# eisdoc.f

          SUBROUTINE EISDOC
    C***BEGIN PROLOGUE  EISDOC
    C***PURPOSE  Documentation for EISPACK, a collection of subprograms for
    C            solving matrix eigen-problems.
    C***LIBRARY   SLATEC (EISPACK)
    C***CATEGORY  D4, Z
    C***TYPE      ALL (EISDOC-A)
    C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
    C***AUTHOR  Vandevender, W. H., (SNLA)
    C***DESCRIPTION
    C
    C                 **********EISPACK Routines**********
    C
    C single double complx
    C ------ ------ ------
    C
    C RS       -    CH     Computes eigenvalues and, optionally,
    C                      eigenvectors of real symmetric
    C                      (complex Hermitian) matrix.
    C
    C RSP      -      -    Compute eigenvalues and, optionally,
    C                      eigenvectors of real symmetric matrix
    C                      packed into a one dimensional array.
    C
    C RG       -    CG     Computes eigenvalues and, optionally,
    C                      eigenvectors of a real (complex) general
    C                      matrix.
    C
    C BISECT   -      -    Compute eigenvalues of symmetric tridiagonal
    C                      matrix given interval using Sturm sequencing.
    C
    C IMTQL1   -      -    Computes eigenvalues of symmetric tridiagonal
    C                      matrix implicit QL method.
    C
    C IMTQL2   -      -    Computes eigenvalues and eigenvectors of
    C                      symmetric tridiagonal matrix using
    C                      implicit QL method.
    C
    C IMTQLV   -      -    Computes eigenvalues of symmetric tridiagonal
    C                      matrix by the implicit QL method.
    C                      Eigenvectors may be computed later.
    C
    C RATQR    -      -    Computes largest or smallest eigenvalues
    C                      of symmetric tridiagonal matrix using
    C                      rational QR method with Newton correction.
    C
    C RST      -      -    Compute eigenvalues and, optionally,
    C                      eigenvectors of real symmetric tridiagonal
    C                      matrix.
    C
    C RT       -      -    Compute eigenvalues and eigenvectors of
    C                      a special real tridiagonal matrix.
    C
    C TQL1     -      -    Compute eigenvalues of symmetric tridiagonal
    C                      matrix by QL method.
    C
    C TQL2     -      -    Compute eigenvalues and eigenvectors
    C                      of symmetric tridiagonal matrix.
    C
    C TQLRAT   -      -    Computes eigenvalues of symmetric
    C                      tridiagonal matrix a rational variant
    C                      of the QL method.
    C
    C TRIDIB   -      -    Computes eigenvalues of symmetric
    C                      tridiagonal matrix given interval using
    C                      Sturm sequencing.
    C
    C TSTURM   -      -    Computes eigenvalues of symmetric tridiagonal
    C                      matrix given interval and eigenvectors
    C                      by Sturm sequencing.  This subroutine
    C                      is a translation of the ALGOL procedure
    C                      TRISTURM by Peters and Wilkinson. HANDBOOK
    C                      FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA,
    C                      418-439(1971).
    C
    C BQR      -      -    Computes some of the eigenvalues of a real
    C                      symmetric matrix using the QR method with
    C                      shifts of origin.
    C
    C RSB      -      -    Computes eigenvalues and, optionally,
    C                      eigenvectors of symmetric band matrix.
    C
    C RSG      -      -    Computes eigenvalues and, optionally,
    C                      eigenvectors of symmetric generalized
    C                      eigenproblem: A*X=(LAMBDA)*B*X
    C
    C RSGAB    -      -    Computes eigenvalues and, optionally,
    C                      eigenvectors of symmetric generalized
    C                      eigenproblem: A*B*X=(LAMBDA)*X
    C
    C RSGBA    -      -    Computes eigenvalues and, optionally,
    C                      eigenvectors of symmetric generalized
    C                      eigenproblem: B*A*X=(LAMBDA)*X
    C
    C RGG      -      -    Computes eigenvalues and eigenvectors
    C                      for real generalized eigenproblem:
    C                      A*X=(LAMBDA)*B*X.
