# SLATEC Keylist Index

- 15-POINT GAUSS-KRONROD RULES
- 21-POINT GAUSS-KRONROD RULES
- 25-POINT CLENSHAW-CURTIS INTEGRATION
- 31-POINT GAUSS-KRONROD RULES
- 3J COEFFICIENTS
- 3J SYMBOLS
- 41-POINT GAUSS-KRONROD RULES
- 51-POINT GAUSS-KRONROD RULES
- 61-POINT GAUSS-KRONROD RULES
- 6J COEFFICIENTS
- 6J SYMBOLS
- ABORT PROGRAM EXECUTION
- ABSOLUTE VALUE
- ABSOLUTE VALUE OF THE LOGARITHM OF THE GAMMA FUNCTION
- ACOSH
- ADAMS METHOD
- ADAMS-BASHFORTH METHOD
- ADAPTIVE QUADRATURE
- AIRY FUNCTION
- ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES
- ALGEBRAICO-LOGARITHMIC
- ANALYSIS OF COVARIANCE
- APPLICATION OF PERMUTATION TO DATA VECTOR
- ARC COSINE
- ARC HYPERBOLIC COSINE
- ARC HYPERBOLIC SINE
- ARC HYPERBOLIC TANGENT
- ARC SINE
- ARC TANGENT
- ARGUMENT OF A COMPLEX NUMBER
- ASINH
- ATANH
- AUTOMATIC INTEGRATOR
- B-SPLINE
- B-SPLINES
- BACKWARD DIFFERENTIATION FORMULAS
- BAIRY FUNCTION
- BANDED
- BANDED MATRIX
- BASE TEN LOGARITHM
- BESSEL FUNCTION
- BESSEL FUNCTION OF ORDER ONE THIRD
- BESSEL FUNCTION OF ORDER TWO THIRDS
- BESSEL FUNCTIONS OF COMPLEX ARGUMENT
- BESSEL FUNCTIONS OF SECOND KIND
- BESSEL FUNCTIONS OF THE FIRST KIND
- BESSEL FUNCTIONS OF THE THIRD KIND
- BICKLEY FUNCTIONS
- BICONJUGATE GRADIENT
- BICONJUGATE GRADIENT SQUARED
- BINOMIAL COEFFICIENTS
- BISECTION
- BLAS
- BOUNDS
- BROWN'S METHOD
- CARTESIAN
- CAUCHY PRINCIPAL VALUE
- CHARACTER COMPARISON
- CHEBYSHEV
- CHEBYSHEV SERIES
- CHEBYSHEV SERIES EXPANSION
- CHOLESKY DECOMPOSITION
- CLEBSCH-GORDAN COEFFICIENTS
- CLENSHAW-CURTIS METHOD
- COEFFICIENTS
- COMPLEMENTARY ERROR FUNCTION
- COMPLEMENTARY INCOMPLETE GAMMA FUNCTION
- COMPLETE BETA FUNCTION
- COMPLETE ELLIPTIC INTEGRAL
- COMPLETE GAMMA FUNCTION
- COMPLEX HERMITIAN
- COMPLEX LINEAR EQUATIONS
- COMPLEX POLYNOMIAL
- COMPLEX VALUED
- COMPLEX VECTORS
- CONDITION NUMBER
- CONSTRAINED LEAST SQUARES
- CONSTRAINTS
- CONVERGENCE ACCELERATION
- CONVERSION
- COPY
- CORRECTION TERM
- COS OR SIN IN WEIGHT FUNCTION
- COSINE
- COSINE FOURIER TRANSFORM
- COTANGENT
- COVARIANCE MATRIX
- CUBE ROOT
- CUBIC HERMITE DIFFERENTIATION
- CUBIC HERMITE EVALUATION
- CUBIC HERMITE INTERPOLATION
- CUBIC POLYNOMIAL EVALUATION
- CUBIC SPLINES
- CURVE FITTING
- CYCLIC REDUCTION
- CYLINDRICAL
- DASSL
- DATA FITTING
- DAWSON'S FUNCTION
- DEGREES
- DEPAC
- DERIVATIVES OF THE GAMMA FUNCTION
- DETERMINANT
- DIAGNOSTICS
- DIAGONAL
- DIFFERENTIAL/ALGEBRAIC
- DIFFERENTIATION OF B-SPLINE
- DIFFERENTIATION OF SPLINES
- DIGAMMA FUNCTION
- DISCLAIMER
- DOCUMENTATION
- DOT PRODUCT
- DOUBLE PRECISION
- DOWNDATE
- DUPLICATION THEOREM
- E1 FUNCTION
- EASY-TO-USE
- EI FUNCTION
- EIGENVALUES
- EIGENVALUES OF A REAL SYMMETRIC MATRIX
- EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX
- EIGENVECTORS
- EIGENVECTORS OF A REAL SYMMETRIC MATRIX
- EISPACK
- ELEMENTARY FUNCTIONS
- ELLIPTIC
- ELLIPTIC INTEGRAL
- ELLIPTIC PDE
- END POINT SINGULARITIES
- EPSILON ALGORITHM
- EQUALITY CONSTRAINTS
- ERF
- ERFC
- ERROR
- ERROR CHECKING
- ERROR FUNCTION
- ERROR MESSAGE
- ERROR MESSAGES
- ERROR NUMBER
- EUCLIDEAN LENGTH
- EUCLIDEAN NORM
- EVALUATION OF B-SPLINE
- EXCHANGE
- EXPONENTIAL
- EXPONENTIAL INTEGRAL
- EXPONENTIALLY SCALED
- EXPONENTIALLY SCALED AIRY FUNCTION
- EXTENDED-RANGE DOUBLE-PRECISION ARITHMETIC
- EXTENDED-RANGE SINGLE-PRECISION ARITHMETIC
- EXTRAPOLATION
- FACTORIAL
- FAST FOURIER TRANSFORM
- FFT
- FFTPACK
- FIRST KIND
- FIRST ORDER
- FISHPACK
- FNLIB
- FOURIER INTEGRALS
- FOURIER TRANSFORM
- FRACTIONAL ORDER
- GAMMA FUNCTION
- GAUSS QUADRATURE
- GAUSS-KRONROD RULES
- GAUSS-KRONROD(PATTERSON) RULES
- GAUSSIAN
- GEAR'S METHOD
- GENERAL MATRIX
- GENERAL SYSTEM OF LINEAR EQUATIONS
- GENERAL-PURPOSE
- GENERALIZED MINIMUM RESIDUAL
- GIVENS ROTATION
- GIVENS TRANSFORMATION
- GLOBALLY ADAPTIVE
- GMRES
- GRADIENTS
- GUIDELINES FOR SELECTION
- H BESSEL FUNCTIONS
- HANKEL FUNCTIONS
- HELMHOLTZ
- HERMITE INTERPOLATION
- HERMITIAN
- HYPERBOLIC BESSEL FUNCTION
- HYPERBOLIC COSINE
- HYPERBOLIC SINE
- HYPERBOLIC TANGENT
- I BESSEL FUNCTION
- I BESSEL FUNCTIONS
- IMPLICIT DIFFERENTIAL SYSTEMS
- INCOMPLETE BETA FUNCTION
- INCOMPLETE CHOLESKY
- INCOMPLETE CHOLESKY FACTORIZATION
- INCOMPLETE ELLIPTIC INTEGRAL
- INCOMPLETE FACTORIZATION
- INCOMPLETE GAMMA FUNCTION
- INCOMPLETE LU FACTORIZATION
- INEQUALITY
- INEQUALITY CONSTRAINTS
- INFINITE INTERVALS
- INITIAL VALUE PROBLEMS
- INITIALIZE
- INNER PRODUCT
- INTEGRAL OF B-SPLINE
- INTEGRAL OF B-SPLINES
- INTEGRAL OF THE FIRST KIND
- INTEGRAL OF THE SECOND KIND
- INTEGRAL OF THE THIRD KIND
- INTEGRALS OF BESSEL FUNCTIONS
- INTEGRAND EXAMINATOR
- INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR
- INTEGRATION
- INTEGRATION BETWEEN ZEROS
- INTEGRATION RULES FOR FUNCTIONS WITH COS OR SIN FACTOR
- INTERCHANGE
- INTERPOLATION
- INVERSE
- INVERSE COSINE FOURIER TRANSFORM
- INVERSE HYPERBOLIC COSINE
- INVERSE HYPERBOLIC SINE
- INVERSE HYPERBOLIC TANGENT
- ITERATIVE IMPROVEMENT
- ITERATIVE INCOMPLETE LU PRECONDITION
- ITERATIVE PRECONDITION
- J BESSEL FUNCTION
- J BESSEL FUNCTIONS
- JACOBIAN
- K BESSEL FUNCTION
- K BESSEL FUNCTIONS
- K-ZERO BESSEL FUNCTION
- L2
- LARGE X
- LEAST SQUARES
- LEGENDRE FUNCTIONS
- LEVEL 2 BLAS
- LEVEL 3 BLAS
- LEVENBERG-MARQUARDT
- LIMITS
- LINEAR
- LINEAR ALGEBRA
- LINEAR CONSTRAINTS
- LINEAR EQUATIONS
- LINEAR LEAST SQUARES
- LINEAR OPTIMIZATION
- LINEAR PROGRAMMING
- LINEAR SYSTEM
- LINEAR SYSTEM SOLVE
- LINPACK
- LOG GAMMA
- LOGARITHM
- LOGARITHM OF GAMMA FUNCTION
- LOGARITHM OF THE COMPLETE BETA FUNCTION
- LOGARITHMIC CONFLUENT HYPERGEOMETRIC FUNCTION
- LOGARITHMIC INTEGRAL
- LOWER TRIANGLE
- LP
- LQ FACTORIZATION
- LR METHOD
- MACHINE CONSTANTS
- MATRIX
- MATRIX FACTORIZATION
- MATRIX READ
- MATRIX TRANSPOSE VECTOR MULTIPLY
- MATRIX VECTOR MULTIPLY
- MAXIMUM COMPONENT
- MINPACK
- MODIFIED BESSEL FUNCTION
- MODIFIED BESSEL FUNCTIONS
- MODIFIED CHEBYSHEV MOMENTS
- MODIFIED GIVENS ROTATION
- MODULUS
- MONOTONE INTERPOLATION
- NEWTON'S METHOD
- NEWTON-COTES
- NON-SYMMETRIC LINEAR SYSTEM
- NON-SYMMETRIC LINEAR SYSTEM SOLVE
- NONADAPTIVE
- NONLINEAR
- NONLINEAR DATA FITTING
- NONLINEAR EQUATIONS
- NONLINEAR LEAST SQUARES
- NONLINEAR SQUARE SYSTEM
- NONNEGATIVITY CONSTRAINTS
- NONSYMMETRIC
- NORMAL
- NORMAL EQUATIONS
- NORMAL EQUATIONS.
- NUMBER SORTING
- NUMERICAL INTEGRATION
- ODE
- ORDER ONE
- ORDER ZERO
- ORDINARY DIFFERENTIAL EQUATIONS
- ORTHOGONAL POLYNOMIAL
- ORTHOGONAL SERIES
- ORTHOGONAL TRIANGULAR
- ORTHOMIN
- ORTHONORMALIZATION
- PACK
- PACKED
- PASSIVE SORTING
- PCHIP
- PDE
- PERMUTATION
- PERRON'S CONTINUED FRACTION
- PHASE
- PIECEWISE CUBIC EVALUATION
- PIECEWISE CUBIC INTERPOLATION
- PIECEWISE POLYNOMIAL
- PLANE ROTATION
- POCHHAMMER
- POISSON
- POLAR
- POLAR ANGEL
- POLYGAMMA FUNCTION
- POLYNOMIAL
- POLYNOMIAL APPROXIMATION
- POLYNOMIAL EVALUATION
- POLYNOMIAL FIT
- POLYNOMIAL INTERPOLATION
- POLYNOMIAL ROOTS
- POLYNOMIAL ZEROS
- POSITIVE DEFINITE
- POWELL HYBRID METHOD
- PRECONDITIONED CONJUGATE GRADIENT
- PREDICTOR-CORRECTOR
- PRINTING
- PSI FUNCTION
- QL METHOD
- QR DECOMPOSITION
- QR FACTORIZATION
- QUADPACK
- QUADRANT
- QUADRATIC PROGRAMMING
- QUADRATURE
- RACAH COEFFICIENTS
- RANDOM NUMBER
- REAL ROOTS
- REARRANGEMENT
- RECALL
- RECIPROCAL GAMMA FUNCTION
- RELATIVE ADDRESS DETERMINATION FUNCTION
- RKF
- ROOTS
- RUNGE-KUTTA-FEHLBERG METHODS
- SAVE
- SCALE
- SDRIVE
- SECOND KIND
- SECOND ORDER
- SEPARABLE
- SEQUENCE OF BESSEL FUNCTIONS
- SEQUENTIAL SORTING
- SHAPE-PRESERVING INTERPOLATION
- SHOOTING
- SINE
- SINGLE PRECISION
- SINGLETON QUICKSORT
- SINGULAR VALUE DECOMPOSITION
- SINGULARITIES AT USER SPECIFIED POINTS
- SLAP
- SLAP SPARSE
- SLATEC
- SMALL X
- SMOOTH INTEGRAND
- SMOOTH INTERPOLANT
- SOLUTIONS
- SOLVE
- SORT
- SORTING
- SPARSE
- SPARSE CONSTRAINTS
- SPARSE ITERATIVE METHODS
- SPECIAL FUNCTIONS
- SPECIAL-PURPOSE
- SPECIAL-PURPOSE INTEGRAL
- SPENCE'S INTEGRAL
- SPHERICAL
- SPLINE INTERPOLATION
- SPLINES
- STIFF
- STOP TEST
- STRING SORTING
- SUM OF MAGNITUDES OF A VECTOR
- SURVEY OF INTEGRATORS
- SYMMETRIC
- SYMMETRIC LINEAR SYSTEM
- SYMMETRIC LINEAR SYSTEM SOLVE
- TABULATED DATA
- TANGENT
- TAYLOR SERIES
- THIRD KIND
- TRANSFORMATION
- TRIAD
- TRIANGULAR
- TRIANGULAR LINEAR SYSTEM
- TRIANGULAR MATRIX
- TRICOMI
- TRIDIAGONAL
- TRIDIAGONAL LINEAR SYSTEM
- TRIGONOMETRIC
- TWO-POINT BOUNDARY VALUE PROBLEM
- UNDERDETERMINED LINEAR SYSTEM
- UNDERDETERMINED LINEAR SYSTEMS
- UNIFORM
- UNITARY
- UNPACK
- UPDATE
- UTILITY ROUTINE
- VECTOR
- VECTOR ADDITION COEFFICIENTS
- VERSION
- WEBER'S FUNCTION
- WEIGHT FUNCTION
- WEIGHTED LEAST SQUARES
- WIGNER COEFFICIENTS
- WORKSPACE CHECKING
- XERMSG
- XERROR
- Y BESSEL FUNCTION
- Y BESSEL FUNCTIONS
- ZEROS

  ### 15-POINT GAUSS-KRONROD RULES

  - dqk15

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = integral of ABS(F) over (A,B)

  - dqk15i

        The original (infinite integration range is mapped
        onto the interval (0,1) and (A,B) is a part of (0,1).
        it is the purpose to compute
        I = Integral of transformed integrand over (A,B),
        J = Integral of ABS(Transformed Integrand) over (A,B).

  - dqk15w

        To compute I = Integral of F*W over (A,B), with error
                       estimate
                   J = Integral of ABS(F*W) over (A,B)

  - qk15

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = integral of ABS(F) over (A,B)

  - qk15i

        The original (infinite integration range is mapped
        onto the interval (0,1) and (A,B) is a part of (0,1).
        it is the purpose to compute
        I = Integral of transformed integrand over (A,B),
        J = Integral of ABS(Transformed Integrand) over (A,B).

  - qk15w

        To compute I = Integral of F*W over (A,B), with error
                       estimate
                   J = Integral of ABS(F*W) over (A,B)

  ### 21-POINT GAUSS-KRONROD RULES

  - dqk21

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk21

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  ### 25-POINT CLENSHAW-CURTIS INTEGRATION

  - dqc25c

        To compute I = Integral of F*W over (A,B) with
        error estimate, where W(X) = 1/(X-C)

  - dqc25s

        To compute I = Integral of F*W over (BL,BR), with error
        estimate, where the weight function W has a singular
        behaviour of ALGEBRAICO-LOGARITHMIC type at the points
        A and/or B. (BL,BR) is a part of (A,B).

  - qc25c

        To compute I = Integral of F*W over (A,B) with
        error estimate, where W(X) = 1/(X-C)

  - qc25s

        To compute I = Integral of F*W over (BL,BR), with error
        estimate, where the weight function W has a singular
        behaviour of ALGEBRAICO-LOGARITHMIC type at the points
        A and/or B. (BL,BR) is a part of (A,B).

  ### 31-POINT GAUSS-KRONROD RULES

  - dqk31

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk31

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  ### 3J COEFFICIENTS

  - drc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - drc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - rc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  ### 3J SYMBOLS

  - drc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - drc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - rc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  ### 41-POINT GAUSS-KRONROD RULES

  - dqk41

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk41

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  ### 51-POINT GAUSS-KRONROD RULES

  - dqk51

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk51

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  ### 61-POINT GAUSS-KRONROD RULES

  - dqk61

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk61

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  ### 6J COEFFICIENTS

  - drc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  ### 6J SYMBOLS

  - drc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  ### ABORT PROGRAM EXECUTION

  - xerhlt

        Abort program execution and print error message.

  ### ABSOLUTE VALUE

  - alngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - clngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - dlngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  ### ABSOLUTE VALUE OF THE LOGARITHM OF THE GAMMA FUNCTION

  - algams

        Compute the logarithm of the absolute value of the Gamma
        function.

  - dlgams

        Compute the logarithm of the absolute value of the Gamma
        function.

  ### ACOSH

  - acosh

        Compute the arc hyperbolic cosine.

  - cacosh

        Compute the arc hyperbolic cosine.

  - dacosh

        Compute the arc hyperbolic cosine.

  ### ADAMS METHOD

  - dintp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in DSTEPS at XOUT.  Must be used in
        conjunction with DSTEPS.

  - dsteps

        Integrate a system of first order ordinary differential
        equations one step.

  - sintrp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in STEPS at XOUT.  Must be used in
        conjunction with STEPS.

  - steps

        Integrate a system of first order ordinary differential
        equations one step.

  ### ADAMS-BASHFORTH METHOD

  - ddeabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - deabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  ### ADAPTIVE QUADRATURE

  - dgaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  - dqnc79

        Integrate a function using a 7-point adaptive Newton-Cotes
        quadrature rule.

  - gaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  - qnc79

        Integrate a function using a 7-point adaptive Newton-Cotes
        quadrature rule.

  ### AIRY FUNCTION

  - ai

        Evaluate the Airy function.

  - cairy

        Compute the Airy function Ai(z) or its derivative dAi/dz
        for complex argument z.  A scaling option is available
        to help avoid underflow and overflow.

  - cbiry

        Compute the Airy function Bi(z) or its derivative dBi/dz
        for complex argument z.  A scaling option is available
        to help avoid overflow.

  - d9aimp

        Evaluate the Airy modulus and phase.

  - dai

        Evaluate the Airy function.

  - r9aimp

        Evaluate the Airy modulus and phase.

  - zairy

        Compute the Airy function Ai(z) or its derivative dAi/dz
        for complex argument z.  A scaling option is available
        to help avoid underflow and overflow.

  - zbiry

        Compute the Airy function Bi(z) or its derivative dBi/dz
        for complex argument z.  A scaling option is available
        to help avoid overflow.

  ### ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES

  - dqaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### ALGEBRAICO-LOGARITHMIC

  - dqwgts

        This function subprogram is used together with the
        routine DQAWS and defines the WEIGHT function.

  - qwgts

        This function subprogram is used together with the
        routine QAWS and defines the WEIGHT function.

  ### ANALYSIS OF COVARIANCE

  - cv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram FC.

  - dcv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram DFC.

  ### APPLICATION OF PERMUTATION TO DATA VECTOR

  - hpperm

        Rearrange a given array according to a prescribed
        permutation vector.

  - ipperm

        Rearrange a given array according to a prescribed
        permutation vector.

  - spperm

        Rearrange a given array according to a prescribed
        permutation vector.

  ### ARC COSINE

  - cacos

        Compute the complex arc cosine.

  ### ARC HYPERBOLIC COSINE

  - acosh

        Compute the arc hyperbolic cosine.

  - cacosh

        Compute the arc hyperbolic cosine.

  - dacosh

        Compute the arc hyperbolic cosine.

  ### ARC HYPERBOLIC SINE

  - asinh

        Compute the arc hyperbolic sine.

  - casinh

        Compute the arc hyperbolic sine.

  - dasinh

        Compute the arc hyperbolic sine.

  ### ARC HYPERBOLIC TANGENT

  - atanh

        Compute the arc hyperbolic tangent.

  - catanh

        Compute the arc hyperbolic tangent.

  - datanh

        Compute the arc hyperbolic tangent.

  ### ARC SINE

  - casin

        Compute the complex arc sine.

  ### ARC TANGENT

  - catan

        Compute the complex arc tangent.

  - catan2

        Compute the complex arc tangent in the proper quadrant.

  - d9atn1

        Evaluate DATAN(X) from first order relative accuracy so
        that DATAN(X) = X + X**3*D9ATN1(X).

  - r9atn1

        Evaluate ATAN(X) from first order relative accuracy so that
        ATAN(X) = X + X**3*R9ATN1(X).

  ### ARGUMENT OF A COMPLEX NUMBER

  - carg

        Compute the argument of a complex number.

  ### ASINH

  - asinh

        Compute the arc hyperbolic sine.

  - casinh

        Compute the arc hyperbolic sine.

  - dasinh

        Compute the arc hyperbolic sine.

  ### ATANH

  - atanh

        Compute the arc hyperbolic tangent.

  - catanh

        Compute the arc hyperbolic tangent.

  - datanh

        Compute the arc hyperbolic tangent.

  ### AUTOMATIC INTEGRATOR

  - dgaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  - dqag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur (e.g.
        SINGULARITIES, DISCONTINUITIES), are provided by the user.

  - dqagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - dqags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - dqawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqawf

        The routine calculates an approximation result to a given
        Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - gaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  - qag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur(e.g. SINGULARITIES,
        DISCONTINUITIES), are provided by the user.

  - qagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
              ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - qags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - qawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qawf

        The routine calculates an approximation result to a given
        Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
         where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### B-SPLINE

  - bint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  - bintk

        Compute the B-representation of a spline which interpolates
        given data.

  - bspdoc

        Documentation for BSPLINE, a package of subprograms for
        working with piecewise polynomial functions
        in B-representation.

  - bspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  - bspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - bsppp

        Convert the B-representation of a B-spline to the piecewise
        polynomial (PP) form.

  - cv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram FC.

  - dbint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  - dbintk

        Compute the B-representation of a spline which interpolates
        given data.

  - dbspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  - dbspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - dbsppp

        Convert the B-representation of a B-spline to the piecewise
        polynomial (PP) form.

  - dcv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram DFC.

  - defc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.

  - dfc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  - dintrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision of
        the X interval.

  - dpfqad

        Compute the integral on (X1,X2) of a product of a
        function F and the ID-th derivative of a B-spline,
        (PP-representation).

  - dppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - dppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  - efc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.

  - fc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  - intrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision
        of the X interval.

  - pfqad

        Compute the integral on (X1,X2) of a product of a function
        F and the ID-th derivative of a B-spline,
        (PP-representation).

  - ppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - ppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  ### B-SPLINES

  - dpchbs

        Piecewise Cubic Hermite to B-Spline converter.

  - pchbs

        Piecewise Cubic Hermite to B-Spline converter.

  ### BACKWARD DIFFERENTIATION FORMULAS

  - ddassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  - ddebdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - debdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - sdassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  ### BAIRY FUNCTION

  - bi

        Evaluate the Bairy function (the Airy function of the
        second kind).

  - bie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  - dbi

        Evaluate the Bairy function (the Airy function of the
        second kind).

  - dbie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  ### BANDED

  - cgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - cgbdi

        Compute the determinant of a complex band matrix using the
        factors from CGBCO or CGBFA.

  - cgbfa

        Factor a band matrix using Gaussian elimination.

  - cgbsl

        Solve the complex band system A*X=B or CTRANS(A)*X=B using
        the factors computed by CGBCO or CGBFA.

  - cnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - cnbdi

        Compute the determinant of a band matrix using the factors
        computed by CNBCO or CNBFA.

  - cnbfa

        Factor a band matrix by elimination.

  - cnbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - cnbir

        Solve a general nonsymmetric banded system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - cnbsl

        Solve a complex band system using the factors computed by
        CNBCO or CNBFA.

  - cpbco

        Factor a complex Hermitian positive definite matrix stored
        in band form and estimate the condition number of the
        matrix.

  - cpbdi

        Compute the determinant of a complex Hermitian positive
        definite band matrix using the factors computed by CPBCO or
        CPBFA.

  - cpbfa

        Factor a complex Hermitian positive definite matrix stored
        in band form.

  - cpbsl

        Solve the complex Hermitian positive definite band system
        using the factors computed by CPBCO or CPBFA.

  - dgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - dgbdi

        Compute the determinant of a band matrix using the factors
        computed by DGBCO or DGBFA.

  - dgbfa

        Factor a band matrix using Gaussian elimination.

  - dgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by DGBCO or DGBFA.

  - dnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - dnbdi

        Compute the determinant of a band matrix using the factors
        computed by DNBCO or DNBFA.

  - dnbfa

        Factor a band matrix by elimination.

  - dnbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - dnbsl

        Solve a real band system using the factors computed by
        DNBCO or DNBFA.

  - dpbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - dpbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by DPBCO or DPBFA.

  - dpbfa

        Factor a real symmetric positive definite matrix stored in
        in band form.

  - dpbsl

        Solve a real symmetric positive definite band system
        using the factors computed by DPBCO or DPBFA.

  - sgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - sgbdi

        Compute the determinant of a band matrix using the factors
        computed by SGBCO or SGBFA.

  - sgbfa

        Factor a band matrix using Gaussian elimination.

  - sgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by SGBCO or SGBFA.

  - snbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - snbdi

        Compute the determinant of a band matrix using the factors
        computed by SNBCO or SNBFA.

  - snbfa

        Factor a real band matrix by elimination.

  - snbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - snbir

        Solve a general nonsymmetric banded system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - snbsl

        Solve a real band system using the factors computed by
        SNBCO or SNBFA.

  - spbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - spbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by SPBCO or SPBFA.

  - spbfa

        Factor a real symmetric positive definite matrix stored in
        band form.

  - spbsl

        Solve a real symmetric positive definite band system
        using the factors computed by SPBCO or SPBFA.

  ### BANDED MATRIX

  - bndacc

        Compute the LU factorization of a banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - bndsol

        Solve the least squares problem for a banded matrix using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dbndac

        Compute the LU factorization of a  banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dbndsl

        Solve the least squares problem for a banded matrix using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  ### BASE TEN LOGARITHM

  - clog10

        Compute the principal value of the complex base 10
        logarithm.

  ### BESSEL FUNCTION

  - besj0

        Compute the Bessel function of the first kind of order
        zero.

  - besj1

        Compute the Bessel function of the first kind of order one.

  - besy0

        Compute the Bessel function of the second kind of order
        zero.

  - besy1

        Compute the Bessel function of the second kind of order
        one.

  - d9b0mp

        Evaluate the modulus and phase for the J0 and Y0 Bessel
        functions.

  - d9b1mp

        Evaluate the modulus and phase for the J1 and Y1 Bessel
        functions.

  - d9knus

        Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
        K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

  - dbesj0

        Compute the Bessel function of the first kind of order
        zero.

  - dbesj1

        Compute the Bessel function of the first kind of order one.

  - dbesy0

        Compute the Bessel function of the second kind of order
        zero.

  - dbesy1

        Compute the Bessel function of the second kind of order
        one.

  - r9knus

        Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
        K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

  ### BESSEL FUNCTION OF ORDER ONE THIRD

  - cairy

        Compute the Airy function Ai(z) or its derivative dAi/dz
        for complex argument z.  A scaling option is available
        to help avoid underflow and overflow.

  - cbiry

        Compute the Airy function Bi(z) or its derivative dBi/dz
        for complex argument z.  A scaling option is available
        to help avoid overflow.

  - zairy

        Compute the Airy function Ai(z) or its derivative dAi/dz
        for complex argument z.  A scaling option is available
        to help avoid underflow and overflow.

  - zbiry

        Compute the Airy function Bi(z) or its derivative dBi/dz
        for complex argument z.  A scaling option is available
        to help avoid overflow.

  ### BESSEL FUNCTION OF ORDER TWO THIRDS

  - cairy

        Compute the Airy function Ai(z) or its derivative dAi/dz
        for complex argument z.  A scaling option is available
        to help avoid underflow and overflow.

  - cbiry

        Compute the Airy function Bi(z) or its derivative dBi/dz
        for complex argument z.  A scaling option is available
        to help avoid overflow.

  - zairy

        Compute the Airy function Ai(z) or its derivative dAi/dz
        for complex argument z.  A scaling option is available
        to help avoid underflow and overflow.

  - zbiry

        Compute the Airy function Bi(z) or its derivative dBi/dz
        for complex argument z.  A scaling option is available
        to help avoid overflow.

  ### BESSEL FUNCTIONS OF COMPLEX ARGUMENT

  - cbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  - cbesi

        Compute a sequence of the Bessel functions I(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - cbesj

        Compute a sequence of the Bessel functions J(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - cbesk

        Compute a sequence of the Bessel functions K(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - cbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  - zbesi

        Compute a sequence of the Bessel functions I(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesj

        Compute a sequence of the Bessel functions J(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesk

        Compute a sequence of the Bessel functions K(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### BESSEL FUNCTIONS OF SECOND KIND

  - cbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### BESSEL FUNCTIONS OF THE FIRST KIND

  - cbesj

        Compute a sequence of the Bessel functions J(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesj

        Compute a sequence of the Bessel functions J(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### BESSEL FUNCTIONS OF THE THIRD KIND

  - cbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  - zbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  ### BICKLEY FUNCTIONS

  - bskin

        Compute repeated integrals of the K-zero Bessel function.

  - dbskin

        Compute repeated integrals of the K-zero Bessel function.

  ### BICONJUGATE GRADIENT

  - dbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - dcgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - sbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - scgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  ### BICONJUGATE GRADIENT SQUARED

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  ### BINOMIAL COEFFICIENTS

  - binom

        Compute the binomial coefficients.

  - dbinom

        Compute the binomial coefficients.

  ### BISECTION

  - dfzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  - fzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  ### BLAS

  - caxpy

        Compute a constant times a vector plus a vector.

  - ccopy

        Copy a vector.

  - cdcdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - cdotc

        Dot product of two complex vectors using the complex
        conjugate of the first vector.

  - cdotu

        Compute the inner product of two vectors.

  - crotg

        Construct a Givens transformation.

  - cscal

        Multiply a vector by a constant.

  - csrot

        Apply a plane Givens rotation.

  - csscal

        Scale a complex vector.

  - cswap

        Interchange two vectors.

  - dasum

        Compute the sum of the magnitudes of the elements of a
        vector.

  - daxpy

        Compute a constant times a vector plus a vector.

  - dcdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dcopy

        Copy a vector.

  - dcopym

        Copy the negative of a vector to a vector.

  - ddot

        Compute the inner product of two vectors.

  - dnrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - drot

        Apply a plane Givens rotation.

  - drotg

        Construct a plane Givens rotation.

  - drotm

        Apply a modified Givens transformation.

  - drotmg

        Construct a modified Givens transformation.

  - dscal

        Multiply a vector by a constant.

  - dsdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dswap

        Interchange two vectors.

  - icamax

        Find the smallest index of the component of a complex
        vector having the maximum sum of magnitudes of real
        and imaginary parts.

  - icopy

        Copy a vector.

  - idamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  - isamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  - iswap

        Interchange two vectors.

  - sasum

        Compute the sum of the magnitudes of the elements of a
        vector.

  - saxpy

        Compute a constant times a vector plus a vector.

  - scasum

        Compute the sum of the magnitudes of the real and
        imaginary elements of a complex vector.

  - scnrm2

        Compute the unitary norm of a complex vector.

  - scopy

        Copy a vector.

  - scopym

        Copy the negative of a vector to a vector.

  - sdot

        Compute the inner product of two vectors.

  - sdsdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - snrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - srot

        Apply a plane Givens rotation.

  - srotg

        Construct a plane Givens rotation.

  - srotm

        Apply a modified Givens transformation.

  - srotmg

        Construct a modified Givens transformation.

  - sscal

        Multiply a vector by a constant.

  - sswap

        Interchange two vectors.

  ### BOUNDS

  - dbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - dbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  - sbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - sbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  ### BROWN'S METHOD

  - dsos

        Solve a square system of nonlinear equations.

  - sos

        Solve a square system of nonlinear equations.

  ### CARTESIAN

  - hw3crt

        Solve the standard seven-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscrt

        Solves the standard five-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  ### CAUCHY PRINCIPAL VALUE

  - dqawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - dqawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqwgtc

        This function subprogram is used together with the
        routine DQAWC and defines the WEIGHT function.

  - qawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - qawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qwgtc

        This function subprogram is used together with the
        routine QAWC and defines the WEIGHT function.

  ### CHARACTER COMPARISON

  - lsame

        Test two characters to determine if they are the same
        letter, except for case.

  ### CHEBYSHEV

  - initds

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - inits

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  ### CHEBYSHEV SERIES

  - csevl

        Evaluate a Chebyshev series.

  - dcsevl

        Evaluate a Chebyshev series.

