# dqawo.f

          SUBROUTINE DQAWO (F, A, B, OMEGA, INTEGR, EPSABS, EPSREL, RESULT,
         +   ABSERR, NEVAL, IER, LENIW, MAXP1, LENW, LAST, IWORK, WORK)
    C***BEGIN PROLOGUE  DQAWO
    C***PURPOSE  Calculate an approximation to a given definite integral
    C            I= Integral of F(X)*W(X) over (A,B), where
    C                   W(X) = COS(OMEGA*X)
    C               or  W(X) = SIN(OMEGA*X),
    C            hopefully satisfying the following claim for accuracy
    C                ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
    C***LIBRARY   SLATEC (QUADPACK)
    C***CATEGORY  H2A2A1
    C***TYPE      DOUBLE PRECISION (QAWO-S, DQAWO-D)
    C***KEYWORDS  AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD,
    C             EXTRAPOLATION, GLOBALLY ADAPTIVE,
    C             INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR, QUADPACK,
    C             QUADRATURE, SPECIAL-PURPOSE
    C***AUTHOR  Piessens, Robert
    C             Applied Mathematics and Programming Division
    C             K. U. Leuven
    C           de Doncker, Elise
    C             Applied Mathematics and Programming Division
    C             K. U. Leuven
    C***DESCRIPTION
    C
    C        Computation of oscillatory integrals
    C        Standard fortran subroutine
    C        Double precision version
    C
    C        PARAMETERS
    C         ON ENTRY
    C            F      - Double precision
    C                     Function subprogram defining the function
    C                     F(X).  The actual name for F needs to be
    C                     declared E X T E R N A L in the driver program.
    C
    C            A      - Double precision
    C                     Lower limit of integration
    C
    C            B      - Double precision
    C                     Upper limit of integration
    C
    C            OMEGA  - Double precision
    C                     Parameter in the integrand weight function
    C
    C            INTEGR - Integer
    C                     Indicates which of the weight functions is used
    C                     INTEGR = 1      W(X) = COS(OMEGA*X)
    C                     INTEGR = 2      W(X) = SIN(OMEGA*X)
    C                     If INTEGR.NE.1.AND.INTEGR.NE.2, the routine will
    C                     end with IER = 6.
    C
    C            EPSABS - Double precision
    C                     Absolute accuracy requested
    C            EPSREL - Double precision
    C                     Relative accuracy requested
    C                     If EPSABS.LE.0 and
    C                     EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
    C                     the routine will end with IER = 6.
    C
    C         ON RETURN
    C            RESULT - Double precision
    C                     Approximation to the integral
    C
    C            ABSERR - Double precision
    C                     Estimate of the modulus of the absolute error,
    C                     which should equal or exceed ABS(I-RESULT)
    C
    C            NEVAL  - Integer
    C                     Number of integrand evaluations
    C
    C            IER    - Integer
    C                     IER = 0 Normal and reliable termination of the
    C                             routine. It is assumed that the requested
    C                             accuracy has been achieved.
    C                   - IER.GT.0 Abnormal termination of the routine.
    C                             The estimates for integral and error are
    C                             less reliable. It is assumed that the
    C                             requested accuracy has not been achieved.
    C            ERROR MESSAGES
    C                     IER = 1 Maximum number of subdivisions allowed
    C                             has been achieved (= LENIW/2). One can
    C                             allow more subdivisions by increasing the
    C                             value of LENIW (and taking the according
    C                             dimension adjustments into account).
    C                             However, if this yields no improvement it
    C                             is advised to analyze the integrand in
    C                             order to determine the integration
    C                             difficulties. If the position of a local
    C                             difficulty can be determined (e.g.
    C                             SINGULARITY, DISCONTINUITY within the
    C                             interval) one will probably gain from
    C                             splitting up the interval at this point
    C                             and calling the integrator on the
    C                             subranges. If possible, an appropriate
    C                             special-purpose integrator should be used
    C                             which is designed for handling the type of
    C                             difficulty involved.
    C                         = 2 The occurrence of roundoff error is
    C                             detected, which prevents the requested
    C                             tolerance from being achieved.
    C                             The error may be under-estimated.