    C
    C BALANC   -    CBAL   Balances a general real (complex)
    C                      matrix and isolates eigenvalues whenever
    C                      possible.
    C
    C BANDR    -      -    Reduces real symmetric band matrix
    C                      to symmetric tridiagonal matrix and,
    C                      optionally, accumulates orthogonal similarity
    C                      transformations.
    C
    C HTRID3   -      -    Reduces complex Hermitian (packed) matrix
    C                      to real symmetric tridiagonal matrix by unitary
    C                      similarity transformations.
    C
    C HTRIDI   -      -    Reduces complex Hermitian matrix to real
    C                      symmetric tridiagonal matrix using unitary
    C                      similarity transformations.
    C
    C TRED1    -      -    Reduce real symmetric matrix to symmetric
    C                      tridiagonal matrix using orthogonal
    C                      similarity transformations.
    C
    C TRED2    -      -    Reduce real symmetric matrix to symmetric
    C                      tridiagonal matrix using and accumulating
    C                      orthogonal transformations.
    C
    C TRED3    -      -    Reduce  symmetric matrix stored in packed
    C                      form to symmetric tridiagonal matrix using
    C                      orthogonal transformations.
    C
    C ELMHES   -    COMHES Reduces real (complex) general matrix to
    C                      upper Hessenberg form using stabilized
    C                      elementary similarity transformations.
    C
    C ORTHES   -    CORTH  Reduces real (complex) general matrix to upper
    C                      Hessenberg form orthogonal (unitary)
    C                      similarity transformations.
    C
    C QZHES    -      -    The first step of the QZ algorithm for solving
    C                      generalized matrix eigenproblems.  Accepts
    C                      a pair of real general matrices and reduces
    C                      one of them to upper Hessenberg and the other
    C                      to upper triangular form using orthogonal
    C                      transformations. Usually followed by QZIT,
    C                      QZVAL, QZ
    C
    C QZIT     -      -    The second step of the QZ algorithm for
    C                      generalized eigenproblems.  Accepts an upper
    C                      Hessenberg and an upper triangular matrix
    C                      and reduces the former to quasi-triangular
    C                      form while preserving the form of the latter.
    C                      Usually preceded by QZHES and followed by QZVAL
    C                      and QZVEC.
    C
    C FIGI     -      -    Transforms certain real non-symmetric
    C                      tridiagonal matrix to symmetric tridiagonal
    C                      matrix.
    C
    C FIGI2    -      -    Transforms certain real non-symmetric
    C                      tridiagonal matrix to symmetric tridiagonal
    C                      matrix.
    C
    C REDUC    -      -    Reduces generalized symmetric eigenproblem
    C                      A*X=(LAMBDA)*B*X, to standard symmetric
    C                      eigenproblem using Cholesky factorization.
    C
    C REDUC2   -      -    Reduces certain generalized symmetric
    C                      eigenproblems standard symmetric eigenproblem,
    C                      using Cholesky factorization.
    C
    C   -      -    COMLR  Computes eigenvalues of a complex upper
    C                      Hessenberg matrix using the modified LR method.
    C
    C   -      -    COMLR2 Computes eigenvalues and eigenvectors of
    C                      complex upper Hessenberg matrix using
    C                      modified LR method.
    C
    C HQR      -    COMQR  Computes eigenvalues of a real (complex)
    C                      upper Hessenberg matrix using the QR method.
    C
    C HQR2     -    COMQR2 Computes eigenvalues and eigenvectors of
    C                      real (complex) upper Hessenberg matrix
    C                      using QR method.
    C
    C INVIT    -    CINVIT Computes eigenvectors of real (complex)
    C                      Hessenberg matrix associated with specified
    C                      eigenvalues by inverse iteration.