  ### CHEBYSHEV SERIES EXPANSION

  - dqcheb

        This routine computes the CHEBYSHEV series expansion
        of degrees 12 and 24 of a function using A
        FAST FOURIER TRANSFORM METHOD
        F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
        F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
        Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

  - qcheb

        This routine computes the CHEBYSHEV series expansion
        of degrees 12 and 24 of a function using A
        FAST FOURIER TRANSFORM METHOD
        F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
        F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
        Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

  ### CHOLESKY DECOMPOSITION

  - cchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - cchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - cchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - cchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - dchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - dchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - dchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - dchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - schdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - schdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - schex

        Update the Cholesky factorization  A=TRANS(R)*R  of A
        positive definite matrix A of order P under diagonal
        permutations of the form TRANS(E)*A*E, where E is a
        permutation matrix.

  - schud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  ### CLEBSCH-GORDAN COEFFICIENTS

  - drc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - drc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - drc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - rc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  ### CLENSHAW-CURTIS METHOD

  - dqawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - dqawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to
        compute J = Integral of ABS(F) over (A,B). For small value
        of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO
        Rule is used. Otherwise a generalized CLENSHAW-CURTIS
        method is used.

  - qawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - qawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)
        and to compute J=Integral of ABS(F) over (A,B). For small
        value of OMEGA or small intervals (A,B) 15-point GAUSS-
        KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

  ### COEFFICIENTS

  - dpolcf

        Compute the coefficients of the polynomial fit (including
        Hermite polynomial fits) produced by a previous call to
        POLINT.

  - polcof

        Compute the coefficients of the polynomial fit (including
        Hermite polynomial fits) produced by a previous call to
        POLINT.

  ### COMPLEMENTARY ERROR FUNCTION

  - derfc

        Compute the complementary error function.

  - erfc

        Compute the complementary error function.

  ### COMPLEMENTARY INCOMPLETE GAMMA FUNCTION

  - d9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and X small.

  - d9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - d9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - dgamic

        Calculate the complementary incomplete Gamma function.

  - dgamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - gamic

        Calculate the complementary incomplete Gamma function.

  - gamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - r9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and for small X.

  - r9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - r9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  ### COMPLETE BETA FUNCTION

  - beta

        Compute the complete Beta function.

  - cbeta

        Compute the complete Beta function.

  - dbeta

        Compute the complete Beta function.

  ### COMPLETE ELLIPTIC INTEGRAL

  - drd

        Compute the incomplete or complete elliptic integral of
        the 2nd kind. For X and Y nonnegative, X+Y and Z positive,
        DRD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - drf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - drj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                          -1/2     -1/2     -1/2     -1
                (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  - rd

        Compute the incomplete or complete elliptic integral of the
        2nd kind.  For X and Y nonnegative, X+Y and Z positive,
         RD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - rf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - rj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                              -1/2     -1/2     -1/2     -1
                    (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  ### COMPLETE GAMMA FUNCTION

  - alngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - c9lgmc

        Compute the log gamma correction factor so that
        LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
        + C9LGMC(Z).

  - cgamma

        Compute the complete Gamma function.

  - clngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - d9lgmc

        Compute the log Gamma correction factor so that
        LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
        + D9LGMC(X).

  - dgamlm

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  - dgamma

        Compute the complete Gamma function.

  - dlngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - gamlim

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  - gamma

        Compute the complete Gamma function.

  - r9lgmc

        Compute the log Gamma correction factor so that
        LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
        + R9LGMC(X).

  ### COMPLEX HERMITIAN

  - chiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - ssiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  ### COMPLEX LINEAR EQUATIONS

  - cgefs

        Solve a general system of linear equations.

  - cgeir

        Solve a general system of linear equations.  Iterative
        refinement is used to obtain an error estimate.

  - dgefs

        Solve a general system of linear equations.

  - sgefs

        Solve a general system of linear equations.

  - sgeir

        Solve a general system of linear equations.  Iterative
        refinement is used to obtain an error estimate.

  ### COMPLEX POLYNOMIAL

  - cpqr79

        Find the zeros of a polynomial with complex coefficients.

  - rpqr79

        Find the zeros of a polynomial with real coefficients.

  ### COMPLEX VALUED

  - cdriv1

        The function of CDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  CDRIV1 allows complex-valued differential
        equations.

  - cdriv2

        The function of CDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  CDRIV2 allows complex-valued differential
        equations.

  - cdriv3

        The function of CDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  CDRIV3
        allows complex-valued differential equations.

  ### COMPLEX VECTORS

  - dcdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dsdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  ### CONDITION NUMBER

  - cgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - cgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - chico

        Factor a complex Hermitian matrix by elimination with sym-
        metric pivoting and estimate the condition of the matrix.

  - chpco

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - cpbco

        Factor a complex Hermitian positive definite matrix stored
        in band form and estimate the condition number of the
        matrix.

  - cpoco

        Factor a complex Hermitian positive definite matrix
        and estimate the condition number of the matrix.

  - cppco

        Factor a complex Hermitian positive definite matrix stored
        in packed form and estimate the condition number of the
        matrix.

  - csico

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting and estimate the condition number of the
        matrix.

  - cspco

        Factor a complex symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - ctrco

        Estimate the condition number of a triangular matrix.

  - dgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - dgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - dpbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - dpoco

        Factor a real symmetric positive definite matrix
        and estimate the condition of the matrix.

  - dppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - dsico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - dspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - dtrco

        Estimate the condition number of a triangular matrix.

  - sgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - sgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - spbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - spoco

        Factor a real symmetric positive definite matrix
        and estimate the condition number of the matrix.

  - sppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - ssico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - sspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - strco

        Estimate the condition number of a triangular matrix.

  ### CONSTRAINED LEAST SQUARES

  - cv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram FC.

  - dcv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram DFC.

  - defc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.

  - dfc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  - dlsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - dwnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  - fc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  - lsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - wnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  ### CONSTRAINTS

  - dbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - dbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  - sbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - sbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  ### CONVERGENCE ACCELERATION

  - dqawf

        The routine calculates an approximation result to a given
        Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqelg

        The routine determines the limit of a given sequence of
        approximations, by means of the Epsilon algorithm of
        P.Wynn. An estimate of the absolute error is also given.
        The condensed Epsilon table is computed. Only those
        elements needed for the computation of the next diagonal
        are preserved.

  - qawf

        The routine calculates an approximation result to a given
        Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
         where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qelg

        The routine determines the limit of a given sequence of
        approximations, by means of the Epsilon algorithm of
        P. Wynn. An estimate of the absolute error is also given.
        The condensed Epsilon table is computed. Only those
        elements needed for the computation of the next diagonal
        are preserved.

  ### CONVERSION

  - dpchbs

        Piecewise Cubic Hermite to B-Spline converter.

  - pchbs

        Piecewise Cubic Hermite to B-Spline converter.

  ### COPY

  - ccopy

        Copy a vector.

  - dcopy

        Copy a vector.

  - dcopym

        Copy the negative of a vector to a vector.

  - icopy

        Copy a vector.

  - scopy

        Copy a vector.

  - scopym

        Copy the negative of a vector to a vector.

  ### CORRECTION TERM

  - c9lgmc

        Compute the log gamma correction factor so that
        LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
        + C9LGMC(Z).

  - d9lgmc

        Compute the log Gamma correction factor so that
        LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
        + D9LGMC(X).

  - r9lgmc

        Compute the log Gamma correction factor so that
        LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
        + R9LGMC(X).

  ### COS OR SIN IN WEIGHT FUNCTION

  - dqwgtf

        This function subprogram is used together with the
        routine DQAWF and defines the WEIGHT function.

  - qwgtf

        This function subprogram is used together with the
        routine QAWF and defines the WEIGHT function.

  ### COSINE

  - cosdg

        Compute the cosine of an argument in degrees.

  - dcosdg

        Compute the cosine of an argument in degrees.

  ### COSINE FOURIER TRANSFORM

  - cosqf

        Compute the forward cosine transform with odd wave numbers.

  - cosqi

        Initialize a work array for COSQF and COSQB.

  - cost

        Compute the cosine transform of a real, even sequence.

  - costi

        Initialize a work array for COST.

  ### COTANGENT

  - ccot

        Compute the cotangent.

  - cot

        Compute the cotangent.

  - dcot

        Compute the cotangent.

  ### COVARIANCE MATRIX

  - dcov

        Calculate the covariance matrix for a nonlinear data
        fitting problem.  It is intended to be used after a
        successful return from either DNLS1 or DNLS1E.

  - scov

        Calculate the covariance matrix for a nonlinear data
        fitting problem.  It is intended to be used after a
        successful return from either SNLS1 or SNLS1E.

  ### CUBE ROOT

  - cbrt

        Compute the cube root.

  - ccbrt

        Compute the cube root.

  - dcbrt

        Compute the cube root.

  ### CUBIC HERMITE DIFFERENTIATION

  - chfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by PCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use CHFEV instead.

  - dchfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by DPCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use DCHFEV instead.

  - dpchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for DPCHIM
        or DPCHIC. If only function values are required, use
        DPCHFE instead.

  - pchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for PCHIM
        or PCHIC.  If only function values are required, use
        PCHFE instead.

  ### CUBIC HERMITE EVALUATION

  - chfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by PCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use CHFEV instead.

  - chfev

        Evaluate a cubic polynomial given in Hermite form at an
        array of points.  While designed for use by PCHFE, it may
        be useful directly as an evaluator for a piecewise cubic
        Hermite function in applications, such as graphing, where
        the interval is known in advance.

  - dchfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by DPCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use DCHFEV instead.

  - dchfev

        Evaluate a cubic polynomial given in Hermite form at an
        array of points.  While designed for use by DPCHFE, it may
        be useful directly as an evaluator for a piecewise cubic
        Hermite function in applications, such as graphing, where
        the interval is known in advance.

  - dpchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for DPCHIM
        or DPCHIC. If only function values are required, use
        DPCHFE instead.

  - dpchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for DPCHIM or DPCHIC.

  - pchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for PCHIM
        or PCHIC.  If only function values are required, use
        PCHFE instead.

  - pchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for PCHIM or PCHIC.

  ### CUBIC HERMITE INTERPOLATION

  - dpchbs

        Piecewise Cubic Hermite to B-Spline converter.

  - dpchcm

        Check a cubic Hermite function for monotonicity.

  - dpchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - dpchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - dpchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  - dpchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See DPCHIC if user control
        is desired over boundary or switch conditions.)

  - dpchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  - pchbs

        Piecewise Cubic Hermite to B-Spline converter.

  - pchcm

        Check a cubic Hermite function for monotonicity.

  - pchdoc

        Documentation for PCHIP, a Fortran package for piecewise
        cubic Hermite interpolation of data.

  - pchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - pchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - pchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  - pchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See PCHIC if user control is
        desired over boundary or switch conditions.)

  - pchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  ### CUBIC POLYNOMIAL EVALUATION

  - chfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by PCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use CHFEV instead.

  - chfev

        Evaluate a cubic polynomial given in Hermite form at an
        array of points.  While designed for use by PCHFE, it may
        be useful directly as an evaluator for a piecewise cubic
        Hermite function in applications, such as graphing, where
        the interval is known in advance.

  - dchfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by DPCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use DCHFEV instead.

  - dchfev

        Evaluate a cubic polynomial given in Hermite form at an
        array of points.  While designed for use by DPCHFE, it may
        be useful directly as an evaluator for a piecewise cubic
        Hermite function in applications, such as graphing, where
        the interval is known in advance.

  ### CUBIC SPLINES

  - bint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  - dbint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  ### CURVE FITTING

  - bndacc

        Compute the LU factorization of a banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - bndsol

        Solve the least squares problem for a banded matrix using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - cv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram FC.

  - dbndac

        Compute the LU factorization of a  banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dbndsl

        Solve the least squares problem for a banded matrix using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dcv

        Evaluate the variance function of the curve obtained
        by the constrained B-spline fitting subprogram DFC.

  - defc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.

  - dfc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  - dhfti

        Solve a least squares problem for banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dlsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - dp1vlu

        Use the coefficients generated by DPOLFT to evaluate the
        polynomial fit of degree L, along with the first NDER of
        its derivatives, at a specified point.

  - dpcoef

        Convert the DPOLFT coefficients to Taylor series form.

  - dpolft

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  - dwnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  - efc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.

  - fc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  - hfti

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.

  - lsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - pcoef

        Convert the POLFIT coefficients to Taylor series form.

  - polfit

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  - pvalue

        Use the coefficients generated by POLFIT to evaluate the
        polynomial fit of degree L, along with the first NDER of
        its derivatives, at a specified point.

  - wnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  ### CYCLIC REDUCTION

  - cmgnbn

        Solve a complex block tridiagonal linear system of
        equations by a cyclic reduction algorithm.

  ### CYLINDRICAL

  - hstcyl

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified
        Helmholtz equation in cylindrical coordinates.

  - hwscyl

        Solve a standard finite difference approximation
        to the Helmholtz equation in cylindrical coordinates.

  ### DASSL

  - ddassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  - sdassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  ### DATA FITTING

  - bint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  - bintk

        Compute the B-representation of a spline which interpolates
        given data.

  - bspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  - bspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - dbint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  - dbintk

        Compute the B-representation of a spline which interpolates
        given data.

  - dbspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  - dbspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - dintrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision of
        the X interval.

  - dlsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - dpcoef

        Convert the DPOLFT coefficients to Taylor series form.

  - dpfqad

        Compute the integral on (X1,X2) of a product of a
        function F and the ID-th derivative of a B-spline,
        (PP-representation).

  - dpolft

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  - dppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - dppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  - dwnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  - intrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision
        of the X interval.

  - lsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - pcoef

        Convert the POLFIT coefficients to Taylor series form.

  - pfqad

        Compute the integral on (X1,X2) of a product of a function
        F and the ID-th derivative of a B-spline,
        (PP-representation).

  - polfit

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  - ppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - ppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  - wnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  ### DAWSON'S FUNCTION

  - daws

        Compute Dawson's function.

  - ddaws

        Compute Dawson's function.

  ### DEGREES

  - cosdg

        Compute the cosine of an argument in degrees.

  - dcosdg

        Compute the cosine of an argument in degrees.

  - dsindg

        Compute the sine of an argument in degrees.

  - sindg

        Compute the sine of an argument in degrees.

  ### DEPAC

  - ddeabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - ddebdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - dderkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - deabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - debdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - derkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - dintp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in DSTEPS at XOUT.  Must be used in
        conjunction with DSTEPS.

  - dsteps

        Integrate a system of first order ordinary differential
        equations one step.

  - sintrp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in STEPS at XOUT.  Must be used in
        conjunction with STEPS.

  - steps

        Integrate a system of first order ordinary differential
        equations one step.

  ### DERIVATIVES OF THE GAMMA FUNCTION

  - dpsifn

        Compute derivatives of the Psi function.

  - psifn

        Compute derivatives of the Psi function.

  ### DETERMINANT

  - cgbdi

        Compute the determinant of a complex band matrix using the
        factors from CGBCO or CGBFA.

  - cgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by CGECO or CGEFA.

  - chidi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix using the factors obtained from CHIFA.

  - chpdi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix stored in packed form using the factors
        obtained from CHPFA.

  - cnbdi

        Compute the determinant of a band matrix using the factors
        computed by CNBCO or CNBFA.

  - cpbdi

        Compute the determinant of a complex Hermitian positive
        definite band matrix using the factors computed by CPBCO or
        CPBFA.

  - cpodi

        Compute the determinant and inverse of a certain complex
        Hermitian positive definite matrix using the factors
        computed by CPOCO, CPOFA, or CQRDC.

  - cppdi

        Compute the determinant and inverse of a complex Hermitian
        positive definite matrix using factors from CPPCO or CPPFA.

  - csidi

        Compute the determinant and inverse of a complex symmetric
        matrix using the factors from CSIFA.

  - cspdi

        Compute the determinant and inverse of a complex symmetric
        matrix stored in packed form using the factors from CSPFA.

  - ctrdi

        Compute the determinant and inverse of a triangular matrix.

  - dgbdi

        Compute the determinant of a band matrix using the factors
        computed by DGBCO or DGBFA.

  - dgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by DGECO or DGEFA.

  - dnbdi

        Compute the determinant of a band matrix using the factors
        computed by DNBCO or DNBFA.

  - dpbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by DPBCO or DPBFA.

  - dpodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by DPOCO, DPOFA or DQRDC.

  - dppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from DPPCO or DPPFA.

  - dsidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from DSIFA.

  - dspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from DSPFA.

  - dtrdi

        Compute the determinant and inverse of a triangular matrix.

  - sgbdi

        Compute the determinant of a band matrix using the factors
        computed by SGBCO or SGBFA.

  - sgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by SGECO or SGEFA.

  - snbdi

        Compute the determinant of a band matrix using the factors
        computed by SNBCO or SNBFA.

  - spbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by SPBCO or SPBFA.

  - spodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by SPOCO, SPOFA or SQRDC.

  - sppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from SPPCO or SPPFA.

  - ssidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from SSIFA.

  - sspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from SSPFA.

  - strdi

        Compute the determinant and inverse of a triangular matrix.

  ### DIAGNOSTICS

  - dcpplt

        Printer Plot of SLAP Column Format Matrix.
        Routine to print out a SLAP Column format matrix in a
        "printer plot" graphical representation.

  - dtin

        Read in SLAP Triad Format Linear System.
        Routine to read in a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - dtout

        Write out SLAP Triad Format Linear System.
        Routine to write out a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - scpplt

        Printer Plot of SLAP Column Format Matrix.
        Routine to print out a SLAP Column format matrix in a
        "printer plot" graphical representation.

  - stin

        Read in SLAP Triad Format Linear System.
        Routine to read in a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - stout

        Write out SLAP Triad Format Linear System.
        Routine to write out a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  ### DIAGONAL

  - dsd2s

        Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up.
        Routine to compute the inverse of the diagonal of the
        matrix A*A', where A is stored in SLAP-Column format.

  - dsds

        Diagonal Scaling Preconditioner SLAP Set Up.
        Routine to compute the inverse of the diagonal of a matrix
        stored in the SLAP Column format.

  - dsdscl

        Diagonal Scaling of system Ax = b.
        This routine scales (and unscales) the system  Ax = b
        by symmetric diagonal scaling.

  - ssd2s

        Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up.
        Routine to compute the inverse of the diagonal of the
        matrix A*A', where A is stored in SLAP-Column format.

  - ssds

        Diagonal Scaling Preconditioner SLAP Set Up.
        Routine to compute the inverse of the diagonal of a matrix
        stored in the SLAP Column format.

  - ssdscl

        Diagonal Scaling of system Ax = b.
        This routine scales (and unscales) the system  Ax = b
        by symmetric diagonal scaling.

  ### DIFFERENTIAL/ALGEBRAIC

  - ddassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  - sdassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  ### DIFFERENTIATION OF B-SPLINE

  - bspvd

        Calculate the value and all derivatives of order less than
        NDERIV of all basis functions which do not vanish at X.

  - bvalu

        Evaluate the B-representation of a B-spline at X for the
        function value or any of its derivatives.

  - dbspvd

        Calculate the value and all derivatives of order less than
        NDERIV of all basis functions which do not vanish at X.

  - dbvalu

        Evaluate the B-representation of a B-spline at X for the
        function value or any of its derivatives.

  ### DIFFERENTIATION OF SPLINES

  - bspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  - dbspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  ### DIGAMMA FUNCTION

  - cpsi

        Compute the Psi (or Digamma) function.

  - dpsi

        Compute the Psi (or Digamma) function.

  - psi

        Compute the Psi (or Digamma) function.

  ### DISCLAIMER

  - aaaaaa

        SLATEC Common Mathematical Library disclaimer and version.

  ### DOCUMENTATION

  - aaaaaa

        SLATEC Common Mathematical Library disclaimer and version.

  - bspdoc

        Documentation for BSPLINE, a package of subprograms for
        working with piecewise polynomial functions
        in B-representation.

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - fftdoc

        Documentation for FFTPACK, a collection of Fast Fourier
        Transform routines.

  - fundoc

        Documentation for FNLIB, a collection of routines for
        evaluating elementary and special functions.

  - pchdoc

        Documentation for PCHIP, a Fortran package for piecewise
        cubic Hermite interpolation of data.

  - qpdoc

        Documentation for QUADPACK, a package of subprograms for
        automatic evaluation of one-dimensional definite integrals.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  ### DOT PRODUCT

  - cdcdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - dcdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dqdota

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dqdoti

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dsdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - sdsdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  ### DOUBLE PRECISION

  - ddriv1

        The function of DDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  DDRIV1 uses double precision arithmetic.

  - ddriv2

        The function of DDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  DDRIV2 uses double precision arithmetic.

  - ddriv3

        The function of DDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  DDRIV3
        uses double precision arithmetic.

  ### DOWNDATE

  - cchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - dchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - schdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  ### DUPLICATION THEOREM

  - drc

        Calculate a double precision approximation to
         DRC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  - drd

        Compute the incomplete or complete elliptic integral of
        the 2nd kind. For X and Y nonnegative, X+Y and Z positive,
        DRD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - drf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - drj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                          -1/2     -1/2     -1/2     -1
                (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  - rc

        Calculate an approximation to
         RC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  - rd

        Compute the incomplete or complete elliptic integral of the
        2nd kind.  For X and Y nonnegative, X+Y and Z positive,
         RD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - rf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - rj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                              -1/2     -1/2     -1/2     -1
                    (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  ### E1 FUNCTION

  - de1

        Compute the exponential integral E1(X).

  - e1

        Compute the exponential integral E1(X).

  ### EASY-TO-USE

  - dnls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  - dnsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.

  - snls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  - snsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.

  ### EI FUNCTION

  - dei

        Compute the exponential integral Ei(X).

  - ei

        Compute the exponential integral Ei(X).

  ### EIGENVALUES

  - bandr

        Reduce a real symmetric band matrix to symmetric
        tridiagonal matrix and, optionally, accumulate
        orthogonal similarity transformations.

  - bisect

        Compute the eigenvalues of a symmetric tridiagonal matrix
        in a given interval using Sturm sequencing.

  - bqr

        Compute some of the eigenvalues of a real symmetric
        matrix using the QR method with shifts of origin.

  - cg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex general matrix.

  - ch

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - cgeev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex general matrix.

  - chiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - cinvit

        Compute the eigenvectors of a complex upper Hessenberg
        associated with specified eigenvalues using inverse
        iteration.

  - combak

        Form the eigenvectors of a complex general matrix from the
        eigenvectors of a upper Hessenberg matrix output from
        COMHES.

  - comhes

        Reduce a complex general matrix to complex upper Hessenberg
        form using stabilized elementary similarity
        transformations.

  - comlr

        Compute the eigenvalues of a complex upper Hessenberg
        matrix using the modified LR method.

  - comlr2

        Compute the eigenvalues and eigenvectors of a complex upper
        Hessenberg matrix using the modified LR method.

  - comqr

        Compute the eigenvalues of complex upper Hessenberg matrix
        using the QR method.

  - comqr2

        Compute the eigenvalues and eigenvectors of a complex upper
        Hessenberg matrix.

  - cortb

        Form the eigenvectors of a complex general matrix from
        eigenvectors of upper Hessenberg matrix output from
        CORTH.

  - corth

        Reduce a complex general matrix to complex upper Hessenberg
        form using unitary similarity transformations.

  - eisdoc

        Documentation for EISPACK, a collection of subprograms for
        solving matrix eigen-problems.

  - elmbak

        Form the eigenvectors of a real general matrix from the
        eigenvectors of the upper Hessenberg matrix output from
        ELMHES.

  - elmhes

        Reduce a real general matrix to upper Hessenberg form
        using stabilized elementary similarity transformations.

  - eltran

        Accumulates the stabilized elementary similarity
        transformations used in the reduction of a real general
        matrix to upper Hessenberg form by ELMHES.

  - figi

        Transforms certain real non-symmetric tridiagonal matrix
        to symmetric tridiagonal matrix.

  - figi2

        Transforms certain real non-symmetric tridiagonal matrix
        to symmetric tridiagonal matrix.

  - hqr

        Compute the eigenvalues of a real upper Hessenberg matrix
        using the QR method.

  - hqr2

        Compute the eigenvalues and eigenvectors of a real upper
        Hessenberg matrix using QR method.

  - htrib3

        Compute the eigenvectors of a complex Hermitian matrix from
        the eigenvectors of a real symmetric tridiagonal matrix
        output from HTRID3.

  - htribk

        Form the eigenvectors of a complex Hermitian matrix from
        the eigenvectors of a real symmetric tridiagonal matrix
        output from HTRIDI.

  - htrid3

        Reduce a complex Hermitian (packed) matrix to a real
        symmetric tridiagonal matrix by unitary similarity
        transformations.

  - htridi

        Reduce a complex Hermitian matrix to a real symmetric
        tridiagonal matrix using unitary similarity
        transformations.

  - imtql1

        Compute the eigenvalues of a symmetric tridiagonal matrix
        using the implicit QL method.

  - imtql2

        Compute the eigenvalues and eigenvectors of a symmetric
        tridiagonal matrix using the implicit QL method.

  - imtqlv

        Compute the eigenvalues of a symmetric tridiagonal matrix
        using the implicit QL method.  Eigenvectors may be computed
        later.

  - invit

        Compute the eigenvectors of a real upper Hessenberg
        matrix associated with specified eigenvalues by inverse
        iteration.

  - minfit

        Compute the singular value decomposition of a rectangular
        matrix and solve the related linear least squares problem.

  - ortbak

        Form the eigenvectors of a general real matrix from the
        eigenvectors of the upper Hessenberg matrix output from
        ORTHES.

  - orthes

        Reduce a real general matrix to upper Hessenberg form
        using orthogonal similarity transformations.

  - ortran

        Accumulate orthogonal similarity transformations in the
        reduction of real general matrix by ORTHES.

  - qzhes

        The first step of the QZ algorithm for solving generalized
        matrix eigenproblems.  Accepts a pair of real general
        matrices and reduces one of them to upper Hessenberg
        and the other to upper triangular form using orthogonal
        transformations. Usually followed by QZIT, QZVAL, QZVEC.

  - qzit

        The second step of the QZ algorithm for generalized
        eigenproblems.  Accepts an upper Hessenberg and an upper
        triangular matrix and reduces the former to
        quasi-triangular form while preserving the form of the
        latter.  Usually preceded by QZHES and followed by QZVAL
        and QZVEC.

  - qzval

        The third step of the QZ algorithm for generalized
        eigenproblems.  Accepts a pair of real matrices, one in
        quasi-triangular form and the other in upper triangular
        form and computes the eigenvalues of the associated
        eigenproblem.  Usually preceded by QZHES, QZIT, and
        followed by QZVEC.

  - qzvec

        The optional fourth step of the QZ algorithm for
        generalized eigenproblems.  Accepts a matrix in
        quasi-triangular form and another in upper triangular
        and computes the eigenvectors of the triangular problem
        and transforms them back to the original coordinates
        Usually preceded by QZHES, QZIT, and QZVAL.

  - ratqr

        Compute the largest or smallest eigenvalues of a symmetric
        tridiagonal matrix using the rational QR method with Newton
        correction.

  - rebak

        Form the eigenvectors of a generalized symmetric
        eigensystem from the eigenvectors of derived matrix output
        from REDUC or REDUC2.

  - rebakb

        Form the eigenvectors of a generalized symmetric
        eigensystem from the eigenvectors of derived matrix output
        from REDUC2.

  - reduc

        Reduce a generalized symmetric eigenproblem to a standard
        symmetric eigenproblem using Cholesky factorization.

  - reduc2

        Reduce a certain generalized symmetric eigenproblem to a
        standard symmetric eigenproblem using Cholesky
        factorization.

  - rg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real general matrix.

  - rgg

        Compute the eigenvalues and eigenvectors for a real
        generalized eigenproblem.

  - rs

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  - rsb

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric band matrix.

  - rsg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsgab

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsgba

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsp

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix packed into a one dimensional
        array.

  - rst

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric tridiagonal matrix.

  - rt

        Compute the eigenvalues and eigenvectors of a special real
        tridiagonal matrix.

  - sgeev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real general matrix.

  - ssiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  - sspev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix stored in packed form.

  - tql2

        Compute the eigenvalues and eigenvectors of symmetric
        tridiagonal matrix.

  - tred1

        Reduce a real symmetric matrix to symmetric tridiagonal
        matrix using orthogonal similarity transformations.

  - tred2

        Reduce a real symmetric matrix to a symmetric tridiagonal
        matrix using and accumulating orthogonal transformations.

  - tred3

        Reduce a real symmetric matrix stored in packed form to
        symmetric tridiagonal matrix using orthogonal
        transformations.

  - tsturm

        Find those eigenvalues of a symmetric tridiagonal matrix
        in a given interval and their associated eigenvectors by
        Sturm sequencing.

  ### EIGENVALUES OF A REAL SYMMETRIC MATRIX

  - tridib

        Compute the eigenvalues of a symmetric tridiagonal matrix
        in a given interval using Sturm sequencing.

  ### EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX

  - tql1

        Compute the eigenvalues of symmetric tridiagonal matrix by
        the QL method.

  - tqlrat

        Compute the eigenvalues of symmetric tridiagonal matrix
        using a rational variant of the QL method.

  ### EIGENVECTORS

  - bakvec

        Form the eigenvectors of a certain real non-symmetric
        tridiagonal matrix from a symmetric tridiagonal matrix
        output from FIGI.

  - balanc

        Balance a real general matrix and isolate eigenvalues
        whenever possible.

  - balbak

        Form the eigenvectors of a real general matrix from the
        eigenvectors of matrix output from BALANC.

  - bandr

        Reduce a real symmetric band matrix to symmetric
        tridiagonal matrix and, optionally, accumulate
        orthogonal similarity transformations.

  - bandv

        Form the eigenvectors of a real symmetric band matrix
        associated with a set of ordered approximate eigenvalues
        by inverse iteration.

  - cbabk2

        Form the eigenvectors of a complex general matrix from the
        eigenvectors of matrix output from CBAL.

  - cbal

        Balance a complex general matrix and isolate eigenvalues
        whenever possible.

  - cg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex general matrix.

  - ch

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - cgeev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex general matrix.

  - chiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - cinvit

        Compute the eigenvectors of a complex upper Hessenberg
        associated with specified eigenvalues using inverse
        iteration.

  - combak

        Form the eigenvectors of a complex general matrix from the
        eigenvectors of a upper Hessenberg matrix output from
        COMHES.

  - comhes

        Reduce a complex general matrix to complex upper Hessenberg
        form using stabilized elementary similarity
        transformations.

  - comlr2

        Compute the eigenvalues and eigenvectors of a complex upper
        Hessenberg matrix using the modified LR method.

  - comqr

        Compute the eigenvalues of complex upper Hessenberg matrix
        using the QR method.

  - comqr2

        Compute the eigenvalues and eigenvectors of a complex upper
        Hessenberg matrix.

  - cortb

        Form the eigenvectors of a complex general matrix from
        eigenvectors of upper Hessenberg matrix output from
        CORTH.

  - corth

        Reduce a complex general matrix to complex upper Hessenberg
        form using unitary similarity transformations.

  - eisdoc

        Documentation for EISPACK, a collection of subprograms for
        solving matrix eigen-problems.

  - elmbak

        Form the eigenvectors of a real general matrix from the
        eigenvectors of the upper Hessenberg matrix output from
        ELMHES.

  - elmhes

        Reduce a real general matrix to upper Hessenberg form
        using stabilized elementary similarity transformations.

  - eltran

        Accumulates the stabilized elementary similarity
        transformations used in the reduction of a real general
        matrix to upper Hessenberg form by ELMHES.

  - figi

        Transforms certain real non-symmetric tridiagonal matrix
        to symmetric tridiagonal matrix.

  - figi2

        Transforms certain real non-symmetric tridiagonal matrix
        to symmetric tridiagonal matrix.

  - hqr

        Compute the eigenvalues of a real upper Hessenberg matrix
        using the QR method.

  - hqr2

        Compute the eigenvalues and eigenvectors of a real upper
        Hessenberg matrix using QR method.

  - htrib3

        Compute the eigenvectors of a complex Hermitian matrix from
        the eigenvectors of a real symmetric tridiagonal matrix
        output from HTRID3.

  - htribk

        Form the eigenvectors of a complex Hermitian matrix from
        the eigenvectors of a real symmetric tridiagonal matrix
        output from HTRIDI.

  - htrid3

        Reduce a complex Hermitian (packed) matrix to a real
        symmetric tridiagonal matrix by unitary similarity
        transformations.

  - htridi

        Reduce a complex Hermitian matrix to a real symmetric
        tridiagonal matrix using unitary similarity
        transformations.

  - imtql1

        Compute the eigenvalues of a symmetric tridiagonal matrix
        using the implicit QL method.

  - imtql2

        Compute the eigenvalues and eigenvectors of a symmetric
        tridiagonal matrix using the implicit QL method.

  - imtqlv

        Compute the eigenvalues of a symmetric tridiagonal matrix
        using the implicit QL method.  Eigenvectors may be computed
        later.

  - invit

        Compute the eigenvectors of a real upper Hessenberg
        matrix associated with specified eigenvalues by inverse
        iteration.

  - minfit

        Compute the singular value decomposition of a rectangular
        matrix and solve the related linear least squares problem.

  - ortbak

        Form the eigenvectors of a general real matrix from the
        eigenvectors of the upper Hessenberg matrix output from
        ORTHES.

  - orthes

        Reduce a real general matrix to upper Hessenberg form
        using orthogonal similarity transformations.

  - ortran

        Accumulate orthogonal similarity transformations in the
        reduction of real general matrix by ORTHES.

  - qzhes

        The first step of the QZ algorithm for solving generalized
        matrix eigenproblems.  Accepts a pair of real general
        matrices and reduces one of them to upper Hessenberg
        and the other to upper triangular form using orthogonal
        transformations. Usually followed by QZIT, QZVAL, QZVEC.