    C                         = 3 Extremely bad integrand behaviour occurs
    C                             at some interior points of the
    C                             integration interval.
    C                         = 4 The algorithm does not converge.
    C                             Roundoff error is detected in the
    C                             extrapolation table. It is presumed that
    C                             the requested tolerance cannot be achieved
    C                             due to roundoff in the extrapolation
    C                             table, and that the returned result is
    C                             the best which can be obtained.
    C                         = 5 The integral is probably divergent, or
    C                             slowly convergent. It must be noted that
    C                             divergence can occur with any other value
    C                             of IER.
    C                         = 6 The input is invalid, because
    C                             (EPSABS.LE.0 and
    C                              EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28))
    C                             or (INTEGR.NE.1 AND INTEGR.NE.2),
    C                             or LENIW.LT.2 OR MAXP1.LT.1 or
    C                             LENW.LT.LENIW*2+MAXP1*25.
    C                             RESULT, ABSERR, NEVAL, LAST are set to
    C                             zero. Except when LENIW, MAXP1 or LENW are
    C                             invalid, WORK(LIMIT*2+1), WORK(LIMIT*3+1),
    C                             IWORK(1), IWORK(LIMIT+1) are set to zero,
    C                             WORK(1) is set to A and WORK(LIMIT+1) to
    C                             B.
    C
    C         DIMENSIONING PARAMETERS
    C            LENIW  - Integer
    C                     Dimensioning parameter for IWORK.
    C                     LENIW/2 equals the maximum number of subintervals
    C                     allowed in the partition of the given integration
    C                     interval (A,B), LENIW.GE.2.
    C                     If LENIW.LT.2, the routine will end with IER = 6.
    C
    C            MAXP1  - Integer
    C                     Gives an upper bound on the number of Chebyshev
    C                     moments which can be stored, i.e. for the
    C                     intervals of lengths ABS(B-A)*2**(-L),
    C                     L=0,1, ..., MAXP1-2, MAXP1.GE.1
    C                     If MAXP1.LT.1, the routine will end with IER = 6.
    C
    C            LENW   - Integer
    C                     Dimensioning parameter for WORK
    C                     LENW must be at least LENIW*2+MAXP1*25.
    C                     If LENW.LT.(LENIW*2+MAXP1*25), the routine will
    C                     end with IER = 6.
    C
    C            LAST   - Integer
    C                     On return, LAST equals the number of subintervals
    C                     produced in the subdivision process, which
    C                     determines the number of significant elements
    C                     actually in the WORK ARRAYS.
    C
    C         WORK ARRAYS
    C            IWORK  - Integer
    C                     Vector of dimension at least LENIW
    C                     on return, the first K elements of which contain
    C                     pointers to the error estimates over the
    C                     subintervals, such that WORK(LIMIT*3+IWORK(1)), ..
    C                     WORK(LIMIT*3+IWORK(K)) form a decreasing
    C                     sequence, with LIMIT = LENW/2 , and K = LAST
    C                     if LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST
    C                     otherwise.
    C                     Furthermore, IWORK(LIMIT+1), ..., IWORK(LIMIT+
    C                     LAST) indicate the subdivision levels of the
    C                     subintervals, such that IWORK(LIMIT+I) = L means
    C                     that the subinterval numbered I is of length
    C                     ABS(B-A)*2**(1-L).
    C
    C            WORK   - Double precision
    C                     Vector of dimension at least LENW
    C                     On return
    C                     WORK(1), ..., WORK(LAST) contain the left
    C                      end points of the subintervals in the
    C                      partition of (A,B),
    C                     WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain
    C                      the right end points,
    C                     WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) contain
    C                      the integral approximations over the
    C                      subintervals,
    C                     WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST)
    C                      contain the error estimates.
    C                     WORK(LIMIT*4+1), ..., WORK(LIMIT*4+MAXP1*25)
    C                      Provide space for storing the Chebyshev moments.
    C                     Note that LIMIT = LENW/2.
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  DQAWOE, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   800101  DATE WRITTEN
    C   890831  Modified array declarations.  (WRB)
    C   890831  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
    C***END PROLOGUE  DQAWO