    C
    C QZVAL    -      -    The third step of the QZ algorithm for
    C                      generalized eigenproblems.  Accepts a pair
    C                      of real matrices, one quasi-triangular form
    C                      and the other in upper triangular form and
    C                      computes the eigenvalues of the associated
    C                      eigenproblem.  Usually preceded by QZHES,
    C                      QZIT, and followed by QZVEC.
    C
    C BANDV    -      -    Forms eigenvectors of real symmetric band
    C                      matrix associated with a set of ordered
    C                      approximate eigenvalue by inverse iteration.
    C
    C QZVEC    -      -    The optional fourth step of the QZ algorithm
    C                      for generalized eigenproblems.  Accepts
    C                      a matrix in quasi-triangular form and another
    C                      in upper triangular and computes the
    C                      eigenvectors of the triangular problem
    C                      and transforms them back to the original
    C                      coordinates Usually preceded by QZHES, QZIT,
    C                      QZVAL.
    C
    C TINVIT   -      -    Eigenvectors of symmetric tridiagonal
    C                      matrix corresponding to some specified
    C                      eigenvalues, using inverse iteration.
    C
    C BAKVEC   -      -    Forms eigenvectors of certain real
    C                      non-symmetric tridiagonal matrix from
    C                      symmetric tridiagonal matrix output from FIGI.
    C
    C BALBAK   -    CBABK2 Forms eigenvectors of real (complex) general
    C                      matrix from eigenvectors of matrix output
    C                      from BALANC (CBAL).
    C
    C ELMBAK   -    COMBAK Forms eigenvectors of real (complex) general
    C                      matrix from eigenvectors of upper Hessenberg
    C                      matrix output from ELMHES (COMHES).
    C
    C ELTRAN   -      -    Accumulates the stabilized elementary
    C                      similarity transformations used in the
    C                      reduction of a real general matrix to upper
    C                      Hessenberg form by ELMHES.
    C
    C HTRIB3   -      -    Computes eigenvectors of complex Hermitian
    C                      matrix from eigenvectors of real symmetric
    C                      tridiagonal matrix output from HTRID3.
    C
    C HTRIBK   -      -    Forms eigenvectors of complex Hermitian
    C                      matrix from eigenvectors of real symmetric
    C                      tridiagonal matrix output from HTRIDI.
    C
    C ORTBAK   -    CORTB  Forms eigenvectors of general real (complex)
    C                      matrix from eigenvectors of upper Hessenberg
    C                      matrix output from ORTHES (CORTH).
    C
    C ORTRAN   -      -    Accumulates orthogonal similarity
    C                      transformations in reduction of real general
    C                      matrix by ORTHES.
    C
    C REBAK    -      -    Forms eigenvectors of generalized symmetric
    C                      eigensystem from eigenvectors of derived
    C                      matrix output from REDUC or REDUC2.
    C
    C REBAKB   -      -    Forms eigenvectors of generalized symmetric
    C                      eigensystem from eigenvectors of derived
    C                      matrix output from REDUC2
    C
    C TRBAK1   -      -    Forms the eigenvectors of real symmetric
    C                      matrix from eigenvectors of symmetric
    C                      tridiagonal matrix formed by TRED1.
    C
    C TRBAK3   -      -    Forms eigenvectors of real symmetric matrix
    C                      from the eigenvectors of symmetric tridiagonal
    C                      matrix formed by TRED3.
    C
    C MINFIT   -      -    Compute Singular Value Decomposition
    C                      of rectangular matrix and solve related
    C                      Linear Least Squares problem.
    C
    C***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
    C                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
    C                 system Routines - EISPACK Guide, Springer-Verlag,
    C                 1976.
    C***ROUTINES CALLED  (NONE)
    C***REVISION HISTORY  (YYMMDD)
    C   811101  DATE WRITTEN
    C   861211  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900723  PURPOSE section revised.  (WRB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  EISDOC