  - qzit

        The second step of the QZ algorithm for generalized
        eigenproblems.  Accepts an upper Hessenberg and an upper
        triangular matrix and reduces the former to
        quasi-triangular form while preserving the form of the
        latter.  Usually preceded by QZHES and followed by QZVAL
        and QZVEC.

  - qzval

        The third step of the QZ algorithm for generalized
        eigenproblems.  Accepts a pair of real matrices, one in
        quasi-triangular form and the other in upper triangular
        form and computes the eigenvalues of the associated
        eigenproblem.  Usually preceded by QZHES, QZIT, and
        followed by QZVEC.

  - qzvec

        The optional fourth step of the QZ algorithm for
        generalized eigenproblems.  Accepts a matrix in
        quasi-triangular form and another in upper triangular
        and computes the eigenvectors of the triangular problem
        and transforms them back to the original coordinates
        Usually preceded by QZHES, QZIT, and QZVAL.

  - ratqr

        Compute the largest or smallest eigenvalues of a symmetric
        tridiagonal matrix using the rational QR method with Newton
        correction.

  - rebak

        Form the eigenvectors of a generalized symmetric
        eigensystem from the eigenvectors of derived matrix output
        from REDUC or REDUC2.

  - rebakb

        Form the eigenvectors of a generalized symmetric
        eigensystem from the eigenvectors of derived matrix output
        from REDUC2.

  - reduc

        Reduce a generalized symmetric eigenproblem to a standard
        symmetric eigenproblem using Cholesky factorization.

  - reduc2

        Reduce a certain generalized symmetric eigenproblem to a
        standard symmetric eigenproblem using Cholesky
        factorization.

  - rg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real general matrix.

  - rgg

        Compute the eigenvalues and eigenvectors for a real
        generalized eigenproblem.

  - rs

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  - rsb

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric band matrix.

  - rsg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsgab

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsgba

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsp

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix packed into a one dimensional
        array.

  - rst

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric tridiagonal matrix.

  - rt

        Compute the eigenvalues and eigenvectors of a special real
        tridiagonal matrix.

  - sgeev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real general matrix.

  - ssiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  - sspev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix stored in packed form.

  - tinvit

        Compute the eigenvectors of symmetric tridiagonal matrix
        corresponding to specified eigenvalues, using inverse
        iteration.

  - tql2

        Compute the eigenvalues and eigenvectors of symmetric
        tridiagonal matrix.

  - tred1

        Reduce a real symmetric matrix to symmetric tridiagonal
        matrix using orthogonal similarity transformations.

  - tred2

        Reduce a real symmetric matrix to a symmetric tridiagonal
        matrix using and accumulating orthogonal transformations.

  - tred3

        Reduce a real symmetric matrix stored in packed form to
        symmetric tridiagonal matrix using orthogonal
        transformations.

  - tsturm

        Find those eigenvalues of a symmetric tridiagonal matrix
        in a given interval and their associated eigenvectors by
        Sturm sequencing.

  ### EIGENVECTORS OF A REAL SYMMETRIC MATRIX

  - trbak1

        Form the eigenvectors of real symmetric matrix from
        the eigenvectors of a symmetric tridiagonal matrix formed
        by TRED1.

  - trbak3

        Form the eigenvectors of a real symmetric matrix from the
        eigenvectors of a symmetric tridiagonal matrix formed
        by TRED3.

  ### EISPACK

  - bakvec

        Form the eigenvectors of a certain real non-symmetric
        tridiagonal matrix from a symmetric tridiagonal matrix
        output from FIGI.

  - balanc

        Balance a real general matrix and isolate eigenvalues
        whenever possible.

  - balbak

        Form the eigenvectors of a real general matrix from the
        eigenvectors of matrix output from BALANC.

  - bandr

        Reduce a real symmetric band matrix to symmetric
        tridiagonal matrix and, optionally, accumulate
        orthogonal similarity transformations.

  - bandv

        Form the eigenvectors of a real symmetric band matrix
        associated with a set of ordered approximate eigenvalues
        by inverse iteration.

  - bisect

        Compute the eigenvalues of a symmetric tridiagonal matrix
        in a given interval using Sturm sequencing.

  - bqr

        Compute some of the eigenvalues of a real symmetric
        matrix using the QR method with shifts of origin.

  - cbabk2

        Form the eigenvectors of a complex general matrix from the
        eigenvectors of matrix output from CBAL.

  - cbal

        Balance a complex general matrix and isolate eigenvalues
        whenever possible.

  - cg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex general matrix.

  - ch

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - cinvit

        Compute the eigenvectors of a complex upper Hessenberg
        associated with specified eigenvalues using inverse
        iteration.

  - combak

        Form the eigenvectors of a complex general matrix from the
        eigenvectors of a upper Hessenberg matrix output from
        COMHES.

  - comhes

        Reduce a complex general matrix to complex upper Hessenberg
        form using stabilized elementary similarity
        transformations.

  - comlr

        Compute the eigenvalues of a complex upper Hessenberg
        matrix using the modified LR method.

  - comlr2

        Compute the eigenvalues and eigenvectors of a complex upper
        Hessenberg matrix using the modified LR method.

  - comqr

        Compute the eigenvalues of complex upper Hessenberg matrix
        using the QR method.

  - comqr2

        Compute the eigenvalues and eigenvectors of a complex upper
        Hessenberg matrix.

  - cortb

        Form the eigenvectors of a complex general matrix from
        eigenvectors of upper Hessenberg matrix output from
        CORTH.

  - corth

        Reduce a complex general matrix to complex upper Hessenberg
        form using unitary similarity transformations.

  - eisdoc

        Documentation for EISPACK, a collection of subprograms for
        solving matrix eigen-problems.

  - elmbak

        Form the eigenvectors of a real general matrix from the
        eigenvectors of the upper Hessenberg matrix output from
        ELMHES.

  - elmhes

        Reduce a real general matrix to upper Hessenberg form
        using stabilized elementary similarity transformations.

  - eltran

        Accumulates the stabilized elementary similarity
        transformations used in the reduction of a real general
        matrix to upper Hessenberg form by ELMHES.

  - figi

        Transforms certain real non-symmetric tridiagonal matrix
        to symmetric tridiagonal matrix.

  - figi2

        Transforms certain real non-symmetric tridiagonal matrix
        to symmetric tridiagonal matrix.

  - hqr

        Compute the eigenvalues of a real upper Hessenberg matrix
        using the QR method.

  - hqr2

        Compute the eigenvalues and eigenvectors of a real upper
        Hessenberg matrix using QR method.

  - htrib3

        Compute the eigenvectors of a complex Hermitian matrix from
        the eigenvectors of a real symmetric tridiagonal matrix
        output from HTRID3.

  - htribk

        Form the eigenvectors of a complex Hermitian matrix from
        the eigenvectors of a real symmetric tridiagonal matrix
        output from HTRIDI.

  - htrid3

        Reduce a complex Hermitian (packed) matrix to a real
        symmetric tridiagonal matrix by unitary similarity
        transformations.

  - htridi

        Reduce a complex Hermitian matrix to a real symmetric
        tridiagonal matrix using unitary similarity
        transformations.

  - imtql1

        Compute the eigenvalues of a symmetric tridiagonal matrix
        using the implicit QL method.

  - imtql2

        Compute the eigenvalues and eigenvectors of a symmetric
        tridiagonal matrix using the implicit QL method.

  - imtqlv

        Compute the eigenvalues of a symmetric tridiagonal matrix
        using the implicit QL method.  Eigenvectors may be computed
        later.

  - invit

        Compute the eigenvectors of a real upper Hessenberg
        matrix associated with specified eigenvalues by inverse
        iteration.

  - minfit

        Compute the singular value decomposition of a rectangular
        matrix and solve the related linear least squares problem.

  - ortbak

        Form the eigenvectors of a general real matrix from the
        eigenvectors of the upper Hessenberg matrix output from
        ORTHES.

  - orthes

        Reduce a real general matrix to upper Hessenberg form
        using orthogonal similarity transformations.

  - ortran

        Accumulate orthogonal similarity transformations in the
        reduction of real general matrix by ORTHES.

  - qzhes

        The first step of the QZ algorithm for solving generalized
        matrix eigenproblems.  Accepts a pair of real general
        matrices and reduces one of them to upper Hessenberg
        and the other to upper triangular form using orthogonal
        transformations. Usually followed by QZIT, QZVAL, QZVEC.

  - qzit

        The second step of the QZ algorithm for generalized
        eigenproblems.  Accepts an upper Hessenberg and an upper
        triangular matrix and reduces the former to
        quasi-triangular form while preserving the form of the
        latter.  Usually preceded by QZHES and followed by QZVAL
        and QZVEC.

  - qzval

        The third step of the QZ algorithm for generalized
        eigenproblems.  Accepts a pair of real matrices, one in
        quasi-triangular form and the other in upper triangular
        form and computes the eigenvalues of the associated
        eigenproblem.  Usually preceded by QZHES, QZIT, and
        followed by QZVEC.

  - qzvec

        The optional fourth step of the QZ algorithm for
        generalized eigenproblems.  Accepts a matrix in
        quasi-triangular form and another in upper triangular
        and computes the eigenvectors of the triangular problem
        and transforms them back to the original coordinates
        Usually preceded by QZHES, QZIT, and QZVAL.

  - ratqr

        Compute the largest or smallest eigenvalues of a symmetric
        tridiagonal matrix using the rational QR method with Newton
        correction.

  - rebak

        Form the eigenvectors of a generalized symmetric
        eigensystem from the eigenvectors of derived matrix output
        from REDUC or REDUC2.

  - rebakb

        Form the eigenvectors of a generalized symmetric
        eigensystem from the eigenvectors of derived matrix output
        from REDUC2.

  - reduc

        Reduce a generalized symmetric eigenproblem to a standard
        symmetric eigenproblem using Cholesky factorization.

  - reduc2

        Reduce a certain generalized symmetric eigenproblem to a
        standard symmetric eigenproblem using Cholesky
        factorization.

  - rg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real general matrix.

  - rgg

        Compute the eigenvalues and eigenvectors for a real
        generalized eigenproblem.

  - rs

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  - rsb

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric band matrix.

  - rsg

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsgab

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsgba

        Compute the eigenvalues and, optionally, the eigenvectors
        of a symmetric generalized eigenproblem.

  - rsp

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix packed into a one dimensional
        array.

  - rst

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric tridiagonal matrix.

  - rt

        Compute the eigenvalues and eigenvectors of a special real
        tridiagonal matrix.

  - sspev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix stored in packed form.

  - tinvit

        Compute the eigenvectors of symmetric tridiagonal matrix
        corresponding to specified eigenvalues, using inverse
        iteration.

  - tql1

        Compute the eigenvalues of symmetric tridiagonal matrix by
        the QL method.

  - tql2

        Compute the eigenvalues and eigenvectors of symmetric
        tridiagonal matrix.

  - tqlrat

        Compute the eigenvalues of symmetric tridiagonal matrix
        using a rational variant of the QL method.

  - trbak1

        Form the eigenvectors of real symmetric matrix from
        the eigenvectors of a symmetric tridiagonal matrix formed
        by TRED1.

  - trbak3

        Form the eigenvectors of a real symmetric matrix from the
        eigenvectors of a symmetric tridiagonal matrix formed
        by TRED3.

  - tred1

        Reduce a real symmetric matrix to symmetric tridiagonal
        matrix using orthogonal similarity transformations.

  - tred2

        Reduce a real symmetric matrix to a symmetric tridiagonal
        matrix using and accumulating orthogonal transformations.

  - tred3

        Reduce a real symmetric matrix stored in packed form to
        symmetric tridiagonal matrix using orthogonal
        transformations.

  - tridib

        Compute the eigenvalues of a symmetric tridiagonal matrix
        in a given interval using Sturm sequencing.

  - tsturm

        Find those eigenvalues of a symmetric tridiagonal matrix
        in a given interval and their associated eigenvectors by
        Sturm sequencing.

  ### ELEMENTARY FUNCTIONS

  - acosh

        Compute the arc hyperbolic cosine.

  - alnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - asinh

        Compute the arc hyperbolic sine.

  - atanh

        Compute the arc hyperbolic tangent.

  - c9ln2r

        Evaluate LOG(1+Z) from second order relative accuracy so
        that  LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

  - cacos

        Compute the complex arc cosine.

  - cacosh

        Compute the arc hyperbolic cosine.

  - carg

        Compute the argument of a complex number.

  - casin

        Compute the complex arc sine.

  - casinh

        Compute the arc hyperbolic sine.

  - catan

        Compute the complex arc tangent.

  - catan2

        Compute the complex arc tangent in the proper quadrant.

  - catanh

        Compute the arc hyperbolic tangent.

  - cbrt

        Compute the cube root.

  - ccbrt

        Compute the cube root.

  - ccosh

        Compute the complex hyperbolic cosine.

  - ccot

        Compute the cotangent.

  - cexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - clnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - clog10

        Compute the principal value of the complex base 10
        logarithm.

  - cosdg

        Compute the cosine of an argument in degrees.

  - cot

        Compute the cotangent.

  - csinh

        Compute the complex hyperbolic sine.

  - ctan

        Compute the complex tangent.

  - ctanh

        Compute the complex hyperbolic tangent.

  - d9atn1

        Evaluate DATAN(X) from first order relative accuracy so
        that DATAN(X) = X + X**3*D9ATN1(X).

  - d9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

  - dacosh

        Compute the arc hyperbolic cosine.

  - dasinh

        Compute the arc hyperbolic sine.

  - datanh

        Compute the arc hyperbolic tangent.

  - dcbrt

        Compute the cube root.

  - dcosdg

        Compute the cosine of an argument in degrees.

  - dcot

        Compute the cotangent.

  - dexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - dlnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - drc

        Calculate a double precision approximation to
         DRC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  - dsindg

        Compute the sine of an argument in degrees.

  - exprel

        Calculate the relative error exponential (EXP(X)-1)/X.

  - fundoc

        Documentation for FNLIB, a collection of routines for
        evaluating elementary and special functions.

  - r9atn1

        Evaluate ATAN(X) from first order relative accuracy so that
        ATAN(X) = X + X**3*R9ATN1(X).

  - r9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

  - rc

        Calculate an approximation to
         RC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  - sindg

        Compute the sine of an argument in degrees.

  ### ELLIPTIC

  - genbun

        Solve by a cyclic reduction algorithm the linear system
        of equations that results from a finite difference
        approximation to certain 2-d elliptic PDE's on a centered
        grid .

  - hstcrt

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in Cartesian coordinates.

  - hstcsp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified Helmholtz
        equation in spherical coordinates assuming axisymmetry
        (no dependence on longitude).

  - hstcyl

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified
        Helmholtz equation in cylindrical coordinates.

  - hstplr

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in polar coordinates.

  - hstssp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz
        equation in spherical coordinates and on the surface of
        the unit sphere (radius of 1).

  - hw3crt

        Solve the standard seven-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscrt

        Solves the standard five-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscsp

        Solve a finite difference approximation to the modified
        Helmholtz equation in spherical coordinates assuming
        axisymmetry  (no dependence on longitude).

  - hwscyl

        Solve a standard finite difference approximation
        to the Helmholtz equation in cylindrical coordinates.

  - hwsplr

        Solve a finite difference approximation to the Helmholtz
        equation in polar coordinates.

  - hwsssp

        Solve a finite difference approximation to the Helmholtz
        equation in spherical coordinates and on the surface of the
        unit sphere (radius of 1).

  - poistg

        Solve a block tridiagonal system of linear equations
        that results from a staggered grid finite difference
        approximation to 2-D elliptic PDE's.

  - sepeli

        Discretize and solve a second and, optionally, a fourth
        order finite difference approximation on a uniform grid to
        the general separable elliptic partial differential
        equation on a rectangle with any combination of periodic or
        mixed boundary conditions.

  - sepx4

        Solve for either the second or fourth order finite
        difference approximation to the solution of a separable
        elliptic partial differential equation on a rectangle.
        Any combination of periodic or mixed boundary conditions is
        allowed.

  ### ELLIPTIC INTEGRAL

  - drc

        Calculate a double precision approximation to
         DRC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  - rc

        Calculate an approximation to
         RC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  ### ELLIPTIC PDE

  - blktri

        Solve a block tridiagonal system of linear equations
        (usually resulting from the discretization of separable
        two-dimensional elliptic equations).

  - cblktr

        Solve a block tridiagonal system of linear equations
        (usually resulting from the discretization of separable
        two-dimensional elliptic equations).

  - cmgnbn

        Solve a complex block tridiagonal linear system of
        equations by a cyclic reduction algorithm.

  - pois3d

        Solve a three-dimensional block tridiagonal linear system
        which arises from a finite difference approximation to a
        three-dimensional Poisson equation using the Fourier
        transform package FFTPAK written by Paul Swarztrauber.

  ### END POINT SINGULARITIES

  - dqags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqwgts

        This function subprogram is used together with the
        routine DQAWS and defines the WEIGHT function.

  - qags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qwgts

        This function subprogram is used together with the
        routine QAWS and defines the WEIGHT function.

  ### EPSILON ALGORITHM

  - dqelg

        The routine determines the limit of a given sequence of
        approximations, by means of the Epsilon algorithm of
        P.Wynn. An estimate of the absolute error is also given.
        The condensed Epsilon table is computed. Only those
        elements needed for the computation of the next diagonal
        are preserved.

  - qelg

        The routine determines the limit of a given sequence of
        approximations, by means of the Epsilon algorithm of
        P. Wynn. An estimate of the absolute error is also given.
        The condensed Epsilon table is computed. Only those
        elements needed for the computation of the next diagonal
        are preserved.

  ### EQUALITY CONSTRAINTS

  - dlsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - dwnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  - lsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - wnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  ### ERF

  - derf

        Compute the error function.

  - erf

        Compute the error function.

  ### ERFC

  - derfc

        Compute the complementary error function.

  - erfc

        Compute the complementary error function.

  ### ERROR

  - fdump

        Symbolic dump (should be locally written).

  - xerclr

        Reset current error number to zero.

  - xercnt

        Allow user control over handling of errors.

  - xerdmp

        Print the error tables and then clear them.

  - xerhlt

        Abort program execution and print error message.

  - xermax

        Set maximum number of times any error message is to be
        printed.

  - xersve

        Record that an error has occurred.

  - xgetf

        Return the current value of the error control flag.

  - xgetua

        Return unit number(s) to which error messages are being
        sent.

  - xgetun

        Return the (first) output file to which error messages
        are being sent.

  - xsetf

        Set the error control flag.

  - xsetua

        Set logical unit numbers (up to 5) to which error
        messages are to be sent.

  - xsetun

        Set output file to which error messages are to be sent.

  ### ERROR CHECKING

  - dchkw

        SLAP WORK/IWORK Array Bounds Checker.
        This routine checks the work array lengths and interfaces
        to the SLATEC error handler if a problem is found.

  - schkw

        SLAP WORK/IWORK Array Bounds Checker.
        This routine checks the work array lengths and interfaces
        to the SLATEC error handler if a problem is found.

  ### ERROR FUNCTION

  - derf

        Compute the error function.

  - erf

        Compute the error function.

  ### ERROR MESSAGE

  - xerbla

        Error handler for the Level 2 and Level 3 BLAS Routines.

  - xermsg

        Process error messages for SLATEC and other libraries.

  ### ERROR MESSAGES

  - j4save

        Save or recall global variables needed by error
        handling routines.

  - xerprn

        Print error messages processed by XERMSG.

  ### ERROR NUMBER

  - j4save

        Save or recall global variables needed by error
        handling routines.

  - numxer

        Return the most recent error number.

  ### EUCLIDEAN LENGTH

  - dnrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - scnrm2

        Compute the unitary norm of a complex vector.

  - snrm2

        Compute the Euclidean length (L2 norm) of a vector.

  ### EUCLIDEAN NORM

  - dnrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - scnrm2

        Compute the unitary norm of a complex vector.

  - snrm2

        Compute the Euclidean length (L2 norm) of a vector.

  ### EVALUATION OF B-SPLINE

  - bspvd

        Calculate the value and all derivatives of order less than
        NDERIV of all basis functions which do not vanish at X.

  - bspvn

        Calculate the value of all (possibly) nonzero basis
        functions at X.

  - bvalu

        Evaluate the B-representation of a B-spline at X for the
        function value or any of its derivatives.

  - dbspvd

        Calculate the value and all derivatives of order less than
        NDERIV of all basis functions which do not vanish at X.

  - dbspvn

        Calculate the value of all (possibly) nonzero basis
        functions at X.

  - dbvalu

        Evaluate the B-representation of a B-spline at X for the
        function value or any of its derivatives.

  ### EXCHANGE

  - cchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - dchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - schex

        Update the Cholesky factorization  A=TRANS(R)*R  of A
        positive definite matrix A of order P under diagonal
        permutations of the form TRANS(E)*A*E, where E is a
        permutation matrix.

  ### EXPONENTIAL

  - cexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - dexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - exprel

        Calculate the relative error exponential (EXP(X)-1)/X.

  ### EXPONENTIAL INTEGRAL

  - bskin

        Compute repeated integrals of the K-zero Bessel function.

  - dbskin

        Compute repeated integrals of the K-zero Bessel function.

  - de1

        Compute the exponential integral E1(X).

  - dei

        Compute the exponential integral Ei(X).

  - dexint

        Compute an M member sequence of exponential integrals
        E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

  - e1

        Compute the exponential integral E1(X).

  - ei

        Compute the exponential integral Ei(X).

  - exint

        Compute an M member sequence of exponential integrals
        E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

  ### EXPONENTIALLY SCALED

  - besi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - besi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - besk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - besk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - beskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - bie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  - dbie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  - dbsi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - dbsi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - dbsk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - dbsk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - dbskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  ### EXPONENTIALLY SCALED AIRY FUNCTION

  - aie

        Calculate the Airy function for a negative argument and an
        exponentially scaled Airy function for a non-negative
        argument.

  - daie

        Calculate the Airy function for a negative argument and an
        exponentially scaled Airy function for a non-negative
        argument.

  ### EXTENDED-RANGE DOUBLE-PRECISION ARITHMETIC

  - dxadd

        To provide double-precision floating-point arithmetic
        with an extended exponent range.

  - dxadj

        To provide double-precision floating-point arithmetic
        with an extended exponent range.

  - dxc210

        To provide double-precision floating-point arithmetic
        with an extended exponent range.

  - dxcon

        To provide double-precision floating-point arithmetic
        with an extended exponent range.

  - dxred

        To provide double-precision floating-point arithmetic
        with an extended exponent range.

  - dxset

        To provide double-precision floating-point arithmetic
        with an extended exponent range.

  ### EXTENDED-RANGE SINGLE-PRECISION ARITHMETIC

  - xadd

        To provide single-precision floating-point arithmetic
        with an extended exponent range.

  - xadj

        To provide single-precision floating-point arithmetic
        with an extended exponent range.

  - xc210

        To provide single-precision floating-point arithmetic
        with an extended exponent range.

  - xcon

        To provide single-precision floating-point arithmetic
        with an extended exponent range.

  - xred

        To provide single-precision floating-point arithmetic
        with an extended exponent range.

  - xset

        To provide single-precision floating-point arithmetic
        with an extended exponent range.

  ### EXTRAPOLATION

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur (e.g.
        SINGULARITIES, DISCONTINUITIES), are provided by the user.

  - dqagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - dqags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqelg

        The routine determines the limit of a given sequence of
        approximations, by means of the Epsilon algorithm of
        P.Wynn. An estimate of the absolute error is also given.
        The condensed Epsilon table is computed. Only those
        elements needed for the computation of the next diagonal
        are preserved.

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur(e.g. SINGULARITIES,
        DISCONTINUITIES), are provided by the user.

  - qagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
              ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - qags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qelg

        The routine determines the limit of a given sequence of
        approximations, by means of the Epsilon algorithm of
        P. Wynn. An estimate of the absolute error is also given.
        The condensed Epsilon table is computed. Only those
        elements needed for the computation of the next diagonal
        are preserved.

  ### FACTORIAL

  - dfac

        Compute the factorial function.

  - fac

        Compute the factorial function.

  ### FAST FOURIER TRANSFORM

  - dqcheb

        This routine computes the CHEBYSHEV series expansion
        of degrees 12 and 24 of a function using A
        FAST FOURIER TRANSFORM METHOD
        F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
        F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
        Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

  - fftdoc

        Documentation for FFTPACK, a collection of Fast Fourier
        Transform routines.

  - qcheb

        This routine computes the CHEBYSHEV series expansion
        of degrees 12 and 24 of a function using A
        FAST FOURIER TRANSFORM METHOD
        F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
        F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
        Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.

  ### FFT

  - fftdoc

        Documentation for FFTPACK, a collection of Fast Fourier
        Transform routines.

  ### FFTPACK

  - cfftb

        Compute the unnormalized inverse of CFFTF.

  - cfftb1

        Compute the unnormalized inverse of CFFTF1.

  - cfftf

        Compute the forward transform of a complex, periodic
        sequence.

  - cfftf1

        Compute the forward transform of a complex, periodic
        sequence.

  - cffti

        Initialize a work array for CFFTF and CFFTB.

  - cffti1

        Initialize a real and an integer work array for CFFTF1 and
        CFFTB1.

  - cosqb

        Compute the unnormalized inverse cosine transform.

  - cosqb1

        Compute the unnormalized inverse of COSQF1.

  - cosqf

        Compute the forward cosine transform with odd wave numbers.

  - cosqf1

        Compute the forward cosine transform with odd wave numbers.

  - cosqi

        Initialize a work array for COSQF and COSQB.

  - cost

        Compute the cosine transform of a real, even sequence.

  - costi

        Initialize a work array for COST.

  - ezfftb

        A simplified real, periodic, backward fast Fourier
        transform.

  - ezfftf

        Compute a simplified real, periodic, fast Fourier forward
        transform.

  - ezffti

        Initialize a work array for EZFFTF and EZFFTB.

  - rfftb

        Compute the backward fast Fourier transform of a real
        coefficient array.

  - rfftb1

        Compute the backward fast Fourier transform of a real
        coefficient array.

  - rfftf

        Compute the forward transform of a real, periodic sequence.

  - rfftf1

        Compute the forward transform of a real, periodic sequence.

  - rffti

        Initialize a work array for RFFTF and RFFTB.

  - rffti1

        Initialize a real and an integer work array for RFFTF1 and
        RFFTB1.

  - sinqb

        Compute the unnormalized inverse of SINQF.

  - sinqf

        Compute the forward sine transform with odd wave numbers.

  - sinqi

        Initialize a work array for SINQF and SINQB.

  - sint

        Compute the sine transform of a real, odd sequence.

  - sinti

        Initialize a work array for SINT.

  ### FIRST KIND

  - besi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - besi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - besi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - besi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - besj0

        Compute the Bessel function of the first kind of order
        zero.

  - besj1

        Compute the Bessel function of the first kind of order one.

  - dbesi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - dbesi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - dbesj0

        Compute the Bessel function of the first kind of order
        zero.

  - dbesj1

        Compute the Bessel function of the first kind of order one.

  - dbsi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - dbsi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  ### FIRST ORDER

  - cexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - d9atn1

        Evaluate DATAN(X) from first order relative accuracy so
        that DATAN(X) = X + X**3*D9ATN1(X).

  - dexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - dpoch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  - exprel

        Calculate the relative error exponential (EXP(X)-1)/X.

  - poch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  - r9atn1

        Evaluate ATAN(X) from first order relative accuracy so that
        ATAN(X) = X + X**3*R9ATN1(X).

  ### FISHPACK

  - blktri

        Solve a block tridiagonal system of linear equations
        (usually resulting from the discretization of separable
        two-dimensional elliptic equations).

  - cblktr

        Solve a block tridiagonal system of linear equations
        (usually resulting from the discretization of separable
        two-dimensional elliptic equations).

  - cmgnbn

        Solve a complex block tridiagonal linear system of
        equations by a cyclic reduction algorithm.

  - genbun

        Solve by a cyclic reduction algorithm the linear system
        of equations that results from a finite difference
        approximation to certain 2-d elliptic PDE's on a centered
        grid .

  - hstcrt

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in Cartesian coordinates.

  - hstcsp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified Helmholtz
        equation in spherical coordinates assuming axisymmetry
        (no dependence on longitude).

  - hstcyl

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified
        Helmholtz equation in cylindrical coordinates.

  - hstplr

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in polar coordinates.

  - hstssp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz
        equation in spherical coordinates and on the surface of
        the unit sphere (radius of 1).

  - hw3crt

        Solve the standard seven-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscrt

        Solves the standard five-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscsp

        Solve a finite difference approximation to the modified
        Helmholtz equation in spherical coordinates assuming
        axisymmetry  (no dependence on longitude).

  - hwscyl

        Solve a standard finite difference approximation
        to the Helmholtz equation in cylindrical coordinates.

  - hwsplr

        Solve a finite difference approximation to the Helmholtz
        equation in polar coordinates.

  - hwsssp

        Solve a finite difference approximation to the Helmholtz
        equation in spherical coordinates and on the surface of the
        unit sphere (radius of 1).

  - pois3d

        Solve a three-dimensional block tridiagonal linear system
        which arises from a finite difference approximation to a
        three-dimensional Poisson equation using the Fourier
        transform package FFTPAK written by Paul Swarztrauber.

  - poistg

        Solve a block tridiagonal system of linear equations
        that results from a staggered grid finite difference
        approximation to 2-D elliptic PDE's.

  - sepeli

        Discretize and solve a second and, optionally, a fourth
        order finite difference approximation on a uniform grid to
        the general separable elliptic partial differential
        equation on a rectangle with any combination of periodic or
        mixed boundary conditions.

  - sepx4

        Solve for either the second or fourth order finite
        difference approximation to the solution of a separable
        elliptic partial differential equation on a rectangle.
        Any combination of periodic or mixed boundary conditions is
        allowed.

  ### FNLIB

  - acosh

        Compute the arc hyperbolic cosine.

  - ai

        Evaluate the Airy function.

  - aie

        Calculate the Airy function for a negative argument and an
        exponentially scaled Airy function for a non-negative
        argument.

  - albeta

        Compute the natural logarithm of the complete Beta
        function.

  - algams

        Compute the logarithm of the absolute value of the Gamma
        function.

  - ali

        Compute the logarithmic integral.

  - alngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - alnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - asinh

        Compute the arc hyperbolic sine.

  - atanh

        Compute the arc hyperbolic tangent.

  - besi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - besi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - besi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - besi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - besj0

        Compute the Bessel function of the first kind of order
        zero.

  - besj1

        Compute the Bessel function of the first kind of order one.

  - besk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - besk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - besk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - besk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - beskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - besks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - besy0

        Compute the Bessel function of the second kind of order
        zero.

  - besy1

        Compute the Bessel function of the second kind of order
        one.

  - beta

        Compute the complete Beta function.

  - betai

        Calculate the incomplete Beta function.

  - bi

        Evaluate the Bairy function (the Airy function of the
        second kind).

  - bie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  - binom

        Compute the binomial coefficients.

  - c0lgmc

        Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative
        accuracy.

  - c9lgmc

        Compute the log gamma correction factor so that
        LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
        + C9LGMC(Z).

  - c9ln2r

        Evaluate LOG(1+Z) from second order relative accuracy so
        that  LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

  - cacos

        Compute the complex arc cosine.

  - cacosh

        Compute the arc hyperbolic cosine.

  - carg

        Compute the argument of a complex number.

  - casin

        Compute the complex arc sine.

  - casinh

        Compute the arc hyperbolic sine.

  - catan

        Compute the complex arc tangent.

  - catan2

        Compute the complex arc tangent in the proper quadrant.

  - catanh

        Compute the arc hyperbolic tangent.

  - cbeta

        Compute the complete Beta function.

  - cbrt

        Compute the cube root.

  - ccbrt

        Compute the cube root.

  - ccosh

        Compute the complex hyperbolic cosine.

  - ccot

        Compute the cotangent.

  - cexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - cgamma

        Compute the complete Gamma function.

  - cgamr

        Compute the reciprocal of the Gamma function.

  - chu

        Compute the logarithmic confluent hypergeometric function.

  - clbeta

        Compute the natural logarithm of the complete Beta
        function.

  - clngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - clnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - clog10

        Compute the principal value of the complex base 10
        logarithm.

  - cosdg

        Compute the cosine of an argument in degrees.

  - cot

        Compute the cotangent.

  - cpsi

        Compute the Psi (or Digamma) function.

  - csevl

        Evaluate a Chebyshev series.

  - csinh

        Compute the complex hyperbolic sine.

  - ctan

        Compute the complex tangent.

  - ctanh

        Compute the complex hyperbolic tangent.

  - d9aimp

        Evaluate the Airy modulus and phase.

  - d9atn1

        Evaluate DATAN(X) from first order relative accuracy so
        that DATAN(X) = X + X**3*D9ATN1(X).

  - d9b0mp

        Evaluate the modulus and phase for the J0 and Y0 Bessel
        functions.

  - d9b1mp

        Evaluate the modulus and phase for the J1 and Y1 Bessel
        functions.

  - d9chu

        Evaluate for large Z  Z**A * U(A,B,Z) where U is the
        logarithmic confluent hypergeometric function.

  - d9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and X small.

  - d9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - d9knus

        Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
        K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

  - d9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - d9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - d9lgmc

        Compute the log Gamma correction factor so that
        LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
        + D9LGMC(X).

  - d9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

  - d9pak

        Pack a base 2 exponent into a floating point number.

  - d9upak

        Unpack a floating point number X so that X = Y*2**N.

  - dai

        Evaluate the Airy function.

  - dacosh

        Compute the arc hyperbolic cosine.

  - daie

        Calculate the Airy function for a negative argument and an
        exponentially scaled Airy function for a non-negative
        argument.

  - dasinh

        Compute the arc hyperbolic sine.

  - datanh

        Compute the arc hyperbolic tangent.

  - daws

        Compute Dawson's function.

  - dbesi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - dbesi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - dbesj0

        Compute the Bessel function of the first kind of order
        zero.

  - dbesj1

        Compute the Bessel function of the first kind of order one.

  - dbesk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - dbesk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - dbesks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbesy0

        Compute the Bessel function of the second kind of order
        zero.

  - dbesy1

        Compute the Bessel function of the second kind of order
        one.

  - dbeta

        Compute the complete Beta function.

  - dbetai

        Calculate the incomplete Beta function.

  - dbi

        Evaluate the Bairy function (the Airy function of the
        second kind).

  - dbie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  - dbinom

        Compute the binomial coefficients.

  - dbsi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - dbsi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - dbsk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - dbsk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - dbskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - dcbrt

        Compute the cube root.

  - dchu

        Compute the logarithmic confluent hypergeometric function.

  - dcosdg

        Compute the cosine of an argument in degrees.

  - dcot

        Compute the cotangent.

  - dcsevl

        Evaluate a Chebyshev series.

  - ddaws

        Compute Dawson's function.

  - de1

        Compute the exponential integral E1(X).

  - dei

        Compute the exponential integral Ei(X).

  - derf

        Compute the error function.

  - derfc

        Compute the complementary error function.

  - dexprl

        Calculate the relative error exponential (EXP(X)-1)/X.

  - dfac

        Compute the factorial function.

  - dgami

        Evaluate the incomplete Gamma function.

  - dgamic

        Calculate the complementary incomplete Gamma function.

  - dgamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - dgamlm

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  - dgamma

        Compute the complete Gamma function.

  - dgamr

        Compute the reciprocal of the Gamma function.

  - dlbeta

        Compute the natural logarithm of the complete Beta
        function.

  - dlgams

        Compute the logarithm of the absolute value of the Gamma
        function.

  - dli

        Compute the logarithmic integral.

  - dlngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - dlnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - dpoch

        Evaluate a generalization of Pochhammer's symbol.

  - dpoch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  - dpsi

        Compute the Psi (or Digamma) function.

  - dsindg

        Compute the sine of an argument in degrees.

  - dspenc

        Compute a form of Spence's integral due to K. Mitchell.

  - e1

        Compute the exponential integral E1(X).

  - ei

        Compute the exponential integral Ei(X).

  - erf

        Compute the error function.

  - erfc

        Compute the complementary error function.

  - exprel

        Calculate the relative error exponential (EXP(X)-1)/X.

  - fac

        Compute the factorial function.

  - gami

        Evaluate the incomplete Gamma function.

  - gamic

        Calculate the complementary incomplete Gamma function.

  - gamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - gamlim

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  - gamma

        Compute the complete Gamma function.

  - gamr

        Compute the reciprocal of the Gamma function.

  - initds

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - inits

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - psi

        Compute the Psi (or Digamma) function.

  - poch

        Evaluate a generalization of Pochhammer's symbol.

  - poch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  - r9aimp

        Evaluate the Airy modulus and phase.

  - r9atn1

        Evaluate ATAN(X) from first order relative accuracy so that
        ATAN(X) = X + X**3*R9ATN1(X).

  - r9chu

        Evaluate for large Z  Z**A * U(A,B,Z) where U is the
        logarithmic confluent hypergeometric function.

  - r9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and for small X.

  - r9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - rand

        Generate a uniformly distributed random number.

  - r9knus

        Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
        K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

  - r9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - r9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - r9lgmc

        Compute the log Gamma correction factor so that
        LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
        + R9LGMC(X).

  - r9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

  - r9pak

        Pack a base 2 exponent into a floating point number.

  - r9upak

        Unpack a floating point number X so that X = Y*2**N.

  - rgauss

        Generate a normally distributed (Gaussian) random number.

  - runif

        Generate a uniformly distributed random number.

  - sindg

        Compute the sine of an argument in degrees.

  - spenc

        Compute a form of Spence's integral due to K. Mitchell.

  ### FOURIER INTEGRALS

  - dqawf

        The routine calculates an approximation result to a given
        Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawf

        The routine calculates an approximation result to a given
        Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
         where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  ### FOURIER TRANSFORM

  - cfftb

        Compute the unnormalized inverse of CFFTF.

  - cfftb1

        Compute the unnormalized inverse of CFFTF1.

  - cfftf

        Compute the forward transform of a complex, periodic
        sequence.

  - cfftf1

        Compute the forward transform of a complex, periodic
        sequence.

  - cffti

        Initialize a work array for CFFTF and CFFTB.

  - cffti1

        Initialize a real and an integer work array for CFFTF1 and
        CFFTB1.

  - cosqb1

        Compute the unnormalized inverse of COSQF1.

  - cosqf1

        Compute the forward cosine transform with odd wave numbers.

  - ezfftb

        A simplified real, periodic, backward fast Fourier
        transform.

  - ezfftf

        Compute a simplified real, periodic, fast Fourier forward
        transform.

  - ezffti

        Initialize a work array for EZFFTF and EZFFTB.

  - rfftb

        Compute the backward fast Fourier transform of a real
        coefficient array.

  - rfftb1

        Compute the backward fast Fourier transform of a real
        coefficient array.

  - rfftf

        Compute the forward transform of a real, periodic sequence.

  - rfftf1

        Compute the forward transform of a real, periodic sequence.

  - rffti

        Initialize a work array for RFFTF and RFFTB.

  - rffti1

        Initialize a real and an integer work array for RFFTF1 and
        RFFTB1.

  - sinqb

        Compute the unnormalized inverse of SINQF.

  - sinqf

        Compute the forward sine transform with odd wave numbers.

  - sinqi

        Initialize a work array for SINQF and SINQB.

  - sint

        Compute the sine transform of a real, odd sequence.

  - sinti

        Initialize a work array for SINT.

  ### FRACTIONAL ORDER

  - beskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - besks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbesks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  ### GAMMA FUNCTION

  - c0lgmc

        Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative
        accuracy.

  ### GAUSS QUADRATURE

  - dgaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  - gaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  ### GAUSS-KRONROD RULES

  - dqag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to
        compute J = Integral of ABS(F) over (A,B). For small value
        of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO
        Rule is used. Otherwise a generalized CLENSHAW-CURTIS
        method is used.

  - qag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)
        and to compute J=Integral of ABS(F) over (A,B). For small
        value of OMEGA or small intervals (A,B) 15-point GAUSS-
        KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

  ### GAUSS-KRONROD(PATTERSON) RULES

  - dqng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### GAUSSIAN

  - rgauss

        Generate a normally distributed (Gaussian) random number.

  ### GEAR'S METHOD

  - cdriv1

        The function of CDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  CDRIV1 allows complex-valued differential
        equations.

  - cdriv2

        The function of CDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  CDRIV2 allows complex-valued differential
        equations.

  - cdriv3

        The function of CDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  CDRIV3
        allows complex-valued differential equations.

  - ddriv1

        The function of DDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  DDRIV1 uses double precision arithmetic.

  - ddriv2

        The function of DDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  DDRIV2 uses double precision arithmetic.

  - ddriv3

        The function of DDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  DDRIV3
        uses double precision arithmetic.

  - sdriv1

        The function of SDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  SDRIV1 uses single precision arithmetic.

  - sdriv2

        The function of SDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  SDRIV2 uses single precision arithmetic.

  - sdriv3

        The function of SDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  SDRIV3
        uses single precision arithmetic.

  ### GENERAL MATRIX

  - cgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - cgeev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex general matrix.

  - cgefa

        Factor a matrix using Gaussian elimination.

  - cgefs

        Solve a general system of linear equations.

  - cgeir

        Solve a general system of linear equations.  Iterative
        refinement is used to obtain an error estimate.

  - dgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - dgefa

        Factor a matrix using Gaussian elimination.

  - dgefs

        Solve a general system of linear equations.

  - sgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - sgeev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real general matrix.

  - sgefa

        Factor a matrix using Gaussian elimination.

  - sgefs

        Solve a general system of linear equations.

  - sgeir

        Solve a general system of linear equations.  Iterative
        refinement is used to obtain an error estimate.

  ### GENERAL SYSTEM OF LINEAR EQUATIONS

  - cgefs

        Solve a general system of linear equations.

  - cgeir

        Solve a general system of linear equations.  Iterative
        refinement is used to obtain an error estimate.

  - dgefs

        Solve a general system of linear equations.

  - sgefs

        Solve a general system of linear equations.

  - sgeir

        Solve a general system of linear equations.  Iterative
        refinement is used to obtain an error estimate.

  ### GENERAL-PURPOSE

  - dqag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur (e.g.
        SINGULARITIES, DISCONTINUITIES), are provided by the user.

  - dqagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - dqags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur(e.g. SINGULARITIES,
        DISCONTINUITIES), are provided by the user.

  - qagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
              ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - qags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### GENERALIZED MINIMUM RESIDUAL

  - dgmres

        Preconditioned GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - dhels

        Internal routine for DGMRES.

  - dheqr

        Internal routine for DGMRES.

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - dorth

        Internal routine for DGMRES.

  - dpigmr

        Internal routine for DGMRES.

  - drlcal

        Internal routine for DGMRES.

  - dsdgmr

        Diagonally scaled GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - dslugm

        Incomplete LU GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - dxlcal

        Internal routine for DGMRES.

  - sgmres

        Preconditioned GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - shels

        Internal routine for SGMRES.

  - sheqr

        Internal routine for SGMRES.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - sorth

        Internal routine for SGMRES.

  - spigmr

        Internal routine for SGMRES.

  - srlcal

        Internal routine for SGMRES.

  - ssdgmr

        Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - sslugm

        Incomplete LU GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - sxlcal

        Internal routine for SGMRES.

  ### GIVENS ROTATION

  - crotg

        Construct a Givens transformation.

  - csrot

        Apply a plane Givens rotation.

  - drot

        Apply a plane Givens rotation.

  - drotg

        Construct a plane Givens rotation.

  - srot

        Apply a plane Givens rotation.

  - srotg

        Construct a plane Givens rotation.

  ### GIVENS TRANSFORMATION

  - crotg

        Construct a Givens transformation.

  - csrot

        Apply a plane Givens rotation.

  - drot

        Apply a plane Givens rotation.

  - drotg

        Construct a plane Givens rotation.

  - srot

        Apply a plane Givens rotation.

  - srotg

        Construct a plane Givens rotation.

  ### GLOBALLY ADAPTIVE

  - dqag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur (e.g.
        SINGULARITIES, DISCONTINUITIES), are provided by the user.

  - dqagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - dqags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur(e.g. SINGULARITIES,
        DISCONTINUITIES), are provided by the user.

  - qagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
              ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - qags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### GMRES

  - isdgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - issgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  ### GRADIENTS

  - chkder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  - dckder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  ### GUIDELINES FOR SELECTION

  - qpdoc

        Documentation for QUADPACK, a package of subprograms for
        automatic evaluation of one-dimensional definite integrals.

  ### H BESSEL FUNCTIONS

  - cbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  - zbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  ### HANKEL FUNCTIONS

  - cbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  - zbesh

        Compute a sequence of the Hankel functions H(m,a,z)
        for superscript m=1 or 2, real nonnegative orders a=b,
        b+1,... where b>0, and nonzero complex argument z.  A
        scaling option is available to help avoid overflow.

  ### HELMHOLTZ

  - hstcrt

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in Cartesian coordinates.

  - hstcsp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified Helmholtz
        equation in spherical coordinates assuming axisymmetry
        (no dependence on longitude).

  - hstcyl

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified
        Helmholtz equation in cylindrical coordinates.

  - hstplr

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in polar coordinates.

  - hstssp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz
        equation in spherical coordinates and on the surface of
        the unit sphere (radius of 1).

  - hw3crt

        Solve the standard seven-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscrt

        Solves the standard five-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscsp

        Solve a finite difference approximation to the modified
        Helmholtz equation in spherical coordinates assuming
        axisymmetry  (no dependence on longitude).

  - hwscyl

        Solve a standard finite difference approximation
        to the Helmholtz equation in cylindrical coordinates.

  - hwsplr

        Solve a finite difference approximation to the Helmholtz
        equation in polar coordinates.

  - hwsssp

        Solve a finite difference approximation to the Helmholtz
        equation in spherical coordinates and on the surface of the
        unit sphere (radius of 1).

  - pois3d

        Solve a three-dimensional block tridiagonal linear system
        which arises from a finite difference approximation to a
        three-dimensional Poisson equation using the Fourier
        transform package FFTPAK written by Paul Swarztrauber.

  - poistg

        Solve a block tridiagonal system of linear equations
        that results from a staggered grid finite difference
        approximation to 2-D elliptic PDE's.

  - sepeli

        Discretize and solve a second and, optionally, a fourth
        order finite difference approximation on a uniform grid to
        the general separable elliptic partial differential
        equation on a rectangle with any combination of periodic or
        mixed boundary conditions.

  - sepx4

        Solve for either the second or fourth order finite
        difference approximation to the solution of a separable
        elliptic partial differential equation on a rectangle.
        Any combination of periodic or mixed boundary conditions is
        allowed.

  ### HERMITE INTERPOLATION

  - dpchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for DPCHIM
        or DPCHIC. If only function values are required, use
        DPCHFE instead.

  - dpchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for DPCHIM or DPCHIC.

  - pchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for PCHIM
        or PCHIC.  If only function values are required, use
        PCHFE instead.

  - pchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for PCHIM or PCHIC.

  ### HERMITIAN

  - chico

        Factor a complex Hermitian matrix by elimination with sym-
        metric pivoting and estimate the condition of the matrix.

  - chidi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix using the factors obtained from CHIFA.

  - chifa

        Factor a complex Hermitian matrix by elimination
        (symmetric pivoting).

  - chisl

        Solve the complex Hermitian system using factors obtained
        from CHIFA.

  - chpco

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - chpdi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix stored in packed form using the factors
        obtained from CHPFA.

  - chpfa

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting.

  - chpsl

        Solve a complex Hermitian system using factors obtained
        from CHPFA.

  - cpofs

        Solve a positive definite symmetric complex system of
        linear equations.

  - cpoir

        Solve a positive definite Hermitian system of linear
        equations.  Iterative refinement is used to obtain an
        error estimate.

  - dpofs

        Solve a positive definite symmetric system of linear
        equations.

  - spofs

        Solve a positive definite symmetric system of linear
        equations.

  - spoir

        Solve a positive definite symmetric system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  ### HYPERBOLIC BESSEL FUNCTION

  - besi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - besi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - besi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - besi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - besk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - besk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - besk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - besk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - dbesi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - dbesi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - dbesk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - dbesk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - dbsi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - dbsi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - dbsk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - dbsk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  ### HYPERBOLIC COSINE

  - ccosh

        Compute the complex hyperbolic cosine.

  ### HYPERBOLIC SINE

  - csinh

        Compute the complex hyperbolic sine.

  ### HYPERBOLIC TANGENT

  - ctanh

        Compute the complex hyperbolic tangent.

  ### I BESSEL FUNCTION

  - besi

        Compute an N member sequence of I Bessel functions
        I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions
        EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative
        ALPHA and X.

  - dbesi

        Compute an N member sequence of I Bessel functions
        I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions
        EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for nonnegative
        ALPHA and X.

  ### I BESSEL FUNCTIONS

  - cbesi

        Compute a sequence of the Bessel functions I(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesi

        Compute a sequence of the Bessel functions I(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### IMPLICIT DIFFERENTIAL SYSTEMS

  - ddassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  - sdassl

        This code solves a system of differential/algebraic
        equations of the form G(T,Y,YPRIME) = 0.

  ### INCOMPLETE BETA FUNCTION

  - betai

        Calculate the incomplete Beta function.

  - dbetai

        Calculate the incomplete Beta function.

  ### INCOMPLETE CHOLESKY

  - dsiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - ssiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  ### INCOMPLETE CHOLESKY FACTORIZATION

  - dsics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  - ssics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  ### INCOMPLETE ELLIPTIC INTEGRAL

  - drd

        Compute the incomplete or complete elliptic integral of
        the 2nd kind. For X and Y nonnegative, X+Y and Z positive,
        DRD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - drf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - drj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                          -1/2     -1/2     -1/2     -1
                (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  - rd

        Compute the incomplete or complete elliptic integral of the
        2nd kind.  For X and Y nonnegative, X+Y and Z positive,
         RD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - rf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - rj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                              -1/2     -1/2     -1/2     -1
                    (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  ### INCOMPLETE FACTORIZATION

  - dllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - sllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  ### INCOMPLETE GAMMA FUNCTION

  - d9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - dgami

        Evaluate the incomplete Gamma function.

  - gami

        Evaluate the incomplete Gamma function.

  - r9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  ### INCOMPLETE LU FACTORIZATION

  - dsilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - ssilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  ### INEQUALITY

  - dbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - dbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  - sbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - sbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  ### INEQUALITY CONSTRAINTS

  - dlsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - dwnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  - lsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - wnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  ### INFINITE INTERVALS

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  ### INITIAL VALUE PROBLEMS

  - cdriv1

        The function of CDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  CDRIV1 allows complex-valued differential
        equations.

  - cdriv2

        The function of CDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  CDRIV2 allows complex-valued differential
        equations.

  - cdriv3

        The function of CDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  CDRIV3
        allows complex-valued differential equations.

  - ddeabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - ddebdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - dderkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - ddriv1

        The function of DDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  DDRIV1 uses double precision arithmetic.

  - ddriv2

        The function of DDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  DDRIV2 uses double precision arithmetic.

  - ddriv3

        The function of DDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  DDRIV3
        uses double precision arithmetic.

  - deabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - debdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - derkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - dintp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in DSTEPS at XOUT.  Must be used in
        conjunction with DSTEPS.

  - dsteps

        Integrate a system of first order ordinary differential
        equations one step.

  - sdriv1

        The function of SDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  SDRIV1 uses single precision arithmetic.

  - sdriv2

        The function of SDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  SDRIV2 uses single precision arithmetic.

  - sdriv3

        The function of SDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  SDRIV3
        uses single precision arithmetic.

  - sintrp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in STEPS at XOUT.  Must be used in
        conjunction with STEPS.

  - steps

        Integrate a system of first order ordinary differential
        equations one step.

  ### INITIALIZE

  - initds

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - inits

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  ### INNER PRODUCT

  - cdcdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - cdotc

        Dot product of two complex vectors using the complex
        conjugate of the first vector.

  - cdotu

        Compute the inner product of two vectors.

  - dcdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - ddot

        Compute the inner product of two vectors.

  - dqdota

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dqdoti

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dsdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - sdot

        Compute the inner product of two vectors.

  - sdsdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  ### INTEGRAL OF B-SPLINE

  - bfqad

        Compute the integral of a product of a function and a
        derivative of a B-spline.

  - dbfqad

        Compute the integral of a product of a function and a
        derivative of a K-th order B-spline.

  ### INTEGRAL OF B-SPLINES

  - bsqad

        Compute the integral of a K-th order B-spline using the
        B-representation.

  - dbsqad

        Compute the integral of a K-th order B-spline using the
        B-representation.

  ### INTEGRAL OF THE FIRST KIND

  - drf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - rf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  ### INTEGRAL OF THE SECOND KIND

  - drd

        Compute the incomplete or complete elliptic integral of
        the 2nd kind. For X and Y nonnegative, X+Y and Z positive,
        DRD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - rd

        Compute the incomplete or complete elliptic integral of the
        2nd kind.  For X and Y nonnegative, X+Y and Z positive,
         RD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  ### INTEGRAL OF THE THIRD KIND

  - drj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                          -1/2     -1/2     -1/2     -1
                (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  - rj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                              -1/2     -1/2     -1/2     -1
                    (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  ### INTEGRALS OF BESSEL FUNCTIONS

  - bskin

        Compute repeated integrals of the K-zero Bessel function.

  - dbskin

        Compute repeated integrals of the K-zero Bessel function.

  ### INTEGRAND EXAMINATOR

  - dqag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### INTEGRATION

  - avint

        Integrate a function tabulated at arbitrarily spaced
        abscissas using overlapping parabolas.

  - davint

        Integrate a function tabulated at arbitrarily spaced
        abscissas using overlapping parabolas.

  - dqnc79

        Integrate a function using a 7-point adaptive Newton-Cotes
        quadrature rule.

  - qnc79

        Integrate a function using a 7-point adaptive Newton-Cotes
        quadrature rule.

  ### INTEGRATION BETWEEN ZEROS

  - dqawf

        The routine calculates an approximation result to a given
        Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawf

        The routine calculates an approximation result to a given
        Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
         where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  ### INTEGRATION RULES FOR FUNCTIONS WITH COS OR SIN FACTOR

  - dqc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to
        compute J = Integral of ABS(F) over (A,B). For small value
        of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO
        Rule is used. Otherwise a generalized CLENSHAW-CURTIS
        method is used.

  - qc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)
        and to compute J=Integral of ABS(F) over (A,B). For small
        value of OMEGA or small intervals (A,B) 15-point GAUSS-
        KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

  ### INTERCHANGE

  - cswap

        Interchange two vectors.

  - dswap

        Interchange two vectors.

  - iswap

        Interchange two vectors.

  - sswap

        Interchange two vectors.

  ### INTERPOLATION

  - bint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  - bintk

        Compute the B-representation of a spline which interpolates
        given data.

  - bspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  - bspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - dbint4

        Compute the B-representation of a cubic spline
        which interpolates given data.

  - dbintk

        Compute the B-representation of a spline which interpolates
        given data.

  - dbspdr

        Use the B-representation to construct a divided difference
        table preparatory to a (right) derivative calculation.

  - dbspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - dintrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision of
        the X interval.

  - dpfqad

        Compute the integral on (X1,X2) of a product of a
        function F and the ID-th derivative of a B-spline,
        (PP-representation).

  - dppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - dppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  - intrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision
        of the X interval.

  - pfqad

        Compute the integral on (X1,X2) of a product of a function
        F and the ID-th derivative of a B-spline,
        (PP-representation).

  - ppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - ppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  ### INVERSE

  - cgbdi

        Compute the determinant of a complex band matrix using the
        factors from CGBCO or CGBFA.

  - cgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by CGECO or CGEFA.

  - chidi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix using the factors obtained from CHIFA.

  - chpdi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix stored in packed form using the factors
        obtained from CHPFA.

  - cpbdi

        Compute the determinant of a complex Hermitian positive
        definite band matrix using the factors computed by CPBCO or
        CPBFA.

  - cpodi

        Compute the determinant and inverse of a certain complex
        Hermitian positive definite matrix using the factors
        computed by CPOCO, CPOFA, or CQRDC.

  - cppdi

        Compute the determinant and inverse of a complex Hermitian
        positive definite matrix using factors from CPPCO or CPPFA.

  - csidi

        Compute the determinant and inverse of a complex symmetric
        matrix using the factors from CSIFA.

  - cspdi

        Compute the determinant and inverse of a complex symmetric
        matrix stored in packed form using the factors from CSPFA.

  - ctrdi

        Compute the determinant and inverse of a triangular matrix.

  - dgbdi

        Compute the determinant of a band matrix using the factors
        computed by DGBCO or DGBFA.

  - dgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by DGECO or DGEFA.

  - dpbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by DPBCO or DPBFA.

  - dpodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by DPOCO, DPOFA or DQRDC.

  - dppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from DPPCO or DPPFA.

  - dsidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from DSIFA.

  - dspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from DSPFA.

  - dtrdi

        Compute the determinant and inverse of a triangular matrix.

  - sgbdi

        Compute the determinant of a band matrix using the factors
        computed by SGBCO or SGBFA.

  - sgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by SGECO or SGEFA.

  - spbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by SPBCO or SPBFA.

  - spodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by SPOCO, SPOFA or SQRDC.

  - sppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from SPPCO or SPPFA.

  - ssidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from SSIFA.

  - sspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from SSPFA.

  - strdi

        Compute the determinant and inverse of a triangular matrix.

  ### INVERSE COSINE FOURIER TRANSFORM

  - cosqb

        Compute the unnormalized inverse cosine transform.

  ### INVERSE HYPERBOLIC COSINE

  - acosh

        Compute the arc hyperbolic cosine.

  - cacosh

        Compute the arc hyperbolic cosine.

  - dacosh

        Compute the arc hyperbolic cosine.

  ### INVERSE HYPERBOLIC SINE

  - asinh

        Compute the arc hyperbolic sine.

  - casinh

        Compute the arc hyperbolic sine.

  - dasinh

        Compute the arc hyperbolic sine.

  ### INVERSE HYPERBOLIC TANGENT

  - atanh

        Compute the arc hyperbolic tangent.

  - catanh

        Compute the arc hyperbolic tangent.

  - datanh

        Compute the arc hyperbolic tangent.

  ### ITERATIVE IMPROVEMENT

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  ### ITERATIVE INCOMPLETE LU PRECONDITION

  - dslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - dslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - dslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - dsluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  - sslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - sslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - sslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - ssluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  ### ITERATIVE PRECONDITION

  - dbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - dcg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - dcgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - dcgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - dgmres

        Preconditioned GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - dhels

        Internal routine for DGMRES.

  - dheqr

        Internal routine for DGMRES.

  - dir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - dllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - domn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - dorth

        Internal routine for DGMRES.

  - dpigmr

        Internal routine for DGMRES.

  - drlcal

        Internal routine for DGMRES.

  - dsdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - dsdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - dsdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - dsdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - dsdgmr

        Diagonally scaled GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - dsdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - dsdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - dsgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - dsiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - dsics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  - dsilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - dsilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - dsjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - dsli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - dsli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - dsllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - dslugm

        Incomplete LU GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - dslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - dslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - dslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - dsluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - dsmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - dsmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  - dxlcal

        Internal routine for DGMRES.

  - isdbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isdcgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - isdomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - issbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isscgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - issomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - sbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - scg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - scgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - scgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - sir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - sgmres

        Preconditioned GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - shels

        Internal routine for SGMRES.

  - sheqr

        Internal routine for SGMRES.

  - sllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - somn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - sorth

        Internal routine for SGMRES.

  - spigmr

        Internal routine for SGMRES.

  - srlcal

        Internal routine for SGMRES.

  - ssdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - ssdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - ssdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - ssdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - ssdgmr

        Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - ssdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - ssdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - ssgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - ssiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - ssics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  - ssilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - ssilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - ssjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - ssli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - ssli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - ssllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - sslugm

        Incomplete LU GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - sslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - sslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - sslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - ssluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - ssmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - ssmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  - sxlcal

        Internal routine for SGMRES.

  ### J BESSEL FUNCTION

  - besj

        Compute an N member sequence of J Bessel functions
        J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA
        and X.

  - dbesj

        Compute an N member sequence of J Bessel functions
        J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA
        and X.

  ### J BESSEL FUNCTIONS

  - cbesj

        Compute a sequence of the Bessel functions J(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesj

        Compute a sequence of the Bessel functions J(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### JACOBIAN

  - chkder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  - dckder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  ### K BESSEL FUNCTION

  - besk

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions
        EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  - dbesk

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions
        EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  ### K BESSEL FUNCTIONS

  - cbesk

        Compute a sequence of the Bessel functions K(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesk

        Compute a sequence of the Bessel functions K(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### K-ZERO BESSEL FUNCTION

  - bskin

        Compute repeated integrals of the K-zero Bessel function.

  - dbskin

        Compute repeated integrals of the K-zero Bessel function.

  ### L2

  - dnrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - scnrm2

        Compute the unitary norm of a complex vector.

  - snrm2

        Compute the Euclidean length (L2 norm) of a vector.

  ### LARGE X

  - d9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - r9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  ### LEAST SQUARES

  - bndacc

        Compute the LU factorization of a banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - bndsol

        Solve the least squares problem for a banded matrix using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dbndac

        Compute the LU factorization of a  banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dbndsl

        Solve the least squares problem for a banded matrix using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - dbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  - dhfti

        Solve a least squares problem for banded matrices using
        sequential accumulation of rows of the data matrix.
        Exactly one right-hand side vector is permitted.

  - dp1vlu

        Use the coefficients generated by DPOLFT to evaluate the
        polynomial fit of degree L, along with the first NDER of
        its derivatives, at a specified point.

  - dpcoef

        Convert the DPOLFT coefficients to Taylor series form.

  - dpolft

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  - pcoef

        Convert the POLFIT coefficients to Taylor series form.

  - polfit

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  - pvalue

        Use the coefficients generated by POLFIT to evaluate the
        polynomial fit of degree L, along with the first NDER of
        its derivatives, at a specified point.

  - sbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - sbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  ### LEGENDRE FUNCTIONS

  - dxlegf

        Compute normalized Legendre polynomials and associated
        Legendre functions.

  - dxnrmp

        Compute normalized Legendre polynomials.

  - dxpmu

        To compute the values of Legendre functions for DXLEGF.
        Method: backward mu-wise recurrence for P(-MU,NU,X) for
        fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,
        P(-MU1,NU1,X) and store in ascending mu order.

  - dxpmup

        To compute the values of Legendre functions for DXLEGF.
        This subroutine transforms an array of Legendre functions
        of the first kind of negative order stored in array PQA
        into Legendre functions of the first kind of positive
        order stored in array PQA. The original array is destroyed.

  - dxpnrm

        To compute the values of Legendre functions for DXLEGF.
        This subroutine transforms an array of Legendre functions
        of the first kind of negative order stored in array PQA
        into normalized Legendre polynomials stored in array PQA.
        The original array is destroyed.

  - dxpqnu

        To compute the values of Legendre functions for DXLEGF.
        This subroutine calculates initial values of P or Q using
        power series, then performs forward nu-wise recurrence to
        obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise
        recurrence is stable for P for all mu and for Q for mu=0,1.

  - dxqmu

        To compute the values of Legendre functions for DXLEGF.
        Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed
        nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).

  - dxqnu

        To compute the values of Legendre functions for DXLEGF.
        Method: backward nu-wise recurrence for Q(MU,NU,X) for
        fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,
        Q(MU1,NU2,X).

  - xlegf

        Compute normalized Legendre polynomials and associated
        Legendre functions.

  - xnrmp

        Compute normalized Legendre polynomials.

  - xpmu

        To compute the values of Legendre functions for XLEGF.
        Method: backward mu-wise recurrence for P(-MU,NU,X) for
        fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,
        P(-MU1,NU1,X) and store in ascending mu order.

  - xpmup

        To compute the values of Legendre functions for XLEGF.
        This subroutine transforms an array of Legendre functions
        of the first kind of negative order stored in array PQA
        into Legendre functions of the first kind of positive
        order stored in array PQA. The original array is destroyed.

  - xpnrm

        To compute the values of Legendre functions for XLEGF.
        This subroutine transforms an array of Legendre functions
        of the first kind of negative order stored in array PQA
        into normalized Legendre polynomials stored in array PQA.
        The original array is destroyed.

  - xpqnu

        To compute the values of Legendre functions for XLEGF.
        This subroutine calculates initial values of P or Q using
        power series, then performs forward nu-wise recurrence to
        obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise
        recurrence is stable for P for all mu and for Q for mu=0,1.

  - xqmu

        To compute the values of Legendre functions for XLEGF.
        Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed
        nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).

  - xqnu

        To compute the values of Legendre functions for XLEGF.
        Method: backward nu-wise recurrence for Q(MU,NU,X) for
        fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,
        Q(MU1,NU2,X).

  ### LEVEL 2 BLAS

  - cgbmv

        Multiply a complex vector by a complex general band matrix.

  - cgemv

        Multiply a complex vector by a complex general matrix.

  - cgerc

        Perform conjugated rank 1 update of a complex general
        matrix.

  - cgeru

        Perform unconjugated rank 1 update of a complex general
        matrix.

  - chbmv

        Multiply a complex vector by a complex Hermitian band
        matrix.

  - chemv

        Multiply a complex vector by a complex Hermitian matrix.

  - cher

        Perform Hermitian rank 1 update of a complex Hermitian
        matrix.

  - cher2

        Perform Hermitian rank 2 update of a complex Hermitian
        matrix.

  - chpmv

        Perform the matrix-vector operation.

  - chpr

        Perform the hermitian rank 1 operation.

  - chpr2

        Perform the hermitian rank 2 operation.

  - ctbmv

        Multiply a complex vector by a complex triangular band
        matrix.

  - ctbsv

        Solve a complex triangular banded system of equations.

  - ctpmv

        Perform one of the matrix-vector operations.

  - ctpsv

        Solve one of the systems of equations.

  - ctrmv

        Multiply a complex vector by a complex triangular matrix.

  - ctrsv

        Solve a complex triangular system of equations.

  - dgbmv

        Perform one of the matrix-vector operations.

  - dgemv

        Perform one of the matrix-vector operations.

  - dger

        Perform the rank 1 operation.

  - dsbmv

        Perform the matrix-vector operation.

  - dspmv

        Perform the matrix-vector operation.

  - dspr

        Perform the symmetric rank 1 operation.

  - dspr2

        Perform the symmetric rank 2 operation.

  - dsymv

        Perform the matrix-vector operation.

  - dsyr

        Perform the symmetric rank 1 operation.

  - dsyr2

        Perform the symmetric rank 2 operation.

  - dtbmv

        Perform one of the matrix-vector operations.

  - dtbsv

        Solve one of the systems of equations.

  - dtpmv

        Perform one of the matrix-vector operations.

  - dtpsv

        Solve one of the systems of equations.

  - dtrmv

        Perform one of the matrix-vector operations.

  - dtrsv

        Solve one of the systems of equations.

  - lsame

        Test two characters to determine if they are the same
        letter, except for case.

  - sgbmv

        Multiply a real vector by a real general band matrix.

  - sgemv

        Multiply a real vector by a real general matrix.

  - sger

        Perform rank 1 update of a real general matrix.

  - ssbmv

        Multiply a real vector by a real symmetric band matrix.

  - sspmv

        Perform the matrix-vector operation.

  - sspr

        Performs the symmetric rank 1 operation.

  - sspr2

        Perform the symmetric rank 2 operation.

  - ssymv

        Multiply a real vector by a real symmetric matrix.

  - ssyr

        Perform symmetric rank 1 update of a real symmetric matrix.

  - ssyr2

        Perform symmetric rank 2 update of a real symmetric matrix.

  - stbmv

        Multiply a real vector by a real triangular band matrix.

  - stbsv

        Solve a real triangular banded system of linear equations.

  - stpmv

        Perform one of the matrix-vector operations.

  - stpsv

        Solve one of the systems of equations.

  - strmv

        Multiply a real vector by a real triangular matrix.

  - strsv

        Solve a real triangular system of linear equations.

  ### LEVEL 3 BLAS

  - cgemm

        Multiply a complex general matrix by a complex general
        matrix.

  - chemm

        Multiply a complex general matrix by a complex Hermitian
        matrix.

  - cher2k

        Perform Hermitian rank 2k update of a complex.

  - cherk

        Perform Hermitian rank k update of a complex Hermitian
        matrix.

  - csymm

        Multiply a complex general matrix by a complex symmetric
        matrix.

  - csyr2k

        Perform symmetric rank 2k update of a complex symmetric
        matrix.

  - csyrk

        Perform symmetric rank k update of a complex symmetric
        matrix.

  - ctrmm

        Multiply a complex general matrix by a complex triangular
        matrix.

  - ctrsm

        Solve a complex triangular system of equations with
        multiple right-hand sides.

  - dgemm

        Perform one of the matrix-matrix operations.

  - dsymm

        Perform one of the matrix-matrix operations.

  - dsyr2k

        Perform one of the symmetric rank 2k operations.

  - dsyrk

        Perform one of the symmetric rank k operations.

  - dtrmm

        Perform one of the matrix-matrix operations.

  - dtrsm

        Solve one of the matrix equations.

  - lsame

        Test two characters to determine if they are the same
        letter, except for case.

  - sgemm

        Multiply a real general matrix by a real general matrix.

  - ssymm

        Multiply a real general matrix by a real symmetric matrix.

  - ssyr2k

        Perform symmetric rank 2k update of a real symmetric matrix

  - ssyrk

        Perform symmetric rank k update of a real symmetric matrix.

  - strmm

        Multiply a real general matrix by a real triangular matrix.

  - strsm

        Solve a real triangular system of equations with multiple
        right-hand sides.

  ### LEVENBERG-MARQUARDT

  - dnls1

        Minimize the sum of the squares of M nonlinear functions
        in N variables by a modification of the Levenberg-Marquardt
        algorithm.

  - dnls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  - snls1

        Minimize the sum of the squares of M nonlinear functions
        in N variables by a modification of the Levenberg-Marquardt
        algorithm.

  - snls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  ### LIMITS

  - dgamlm

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  - gamlim

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  ### LINEAR

  - dbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - dbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  - sbocls

        Solve the bounded and constrained least squares
        problem consisting of solving the equation
                  E*X = F  (in the least squares sense)
         subject to the linear constraints
                        C*X = Y.

  - sbols

        Solve the problem
             E*X = F (in the least  squares  sense)
        with bounds on selected X values.

  ### LINEAR ALGEBRA

  - caxpy

        Compute a constant times a vector plus a vector.

  - cchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - cchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - cchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - cchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - ccopy

        Copy a vector.

  - cdcdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - cdotc

        Dot product of two complex vectors using the complex
        conjugate of the first vector.

  - cdotu

        Compute the inner product of two vectors.

  - cgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - cgbdi

        Compute the determinant of a complex band matrix using the
        factors from CGBCO or CGBFA.

  - cgbfa

        Factor a band matrix using Gaussian elimination.

  - cgbmv

        Multiply a complex vector by a complex general band matrix.

  - cgbsl

        Solve the complex band system A*X=B or CTRANS(A)*X=B using
        the factors computed by CGBCO or CGBFA.

  - cgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - cgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by CGECO or CGEFA.

  - cgefa

        Factor a matrix using Gaussian elimination.

  - cgemm

        Multiply a complex general matrix by a complex general
        matrix.

  - cgemv

        Multiply a complex vector by a complex general matrix.

  - cgerc

        Perform conjugated rank 1 update of a complex general
        matrix.

  - cgeru

        Perform unconjugated rank 1 update of a complex general
        matrix.

  - cgesl

        Solve the complex system A*X=B or CTRANS(A)*X=B using the
        factors computed by CGECO or CGEFA.

  - cgtsl

        Solve a tridiagonal linear system.

  - chbmv

        Multiply a complex vector by a complex Hermitian band
        matrix.

  - chemm

        Multiply a complex general matrix by a complex Hermitian
        matrix.

  - chemv

        Multiply a complex vector by a complex Hermitian matrix.

  - cher

        Perform Hermitian rank 1 update of a complex Hermitian
        matrix.

  - cher2

        Perform Hermitian rank 2 update of a complex Hermitian
        matrix.

  - cher2k

        Perform Hermitian rank 2k update of a complex.

  - cherk

        Perform Hermitian rank k update of a complex Hermitian
        matrix.

  - chico

        Factor a complex Hermitian matrix by elimination with sym-
        metric pivoting and estimate the condition of the matrix.

  - chidi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix using the factors obtained from CHIFA.

  - chifa

        Factor a complex Hermitian matrix by elimination
        (symmetric pivoting).

  - chisl

        Solve the complex Hermitian system using factors obtained
        from CHIFA.

  - chpco

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - chpdi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix stored in packed form using the factors
        obtained from CHPFA.

  - chpfa

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting.

  - chpmv

        Perform the matrix-vector operation.

  - chpr

        Perform the hermitian rank 1 operation.

  - chpr2

        Perform the hermitian rank 2 operation.

  - chpsl

        Solve a complex Hermitian system using factors obtained
        from CHPFA.

  - cpbco

        Factor a complex Hermitian positive definite matrix stored
        in band form and estimate the condition number of the
        matrix.

  - cpbdi

        Compute the determinant of a complex Hermitian positive
        definite band matrix using the factors computed by CPBCO or
        CPBFA.

  - cpbfa

        Factor a complex Hermitian positive definite matrix stored
        in band form.

  - cpbsl

        Solve the complex Hermitian positive definite band system
        using the factors computed by CPBCO or CPBFA.

  - cpoco

        Factor a complex Hermitian positive definite matrix
        and estimate the condition number of the matrix.

  - cpodi

        Compute the determinant and inverse of a certain complex
        Hermitian positive definite matrix using the factors
        computed by CPOCO, CPOFA, or CQRDC.

  - cpofa

        Factor a complex Hermitian positive definite matrix.

  - cposl

        Solve the complex Hermitian positive definite linear system
        using the factors computed by CPOCO or CPOFA.

  - cppco

        Factor a complex Hermitian positive definite matrix stored
        in packed form and estimate the condition number of the
        matrix.

  - cppdi

        Compute the determinant and inverse of a complex Hermitian
        positive definite matrix using factors from CPPCO or CPPFA.

  - cppfa

        Factor a complex Hermitian positive definite matrix stored
        in packed form.

  - cppsl

        Solve the complex Hermitian positive definite system using
        the factors computed by CPPCO or CPPFA.

  - cptsl

        Solve a positive definite tridiagonal linear system.

  - cqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - cqrsl

        Apply the output of CQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - crotg

        Construct a Givens transformation.

  - cscal

        Multiply a vector by a constant.

  - csico

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting and estimate the condition number of the
        matrix.

  - csidi

        Compute the determinant and inverse of a complex symmetric
        matrix using the factors from CSIFA.

  - csifa

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting.

  - csisl

        Solve a complex symmetric system using the factors obtained
        from CSIFA.

  - cspco

        Factor a complex symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - cspdi

        Compute the determinant and inverse of a complex symmetric
        matrix stored in packed form using the factors from CSPFA.

  - cspfa

        Factor a complex symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - cspsl

        Solve a complex symmetric system using the factors obtained
        from CSPFA.

  - csrot

        Apply a plane Givens rotation.

  - csscal

        Scale a complex vector.

  - csvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - cswap

        Interchange two vectors.

  - csymm

        Multiply a complex general matrix by a complex symmetric
        matrix.

  - csyr2k

        Perform symmetric rank 2k update of a complex symmetric
        matrix.

  - csyrk

        Perform symmetric rank k update of a complex symmetric
        matrix.

  - ctbmv

        Multiply a complex vector by a complex triangular band
        matrix.

  - ctbsv

        Solve a complex triangular banded system of equations.

  - ctpmv

        Perform one of the matrix-vector operations.

  - ctpsv

        Solve one of the systems of equations.

  - ctrco

        Estimate the condition number of a triangular matrix.

  - ctrdi

        Compute the determinant and inverse of a triangular matrix.

  - ctrmm

        Multiply a complex general matrix by a complex triangular
        matrix.

  - ctrmv

        Multiply a complex vector by a complex triangular matrix.

  - ctrsl

        Solve a system of the form  T*X=B or CTRANS(T)*X=B, where
        T is a triangular matrix.  Here CTRANS(T) is the conjugate
        transpose.

  - ctrsm

        Solve a complex triangular system of equations with
        multiple right-hand sides.

  - ctrsv

        Solve a complex triangular system of equations.

  - dasum

        Compute the sum of the magnitudes of the elements of a
        vector.

  - daxpy

        Compute a constant times a vector plus a vector.

  - dcdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - dchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - dchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - dchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - dcopy

        Copy a vector.

  - ddot

        Compute the inner product of two vectors.

  - dgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - dgbdi

        Compute the determinant of a band matrix using the factors
        computed by DGBCO or DGBFA.

  - dgbfa

        Factor a band matrix using Gaussian elimination.

  - dgbmv

        Perform one of the matrix-vector operations.

  - dgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by DGBCO or DGBFA.

  - dgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - dgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by DGECO or DGEFA.

  - dgefa

        Factor a matrix using Gaussian elimination.

  - dgemm

        Perform one of the matrix-matrix operations.

  - dgemv

        Perform one of the matrix-vector operations.

  - dger

        Perform the rank 1 operation.

  - dgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors computed by DGECO or DGEFA.

  - dgtsl

        Solve a tridiagonal linear system.

  - dnrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - dpbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - dpbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by DPBCO or DPBFA.

  - dpbfa

        Factor a real symmetric positive definite matrix stored in
        in band form.

  - dpbsl

        Solve a real symmetric positive definite band system
        using the factors computed by DPBCO or DPBFA.

  - dpoco

        Factor a real symmetric positive definite matrix
        and estimate the condition of the matrix.

  - dpodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by DPOCO, DPOFA or DQRDC.

  - dpofa

        Factor a real symmetric positive definite matrix.

  - dposl

        Solve the real symmetric positive definite linear system
        using the factors computed by DPOCO or DPOFA.

  - dppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - dppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from DPPCO or DPPFA.

  - dppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - dppsl

        Solve the real symmetric positive definite system using
        the factors computed by DPPCO or DPPFA.

  - dptsl

        Solve a positive definite tridiagonal linear system.

  - dqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - dqrsl

        Apply the output of DQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - drot

        Apply a plane Givens rotation.

  - drotg

        Construct a plane Givens rotation.

  - drotm

        Apply a modified Givens transformation.

  - drotmg

        Construct a modified Givens transformation.

  - dsbmv

        Perform the matrix-vector operation.

  - dscal

        Multiply a vector by a constant.

  - dsdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dsico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - dsidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from DSIFA.

  - dsifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - dsisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - dspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - dspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from DSPFA.

  - dspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - dspmv

        Perform the matrix-vector operation.

  - dspr

        Perform the symmetric rank 1 operation.

  - dspr2

        Perform the symmetric rank 2 operation.

  - dspsl

        Solve a real symmetric system using the factors obtained
        from DSPFA.

  - dsvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - dswap

        Interchange two vectors.

  - dsymm

        Perform one of the matrix-matrix operations.

  - dsymv

        Perform the matrix-vector operation.

  - dsyr

        Perform the symmetric rank 1 operation.

  - dsyr2

        Perform the symmetric rank 2 operation.

  - dsyr2k

        Perform one of the symmetric rank 2k operations.

  - dsyrk

        Perform one of the symmetric rank k operations.

  - dtbmv

        Perform one of the matrix-vector operations.

  - dtbsv

        Solve one of the systems of equations.

  - dtpmv

        Perform one of the matrix-vector operations.

  - dtpsv

        Solve one of the systems of equations.

  - dtrco

        Estimate the condition number of a triangular matrix.

  - dtrdi

        Compute the determinant and inverse of a triangular matrix.

  - dtrmm

        Perform one of the matrix-matrix operations.

  - dtrmv

        Perform one of the matrix-vector operations.

  - dtrsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  - dtrsm

        Solve one of the matrix equations.

  - dtrsv

        Solve one of the systems of equations.

  - icamax

        Find the smallest index of the component of a complex
        vector having the maximum sum of magnitudes of real
        and imaginary parts.

  - icopy

        Copy a vector.

  - idamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  - isamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  - iswap

        Interchange two vectors.

  - sasum

        Compute the sum of the magnitudes of the elements of a
        vector.

  - saxpy

        Compute a constant times a vector plus a vector.

  - scasum

        Compute the sum of the magnitudes of the real and
        imaginary elements of a complex vector.

  - schdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - schdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - schex

        Update the Cholesky factorization  A=TRANS(R)*R  of A
        positive definite matrix A of order P under diagonal
        permutations of the form TRANS(E)*A*E, where E is a
        permutation matrix.

  - schud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - scnrm2

        Compute the unitary norm of a complex vector.

  - scopy

        Copy a vector.

  - sdot

        Compute the inner product of two vectors.

  - sdsdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - sgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - sgbdi

        Compute the determinant of a band matrix using the factors
        computed by SGBCO or SGBFA.

  - sgbfa

        Factor a band matrix using Gaussian elimination.

  - sgbmv

        Multiply a real vector by a real general band matrix.

  - sgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by SGBCO or SGBFA.

  - sgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - sgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by SGECO or SGEFA.

  - sgefa

        Factor a matrix using Gaussian elimination.

  - sgemm

        Multiply a real general matrix by a real general matrix.

  - sgemv

        Multiply a real vector by a real general matrix.

  - sger

        Perform rank 1 update of a real general matrix.

  - sgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors of SGECO or SGEFA.

  - sgtsl

        Solve a tridiagonal linear system.

  - snrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - spbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - spbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by SPBCO or SPBFA.

  - spbfa

        Factor a real symmetric positive definite matrix stored in
        band form.

  - spbsl

        Solve a real symmetric positive definite band system
        using the factors computed by SPBCO or SPBFA.

  - spoco

        Factor a real symmetric positive definite matrix
        and estimate the condition number of the matrix.

  - spodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by SPOCO, SPOFA or SQRDC.

  - spofa

        Factor a real symmetric positive definite matrix.

  - sposl

        Solve the real symmetric positive definite linear system
        using the factors computed by SPOCO or SPOFA.

  - sppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - sppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from SPPCO or SPPFA.

  - sppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - sppsl

        Solve the real symmetric positive definite system using
        the factors computed by SPPCO or SPPFA.

  - sptsl

        Solve a positive definite tridiagonal linear system.

  - sqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - sqrsl

        Apply the output of SQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - srot

        Apply a plane Givens rotation.

  - srotg

        Construct a plane Givens rotation.

  - srotm

        Apply a modified Givens transformation.

  - srotmg

        Construct a modified Givens transformation.

  - ssbmv

        Multiply a real vector by a real symmetric band matrix.

  - sscal

        Multiply a vector by a constant.

  - ssico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - ssidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from SSIFA.

  - ssifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - ssisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - sspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - sspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from SSPFA.

  - sspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - sspmv

        Perform the matrix-vector operation.

  - sspr

        Performs the symmetric rank 1 operation.

  - sspr2

        Perform the symmetric rank 2 operation.

  - sspsl

        Solve a real symmetric system using the factors obtained
        from SSPFA.

  - ssvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - sswap

        Interchange two vectors.

  - ssymm

        Multiply a real general matrix by a real symmetric matrix.

  - ssymv

        Multiply a real vector by a real symmetric matrix.

  - ssyr

        Perform symmetric rank 1 update of a real symmetric matrix.

  - ssyr2

        Perform symmetric rank 2 update of a real symmetric matrix.

  - ssyr2k

        Perform symmetric rank 2k update of a real symmetric matrix

  - ssyrk

        Perform symmetric rank k update of a real symmetric matrix.

  - stbmv

        Multiply a real vector by a real triangular band matrix.

  - stbsv

        Solve a real triangular banded system of linear equations.

  - stpmv

        Perform one of the matrix-vector operations.

  - stpsv

        Solve one of the systems of equations.

  - strco

        Estimate the condition number of a triangular matrix.

  - strdi

        Compute the determinant and inverse of a triangular matrix.

  - strmm

        Multiply a real general matrix by a real triangular matrix.

  - strmv

        Multiply a real vector by a real triangular matrix.

  - strsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  - strsm

        Solve a real triangular system of equations with multiple
        right-hand sides.

  - strsv

        Solve a real triangular system of linear equations.

  ### LINEAR CONSTRAINTS

  - dsplp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  - splp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  ### LINEAR EQUATIONS

  - cnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - cnbdi

        Compute the determinant of a band matrix using the factors
        computed by CNBCO or CNBFA.

  - cnbfa

        Factor a band matrix by elimination.

  - cnbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - cnbir

        Solve a general nonsymmetric banded system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - cnbsl

        Solve a complex band system using the factors computed by
        CNBCO or CNBFA.

  - cpofs

        Solve a positive definite symmetric complex system of
        linear equations.

  - cpoir

        Solve a positive definite Hermitian system of linear
        equations.  Iterative refinement is used to obtain an
        error estimate.

  - dnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - dnbdi

        Compute the determinant of a band matrix using the factors
        computed by DNBCO or DNBFA.

  - dnbfa

        Factor a band matrix by elimination.

  - dnbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - dnbsl

        Solve a real band system using the factors computed by
        DNBCO or DNBFA.

  - dpofs

        Solve a positive definite symmetric system of linear
        equations.

  - snbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - snbdi

        Compute the determinant of a band matrix using the factors
        computed by SNBCO or SNBFA.

  - snbfa

        Factor a real band matrix by elimination.

  - snbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - snbir

        Solve a general nonsymmetric banded system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - snbsl

        Solve a real band system using the factors computed by
        SNBCO or SNBFA.

  - spofs

        Solve a positive definite symmetric system of linear
        equations.

  - spoir

        Solve a positive definite symmetric system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  ### LINEAR LEAST SQUARES

  - dglss

        Solve a linear least squares problems by performing a QR
        factorization of the input matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - dllsia

        Solve linear least squares problems by performing a QR
        factorization of the input matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - dulsia

        Solve an underdetermined linear system of equations by
        performing an LQ factorization of the matrix using
        Householder transformations.  Emphasis is put on detecting
        possible rank deficiency.

  - hfti

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.

  - llsia

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - sglss

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - ulsia

        Solve an underdetermined linear system of equations by
        performing an LQ factorization of the matrix using
        Householder transformations.  Emphasis is put on detecting
        possible rank deficiency.

  ### LINEAR OPTIMIZATION

  - dsplp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  - splp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  ### LINEAR PROGRAMMING

  - dsplp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  - splp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  ### LINEAR SYSTEM

  - dbhin

        Read a Sparse Linear System in the Boeing/Harwell Format.
        The matrix is read in and if the right hand side is also
        present in the input file then it too is read in.  The
        matrix is then modified to be in the SLAP Column format.

  - dcpplt

        Printer Plot of SLAP Column Format Matrix.
        Routine to print out a SLAP Column format matrix in a
        "printer plot" graphical representation.

  - dir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - ds2lt

        Lower Triangle Preconditioner SLAP Set Up.
        Routine to store the lower triangle of a matrix stored
        in the SLAP Column format.

  - ds2y

        SLAP Triad to SLAP Column Format Converter.
        Routine to convert from the SLAP Triad to SLAP Column
        format.

  - dsgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - dsics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  - dsilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - dsjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - dsmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - dtin

        Read in SLAP Triad Format Linear System.
        Routine to read in a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - dtout

        Write out SLAP Triad Format Linear System.
        Routine to write out a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - isdcg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - isdir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - issgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - issir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - sbhin

        Read a Sparse Linear System in the Boeing/Harwell Format.
        The matrix is read in and if the right hand side is also
        present in the input file then it too is read in.  The
        matrix is then modified to be in the SLAP Column format.

  - sir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - scpplt

        Printer Plot of SLAP Column Format Matrix.
        Routine to print out a SLAP Column format matrix in a
        "printer plot" graphical representation.

  - ss2lt

        Lower Triangle Preconditioner SLAP Set Up.
        Routine to store the lower triangle of a matrix stored
        in the SLAP Column format.

  - ss2y

        SLAP Triad to SLAP Column Format Converter.
        Routine to convert from the SLAP Triad to SLAP Column
        format.

  - ssgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - ssics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  - ssilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - ssjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - ssmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - stin

        Read in SLAP Triad Format Linear System.
        Routine to read in a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - stout

        Write out SLAP Triad Format Linear System.
        Routine to write out a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  ### LINEAR SYSTEM SOLVE

  - dsdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - dsli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - dsli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - dsllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - dsluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - dsmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  - ssdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - ssli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - ssli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - ssllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - ssluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - ssmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  ### LINPACK

  - cchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - cchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - cchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - cchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - cgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - cgbdi

        Compute the determinant of a complex band matrix using the
        factors from CGBCO or CGBFA.

  - cgbfa

        Factor a band matrix using Gaussian elimination.

  - cgbsl

        Solve the complex band system A*X=B or CTRANS(A)*X=B using
        the factors computed by CGBCO or CGBFA.

  - cgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - cgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by CGECO or CGEFA.

  - cgefa

        Factor a matrix using Gaussian elimination.

  - cgesl

        Solve the complex system A*X=B or CTRANS(A)*X=B using the
        factors computed by CGECO or CGEFA.

  - cgtsl

        Solve a tridiagonal linear system.

  - chico

        Factor a complex Hermitian matrix by elimination with sym-
        metric pivoting and estimate the condition of the matrix.

  - chidi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix using the factors obtained from CHIFA.

  - chifa

        Factor a complex Hermitian matrix by elimination
        (symmetric pivoting).

  - chisl

        Solve the complex Hermitian system using factors obtained
        from CHIFA.

  - chpco

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - chpdi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix stored in packed form using the factors
        obtained from CHPFA.

  - chpfa

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting.

  - chpsl

        Solve a complex Hermitian system using factors obtained
        from CHPFA.

  - cpbco

        Factor a complex Hermitian positive definite matrix stored
        in band form and estimate the condition number of the
        matrix.

  - cpbdi

        Compute the determinant of a complex Hermitian positive
        definite band matrix using the factors computed by CPBCO or
        CPBFA.

  - cpbfa

        Factor a complex Hermitian positive definite matrix stored
        in band form.

  - cpbsl

        Solve the complex Hermitian positive definite band system
        using the factors computed by CPBCO or CPBFA.

  - cpoco

        Factor a complex Hermitian positive definite matrix
        and estimate the condition number of the matrix.

  - cpodi

        Compute the determinant and inverse of a certain complex
        Hermitian positive definite matrix using the factors
        computed by CPOCO, CPOFA, or CQRDC.

  - cpofa

        Factor a complex Hermitian positive definite matrix.

  - cposl

        Solve the complex Hermitian positive definite linear system
        using the factors computed by CPOCO or CPOFA.

  - cppco

        Factor a complex Hermitian positive definite matrix stored
        in packed form and estimate the condition number of the
        matrix.

  - cppdi

        Compute the determinant and inverse of a complex Hermitian
        positive definite matrix using factors from CPPCO or CPPFA.

  - cppfa

        Factor a complex Hermitian positive definite matrix stored
        in packed form.

  - cppsl

        Solve the complex Hermitian positive definite system using
        the factors computed by CPPCO or CPPFA.

  - cptsl

        Solve a positive definite tridiagonal linear system.

  - cqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - cqrsl

        Apply the output of CQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - csico

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting and estimate the condition number of the
        matrix.

  - csidi

        Compute the determinant and inverse of a complex symmetric
        matrix using the factors from CSIFA.

  - csifa

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting.

  - csisl

        Solve a complex symmetric system using the factors obtained
        from CSIFA.

  - cspco

        Factor a complex symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - cspdi

        Compute the determinant and inverse of a complex symmetric
        matrix stored in packed form using the factors from CSPFA.

  - cspfa

        Factor a complex symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - cspsl

        Solve a complex symmetric system using the factors obtained
        from CSPFA.

  - csvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - ctrco

        Estimate the condition number of a triangular matrix.

  - ctrdi

        Compute the determinant and inverse of a triangular matrix.

  - ctrsl

        Solve a system of the form  T*X=B or CTRANS(T)*X=B, where
        T is a triangular matrix.  Here CTRANS(T) is the conjugate
        transpose.

  - dchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - dchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - dchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - dchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - dgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - dgbdi

        Compute the determinant of a band matrix using the factors
        computed by DGBCO or DGBFA.

  - dgbfa

        Factor a band matrix using Gaussian elimination.

  - dgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by DGBCO or DGBFA.

  - dgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - dgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by DGECO or DGEFA.

  - dgefa

        Factor a matrix using Gaussian elimination.

  - dgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors computed by DGECO or DGEFA.

  - dgtsl

        Solve a tridiagonal linear system.

  - dpbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - dpbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by DPBCO or DPBFA.

  - dpbfa

        Factor a real symmetric positive definite matrix stored in
        in band form.

  - dpbsl

        Solve a real symmetric positive definite band system
        using the factors computed by DPBCO or DPBFA.

  - dpoco

        Factor a real symmetric positive definite matrix
        and estimate the condition of the matrix.

  - dpodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by DPOCO, DPOFA or DQRDC.

  - dpofa

        Factor a real symmetric positive definite matrix.

  - dposl

        Solve the real symmetric positive definite linear system
        using the factors computed by DPOCO or DPOFA.

  - dppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - dppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from DPPCO or DPPFA.

  - dppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - dppsl

        Solve the real symmetric positive definite system using
        the factors computed by DPPCO or DPPFA.

  - dptsl

        Solve a positive definite tridiagonal linear system.

  - dqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - dqrsl

        Apply the output of DQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - dsico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - dsidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from DSIFA.

  - dsifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - dsisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - dspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - dspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from DSPFA.

  - dspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - dspsl

        Solve a real symmetric system using the factors obtained
        from DSPFA.

  - dsvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - dtrco

        Estimate the condition number of a triangular matrix.

  - dtrdi

        Compute the determinant and inverse of a triangular matrix.

  - dtrsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  - schdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - schdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - schex

        Update the Cholesky factorization  A=TRANS(R)*R  of A
        positive definite matrix A of order P under diagonal
        permutations of the form TRANS(E)*A*E, where E is a
        permutation matrix.

  - schud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - sgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - sgbdi

        Compute the determinant of a band matrix using the factors
        computed by SGBCO or SGBFA.

  - sgbfa

        Factor a band matrix using Gaussian elimination.

  - sgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by SGBCO or SGBFA.

  - sgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - sgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by SGECO or SGEFA.

  - sgefa

        Factor a matrix using Gaussian elimination.

  - sgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors of SGECO or SGEFA.

  - sgtsl

        Solve a tridiagonal linear system.

  - spbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - spbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by SPBCO or SPBFA.

  - spbfa

        Factor a real symmetric positive definite matrix stored in
        band form.

  - spbsl

        Solve a real symmetric positive definite band system
        using the factors computed by SPBCO or SPBFA.

  - spoco

        Factor a real symmetric positive definite matrix
        and estimate the condition number of the matrix.

  - spodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by SPOCO, SPOFA or SQRDC.

  - spofa

        Factor a real symmetric positive definite matrix.

  - sposl

        Solve the real symmetric positive definite linear system
        using the factors computed by SPOCO or SPOFA.

  - sppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - sppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from SPPCO or SPPFA.

  - sppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - sppsl

        Solve the real symmetric positive definite system using
        the factors computed by SPPCO or SPPFA.

  - sptsl

        Solve a positive definite tridiagonal linear system.

  - sqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - sqrsl

        Apply the output of SQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - ssico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - ssidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from SSIFA.

  - ssifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - ssisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - sspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - sspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from SSPFA.

  - sspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - sspsl

        Solve a real symmetric system using the factors obtained
        from SSPFA.

  - ssvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - strco

        Estimate the condition number of a triangular matrix.

  - strdi

        Compute the determinant and inverse of a triangular matrix.

  - strsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  ### LOG GAMMA

  - c9lgmc

        Compute the log gamma correction factor so that
        LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
        + C9LGMC(Z).

  - d9lgmc

        Compute the log Gamma correction factor so that
        LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
        + D9LGMC(X).

  - r9lgmc

        Compute the log Gamma correction factor so that
        LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
        + R9LGMC(X).

  ### LOGARITHM

  - alngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - alnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - c9lgmc

        Compute the log gamma correction factor so that
        LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
        + C9LGMC(Z).

  - c9ln2r

        Evaluate LOG(1+Z) from second order relative accuracy so
        that  LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

  - clngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - clnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - d9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - d9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - d9lgmc

        Compute the log Gamma correction factor so that
        LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
        + D9LGMC(X).

  - d9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

  - dlngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - dlnrel

        Evaluate ln(1+X) accurate in the sense of relative error.

  - r9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - r9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - r9lgmc

        Compute the log Gamma correction factor so that
        LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
        + R9LGMC(X).

  - r9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

  ### LOGARITHM OF GAMMA FUNCTION

  - dgamln

        Compute the logarithm of the Gamma function

  - gamln

        Compute the logarithm of the Gamma function

  ### LOGARITHM OF THE COMPLETE BETA FUNCTION

  - albeta

        Compute the natural logarithm of the complete Beta
        function.

  - clbeta

        Compute the natural logarithm of the complete Beta
        function.

  - dlbeta

        Compute the natural logarithm of the complete Beta
        function.

  ### LOGARITHMIC CONFLUENT HYPERGEOMETRIC FUNCTION

  - chu

        Compute the logarithmic confluent hypergeometric function.

  - d9chu

        Evaluate for large Z  Z**A * U(A,B,Z) where U is the
        logarithmic confluent hypergeometric function.

  - dchu

        Compute the logarithmic confluent hypergeometric function.

  - r9chu

        Evaluate for large Z  Z**A * U(A,B,Z) where U is the
        logarithmic confluent hypergeometric function.

  ### LOGARITHMIC INTEGRAL

  - ali

        Compute the logarithmic integral.

  - dli

        Compute the logarithmic integral.

  ### LOWER TRIANGLE

  - ds2lt

        Lower Triangle Preconditioner SLAP Set Up.
        Routine to store the lower triangle of a matrix stored
        in the SLAP Column format.

  - ss2lt

        Lower Triangle Preconditioner SLAP Set Up.
        Routine to store the lower triangle of a matrix stored
        in the SLAP Column format.

  ### LP

  - dsplp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  - splp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  ### LQ FACTORIZATION

  - dglss

        Solve a linear least squares problems by performing a QR
        factorization of the input matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - dulsia

        Solve an underdetermined linear system of equations by
        performing an LQ factorization of the matrix using
        Householder transformations.  Emphasis is put on detecting
        possible rank deficiency.

  - sglss

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - ulsia

        Solve an underdetermined linear system of equations by
        performing an LQ factorization of the matrix using
        Householder transformations.  Emphasis is put on detecting
        possible rank deficiency.

  ### LR METHOD

  - comlr

        Compute the eigenvalues of a complex upper Hessenberg
        matrix using the modified LR method.

  - comlr2

        Compute the eigenvalues and eigenvectors of a complex upper
        Hessenberg matrix using the modified LR method.

  ### MACHINE CONSTANTS

  - d1mach_IRIX

        Return floating point machine dependent constants.

  - i1mach_IRIX

        Return integer machine dependent constants.

  - d1mach_GENERIC

        Return floating point machine dependent constants.

  - d1mach_IRIX6

        Return floating point machine dependent constants.

  - d1mach_Linux

        Return floating point machine dependent constants.

  - d1mach_OSF1

        Return floating point machine dependent constants.

  - i1mach_GENERIC

        Return integer machine dependent constants.

  - i1mach_IRIX6

        Return integer machine dependent constants.

  - i1mach_Linux

        Return integer machine dependent constants.

  - i1mach_OSF1

        Return integer machine dependent constants.

  - r1mach_IRIX

        Return floating point machine dependent constants.

  - r1mach_GENERIC

        Return floating point machine dependent constants.

  - r1mach_IRIX6

        Return floating point machine dependent constants.

  - r1mach_Linux

        Return floating point machine dependent constants.

  - r1mach_OSF1

        Return floating point machine dependent constants.

  ### MATRIX

  - cchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - cchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - cchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - cchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - cgbdi

        Compute the determinant of a complex band matrix using the
        factors from CGBCO or CGBFA.

  - cgbsl

        Solve the complex band system A*X=B or CTRANS(A)*X=B using
        the factors computed by CGBCO or CGBFA.

  - cgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by CGECO or CGEFA.

  - cgesl

        Solve the complex system A*X=B or CTRANS(A)*X=B using the
        factors computed by CGECO or CGEFA.

  - cgtsl

        Solve a tridiagonal linear system.

  - chidi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix using the factors obtained from CHIFA.

  - chiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - chisl

        Solve the complex Hermitian system using factors obtained
        from CHIFA.

  - chpdi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix stored in packed form using the factors
        obtained from CHPFA.

  - chpsl

        Solve a complex Hermitian system using factors obtained
        from CHPFA.

  - cpbdi

        Compute the determinant of a complex Hermitian positive
        definite band matrix using the factors computed by CPBCO or
        CPBFA.

  - cpbsl

        Solve the complex Hermitian positive definite band system
        using the factors computed by CPBCO or CPBFA.

  - cpodi

        Compute the determinant and inverse of a certain complex
        Hermitian positive definite matrix using the factors
        computed by CPOCO, CPOFA, or CQRDC.

  - cposl

        Solve the complex Hermitian positive definite linear system
        using the factors computed by CPOCO or CPOFA.

  - cppdi

        Compute the determinant and inverse of a complex Hermitian
        positive definite matrix using factors from CPPCO or CPPFA.

  - cppsl

        Solve the complex Hermitian positive definite system using
        the factors computed by CPPCO or CPPFA.

  - cptsl

        Solve a positive definite tridiagonal linear system.

  - cqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - cqrsl

        Apply the output of CQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - csidi

        Compute the determinant and inverse of a complex symmetric
        matrix using the factors from CSIFA.

  - csisl

        Solve a complex symmetric system using the factors obtained
        from CSIFA.

  - cspdi

        Compute the determinant and inverse of a complex symmetric
        matrix stored in packed form using the factors from CSPFA.

  - cspsl

        Solve a complex symmetric system using the factors obtained
        from CSPFA.

  - csvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - dchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - dchdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - dchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - dchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - dgbdi

        Compute the determinant of a band matrix using the factors
        computed by DGBCO or DGBFA.

  - dgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by DGBCO or DGBFA.

  - dgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by DGECO or DGEFA.

  - dgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors computed by DGECO or DGEFA.

  - dgtsl

        Solve a tridiagonal linear system.

  - dpbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by DPBCO or DPBFA.

  - dpbsl

        Solve a real symmetric positive definite band system
        using the factors computed by DPBCO or DPBFA.

  - dpodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by DPOCO, DPOFA or DQRDC.

  - dposl

        Solve the real symmetric positive definite linear system
        using the factors computed by DPOCO or DPOFA.

  - dppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from DPPCO or DPPFA.

  - dppsl

        Solve the real symmetric positive definite system using
        the factors computed by DPPCO or DPPFA.

  - dptsl

        Solve a positive definite tridiagonal linear system.

  - dqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - dqrsl

        Apply the output of DQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - dsidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from DSIFA.

  - dsisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - dspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from DSPFA.

  - dspsl

        Solve a real symmetric system using the factors obtained
        from DSPFA.

  - dsvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - schdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - schdd

        Downdate an augmented Cholesky decomposition or the
        triangular factor of an augmented QR decomposition.

  - schex

        Update the Cholesky factorization  A=TRANS(R)*R  of A
        positive definite matrix A of order P under diagonal
        permutations of the form TRANS(E)*A*E, where E is a
        permutation matrix.

  - schud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - sgbdi

        Compute the determinant of a band matrix using the factors
        computed by SGBCO or SGBFA.

  - sgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by SGBCO or SGBFA.

  - sgedi

        Compute the determinant and inverse of a matrix using the
        factors computed by SGECO or SGEFA.

  - sgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors of SGECO or SGEFA.

  - sgtsl

        Solve a tridiagonal linear system.

  - spbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by SPBCO or SPBFA.

  - spbsl

        Solve a real symmetric positive definite band system
        using the factors computed by SPBCO or SPBFA.

  - spodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by SPOCO, SPOFA or SQRDC.

  - sposl

        Solve the real symmetric positive definite linear system
        using the factors computed by SPOCO or SPOFA.

  - sppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from SPPCO or SPPFA.

  - sppsl

        Solve the real symmetric positive definite system using
        the factors computed by SPPCO or SPPFA.

  - sptsl

        Solve a positive definite tridiagonal linear system.

  - sqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - sqrsl

        Apply the output of SQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - ssidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from SSIFA.

  - ssiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  - ssisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - sspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from SSPFA.

  - sspsl

        Solve a real symmetric system using the factors obtained
        from SSPFA.

  - ssvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - strdi

        Compute the determinant and inverse of a triangular matrix.

  ### MATRIX FACTORIZATION

  - cgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - cgbfa

        Factor a band matrix using Gaussian elimination.

  - cgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - cgefa

        Factor a matrix using Gaussian elimination.

  - chico

        Factor a complex Hermitian matrix by elimination with sym-
        metric pivoting and estimate the condition of the matrix.

  - chifa

        Factor a complex Hermitian matrix by elimination
        (symmetric pivoting).

  - chpco

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - chpfa

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting.

  - cnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - cnbfa

        Factor a band matrix by elimination.

  - cpbco

        Factor a complex Hermitian positive definite matrix stored
        in band form and estimate the condition number of the
        matrix.

  - cpbfa

        Factor a complex Hermitian positive definite matrix stored
        in band form.

  - cpoco

        Factor a complex Hermitian positive definite matrix
        and estimate the condition number of the matrix.

  - cpofa

        Factor a complex Hermitian positive definite matrix.

  - cppco

        Factor a complex Hermitian positive definite matrix stored
        in packed form and estimate the condition number of the
        matrix.

  - cppfa

        Factor a complex Hermitian positive definite matrix stored
        in packed form.

  - csico

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting and estimate the condition number of the
        matrix.

  - csifa

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting.

  - cspco

        Factor a complex symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - cspfa

        Factor a complex symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - dgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - dgbfa

        Factor a band matrix using Gaussian elimination.

  - dgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - dgefa

        Factor a matrix using Gaussian elimination.

  - dnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - dnbfa

        Factor a band matrix by elimination.

  - dpbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - dpbfa

        Factor a real symmetric positive definite matrix stored in
        in band form.

  - dpoco

        Factor a real symmetric positive definite matrix
        and estimate the condition of the matrix.

  - dpofa

        Factor a real symmetric positive definite matrix.

  - dppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - dppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - dsico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - dsifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - dspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - dspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - sgbco

        Factor a band matrix by Gaussian elimination and
        estimate the condition number of the matrix.

  - sgbfa

        Factor a band matrix using Gaussian elimination.

  - sgeco

        Factor a matrix using Gaussian elimination and estimate
        the condition number of the matrix.

  - sgefa

        Factor a matrix using Gaussian elimination.

  - snbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - snbfa

        Factor a real band matrix by elimination.

  - spbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - spbfa

        Factor a real symmetric positive definite matrix stored in
        band form.

  - spoco

        Factor a real symmetric positive definite matrix
        and estimate the condition number of the matrix.

  - spofa

        Factor a real symmetric positive definite matrix.

  - sppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - sppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - ssico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - ssifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - sspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - sspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  ### MATRIX READ

  - dbhin

        Read a Sparse Linear System in the Boeing/Harwell Format.
        The matrix is read in and if the right hand side is also
        present in the input file then it too is read in.  The
        matrix is then modified to be in the SLAP Column format.

  - sbhin

        Read a Sparse Linear System in the Boeing/Harwell Format.
        The matrix is read in and if the right hand side is also
        present in the input file then it too is read in.  The
        matrix is then modified to be in the SLAP Column format.

  ### MATRIX TRANSPOSE VECTOR MULTIPLY

  - dsmtv

        SLAP Column Format Sparse Matrix Transpose Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A'*X, where ' denotes transpose.

  - ssmtv

        SLAP Column Format Sparse Matrix Transpose Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A'*X, where ' denotes transpose.

  ### MATRIX VECTOR MULTIPLY

  - dsmv

        SLAP Column Format Sparse Matrix Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A*X.

  - ssmv

        SLAP Column Format Sparse Matrix Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A*X.

  ### MAXIMUM COMPONENT

  - icamax

        Find the smallest index of the component of a complex
        vector having the maximum sum of magnitudes of real
        and imaginary parts.

  - idamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  - isamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  ### MINPACK

  - chkder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  - dckder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  ### MODIFIED BESSEL FUNCTION

  - besi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - besi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - besi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - besi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - besk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - besk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - besk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - besk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - beskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - besks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbesi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - dbesi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - dbesk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - dbesk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - dbesks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbsi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - dbsi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - dbsk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - dbsk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - dbskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  ### MODIFIED BESSEL FUNCTIONS

  - cbesi

        Compute a sequence of the Bessel functions I(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - cbesk

        Compute a sequence of the Bessel functions K(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesi

        Compute a sequence of the Bessel functions I(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesk

        Compute a sequence of the Bessel functions K(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### MODIFIED CHEBYSHEV MOMENTS

  - dqmomo

        This routine computes modified Chebyshev moments.  The K-th
        modified Chebyshev moment is defined as the integral over
        (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
        polynomial of degree K.

  - qmomo

        This routine computes modified Chebyshev moments.  The K-th
        modified Chebyshev moment is defined as the integral over
        (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
        polynomial of degree K.

  ### MODIFIED GIVENS ROTATION

  - drotm

        Apply a modified Givens transformation.

  - drotmg

        Construct a modified Givens transformation.

  - srotm

        Apply a modified Givens transformation.

  - srotmg

        Construct a modified Givens transformation.

  ### MODULUS

  - d9aimp

        Evaluate the Airy modulus and phase.

  - d9b0mp

        Evaluate the modulus and phase for the J0 and Y0 Bessel
        functions.

  - d9b1mp

        Evaluate the modulus and phase for the J1 and Y1 Bessel
        functions.

  - r9aimp

        Evaluate the Airy modulus and phase.

  ### MONOTONE INTERPOLATION

  - dpchcm

        Check a cubic Hermite function for monotonicity.

  - dpchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - dpchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See DPCHIC if user control
        is desired over boundary or switch conditions.)

  - pchcm

        Check a cubic Hermite function for monotonicity.

  - pchdoc

        Documentation for PCHIP, a Fortran package for piecewise
        cubic Hermite interpolation of data.

  - pchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - pchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See PCHIC if user control is
        desired over boundary or switch conditions.)

  ### NEWTON'S METHOD

  - dsos

        Solve a square system of nonlinear equations.

  - sos

        Solve a square system of nonlinear equations.

  ### NEWTON-COTES

  - dqnc79

        Integrate a function using a 7-point adaptive Newton-Cotes
        quadrature rule.

  - qnc79

        Integrate a function using a 7-point adaptive Newton-Cotes
        quadrature rule.

  ### NON-SYMMETRIC LINEAR SYSTEM

  - dbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - dcgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - dgmres

        Preconditioned GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - dhels

        Internal routine for DGMRES.

  - dheqr

        Internal routine for DGMRES.

  - domn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - dorth

        Internal routine for DGMRES.

  - dpigmr

        Internal routine for DGMRES.

  - drlcal

        Internal routine for DGMRES.

  - dsdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - dsdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - dsdgmr

        Diagonally scaled GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - dsilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - dslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - dslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - dslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - dslugm

        Incomplete LU GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - dsluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  - dxlcal

        Internal routine for DGMRES.

  - isdbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isdcgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - isdomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - issbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isscgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - issomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - sbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - scgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - sgmres

        Preconditioned GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - shels

        Internal routine for SGMRES.

  - sheqr

        Internal routine for SGMRES.

  - somn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - sorth

        Internal routine for SGMRES.

  - spigmr

        Internal routine for SGMRES.

  - srlcal

        Internal routine for SGMRES.

  - ssdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - ssdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - ssdgmr

        Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - ssilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - sslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - sslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - sslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - sslugm

        Incomplete LU GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - ssluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  - sxlcal

        Internal routine for SGMRES.

  ### NON-SYMMETRIC LINEAR SYSTEM SOLVE

  - dcgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - dsdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - dsdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - dslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - dslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - dslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - scgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - ssdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - ssdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - sslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - sslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - sslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  ### NONADAPTIVE

  - dqng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### NONLINEAR

  - chkder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  - dckder

        Check the gradients of M nonlinear functions in N
        variables, evaluated at a point X, for consistency
        with the functions themselves.

  - dfzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  ### NONLINEAR DATA FITTING

  - dcov

        Calculate the covariance matrix for a nonlinear data
        fitting problem.  It is intended to be used after a
        successful return from either DNLS1 or DNLS1E.

  - dnls1

        Minimize the sum of the squares of M nonlinear functions
        in N variables by a modification of the Levenberg-Marquardt
        algorithm.

  - dnls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  - scov

        Calculate the covariance matrix for a nonlinear data
        fitting problem.  It is intended to be used after a
        successful return from either SNLS1 or SNLS1E.

  - snls1

        Minimize the sum of the squares of M nonlinear functions
        in N variables by a modification of the Levenberg-Marquardt
        algorithm.

  - snls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  ### NONLINEAR EQUATIONS

  - dsos

        Solve a square system of nonlinear equations.

  - fzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  - sos

        Solve a square system of nonlinear equations.

  ### NONLINEAR LEAST SQUARES

  - dcov

        Calculate the covariance matrix for a nonlinear data
        fitting problem.  It is intended to be used after a
        successful return from either DNLS1 or DNLS1E.

  - dnls1

        Minimize the sum of the squares of M nonlinear functions
        in N variables by a modification of the Levenberg-Marquardt
        algorithm.

  - dnls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  - scov

        Calculate the covariance matrix for a nonlinear data
        fitting problem.  It is intended to be used after a
        successful return from either SNLS1 or SNLS1E.

  - snls1

        Minimize the sum of the squares of M nonlinear functions
        in N variables by a modification of the Levenberg-Marquardt
        algorithm.

  - snls1e

        An easy-to-use code which minimizes the sum of the squares
        of M nonlinear functions in N variables by a modification
        of the Levenberg-Marquardt algorithm.

  ### NONLINEAR SQUARE SYSTEM

  - dnsq

        Find a zero of a system of a N nonlinear functions in N
        variables by a modification of the Powell hybrid method.

  - dnsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.

  - snsq

        Find a zero of a system of a N nonlinear functions in N
        variables by a modification of the Powell hybrid method.

  - snsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.

  ### NONNEGATIVITY CONSTRAINTS

  - dwnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  - wnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  ### NONSYMMETRIC

  - cnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - cnbdi

        Compute the determinant of a band matrix using the factors
        computed by CNBCO or CNBFA.

  - cnbfa

        Factor a band matrix by elimination.

  - cnbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - cnbir

        Solve a general nonsymmetric banded system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - cnbsl

        Solve a complex band system using the factors computed by
        CNBCO or CNBFA.

  - dnbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - dnbdi

        Compute the determinant of a band matrix using the factors
        computed by DNBCO or DNBFA.

  - dnbfa

        Factor a band matrix by elimination.

  - dnbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - dnbsl

        Solve a real band system using the factors computed by
        DNBCO or DNBFA.

  - snbco

        Factor a band matrix using Gaussian elimination and
        estimate the condition number.

  - snbdi

        Compute the determinant of a band matrix using the factors
        computed by SNBCO or SNBFA.

  - snbfa

        Factor a real band matrix by elimination.

  - snbfs

        Solve a general nonsymmetric banded system of linear
        equations.

  - snbir

        Solve a general nonsymmetric banded system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - snbsl

        Solve a real band system using the factors computed by
        SNBCO or SNBFA.

  ### NORMAL

  - rgauss

        Generate a normally distributed (Gaussian) random number.

  ### NORMAL EQUATIONS

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - isdcgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isscgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  ### NORMAL EQUATIONS.

  - dcgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - scgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  ### NUMBER SORTING

  - dpsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - ipsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - spsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  ### NUMERICAL INTEGRATION

  - dgaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  - dpchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - dpchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  - gaus8

        Integrate a real function of one variable over a finite
        interval using an adaptive 8-point Legendre-Gauss
        algorithm.  Intended primarily for high accuracy
        integration or integration of smooth functions.

  - pchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - pchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  ### ODE

  - cdriv1

        The function of CDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  CDRIV1 allows complex-valued differential
        equations.

  - cdriv2

        The function of CDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  CDRIV2 allows complex-valued differential
        equations.

  - cdriv3

        The function of CDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  CDRIV3
        allows complex-valued differential equations.

  - ddeabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - ddebdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - dderkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - ddriv1

        The function of DDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  DDRIV1 uses double precision arithmetic.

  - ddriv2

        The function of DDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  DDRIV2 uses double precision arithmetic.

  - ddriv3

        The function of DDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  DDRIV3
        uses double precision arithmetic.

  - deabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - debdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - derkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - dintp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in DSTEPS at XOUT.  Must be used in
        conjunction with DSTEPS.

  - dsteps

        Integrate a system of first order ordinary differential
        equations one step.

  - sdriv1

        The function of SDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  SDRIV1 uses single precision arithmetic.

  - sdriv2

        The function of SDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  SDRIV2 uses single precision arithmetic.

  - sdriv3

        The function of SDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  SDRIV3
        uses single precision arithmetic.

  - sintrp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in STEPS at XOUT.  Must be used in
        conjunction with STEPS.

  - steps

        Integrate a system of first order ordinary differential
        equations one step.

  ### ORDER ONE

  - besi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - besi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - besj1

        Compute the Bessel function of the first kind of order one.

  - besk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - besk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - besy1

        Compute the Bessel function of the second kind of order
        one.

  - dbesi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - dbesj1

        Compute the Bessel function of the first kind of order one.

  - dbesk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - dbesy1

        Compute the Bessel function of the second kind of order
        one.

  - dbsi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - dbsk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  ### ORDER ZERO

  - besi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - besi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - besj0

        Compute the Bessel function of the first kind of order
        zero.

  - besk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - besk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - besy0

        Compute the Bessel function of the second kind of order
        zero.

  - dbesi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - dbesj0

        Compute the Bessel function of the first kind of order
        zero.

  - dbesk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - dbesy0

        Compute the Bessel function of the second kind of order
        zero.

  - dbsi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - dbsk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  ### ORDINARY DIFFERENTIAL EQUATIONS

  - cdriv1

        The function of CDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  CDRIV1 allows complex-valued differential
        equations.

  - cdriv2

        The function of CDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  CDRIV2 allows complex-valued differential
        equations.

  - cdriv3

        The function of CDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  CDRIV3
        allows complex-valued differential equations.

  - ddeabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - ddebdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - dderkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - ddriv1

        The function of DDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  DDRIV1 uses double precision arithmetic.

  - ddriv2

        The function of DDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  DDRIV2 uses double precision arithmetic.

  - ddriv3

        The function of DDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  DDRIV3
        uses double precision arithmetic.

  - deabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - debdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - derkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - dintp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in DSTEPS at XOUT.  Must be used in
        conjunction with DSTEPS.

  - dsteps

        Integrate a system of first order ordinary differential
        equations one step.

  - sdriv1

        The function of SDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  SDRIV1 uses single precision arithmetic.

  - sdriv2

        The function of SDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  SDRIV2 uses single precision arithmetic.

  - sdriv3

        The function of SDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  SDRIV3
        uses single precision arithmetic.

  - sintrp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in STEPS at XOUT.  Must be used in
        conjunction with STEPS.

  - steps

        Integrate a system of first order ordinary differential
        equations one step.

  ### ORTHOGONAL POLYNOMIAL

  - initds

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - inits

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  ### ORTHOGONAL SERIES

  - initds

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - inits

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  ### ORTHOGONAL TRIANGULAR

  - cqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - cqrsl

        Apply the output of CQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - dqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - dqrsl

        Apply the output of DQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - sqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - sqrsl

        Apply the output of SQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  ### ORTHOMIN

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - domn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - isdomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - issomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - somn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  ### ORTHONORMALIZATION

  - bvsup

        Solve a linear two-point boundary value problem using
        superposition coupled with an orthonormalization procedure
        and a variable-step integration scheme.

  - dbvsup

        Solve a linear two-point boundary value problem using
        superposition coupled with an orthonormalization procedure
        and a variable-step integration scheme.

  ### PACK

  - d9pak

        Pack a base 2 exponent into a floating point number.

  - r9pak

        Pack a base 2 exponent into a floating point number.

  ### PACKED

  - chpco

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - chpdi

        Compute the determinant, inertia and inverse of a complex
        Hermitian matrix stored in packed form using the factors
        obtained from CHPFA.

  - chpfa

        Factor a complex Hermitian matrix stored in packed form by
        elimination with symmetric pivoting.

  - chpsl

        Solve a complex Hermitian system using factors obtained
        from CHPFA.

  - cppco

        Factor a complex Hermitian positive definite matrix stored
        in packed form and estimate the condition number of the
        matrix.

  - cppdi

        Compute the determinant and inverse of a complex Hermitian
        positive definite matrix using factors from CPPCO or CPPFA.

  - cppfa

        Factor a complex Hermitian positive definite matrix stored
        in packed form.

  - cppsl

        Solve the complex Hermitian positive definite system using
        the factors computed by CPPCO or CPPFA.

  - cspco

        Factor a complex symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - cspdi

        Compute the determinant and inverse of a complex symmetric
        matrix stored in packed form using the factors from CSPFA.

  - cspfa

        Factor a complex symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - cspsl

        Solve a complex symmetric system using the factors obtained
        from CSPFA.

  - dppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - dppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from DPPCO or DPPFA.

  - dppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - dppsl

        Solve the real symmetric positive definite system using
        the factors computed by DPPCO or DPPFA.

  - dspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - dspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from DSPFA.

  - dspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - dspsl

        Solve a real symmetric system using the factors obtained
        from DSPFA.

  - sppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - sppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from SPPCO or SPPFA.

  - sppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - sppsl

        Solve the real symmetric positive definite system using
        the factors computed by SPPCO or SPPFA.

  - sspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - sspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from SSPFA.

  - sspev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix stored in packed form.

  - sspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - sspsl

        Solve a real symmetric system using the factors obtained
        from SSPFA.

  ### PASSIVE SORTING

  - dpsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - hpsort

        Return the permutation vector generated by sorting a
        substring within a character array and, optionally,
        rearrange the elements of the array.  The array may be
        sorted in forward or reverse lexicographical order.  A
        slightly modified quicksort algorithm is used.

  - ipsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - spsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  ### PCHIP

  - chfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by PCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use CHFEV instead.

  - chfev

        Evaluate a cubic polynomial given in Hermite form at an
        array of points.  While designed for use by PCHFE, it may
        be useful directly as an evaluator for a piecewise cubic
        Hermite function in applications, such as graphing, where
        the interval is known in advance.

  - dchfdv

        Evaluate a cubic polynomial given in Hermite form and its
        first derivative at an array of points.  While designed for
        use by DPCHFD, it may be useful directly as an evaluator
        for a piecewise cubic Hermite function in applications,
        such as graphing, where the interval is known in advance.
        If only function values are required, use DCHFEV instead.

  - dchfev

        Evaluate a cubic polynomial given in Hermite form at an
        array of points.  While designed for use by DPCHFE, it may
        be useful directly as an evaluator for a piecewise cubic
        Hermite function in applications, such as graphing, where
        the interval is known in advance.

  - dpchcm

        Check a cubic Hermite function for monotonicity.

  - dpchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for DPCHIM
        or DPCHIC. If only function values are required, use
        DPCHFE instead.

  - dpchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for DPCHIM or DPCHIC.

  - dpchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - dpchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - dpchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  - dpchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See DPCHIC if user control
        is desired over boundary or switch conditions.)

  - dpchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  - pchcm

        Check a cubic Hermite function for monotonicity.

  - pchdoc

        Documentation for PCHIP, a Fortran package for piecewise
        cubic Hermite interpolation of data.

  - pchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for PCHIM
        or PCHIC.  If only function values are required, use
        PCHFE instead.

  - pchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for PCHIM or PCHIC.

  - pchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - pchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - pchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  - pchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See PCHIC if user control is
        desired over boundary or switch conditions.)

  - pchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  ### PDE

  - genbun

        Solve by a cyclic reduction algorithm the linear system
        of equations that results from a finite difference
        approximation to certain 2-d elliptic PDE's on a centered
        grid .

  - hstcrt

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in Cartesian coordinates.

  - hstcsp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified Helmholtz
        equation in spherical coordinates assuming axisymmetry
        (no dependence on longitude).

  - hstcyl

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified
        Helmholtz equation in cylindrical coordinates.

  - hstplr

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in polar coordinates.

  - hstssp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz
        equation in spherical coordinates and on the surface of
        the unit sphere (radius of 1).

  - hw3crt

        Solve the standard seven-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscrt

        Solves the standard five-point finite difference
        approximation to the Helmholtz equation in Cartesian
        coordinates.

  - hwscsp

        Solve a finite difference approximation to the modified
        Helmholtz equation in spherical coordinates assuming
        axisymmetry  (no dependence on longitude).

  - hwscyl

        Solve a standard finite difference approximation
        to the Helmholtz equation in cylindrical coordinates.

  - hwsplr

        Solve a finite difference approximation to the Helmholtz
        equation in polar coordinates.

  - hwsssp

        Solve a finite difference approximation to the Helmholtz
        equation in spherical coordinates and on the surface of the
        unit sphere (radius of 1).

  - poistg

        Solve a block tridiagonal system of linear equations
        that results from a staggered grid finite difference
        approximation to 2-D elliptic PDE's.

  - sepeli

        Discretize and solve a second and, optionally, a fourth
        order finite difference approximation on a uniform grid to
        the general separable elliptic partial differential
        equation on a rectangle with any combination of periodic or
        mixed boundary conditions.

  - sepx4

        Solve for either the second or fourth order finite
        difference approximation to the solution of a separable
        elliptic partial differential equation on a rectangle.
        Any combination of periodic or mixed boundary conditions is
        allowed.

  ### PERMUTATION

  - dpperm

        Rearrange a given array according to a prescribed
        permutation vector.

  ### PERRON'S CONTINUED FRACTION

  - d9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - r9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  ### PHASE

  - d9aimp

        Evaluate the Airy modulus and phase.

  - d9b0mp

        Evaluate the modulus and phase for the J0 and Y0 Bessel
        functions.

  - d9b1mp

        Evaluate the modulus and phase for the J1 and Y1 Bessel
        functions.

  - r9aimp

        Evaluate the Airy modulus and phase.

  ### PIECEWISE CUBIC EVALUATION

  - dpchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for DPCHIM
        or DPCHIC. If only function values are required, use
        DPCHFE instead.

  - dpchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for DPCHIM or DPCHIC.

  - pchfd

        Evaluate a piecewise cubic Hermite function and its first
        derivative at an array of points.  May be used by itself
        for Hermite interpolation, or as an evaluator for PCHIM
        or PCHIC.  If only function values are required, use
        PCHFE instead.

  - pchfe

        Evaluate a piecewise cubic Hermite function at an array of
        points.  May be used by itself for Hermite interpolation,
        or as an evaluator for PCHIM or PCHIC.

  ### PIECEWISE CUBIC INTERPOLATION

  - dpchbs

        Piecewise Cubic Hermite to B-Spline converter.

  - dpchcm

        Check a cubic Hermite function for monotonicity.

  - dpchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - dpchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See DPCHIC if user control
        is desired over boundary or switch conditions.)

  - dpchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  - pchbs

        Piecewise Cubic Hermite to B-Spline converter.

  - pchcm

        Check a cubic Hermite function for monotonicity.

  - pchdoc

        Documentation for PCHIP, a Fortran package for piecewise
        cubic Hermite interpolation of data.

  - pchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - pchim

        Set derivatives needed to determine a monotone piecewise
        cubic Hermite interpolant to given data.  Boundary values
        are provided which are compatible with monotonicity.  The
        interpolant will have an extremum at each point where mono-
        tonicity switches direction.  (See PCHIC if user control is
        desired over boundary or switch conditions.)

  - pchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  ### PIECEWISE POLYNOMIAL

  - bsppp

        Convert the B-representation of a B-spline to the piecewise
        polynomial (PP) form.

  - dbsppp

        Convert the B-representation of a B-spline to the piecewise
        polynomial (PP) form.

  ### PLANE ROTATION

  - csrot

        Apply a plane Givens rotation.

  - drot

        Apply a plane Givens rotation.

  - srot

        Apply a plane Givens rotation.

  ### POCHHAMMER

  - dpoch

        Evaluate a generalization of Pochhammer's symbol.

  - dpoch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  - poch

        Evaluate a generalization of Pochhammer's symbol.

  - poch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  ### POISSON

  - pois3d

        Solve a three-dimensional block tridiagonal linear system
        which arises from a finite difference approximation to a
        three-dimensional Poisson equation using the Fourier
        transform package FFTPAK written by Paul Swarztrauber.

  ### POLAR

  - hstplr

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz equation
        in polar coordinates.

  - hwsplr

        Solve a finite difference approximation to the Helmholtz
        equation in polar coordinates.

  ### POLAR ANGEL

  - catan2

        Compute the complex arc tangent in the proper quadrant.

  ### POLYGAMMA FUNCTION

  - dpsifn

        Compute derivatives of the Psi function.

  - psifn

        Compute derivatives of the Psi function.

  ### POLYNOMIAL

  - dpolcf

        Compute the coefficients of the polynomial fit (including
        Hermite polynomial fits) produced by a previous call to
        POLINT.

  - polcof

        Compute the coefficients of the polynomial fit (including
        Hermite polynomial fits) produced by a previous call to
        POLINT.

  ### POLYNOMIAL APPROXIMATION

  - dp1vlu

        Use the coefficients generated by DPOLFT to evaluate the
        polynomial fit of degree L, along with the first NDER of
        its derivatives, at a specified point.

  - pvalue

        Use the coefficients generated by POLFIT to evaluate the
        polynomial fit of degree L, along with the first NDER of
        its derivatives, at a specified point.

  ### POLYNOMIAL EVALUATION

  - dpolvl

        Calculate the value of a polynomial and its first NDER
        derivatives where the polynomial was produced by a previous
        call to DPLINT.

  - polyvl

        Calculate the value of a polynomial and its first NDER
        derivatives where the polynomial was produced by a previous
        call to POLINT.

  ### POLYNOMIAL FIT

  - dpcoef

        Convert the DPOLFT coefficients to Taylor series form.

  - dpolft

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  - pcoef

        Convert the POLFIT coefficients to Taylor series form.

  - polfit

        Fit discrete data in a least squares sense by polynomials
        in one variable.

  ### POLYNOMIAL INTERPOLATION

  - dplint

        Produce the polynomial which interpolates a set of discrete
        data points.

  - polint

        Produce the polynomial which interpolates a set of discrete
        data points.

  ### POLYNOMIAL ROOTS

  - cpqr79

        Find the zeros of a polynomial with complex coefficients.

  - cpzero

        Find the zeros of a polynomial with complex coefficients.

  - rpqr79

        Find the zeros of a polynomial with real coefficients.

  - rpzero

        Find the zeros of a polynomial with real coefficients.

  ### POLYNOMIAL ZEROS

  - cpqr79

        Find the zeros of a polynomial with complex coefficients.

  - cpzero

        Find the zeros of a polynomial with complex coefficients.

  - rpqr79

        Find the zeros of a polynomial with real coefficients.

  - rpzero

        Find the zeros of a polynomial with real coefficients.

  ### POSITIVE DEFINITE

  - cchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - cchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - cpbco

        Factor a complex Hermitian positive definite matrix stored
        in band form and estimate the condition number of the
        matrix.

  - cpbdi

        Compute the determinant of a complex Hermitian positive
        definite band matrix using the factors computed by CPBCO or
        CPBFA.

  - cpbfa

        Factor a complex Hermitian positive definite matrix stored
        in band form.

  - cpbsl

        Solve the complex Hermitian positive definite band system
        using the factors computed by CPBCO or CPBFA.

  - cpoco

        Factor a complex Hermitian positive definite matrix
        and estimate the condition number of the matrix.

  - cpodi

        Compute the determinant and inverse of a certain complex
        Hermitian positive definite matrix using the factors
        computed by CPOCO, CPOFA, or CQRDC.

  - cpofa

        Factor a complex Hermitian positive definite matrix.

  - cpofs

        Solve a positive definite symmetric complex system of
        linear equations.

  - cpoir

        Solve a positive definite Hermitian system of linear
        equations.  Iterative refinement is used to obtain an
        error estimate.

  - cposl

        Solve the complex Hermitian positive definite linear system
        using the factors computed by CPOCO or CPOFA.

  - cppco

        Factor a complex Hermitian positive definite matrix stored
        in packed form and estimate the condition number of the
        matrix.

  - cppdi

        Compute the determinant and inverse of a complex Hermitian
        positive definite matrix using factors from CPPCO or CPPFA.

  - cppfa

        Factor a complex Hermitian positive definite matrix stored
        in packed form.

  - cppsl

        Solve the complex Hermitian positive definite system using
        the factors computed by CPPCO or CPPFA.

  - cptsl

        Solve a positive definite tridiagonal linear system.

  - dchdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - dchex

        Update the Cholesky factorization  A=TRANS(R)*R  of a
        positive definite matrix A of order P under diagonal
        permutations of the form  TRANS(E)*A*E, where E is a
        permutation matrix.

  - dpbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - dpbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by DPBCO or DPBFA.

  - dpbfa

        Factor a real symmetric positive definite matrix stored in
        in band form.

  - dpbsl

        Solve a real symmetric positive definite band system
        using the factors computed by DPBCO or DPBFA.

  - dpoco

        Factor a real symmetric positive definite matrix
        and estimate the condition of the matrix.

  - dpodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by DPOCO, DPOFA or DQRDC.

  - dpofa

        Factor a real symmetric positive definite matrix.

  - dpofs

        Solve a positive definite symmetric system of linear
        equations.

  - dposl

        Solve the real symmetric positive definite linear system
        using the factors computed by DPOCO or DPOFA.

  - dppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - dppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from DPPCO or DPPFA.

  - dppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - dppsl

        Solve the real symmetric positive definite system using
        the factors computed by DPPCO or DPPFA.

  - dptsl

        Solve a positive definite tridiagonal linear system.

  - schdc

        Compute the Cholesky decomposition of a positive definite
        matrix.  A pivoting option allows the user to estimate the
        condition number of a positive definite matrix or determine
        the rank of a positive semidefinite matrix.

  - schex

        Update the Cholesky factorization  A=TRANS(R)*R  of A
        positive definite matrix A of order P under diagonal
        permutations of the form TRANS(E)*A*E, where E is a
        permutation matrix.

  - spbco

        Factor a real symmetric positive definite matrix stored in
        band form and estimate the condition number of the matrix.

  - spbdi

        Compute the determinant of a symmetric positive definite
        band matrix using the factors computed by SPBCO or SPBFA.

  - spbfa

        Factor a real symmetric positive definite matrix stored in
        band form.

  - spbsl

        Solve a real symmetric positive definite band system
        using the factors computed by SPBCO or SPBFA.

  - spoco

        Factor a real symmetric positive definite matrix
        and estimate the condition number of the matrix.

  - spodi

        Compute the determinant and inverse of a certain real
        symmetric positive definite matrix using the factors
        computed by SPOCO, SPOFA or SQRDC.

  - spofa

        Factor a real symmetric positive definite matrix.

  - spofs

        Solve a positive definite symmetric system of linear
        equations.

  - spoir

        Solve a positive definite symmetric system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - sposl

        Solve the real symmetric positive definite linear system
        using the factors computed by SPOCO or SPOFA.

  - sppco

        Factor a symmetric positive definite matrix stored in
        packed form and estimate the condition number of the
        matrix.

  - sppdi

        Compute the determinant and inverse of a real symmetric
        positive definite matrix using factors from SPPCO or SPPFA.

  - sppfa

        Factor a real symmetric positive definite matrix stored in
        packed form.

  - sppsl

        Solve the real symmetric positive definite system using
        the factors computed by SPPCO or SPPFA.

  - sptsl

        Solve a positive definite tridiagonal linear system.

  ### POWELL HYBRID METHOD

  - dnsq

        Find a zero of a system of a N nonlinear functions in N
        variables by a modification of the Powell hybrid method.

  - dnsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.

  - snsq

        Find a zero of a system of a N nonlinear functions in N
        variables by a modification of the Powell hybrid method.

  - snsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.

  ### PRECONDITIONED CONJUGATE GRADIENT

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  ### PREDICTOR-CORRECTOR

  - ddeabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - deabm

        Solve an initial value problem in ordinary differential
        equations using an Adams-Bashforth method.

  - dintp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in DSTEPS at XOUT.  Must be used in
        conjunction with DSTEPS.

  - dsteps

        Integrate a system of first order ordinary differential
        equations one step.

  - sintrp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in STEPS at XOUT.  Must be used in
        conjunction with STEPS.

  - steps

        Integrate a system of first order ordinary differential
        equations one step.

  ### PRINTING

  - xerprn

        Print error messages processed by XERMSG.

  ### PSI FUNCTION

  - cpsi

        Compute the Psi (or Digamma) function.

  - dpsi

        Compute the Psi (or Digamma) function.

  - dpsifn

        Compute derivatives of the Psi function.

  - dxpsi

        To compute values of the Psi function for DXLEGF.

  - psifn

        Compute derivatives of the Psi function.

  - psi

        Compute the Psi (or Digamma) function.

  - xpsi

        To compute values of the Psi function for XLEGF.

  ### QL METHOD

  - tql1

        Compute the eigenvalues of symmetric tridiagonal matrix by
        the QL method.

  - tqlrat

        Compute the eigenvalues of symmetric tridiagonal matrix
        using a rational variant of the QL method.

  ### QR DECOMPOSITION

  - cqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - dqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  - sqrdc

        Use Householder transformations to compute the QR
        factorization of an N by P matrix.  Column pivoting is a
        users option.

  ### QR FACTORIZATION

  - dglss

        Solve a linear least squares problems by performing a QR
        factorization of the input matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - dllsia

        Solve linear least squares problems by performing a QR
        factorization of the input matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - hfti

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.

  - llsia

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - sglss

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  ### QUADPACK

  - dqag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur (e.g.
        SINGULARITIES, DISCONTINUITIES), are provided by the user.

  - dqagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - dqags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - dqawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqawf

        The routine calculates an approximation result to a given
        Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqc25c

        To compute I = Integral of F*W over (A,B) with
        error estimate, where W(X) = 1/(X-C)

  - dqc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to
        compute J = Integral of ABS(F) over (A,B). For small value
        of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO
        Rule is used. Otherwise a generalized CLENSHAW-CURTIS
        method is used.

  - dqc25s

        To compute I = Integral of F*W over (BL,BR), with error
        estimate, where the weight function W has a singular
        behaviour of ALGEBRAICO-LOGARITHMIC type at the points
        A and/or B. (BL,BR) is a part of (A,B).

  - dqk15

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = integral of ABS(F) over (A,B)

  - dqk15i

        The original (infinite integration range is mapped
        onto the interval (0,1) and (A,B) is a part of (0,1).
        it is the purpose to compute
        I = Integral of transformed integrand over (A,B),
        J = Integral of ABS(Transformed Integrand) over (A,B).

  - dqk15w

        To compute I = Integral of F*W over (A,B), with error
                       estimate
                   J = Integral of ABS(F*W) over (A,B)

  - dqk21

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk31

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk41

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk51

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk61

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqmomo

        This routine computes modified Chebyshev moments.  The K-th
        modified Chebyshev moment is defined as the integral over
        (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
        polynomial of degree K.

  - dqng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur(e.g. SINGULARITIES,
        DISCONTINUITIES), are provided by the user.

  - qagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
              ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - qags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - qawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qawf

        The routine calculates an approximation result to a given
        Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
         where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qc25c

        To compute I = Integral of F*W over (A,B) with
        error estimate, where W(X) = 1/(X-C)

  - qc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)
        and to compute J=Integral of ABS(F) over (A,B). For small
        value of OMEGA or small intervals (A,B) 15-point GAUSS-
        KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

  - qc25s

        To compute I = Integral of F*W over (BL,BR), with error
        estimate, where the weight function W has a singular
        behaviour of ALGEBRAICO-LOGARITHMIC type at the points
        A and/or B. (BL,BR) is a part of (A,B).

  - qk15

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = integral of ABS(F) over (A,B)

  - qk15i

        The original (infinite integration range is mapped
        onto the interval (0,1) and (A,B) is a part of (0,1).
        it is the purpose to compute
        I = Integral of transformed integrand over (A,B),
        J = Integral of ABS(Transformed Integrand) over (A,B).

  - qk15w

        To compute I = Integral of F*W over (A,B), with error
                       estimate
                   J = Integral of ABS(F*W) over (A,B)

  - qk21

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk31

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk41

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk51

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk61

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qmomo

        This routine computes modified Chebyshev moments.  The K-th
        modified Chebyshev moment is defined as the integral over
        (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
        polynomial of degree K.

  - qng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qpdoc

        Documentation for QUADPACK, a package of subprograms for
        automatic evaluation of one-dimensional definite integrals.

  ### QUADRANT

  - catan2

        Compute the complex arc tangent in the proper quadrant.

  ### QUADRATIC PROGRAMMING

  - dlsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - dwnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  - lsei

        Solve a linearly constrained least squares problem with
        equality and inequality constraints, and optionally compute
        a covariance matrix.

  - wnnls

        Solve a linearly constrained least squares problem with
        equality constraints and nonnegativity constraints on
        selected variables.

  ### QUADRATURE

  - avint

        Integrate a function tabulated at arbitrarily spaced
        abscissas using overlapping parabolas.

  - bfqad

        Compute the integral of a product of a function and a
        derivative of a B-spline.

  - bsqad

        Compute the integral of a K-th order B-spline using the
        B-representation.

  - davint

        Integrate a function tabulated at arbitrarily spaced
        abscissas using overlapping parabolas.

  - dbfqad

        Compute the integral of a product of a function and a
        derivative of a K-th order B-spline.

  - dbsqad

        Compute the integral of a K-th order B-spline using the
        B-representation.

  - dpchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - dpchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  - dpfqad

        Compute the integral on (X1,X2) of a product of a
        function F and the ID-th derivative of a B-spline,
        (PP-representation).

  - dppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - dqag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur (e.g.
        SINGULARITIES, DISCONTINUITIES), are provided by the user.

  - dqagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - dqags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - dqawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqawf

        The routine calculates an approximation result to a given
        Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqc25c

        To compute I = Integral of F*W over (A,B) with
        error estimate, where W(X) = 1/(X-C)

  - dqc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) or W(X)=SIN(OMEGA*X) and to
        compute J = Integral of ABS(F) over (A,B). For small value
        of OMEGA or small intervals (A,B) the 15-point GAUSS-KRONRO
        Rule is used. Otherwise a generalized CLENSHAW-CURTIS
        method is used.

  - dqc25s

        To compute I = Integral of F*W over (BL,BR), with error
        estimate, where the weight function W has a singular
        behaviour of ALGEBRAICO-LOGARITHMIC type at the points
        A and/or B. (BL,BR) is a part of (A,B).

  - dqk15

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = integral of ABS(F) over (A,B)

  - dqk15i

        The original (infinite integration range is mapped
        onto the interval (0,1) and (A,B) is a part of (0,1).
        it is the purpose to compute
        I = Integral of transformed integrand over (A,B),
        J = Integral of ABS(Transformed Integrand) over (A,B).

  - dqk15w

        To compute I = Integral of F*W over (A,B), with error
                       estimate
                   J = Integral of ABS(F*W) over (A,B)

  - dqk21

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk31

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk41

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk51

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqk61

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - dqmomo

        This routine computes modified Chebyshev moments.  The K-th
        modified Chebyshev moment is defined as the integral over
        (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
        polynomial of degree K.

  - dqng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - pchia

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an arbitrary interval.

  - pchid

        Evaluate the definite integral of a piecewise cubic
        Hermite function over an interval whose endpoints are data
        points.

  - pfqad

        Compute the integral on (X1,X2) of a product of a function
        F and the ID-th derivative of a B-spline,
        (PP-representation).

  - ppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - qag

        The routine calculates an approximation result to a given
        definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qage

        The routine calculates an approximation result to a given
        definite integral   I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur(e.g. SINGULARITIES,
        DISCONTINUITIES), are provided by the user.

  - qagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
              ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - qags

        The routine calculates an approximation result to a given
        Definite integral  I = Integral of F over (A,B),
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - qawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qawf

        The routine calculates an approximation result to a given
        Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
         where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qc25c

        To compute I = Integral of F*W over (A,B) with
        error estimate, where W(X) = 1/(X-C)

  - qc25f

        To compute the integral I=Integral of F(X) over (A,B)
        Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)
        and to compute J=Integral of ABS(F) over (A,B). For small
        value of OMEGA or small intervals (A,B) 15-point GAUSS-
        KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us

  - qc25s

        To compute I = Integral of F*W over (BL,BR), with error
        estimate, where the weight function W has a singular
        behaviour of ALGEBRAICO-LOGARITHMIC type at the points
        A and/or B. (BL,BR) is a part of (A,B).

  - qk15

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = integral of ABS(F) over (A,B)

  - qk15i

        The original (infinite integration range is mapped
        onto the interval (0,1) and (A,B) is a part of (0,1).
        it is the purpose to compute
        I = Integral of transformed integrand over (A,B),
        J = Integral of ABS(Transformed Integrand) over (A,B).

  - qk15w

        To compute I = Integral of F*W over (A,B), with error
                       estimate
                   J = Integral of ABS(F*W) over (A,B)

  - qk21

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk31

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk41

        To compute I = Integral of F over (A,B), with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk51

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qk61

        To compute I = Integral of F over (A,B) with error
                       estimate
                   J = Integral of ABS(F) over (A,B)

  - qmomo

        This routine computes modified Chebyshev moments.  The K-th
        modified Chebyshev moment is defined as the integral over
        (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
        polynomial of degree K.

  - qng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qpdoc

        Documentation for QUADPACK, a package of subprograms for
        automatic evaluation of one-dimensional definite integrals.

  ### RACAH COEFFICIENTS

  - drc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - drc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - drc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - rc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  ### RANDOM NUMBER

  - rand

        Generate a uniformly distributed random number.

  - rgauss

        Generate a normally distributed (Gaussian) random number.

  - runif

        Generate a uniformly distributed random number.

  ### REAL ROOTS

  - cpzero

        Find the zeros of a polynomial with complex coefficients.

  - rpzero

        Find the zeros of a polynomial with real coefficients.

  ### REARRANGEMENT

  - dpperm

        Rearrange a given array according to a prescribed
        permutation vector.

  ### RECALL

  - j4save

        Save or recall global variables needed by error
        handling routines.

  ### RECIPROCAL GAMMA FUNCTION

  - cgamr

        Compute the reciprocal of the Gamma function.

  - dgamr

        Compute the reciprocal of the Gamma function.

  - gamr

        Compute the reciprocal of the Gamma function.

  ### RELATIVE ADDRESS DETERMINATION FUNCTION

  - idloc

        Subsidiary to DSPLP

  - iploc

        Subsidiary to SPLP

  ### RKF

  - dderkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - derkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  ### ROOTS

  - cbrt

        Compute the cube root.

  - ccbrt

        Compute the cube root.

  - dcbrt

        Compute the cube root.

  - dfzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  - dsos

        Solve a square system of nonlinear equations.

  - fzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  - sos

        Solve a square system of nonlinear equations.

  ### RUNGE-KUTTA-FEHLBERG METHODS

  - dderkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  - derkf

        Solve an initial value problem in ordinary differential
        equations using a Runge-Kutta-Fehlberg scheme.

  ### SAVE

  - j4save

        Save or recall global variables needed by error
        handling routines.

  ### SCALE

  - cscal

        Multiply a vector by a constant.

  - csscal

        Scale a complex vector.

  - dscal

        Multiply a vector by a constant.

  - sscal

        Multiply a vector by a constant.

  ### SDRIVE

  - cdriv1

        The function of CDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  CDRIV1 allows complex-valued differential
        equations.

  - cdriv2

        The function of CDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  CDRIV2 allows complex-valued differential
        equations.

  - cdriv3

        The function of CDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  CDRIV3
        allows complex-valued differential equations.

  - ddriv1

        The function of DDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  DDRIV1 uses double precision arithmetic.

  - ddriv2

        The function of DDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  DDRIV2 uses double precision arithmetic.

  - ddriv3

        The function of DDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  DDRIV3
        uses double precision arithmetic.

  - sdriv1

        The function of SDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  SDRIV1 uses single precision arithmetic.

  - sdriv2

        The function of SDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  SDRIV2 uses single precision arithmetic.

  - sdriv3

        The function of SDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  SDRIV3
        uses single precision arithmetic.

  ### SECOND KIND

  - besy0

        Compute the Bessel function of the second kind of order
        zero.

  - besy1

        Compute the Bessel function of the second kind of order
        one.

  - dbesy0

        Compute the Bessel function of the second kind of order
        zero.

  - dbesy1

        Compute the Bessel function of the second kind of order
        one.

  ### SECOND ORDER

  - c9ln2r

        Evaluate LOG(1+Z) from second order relative accuracy so
        that  LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).

  - d9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)

  - r9ln2r

        Evaluate LOG(1+X) from second order relative accuracy so
        that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).

  ### SEPARABLE

  - sepeli

        Discretize and solve a second and, optionally, a fourth
        order finite difference approximation on a uniform grid to
        the general separable elliptic partial differential
        equation on a rectangle with any combination of periodic or
        mixed boundary conditions.

  - sepx4

        Solve for either the second or fourth order finite
        difference approximation to the solution of a separable
        elliptic partial differential equation on a rectangle.
        Any combination of periodic or mixed boundary conditions is
        allowed.

  ### SEQUENCE OF BESSEL FUNCTIONS

  - beskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - besks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbesks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  ### SEQUENTIAL SORTING

  - dqpsrt

        This routine maintains the descending ordering in the
        list of the local error estimated resulting from the
        interval subdivision process. At each call two error
        estimates are inserted using the sequential search
        method, top-down for the largest error estimate and
        bottom-up for the smallest error estimate.

  - qpsrt

        Subsidiary to QAGE, QAGIE, QAGPE, QAGSE, QAWCE, QAWOE and
        QAWSE

  ### SHAPE-PRESERVING INTERPOLATION

  - dpchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  - pchic

        Set derivatives needed to determine a piecewise monotone
        piecewise cubic Hermite interpolant to given data.
        User control is available over boundary conditions and/or
        treatment of points where monotonicity switches direction.

  ### SHOOTING

  - bvsup

        Solve a linear two-point boundary value problem using
        superposition coupled with an orthonormalization procedure
        and a variable-step integration scheme.

  - dbvsup

        Solve a linear two-point boundary value problem using
        superposition coupled with an orthonormalization procedure
        and a variable-step integration scheme.

  ### SINE

  - dsindg

        Compute the sine of an argument in degrees.

  - sindg

        Compute the sine of an argument in degrees.

  ### SINGLE PRECISION

  - sdriv1

        The function of SDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  SDRIV1 uses single precision arithmetic.

  - sdriv2

        The function of SDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  SDRIV2 uses single precision arithmetic.

  - sdriv3

        The function of SDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  SDRIV3
        uses single precision arithmetic.

  ### SINGLETON QUICKSORT

  - dpsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - dsort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - hpsort

        Return the permutation vector generated by sorting a
        substring within a character array and, optionally,
        rearrange the elements of the array.  The array may be
        sorted in forward or reverse lexicographical order.  A
        slightly modified quicksort algorithm is used.

  - ipsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - isort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - qs2i1d

        Sort an integer array, moving an integer and DP array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the double pre-
        cision array A.  The array IA may be sorted in increasing
        order or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - qs2i1r

        Sort an integer array, moving an integer and real array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the real array A.
        The array IA may be sorted in increasing order or decreas-
        ing order.  A slightly modified QUICKSORT algorithm is
        used.

  - spsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - ssort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  ### SINGULAR VALUE DECOMPOSITION

  - csvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - dsvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  - ssvdc

        Perform the singular value decomposition of a rectangular
        matrix.

  ### SINGULARITIES AT USER SPECIFIED POINTS

  - dqagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur (e.g.
        SINGULARITIES, DISCONTINUITIES), are provided by the user.

  - dqagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  - qagp

        The routine calculates an approximation result to a given
        definite integral I = Integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        break points of the integration interval, where local
        difficulties of the integrand may occur(e.g. SINGULARITIES,
        DISCONTINUITIES), are provided by the user.

  - qagpe

        Approximate a given definite integral I = Integral of F
        over (A,B), hopefully satisfying the accuracy claim:
              ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
        Break points of the integration interval, where local
        difficulties of the integrand may occur (e.g. singularities
        or discontinuities) are provided by the user.

  ### SLAP

  - dbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - dcg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - dcgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - dcgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - dchkw

        SLAP WORK/IWORK Array Bounds Checker.
        This routine checks the work array lengths and interfaces
        to the SLATEC error handler if a problem is found.

  - dgmres

        Preconditioned GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - dhels

        Internal routine for DGMRES.

  - dheqr

        Internal routine for DGMRES.

  - dir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - dllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - domn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - dorth

        Internal routine for DGMRES.

  - dpigmr

        Internal routine for DGMRES.

  - drlcal

        Internal routine for DGMRES.

  - dsdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - dsdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - dsdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - dsdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - dsdgmr

        Diagonally scaled GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - dsdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - dsdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - dsgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - dsiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - dsilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - dsilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - dsjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - dsli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - dsli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - dsllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - dslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - dslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - dslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - dslugm

        Incomplete LU GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - dslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - dslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - dslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - dsluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  - dsluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - dsmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - dsmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  - dsmtv

        SLAP Column Format Sparse Matrix Transpose Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A'*X, where ' denotes transpose.

  - dsmv

        SLAP Column Format Sparse Matrix Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A*X.

  - dxlcal

        Internal routine for DGMRES.

  - isdbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isdcgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - isdgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - isdir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - issbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isscgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - issgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - issir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - issomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - qs2i1d

        Sort an integer array, moving an integer and DP array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the double pre-
        cision array A.  The array IA may be sorted in increasing
        order or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - qs2i1r

        Sort an integer array, moving an integer and real array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the real array A.
        The array IA may be sorted in increasing order or decreas-
        ing order.  A slightly modified QUICKSORT algorithm is
        used.

  - sbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - scg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - scgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - scgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - schkw

        SLAP WORK/IWORK Array Bounds Checker.
        This routine checks the work array lengths and interfaces
        to the SLATEC error handler if a problem is found.

  - sir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - sgmres

        Preconditioned GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - shels

        Internal routine for SGMRES.

  - sheqr

        Internal routine for SGMRES.

  - sllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - somn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - sorth

        Internal routine for SGMRES.

  - spigmr

        Internal routine for SGMRES.

  - srlcal

        Internal routine for SGMRES.

  - ssdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - ssdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - ssdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - ssdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - ssdgmr

        Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - ssdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - ssdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - ssgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - ssiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - ssilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - ssilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - ssjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - ssli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - ssli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - ssllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - sslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - sslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - sslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - sslugm

        Incomplete LU GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - sslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - sslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - sslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - ssluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  - ssluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - ssmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - ssmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  - ssmtv

        SLAP Column Format Sparse Matrix Transpose Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A'*X, where ' denotes transpose.

  - ssmv

        SLAP Column Format Sparse Matrix Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A*X.

  - sxlcal

        Internal routine for SGMRES.

  ### SLAP SPARSE

  - dbhin

        Read a Sparse Linear System in the Boeing/Harwell Format.
        The matrix is read in and if the right hand side is also
        present in the input file then it too is read in.  The
        matrix is then modified to be in the SLAP Column format.

  - dcpplt

        Printer Plot of SLAP Column Format Matrix.
        Routine to print out a SLAP Column format matrix in a
        "printer plot" graphical representation.

  - ds2lt

        Lower Triangle Preconditioner SLAP Set Up.
        Routine to store the lower triangle of a matrix stored
        in the SLAP Column format.

  - ds2y

        SLAP Triad to SLAP Column Format Converter.
        Routine to convert from the SLAP Triad to SLAP Column
        format.

  - dsd2s

        Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up.
        Routine to compute the inverse of the diagonal of the
        matrix A*A', where A is stored in SLAP-Column format.

  - dsds

        Diagonal Scaling Preconditioner SLAP Set Up.
        Routine to compute the inverse of the diagonal of a matrix
        stored in the SLAP Column format.

  - dsdscl

        Diagonal Scaling of system Ax = b.
        This routine scales (and unscales) the system  Ax = b
        by symmetric diagonal scaling.

  - dsics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  - dtin

        Read in SLAP Triad Format Linear System.
        Routine to read in a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - dtout

        Write out SLAP Triad Format Linear System.
        Routine to write out a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - sbhin

        Read a Sparse Linear System in the Boeing/Harwell Format.
        The matrix is read in and if the right hand side is also
        present in the input file then it too is read in.  The
        matrix is then modified to be in the SLAP Column format.

  - scpplt

        Printer Plot of SLAP Column Format Matrix.
        Routine to print out a SLAP Column format matrix in a
        "printer plot" graphical representation.

  - ss2lt

        Lower Triangle Preconditioner SLAP Set Up.
        Routine to store the lower triangle of a matrix stored
        in the SLAP Column format.

  - ss2y

        SLAP Triad to SLAP Column Format Converter.
        Routine to convert from the SLAP Triad to SLAP Column
        format.

  - ssd2s

        Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up.
        Routine to compute the inverse of the diagonal of the
        matrix A*A', where A is stored in SLAP-Column format.

  - ssds

        Diagonal Scaling Preconditioner SLAP Set Up.
        Routine to compute the inverse of the diagonal of a matrix
        stored in the SLAP Column format.

  - ssdscl

        Diagonal Scaling of system Ax = b.
        This routine scales (and unscales) the system  Ax = b
        by symmetric diagonal scaling.

  - ssics

        Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
        Routine to generate the Incomplete Cholesky decomposition,
        L*D*L-trans, of a symmetric positive definite matrix, A,
        which is stored in SLAP Column format.  The unit lower
        triangular matrix L is stored by rows, and the inverse of
        the diagonal matrix D is stored.

  - stin

        Read in SLAP Triad Format Linear System.
        Routine to read in a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  - stout

        Write out SLAP Triad Format Linear System.
        Routine to write out a SLAP Triad format matrix and right
        hand side and solution to the system, if known.

  ### SLATEC

  - idloc

        Subsidiary to DSPLP

  - iploc

        Subsidiary to SPLP

  ### SMALL X

  - d9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and X small.

  - d9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - r9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and for small X.

  - r9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  ### SMOOTH INTEGRAND

  - dqng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qng

        The routine calculates an approximation result to a
        given definite integral I = integral of F over (A,B),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### SMOOTH INTERPOLANT

  - dintp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in DSTEPS at XOUT.  Must be used in
        conjunction with DSTEPS.

  - sintrp

        Approximate the solution at XOUT by evaluating the
        polynomial computed in STEPS at XOUT.  Must be used in
        conjunction with STEPS.

  ### SOLUTIONS

  - dsos

        Solve a square system of nonlinear equations.

  - sos

        Solve a square system of nonlinear equations.

  ### SOLVE

  - cgbsl

        Solve the complex band system A*X=B or CTRANS(A)*X=B using
        the factors computed by CGBCO or CGBFA.

  - cgesl

        Solve the complex system A*X=B or CTRANS(A)*X=B using the
        factors computed by CGECO or CGEFA.

  - cgtsl

        Solve a tridiagonal linear system.

  - chisl

        Solve the complex Hermitian system using factors obtained
        from CHIFA.

  - chpsl

        Solve a complex Hermitian system using factors obtained
        from CHPFA.

  - cnbsl

        Solve a complex band system using the factors computed by
        CNBCO or CNBFA.

  - cpbsl

        Solve the complex Hermitian positive definite band system
        using the factors computed by CPBCO or CPBFA.

  - cposl

        Solve the complex Hermitian positive definite linear system
        using the factors computed by CPOCO or CPOFA.

  - cppsl

        Solve the complex Hermitian positive definite system using
        the factors computed by CPPCO or CPPFA.

  - cptsl

        Solve a positive definite tridiagonal linear system.

  - cqrsl

        Apply the output of CQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - csisl

        Solve a complex symmetric system using the factors obtained
        from CSIFA.

  - cspsl

        Solve a complex symmetric system using the factors obtained
        from CSPFA.

  - dgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by DGBCO or DGBFA.

  - dgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors computed by DGECO or DGEFA.

  - dgtsl

        Solve a tridiagonal linear system.

  - dnbsl

        Solve a real band system using the factors computed by
        DNBCO or DNBFA.

  - dpbsl

        Solve a real symmetric positive definite band system
        using the factors computed by DPBCO or DPBFA.

  - dposl

        Solve the real symmetric positive definite linear system
        using the factors computed by DPOCO or DPOFA.

  - dppsl

        Solve the real symmetric positive definite system using
        the factors computed by DPPCO or DPPFA.

  - dptsl

        Solve a positive definite tridiagonal linear system.

  - dqrsl

        Apply the output of DQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - dsisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - dspsl

        Solve a real symmetric system using the factors obtained
        from DSPFA.

  - sgbsl

        Solve the real band system A*X=B or TRANS(A)*X=B using
        the factors computed by SGBCO or SGBFA.

  - sgesl

        Solve the real system A*X=B or TRANS(A)*X=B using the
        factors of SGECO or SGEFA.

  - sgtsl

        Solve a tridiagonal linear system.

  - snbsl

        Solve a real band system using the factors computed by
        SNBCO or SNBFA.

  - spbsl

        Solve a real symmetric positive definite band system
        using the factors computed by SPBCO or SPBFA.

  - sposl

        Solve the real symmetric positive definite linear system
        using the factors computed by SPOCO or SPOFA.

  - sppsl

        Solve the real symmetric positive definite system using
        the factors computed by SPPCO or SPPFA.

  - sptsl

        Solve a positive definite tridiagonal linear system.

  - sqrsl

        Apply the output of SQRDC to compute coordinate transfor-
        mations, projections, and least squares solutions.

  - ssisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - sspsl

        Solve a real symmetric system using the factors obtained
        from SSPFA.

  ### SORT

  - dpsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - dsort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - hpsort

        Return the permutation vector generated by sorting a
        substring within a character array and, optionally,
        rearrange the elements of the array.  The array may be
        sorted in forward or reverse lexicographical order.  A
        slightly modified quicksort algorithm is used.

  - ipsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - isort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - qs2i1d

        Sort an integer array, moving an integer and DP array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the double pre-
        cision array A.  The array IA may be sorted in increasing
        order or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - qs2i1r

        Sort an integer array, moving an integer and real array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the real array A.
        The array IA may be sorted in increasing order or decreas-
        ing order.  A slightly modified QUICKSORT algorithm is
        used.

  - spsort

        Return the permutation vector generated by sorting a given
        array and, optionally, rearrange the elements of the array.
        The array may be sorted in increasing or decreasing order.
        A slightly modified quicksort algorithm is used.

  - ssort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  ### SORTING

  - dsort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - isort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - qs2i1d

        Sort an integer array, moving an integer and DP array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the double pre-
        cision array A.  The array IA may be sorted in increasing
        order or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  - qs2i1r

        Sort an integer array, moving an integer and real array.
        This routine sorts the integer array IA and makes the same
        interchanges in the integer array JA and the real array A.
        The array IA may be sorted in increasing order or decreas-
        ing order.  A slightly modified QUICKSORT algorithm is
        used.

  - ssort

        Sort an array and optionally make the same interchanges in
        an auxiliary array.  The array may be sorted in increasing
        or decreasing order.  A slightly modified QUICKSORT
        algorithm is used.

  ### SPARSE

  - dbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - dcg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - dcgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - dcgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - dgmres

        Preconditioned GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - dhels

        Internal routine for DGMRES.

  - dheqr

        Internal routine for DGMRES.

  - dir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - dllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - domn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - dorth

        Internal routine for DGMRES.

  - dpigmr

        Internal routine for DGMRES.

  - drlcal

        Internal routine for DGMRES.

  - dsdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - dsdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - dsdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - dsdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - dsdgmr

        Diagonally scaled GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - dsdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - dsdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - dsgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - dsiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - dsilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - dsilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - dsjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - dsli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - dsli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - dsllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - dslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - dslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - dslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - dslugm

        Incomplete LU GMRES iterative sparse Ax=b solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - dslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - dslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - dslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - dsluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  - dsluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - dsmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - dsmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  - dsmtv

        SLAP Column Format Sparse Matrix Transpose Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A'*X, where ' denotes transpose.

  - dsmv

        SLAP Column Format Sparse Matrix Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A*X.

  - dxlcal

        Internal routine for DGMRES.

  - isdbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isdcgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - isdgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - isdir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - issbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscgn

        Preconditioned CG on Normal Equations Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme applied to the normal equations.
        It returns a non-zero if the error estimate (the type of
        which is determined by ITOL) is less than the user
        specified tolerance TOL.

  - isscgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - issgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - issir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - issomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - sbcg

        Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient method.

  - scg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - scgn

        Preconditioned CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        Preconditioned Conjugate Gradient method applied to the
        normal equations  AA'y = b, x=A'y.

  - scgs

        Preconditioned BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a Non-Symmetric linear system  Ax = b
        using the Preconditioned BiConjugate Gradient Squared
        method.

  - sir

        Preconditioned Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        iterative refinement with a matrix splitting.

  - sgmres

        Preconditioned GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with preconditioning to solve
        non-symmetric linear systems of the form: Ax = b.

  - shels

        Internal routine for SGMRES.

  - sheqr

        Internal routine for SGMRES.

  - sllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - somn

        Preconditioned Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Preconditioned Orthomin method.

  - sorth

        Internal routine for SGMRES.

  - spigmr

        Internal routine for SGMRES.

  - srlcal

        Internal routine for SGMRES.

  - ssdbcg

        Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with diagonal scaling.

  - ssdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - ssdcgn

        Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
        Routine to solve a general linear system  Ax = b  using
        diagonal scaling with the Conjugate Gradient method
        applied to the the normal equations, viz.,  AA'y = b,
        where  x = A'y.

  - ssdcgs

        Diagonally Scaled CGS Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with diagonal scaling.

  - ssdgmr

        Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with diagonal scaling to solve possibly
        non-symmetric linear systems of the form: Ax = b.

  - ssdi

        Diagonal Matrix Vector Multiply.
        Routine to calculate the product  X = DIAG*B, where DIAG
        is a diagonal matrix.

  - ssdomn

        Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with diagonal scaling.

  - ssgs

        Gauss-Seidel Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Gauss-Seidel iteration.

  - ssiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - ssilur

        Incomplete LU Iterative Refinement Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        the incomplete LU decomposition with iterative refinement.

  - ssilus

        Incomplete LU Decomposition Preconditioner SLAP Set Up.
        Routine to generate the incomplete LDU decomposition of a
        matrix.  The unit lower triangular factor L is stored by
        rows and the unit upper triangular factor U is stored by
        columns.  The inverse of the diagonal matrix D is stored.
        No fill in is allowed.

  - ssjac

        Jacobi's Method Iterative Sparse Ax = b Solver.
        Routine to solve a general linear system  Ax = b  using
        Jacobi iteration.

  - ssli

        SLAP MSOLVE for Lower Triangle Matrix.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                  -1
        computes L  B = X.

  - ssli2

        SLAP Lower Triangle Matrix Backsolve.
        Routine to solve a system of the form  Lx = b , where L
        is a lower triangular matrix.

  - ssllti

        SLAP MSOLVE for LDL' (IC) Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes (LDL')  B = X.

  - sslubc

        Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient method with Incomplete LU
        decomposition preconditioning.

  - sslucn

        Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
        Routine to solve a general linear system  Ax = b  using the
        incomplete LU decomposition with the Conjugate Gradient
        method applied to the normal equations, viz.,  AA'y = b,
        x = A'y.

  - sslucs

        Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
        Routine to solve a linear system  Ax = b  using the
        BiConjugate Gradient Squared method with Incomplete LU
        decomposition preconditioning.

  - sslugm

        Incomplete LU GMRES Iterative Sparse Ax=b Solver.
        This routine uses the generalized minimum residual
        (GMRES) method with incomplete LU factorization for
        preconditioning to solve possibly non-symmetric linear
        systems of the form: Ax = b.

  - sslui

        SLAP MSOLVE for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MSOLVE calling convention and the routine that actually
                       -1
        computes  (LDU)  B = X.

  - sslui2

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  L*D*U X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix.

  - sslui4

        SLAP Backsolve for LDU Factorization.
        Routine to solve a system of the form  (L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - ssluom

        Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
        Routine to solve a general linear system  Ax = b  using
        the Orthomin method with Incomplete LU decomposition.

  - ssluti

        SLAP MTSOLV for LDU Factorization.
        This routine acts as an interface between the SLAP generic
        MTSOLV calling convention and the routine that actually
                       -T
        computes  (LDU)  B = X.

  - ssmmi2

        SLAP Backsolve for LDU Factorization of Normal Equations.
        To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
        where L is a unit lower triangular matrix, D is a diagonal
        matrix, and U is a unit upper triangular matrix and '
        denotes transpose.

  - ssmmti

        SLAP MSOLVE for LDU Factorization of Normal Equations.
        This routine acts as an interface between the SLAP generic
        MMTSLV calling convention and the routine that actually
                                -1
        computes  [(LDU)*(LDU)']  B = X.

  - ssmtv

        SLAP Column Format Sparse Matrix Transpose Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A'*X, where ' denotes transpose.

  - ssmv

        SLAP Column Format Sparse Matrix Vector Product.
        Routine to calculate the sparse matrix vector product:
        Y = A*X.

  - sxlcal

        Internal routine for SGMRES.

  ### SPARSE CONSTRAINTS

  - dsplp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  - splp

        Solve linear programming problems involving at
        most a few thousand constraints and variables.
        Takes advantage of sparsity in the constraint matrix.

  ### SPARSE ITERATIVE METHODS

  - dlpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  - slpdoc

        Sparse Linear Algebra Package Version 2.0.2 Documentation.
        Routines to solve large sparse symmetric and nonsymmetric
        positive definite linear systems, Ax = b, using precondi-
        tioned iterative methods.

  ### SPECIAL FUNCTIONS

  - ai

        Evaluate the Airy function.

  - aie

        Calculate the Airy function for a negative argument and an
        exponentially scaled Airy function for a non-negative
        argument.

  - albeta

        Compute the natural logarithm of the complete Beta
        function.

  - algams

        Compute the logarithm of the absolute value of the Gamma
        function.

  - ali

        Compute the logarithmic integral.

  - alngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - besi

        Compute an N member sequence of I Bessel functions
        I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions
        EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative
        ALPHA and X.

  - besi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - besi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - besi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - besi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - besj

        Compute an N member sequence of J Bessel functions
        J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA
        and X.

  - besj0

        Compute the Bessel function of the first kind of order
        zero.

  - besj1

        Compute the Bessel function of the first kind of order one.

  - besk

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions
        EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  - besk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - besk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - besk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - besk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - beskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - besks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - besy

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  - besy0

        Compute the Bessel function of the second kind of order
        zero.

  - besy1

        Compute the Bessel function of the second kind of order
        one.

  - beta

        Compute the complete Beta function.

  - betai

        Calculate the incomplete Beta function.

  - bi

        Evaluate the Bairy function (the Airy function of the
        second kind).

  - bie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  - binom

        Compute the binomial coefficients.

  - c0lgmc

        Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative
        accuracy.

  - c9lgmc

        Compute the log gamma correction factor so that
        LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
        + C9LGMC(Z).

  - cbeta

        Compute the complete Beta function.

  - cgamma

        Compute the complete Gamma function.

  - cgamr

        Compute the reciprocal of the Gamma function.

  - chu

        Compute the logarithmic confluent hypergeometric function.

  - clbeta

        Compute the natural logarithm of the complete Beta
        function.

  - clngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - cpsi

        Compute the Psi (or Digamma) function.

  - csevl

        Evaluate a Chebyshev series.

  - d9aimp

        Evaluate the Airy modulus and phase.

  - d9b0mp

        Evaluate the modulus and phase for the J0 and Y0 Bessel
        functions.

  - d9b1mp

        Evaluate the modulus and phase for the J1 and Y1 Bessel
        functions.

  - d9chu

        Evaluate for large Z  Z**A * U(A,B,Z) where U is the
        logarithmic confluent hypergeometric function.

  - d9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and X small.

  - d9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - d9knus

        Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
        K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

  - d9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - d9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - d9lgmc

        Compute the log Gamma correction factor so that
        LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
        + D9LGMC(X).

  - dai

        Evaluate the Airy function.

  - daie

        Calculate the Airy function for a negative argument and an
        exponentially scaled Airy function for a non-negative
        argument.

  - daws

        Compute Dawson's function.

  - dbesi

        Compute an N member sequence of I Bessel functions
        I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions
        EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for nonnegative
        ALPHA and X.

  - dbesi0

        Compute the hyperbolic Bessel function of the first kind
        of order zero.

  - dbesi1

        Compute the modified (hyperbolic) Bessel function of the
        first kind of order one.

  - dbesj

        Compute an N member sequence of J Bessel functions
        J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA
        and X.

  - dbesj0

        Compute the Bessel function of the first kind of order
        zero.

  - dbesj1

        Compute the Bessel function of the first kind of order one.

  - dbesk

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions
        EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  - dbesk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - dbesk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - dbesks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbesy

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  - dbesy0

        Compute the Bessel function of the second kind of order
        zero.

  - dbesy1

        Compute the Bessel function of the second kind of order
        one.

  - dbeta

        Compute the complete Beta function.

  - dbetai

        Calculate the incomplete Beta function.

  - dbi

        Evaluate the Bairy function (the Airy function of the
        second kind).

  - dbie

        Calculate the Bairy function for a negative argument and an
        exponentially scaled Bairy function for a non-negative
        argument.

  - dbinom

        Compute the binomial coefficients.

  - dbsi0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order zero.

  - dbsi1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the first kind of order one.

  - dbsk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - dbsk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - dbskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - dchu

        Compute the logarithmic confluent hypergeometric function.

  - dcsevl

        Evaluate a Chebyshev series.

  - ddaws

        Compute Dawson's function.

  - de1

        Compute the exponential integral E1(X).

  - dei

        Compute the exponential integral Ei(X).

  - derf

        Compute the error function.

  - derfc

        Compute the complementary error function.

  - dexint

        Compute an M member sequence of exponential integrals
        E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

  - dfac

        Compute the factorial function.

  - dgami

        Evaluate the incomplete Gamma function.

  - dgamic

        Calculate the complementary incomplete Gamma function.

  - dgamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - dgamlm

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  - dgamma

        Compute the complete Gamma function.

  - dgamr

        Compute the reciprocal of the Gamma function.

  - dlbeta

        Compute the natural logarithm of the complete Beta
        function.

  - dlgams

        Compute the logarithm of the absolute value of the Gamma
        function.

  - dli

        Compute the logarithmic integral.

  - dlngam

        Compute the logarithm of the absolute value of the Gamma
        function.

  - dpoch

        Evaluate a generalization of Pochhammer's symbol.

  - dpoch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  - dpsi

        Compute the Psi (or Digamma) function.

  - dspenc

        Compute a form of Spence's integral due to K. Mitchell.

  - e1

        Compute the exponential integral E1(X).

  - ei

        Compute the exponential integral Ei(X).

  - erf

        Compute the error function.

  - erfc

        Compute the complementary error function.

  - exint

        Compute an M member sequence of exponential integrals
        E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.

  - fac

        Compute the factorial function.

  - fundoc

        Documentation for FNLIB, a collection of routines for
        evaluating elementary and special functions.

  - gami

        Evaluate the incomplete Gamma function.

  - gamic

        Calculate the complementary incomplete Gamma function.

  - gamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - gamlim

        Compute the minimum and maximum bounds for the argument in
        the Gamma function.

  - gamma

        Compute the complete Gamma function.

  - gamr

        Compute the reciprocal of the Gamma function.

  - initds

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - inits

        Determine the number of terms needed in an orthogonal
        polynomial series so that it meets a specified accuracy.

  - psi

        Compute the Psi (or Digamma) function.

  - poch

        Evaluate a generalization of Pochhammer's symbol.

  - poch1

        Calculate a generalization of Pochhammer's symbol starting
        from first order.

  - r9aimp

        Evaluate the Airy modulus and phase.

  - r9chu

        Evaluate for large Z  Z**A * U(A,B,Z) where U is the
        logarithmic confluent hypergeometric function.

  - r9gmic

        Compute the complementary incomplete Gamma function for A
        near a negative integer and for small X.

  - r9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - rand

        Generate a uniformly distributed random number.

  - r9knus

        Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
        K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.

  - r9lgic

        Compute the log complementary incomplete Gamma function
        for large X and for A .LE. X.

  - r9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - r9lgmc

        Compute the log Gamma correction factor so that
        LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
        + R9LGMC(X).

  - rgauss

        Generate a normally distributed (Gaussian) random number.

  - runif

        Generate a uniformly distributed random number.

  - spenc

        Compute a form of Spence's integral due to K. Mitchell.

  ### SPECIAL-PURPOSE

  - dqawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - dqawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - dqawo

        Calculate an approximation to a given definite integral
        I= Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
           or  W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawoe

        Calculate an approximation to a given definite integral
        I = Integral of F(X)*W(X) over (A,B), where
                 W(X) = COS(OMEGA*X)
             or  W(X)=SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
             ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawc

        The routine calculates an approximation result to a
        Cauchy principal value I = INTEGRAL of F*W over (A,B)
        (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).

  - qawce

        The routine calculates an approximation result to a
        CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
        (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
        following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qawo

        Calculate an approximation to a given definite integral
         I = Integral of F(X)*W(X) over (A,B), where
               W(X) = COS(OMEGA*X)
            or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawoe

        Calculate an approximation to a given definite integral
           I = Integral of F(X)*W(X) over (A,B), where
              W(X) = COS(OMEGA*X)
           or W(X) = SIN(OMEGA*X),
        hopefully satisfying the following claim for accuracy
           ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qaws

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qawse

        The routine calculates an approximation result to a given
        definite integral I = Integral of F*W over (A,B),
        (where W shows a singular behaviour at the end points,
        see parameter INTEGR).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  ### SPECIAL-PURPOSE INTEGRAL

  - dqawf

        The routine calculates an approximation result to a given
        Fourier integral I=Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - dqawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawf

        The routine calculates an approximation result to a given
        Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
        where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  - qawfe

        The routine calculates an approximation result to a
        given Fourier integral
        I = Integral of F(X)*W(X) over (A,INFINITY)
         where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.EPSABS.

  ### SPENCE'S INTEGRAL

  - dspenc

        Compute a form of Spence's integral due to K. Mitchell.

  - spenc

        Compute a form of Spence's integral due to K. Mitchell.

  ### SPHERICAL

  - hstcsp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the modified Helmholtz
        equation in spherical coordinates assuming axisymmetry
        (no dependence on longitude).

  - hstssp

        Solve the standard five-point finite difference
        approximation on a staggered grid to the Helmholtz
        equation in spherical coordinates and on the surface of
        the unit sphere (radius of 1).

  - hwscsp

        Solve a finite difference approximation to the modified
        Helmholtz equation in spherical coordinates assuming
        axisymmetry  (no dependence on longitude).

  - hwsssp

        Solve a finite difference approximation to the Helmholtz
        equation in spherical coordinates and on the surface of the
        unit sphere (radius of 1).

  ### SPLINE INTERPOLATION

  - dpchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  - pchsp

        Set derivatives needed to determine the Hermite represen-
        tation of the cubic spline interpolant to given data, with
        specified boundary conditions.

  ### SPLINES

  - bspdoc

        Documentation for BSPLINE, a package of subprograms for
        working with piecewise polynomial functions
        in B-representation.

  - bspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - dbspev

        Calculate the value of the spline and its derivatives from
        the B-representation.

  - dintrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision of
        the X interval.

  - dpfqad

        Compute the integral on (X1,X2) of a product of a
        function F and the ID-th derivative of a B-spline,
        (PP-representation).

  - dppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - dppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  - intrv

        Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
        such that XT(ILEFT) .LE. X where XT(*) is a subdivision
        of the X interval.

  - pfqad

        Compute the integral on (X1,X2) of a product of a function
        F and the ID-th derivative of a B-spline,
        (PP-representation).

  - ppqad

        Compute the integral on (X1,X2) of a K-th order B-spline
        using the piecewise polynomial (PP) representation.

  - ppval

        Calculate the value of the IDERIV-th derivative of the
        B-spline from the PP-representation.

  ### STIFF

  - cdriv1

        The function of CDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  CDRIV1 allows complex-valued differential
        equations.

  - cdriv2

        The function of CDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  CDRIV2 allows complex-valued differential
        equations.

  - cdriv3

        The function of CDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  CDRIV3
        allows complex-valued differential equations.

  - ddebdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - ddriv1

        The function of DDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  DDRIV1 uses double precision arithmetic.

  - ddriv2

        The function of DDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  DDRIV2 uses double precision arithmetic.

  - ddriv3

        The function of DDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  DDRIV3
        uses double precision arithmetic.

  - debdf

        Solve an initial value problem in ordinary differential
        equations using backward differentiation formulas.  It is
        intended primarily for stiff problems.

  - sdriv1

        The function of SDRIV1 is to solve N (200 or fewer)
        ordinary differential equations of the form
        dY(I)/dT = F(Y(I),T), given the initial conditions
        Y(I) = YI.  SDRIV1 uses single precision arithmetic.

  - sdriv2

        The function of SDRIV2 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  SDRIV2 uses single precision arithmetic.

  - sdriv3

        The function of SDRIV3 is to solve N ordinary differential
        equations of the form dY(I)/dT = F(Y(I),T), given the
        initial conditions Y(I) = YI.  The program has options to
        allow the solution of both stiff and non-stiff differential
        equations.  Other important options are available.  SDRIV3
        uses single precision arithmetic.

  ### STOP TEST

  - isdbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdcgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - isdgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - isdir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isdomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  - issbcg

        Preconditioned BiConjugate Gradient Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscg

        Preconditioned Conjugate Gradient Stop Test.
        This routine calculates the stop test for the Conjugate
        Gradient iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - isscgs

        Preconditioned BiConjugate Gradient Squared Stop Test.
        This routine calculates the stop test for the BiConjugate
        Gradient Squared iteration scheme.  It returns a non-zero
        if the error estimate (the type of which is determined by
        ITOL) is less than the user specified tolerance TOL.

  - issgmr

        Generalized Minimum Residual Stop Test.
        This routine calculates the stop test for the Generalized
        Minimum RESidual (GMRES) iteration scheme.  It returns a
        non-zero if the error estimate (the type of which is
        determined by ITOL) is less than the user specified
        tolerance TOL.

  - issir

        Preconditioned Iterative Refinement Stop Test.
        This routine calculates the stop test for the iterative
        refinement iteration scheme.  It returns a non-zero if the
        error estimate (the type of which is determined by ITOL)
        is less than the user specified tolerance TOL.

  - issomn

        Preconditioned Orthomin Stop Test.
        This routine calculates the stop test for the Orthomin
        iteration scheme.  It returns a non-zero if the error
        estimate (the type of which is determined by ITOL) is
        less than the user specified tolerance TOL.

  ### STRING SORTING

  - hpsort

        Return the permutation vector generated by sorting a
        substring within a character array and, optionally,
        rearrange the elements of the array.  The array may be
        sorted in forward or reverse lexicographical order.  A
        slightly modified quicksort algorithm is used.

  ### SUM OF MAGNITUDES OF A VECTOR

  - dasum

        Compute the sum of the magnitudes of the elements of a
        vector.

  - sasum

        Compute the sum of the magnitudes of the elements of a
        vector.

  - scasum

        Compute the sum of the magnitudes of the real and
        imaginary elements of a complex vector.

  ### SURVEY OF INTEGRATORS

  - qpdoc

        Documentation for QUADPACK, a package of subprograms for
        automatic evaluation of one-dimensional definite integrals.

  ### SYMMETRIC

  - chiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a complex Hermitian matrix.

  - cpofs

        Solve a positive definite symmetric complex system of
        linear equations.

  - cpoir

        Solve a positive definite Hermitian system of linear
        equations.  Iterative refinement is used to obtain an
        error estimate.

  - csico

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting and estimate the condition number of the
        matrix.

  - csidi

        Compute the determinant and inverse of a complex symmetric
        matrix using the factors from CSIFA.

  - csifa

        Factor a complex symmetric matrix by elimination with
        symmetric pivoting.

  - csisl

        Solve a complex symmetric system using the factors obtained
        from CSIFA.

  - cspco

        Factor a complex symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - cspdi

        Compute the determinant and inverse of a complex symmetric
        matrix stored in packed form using the factors from CSPFA.

  - cspfa

        Factor a complex symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - cspsl

        Solve a complex symmetric system using the factors obtained
        from CSPFA.

  - dpofs

        Solve a positive definite symmetric system of linear
        equations.

  - dsico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - dsidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from DSIFA.

  - dsifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - dsisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - dspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - dspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from DSPFA.

  - dspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - dspsl

        Solve a real symmetric system using the factors obtained
        from DSPFA.

  - spofs

        Solve a positive definite symmetric system of linear
        equations.

  - spoir

        Solve a positive definite symmetric system of linear
        equations.  Iterative refinement is used to obtain an error
        estimate.

  - ssico

        Factor a symmetric matrix by elimination with symmetric
        pivoting and estimate the condition number of the matrix.

  - ssidi

        Compute the determinant, inertia and inverse of a real
        symmetric matrix using the factors from SSIFA.

  - ssiev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix.

  - ssifa

        Factor a real symmetric matrix by elimination with
        symmetric pivoting.

  - ssisl

        Solve a real symmetric system using the factors obtained
        from SSIFA.

  - sspco

        Factor a real symmetric matrix stored in packed form
        by elimination with symmetric pivoting and estimate the
        condition number of the matrix.

  - sspdi

        Compute the determinant, inertia, inverse of a real
        symmetric matrix stored in packed form using the factors
        from SSPFA.

  - sspev

        Compute the eigenvalues and, optionally, the eigenvectors
        of a real symmetric matrix stored in packed form.

  - sspfa

        Factor a real symmetric matrix stored in packed form by
        elimination with symmetric pivoting.

  - sspsl

        Solve a real symmetric system using the factors obtained
        from SSPFA.

  ### SYMMETRIC LINEAR SYSTEM

  - dcg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - dsdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - dsiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  - scg

        Preconditioned Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.

  - ssdcg

        Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the Preconditioned Conjugate
        Gradient method.  The preconditioner is diagonal scaling.

  - ssiccg

        Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
        Routine to solve a symmetric positive definite linear
        system  Ax = b  using the incomplete Cholesky
        Preconditioned Conjugate Gradient method.

  ### SYMMETRIC LINEAR SYSTEM SOLVE

  - dllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  - sllti2

        SLAP Backsolve routine for LDL' Factorization.
        Routine to solve a system of the form  L*D*L' X = B,
        where L is a unit lower triangular matrix and D is a
        diagonal matrix and ' means transpose.

  ### TABULATED DATA

  - avint

        Integrate a function tabulated at arbitrarily spaced
        abscissas using overlapping parabolas.

  - davint

        Integrate a function tabulated at arbitrarily spaced
        abscissas using overlapping parabolas.

  ### TANGENT

  - ctan

        Compute the complex tangent.

  ### TAYLOR SERIES

  - drc

        Calculate a double precision approximation to
         DRC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  - drd

        Compute the incomplete or complete elliptic integral of
        the 2nd kind. For X and Y nonnegative, X+Y and Z positive,
        DRD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - drf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - drj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                          -1/2     -1/2     -1/2     -1
                (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  - rc

        Calculate an approximation to
         RC(X,Y) = Integral from zero to infinity of
                          -1/2     -1
                (1/2)(t+X)    (t+Y)  dt,
        where X is nonnegative and Y is positive.

  - rd

        Compute the incomplete or complete elliptic integral of the
        2nd kind.  For X and Y nonnegative, X+Y and Z positive,
         RD(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -3/2
                  (3/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X or Y is zero, the integral is complete.

  - rf

        Compute the incomplete or complete elliptic integral of the
        1st kind.  For X, Y, and Z non-negative and at most one of
        them zero, RF(X,Y,Z) = Integral from zero to infinity of
                            -1/2     -1/2     -1/2
                  (1/2)(t+X)    (t+Y)    (t+Z)    dt.
        If X, Y or Z is zero, the integral is complete.

  - rj

        Compute the incomplete or complete (X or Y or Z is zero)
        elliptic integral of the 3rd kind.  For X, Y, and Z non-
        negative, at most one of them zero, and P positive,
         RJ(X,Y,Z,P) = Integral from zero to infinity of
                              -1/2     -1/2     -1/2     -1
                    (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.

  ### THIRD KIND

  - besk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - besk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - besk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - besk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - beskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  - besks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbesk0

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order zero.

  - dbesk1

        Compute the modified (hyperbolic) Bessel function of the
        third kind of order one.

  - dbesks

        Compute a sequence of modified Bessel functions of the
        third kind of fractional order.

  - dbsk0e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order zero.

  - dbsk1e

        Compute the exponentially scaled modified (hyperbolic)
        Bessel function of the third kind of order one.

  - dbskes

        Compute a sequence of exponentially scaled modified Bessel
        functions of the third kind of fractional order.

  ### TRANSFORMATION

  - dqagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
        OR I = Integral of F over (-INFINITY,BOUND)
        OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - dqagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
        or I = Integral of F over (-INFINITY,BOUND)
        or I = Integral of F over (-INFINITY,+INFINITY),
        hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  - qagi

        The routine calculates an approximation result to a given
        INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
                OR I = Integral of F over (-INFINITY,BOUND)
                OR I = Integral of F over (-INFINITY,+INFINITY)
        Hopefully satisfying following claim for accuracy
        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

  - qagie

        The routine calculates an approximation result to a given
        integral   I = Integral of F over (BOUND,+INFINITY)
                or I = Integral of F over (-INFINITY,BOUND)
                or I = Integral of F over (-INFINITY,+INFINITY),
                hopefully satisfying following claim for accuracy
                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))

  ### TRIAD

  - caxpy

        Compute a constant times a vector plus a vector.

  - daxpy

        Compute a constant times a vector plus a vector.

  - saxpy

        Compute a constant times a vector plus a vector.

  ### TRIANGULAR

  - strdi

        Compute the determinant and inverse of a triangular matrix.

  ### TRIANGULAR LINEAR SYSTEM

  - ctrsl

        Solve a system of the form  T*X=B or CTRANS(T)*X=B, where
        T is a triangular matrix.  Here CTRANS(T) is the conjugate
        transpose.

  - dtrsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  - strsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  ### TRIANGULAR MATRIX

  - ctrco

        Estimate the condition number of a triangular matrix.

  - ctrdi

        Compute the determinant and inverse of a triangular matrix.

  - ctrsl

        Solve a system of the form  T*X=B or CTRANS(T)*X=B, where
        T is a triangular matrix.  Here CTRANS(T) is the conjugate
        transpose.

  - dtrco

        Estimate the condition number of a triangular matrix.

  - dtrdi

        Compute the determinant and inverse of a triangular matrix.

  - dtrsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  - strco

        Estimate the condition number of a triangular matrix.

  - strsl

        Solve a system of the form  T*X=B or TRANS(T)*X=B, where
        T is a triangular matrix.

  ### TRICOMI

  - d9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - d9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  - dgamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - gamit

        Calculate Tricomi's form of the incomplete Gamma function.

  - r9gmit

        Compute Tricomi's incomplete Gamma function for small
        arguments.

  - r9lgit

        Compute the logarithm of Tricomi's incomplete Gamma
        function with Perron's continued fraction for large X and
        A .GE. X.

  ### TRIDIAGONAL

  - cgtsl

        Solve a tridiagonal linear system.

  - cptsl

        Solve a positive definite tridiagonal linear system.

  - dgtsl

        Solve a tridiagonal linear system.

  - dptsl

        Solve a positive definite tridiagonal linear system.

  - genbun

        Solve by a cyclic reduction algorithm the linear system
        of equations that results from a finite difference
        approximation to certain 2-d elliptic PDE's on a centered
        grid .

  - poistg

        Solve a block tridiagonal system of linear equations
        that results from a staggered grid finite difference
        approximation to 2-D elliptic PDE's.

  - sgtsl

        Solve a tridiagonal linear system.

  - sptsl

        Solve a positive definite tridiagonal linear system.

  ### TRIDIAGONAL LINEAR SYSTEM

  - blktri

        Solve a block tridiagonal system of linear equations
        (usually resulting from the discretization of separable
        two-dimensional elliptic equations).

  - cblktr

        Solve a block tridiagonal system of linear equations
        (usually resulting from the discretization of separable
        two-dimensional elliptic equations).

  - cmgnbn

        Solve a complex block tridiagonal linear system of
        equations by a cyclic reduction algorithm.

  ### TRIGONOMETRIC

  - cacos

        Compute the complex arc cosine.

  - casin

        Compute the complex arc sine.

  - catan

        Compute the complex arc tangent.

  - catan2

        Compute the complex arc tangent in the proper quadrant.

  - ccot

        Compute the cotangent.

  - cosdg

        Compute the cosine of an argument in degrees.

  - cot

        Compute the cotangent.

  - ctan

        Compute the complex tangent.

  - d9atn1

        Evaluate DATAN(X) from first order relative accuracy so
        that DATAN(X) = X + X**3*D9ATN1(X).

  - dcosdg

        Compute the cosine of an argument in degrees.

  - dcot

        Compute the cotangent.

  - dsindg

        Compute the sine of an argument in degrees.

  - r9atn1

        Evaluate ATAN(X) from first order relative accuracy so that
        ATAN(X) = X + X**3*R9ATN1(X).

  - sindg

        Compute the sine of an argument in degrees.

  ### TWO-POINT BOUNDARY VALUE PROBLEM

  - bvsup

        Solve a linear two-point boundary value problem using
        superposition coupled with an orthonormalization procedure
        and a variable-step integration scheme.

  - dbvsup

        Solve a linear two-point boundary value problem using
        superposition coupled with an orthonormalization procedure
        and a variable-step integration scheme.

  ### UNDERDETERMINED LINEAR SYSTEM

  - dulsia

        Solve an underdetermined linear system of equations by
        performing an LQ factorization of the matrix using
        Householder transformations.  Emphasis is put on detecting
        possible rank deficiency.

  - ulsia

        Solve an underdetermined linear system of equations by
        performing an LQ factorization of the matrix using
        Householder transformations.  Emphasis is put on detecting
        possible rank deficiency.

  ### UNDERDETERMINED LINEAR SYSTEMS

  - dglss

        Solve a linear least squares problems by performing a QR
        factorization of the input matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  - sglss

        Solve a linear least squares problems by performing a QR
        factorization of the matrix using Householder
        transformations.  Emphasis is put on detecting possible
        rank deficiency.

  ### UNIFORM

  - rand

        Generate a uniformly distributed random number.

  - runif

        Generate a uniformly distributed random number.

  ### UNITARY

  - dnrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - scnrm2

        Compute the unitary norm of a complex vector.

  - snrm2

        Compute the Euclidean length (L2 norm) of a vector.

  ### UNPACK

  - d9upak

        Unpack a floating point number X so that X = Y*2**N.

  - r9upak

        Unpack a floating point number X so that X = Y*2**N.

  ### UPDATE

  - cchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - dchud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  - schud

        Update an augmented Cholesky decomposition of the
        triangular part of an augmented QR decomposition.

  ### UTILITY ROUTINE

  - dpchcm

        Check a cubic Hermite function for monotonicity.

  - pchcm

        Check a cubic Hermite function for monotonicity.

  ### VECTOR

  - caxpy

        Compute a constant times a vector plus a vector.

  - ccopy

        Copy a vector.

  - cdcdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - cdotc

        Dot product of two complex vectors using the complex
        conjugate of the first vector.

  - cdotu

        Compute the inner product of two vectors.

  - crotg

        Construct a Givens transformation.

  - cscal

        Multiply a vector by a constant.

  - csrot

        Apply a plane Givens rotation.

  - csscal

        Scale a complex vector.

  - cswap

        Interchange two vectors.

  - daxpy

        Compute a constant times a vector plus a vector.

  - dcdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dcopy

        Copy a vector.

  - dcopym

        Copy the negative of a vector to a vector.

  - ddot

        Compute the inner product of two vectors.

  - dnrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - drot

        Apply a plane Givens rotation.

  - drotg

        Construct a plane Givens rotation.

  - drotm

        Apply a modified Givens transformation.

  - drotmg

        Construct a modified Givens transformation.

  - dscal

        Multiply a vector by a constant.

  - dsdot

        Compute the inner product of two vectors with extended
        precision accumulation and result.

  - dswap

        Interchange two vectors.

  - icamax

        Find the smallest index of the component of a complex
        vector having the maximum sum of magnitudes of real
        and imaginary parts.

  - icopy

        Copy a vector.

  - idamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  - isamax

        Find the smallest index of that component of a vector
        having the maximum magnitude.

  - iswap

        Interchange two vectors.

  - saxpy

        Compute a constant times a vector plus a vector.

  - scnrm2

        Compute the unitary norm of a complex vector.

  - scopy

        Copy a vector.

  - scopym

        Copy the negative of a vector to a vector.

  - sdot

        Compute the inner product of two vectors.

  - sdsdot

        Compute the inner product of two vectors with extended
        precision accumulation.

  - snrm2

        Compute the Euclidean length (L2 norm) of a vector.

  - srot

        Apply a plane Givens rotation.

  - srotg

        Construct a plane Givens rotation.

  - srotm

        Apply a modified Givens transformation.

  - srotmg

        Construct a modified Givens transformation.

  - sscal

        Multiply a vector by a constant.

  - sswap

        Interchange two vectors.

  ### VECTOR ADDITION COEFFICIENTS

  - drc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - drc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - drc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - rc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  ### VERSION

  - aaaaaa

        SLATEC Common Mathematical Library disclaimer and version.

  ### WEBER'S FUNCTION

  - cbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### WEIGHT FUNCTION

  - dqwgtc

        This function subprogram is used together with the
        routine DQAWC and defines the WEIGHT function.

  - dqwgts

        This function subprogram is used together with the
        routine DQAWS and defines the WEIGHT function.

  - qwgtc

        This function subprogram is used together with the
        routine QAWC and defines the WEIGHT function.

  - qwgts

        This function subprogram is used together with the
        routine QAWS and defines the WEIGHT function.

  ### WEIGHTED LEAST SQUARES

  - dfc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  - efc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.

  - fc

        Fit a piecewise polynomial curve to discrete data.
        The piecewise polynomials are represented as B-splines.
        The fitting is done in a weighted least squares sense.
        Equality and inequality constraints can be imposed on the
        fitted curve.

  ### WIGNER COEFFICIENTS

  - drc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - drc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - drc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jj

        Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
                                       (-M2-M3 M2 M3)
        for all allowed values of L1, the other parameters
        being held fixed.

  - rc3jm

        Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
                                       (M1 M2 -M1-M2)
        for all allowed values of M2, the other parameters
        being held fixed.

  - rc6j

        Evaluate the 6j symbol h(L1) = {L1 L2 L3}
                                       {L4 L5 L6}
        for all allowed values of L1, the other parameters
        being held fixed.

  ### WORKSPACE CHECKING

  - dchkw

        SLAP WORK/IWORK Array Bounds Checker.
        This routine checks the work array lengths and interfaces
        to the SLATEC error handler if a problem is found.

  - schkw

        SLAP WORK/IWORK Array Bounds Checker.
        This routine checks the work array lengths and interfaces
        to the SLATEC error handler if a problem is found.

  ### XERMSG

  - fdump

        Symbolic dump (should be locally written).

  ### XERROR

  - j4save

        Save or recall global variables needed by error
        handling routines.

  - numxer

        Return the most recent error number.

  - xerclr

        Reset current error number to zero.

  - xercnt

        Allow user control over handling of errors.

  - xerdmp

        Print the error tables and then clear them.

  - xerhlt

        Abort program execution and print error message.

  - xermax

        Set maximum number of times any error message is to be
        printed.

  - xermsg

        Process error messages for SLATEC and other libraries.

  - xerprn

        Print error messages processed by XERMSG.

  - xersve

        Record that an error has occurred.

  - xgetf

        Return the current value of the error control flag.

  - xgetua

        Return unit number(s) to which error messages are being
        sent.

  - xgetun

        Return the (first) output file to which error messages
        are being sent.

  - xsetf

        Set the error control flag.

  - xsetua

        Set logical unit numbers (up to 5) to which error
        messages are to be sent.

  - xsetun

        Set output file to which error messages are to be sent.

  ### Y BESSEL FUNCTION

  - besy

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  - dbesy

        Implement forward recursion on the three term recursion
        relation for a sequence of non-negative order Bessel
        functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
        X and non-negative orders FNU.

  ### Y BESSEL FUNCTIONS

  - cbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  - zbesy

        Compute a sequence of the Bessel functions Y(a,z) for
        complex argument z and real nonnegative orders a=b,b+1,
        b+2,... where b>0.  A scaling option is available to
        help avoid overflow.

  ### ZEROS

  - dfzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  - dnsq

        Find a zero of a system of a N nonlinear functions in N
        variables by a modification of the Powell hybrid method.

  - dnsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.

  - fzero

        Search for a zero of a function F(X) in a given interval
        (B,C).  It is designed primarily for problems where F(B)
        and F(C) have opposite signs.

  - snsq

        Find a zero of a system of a N nonlinear functions in N
        variables by a modification of the Powell hybrid method.

  - snsqe

        An easy-to-use code to find a zero of a system of N
        nonlinear functions in N variables by a modification of
        the Powell hybrid method.