EISDOC(3)

SYNOPSIS
SUBROUTINE EISDOC

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

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4, Z

TYPE
ALL (EISDOC-A)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Vandevender, W. H., (SNLA)

DESCRIPTION
**********EISPACK Routines********** single double complx ------ ------ ------ RS - CH Computes eigenvalues and, optionally, eigenvectors of real symmetric (complex Hermitian) matrix. RSP - - Compute eigenvalues and, optionally, eigenvectors of real symmetric matrix packed into a one dimensional array. RG - CG Computes eigenvalues and, optionally, eigenvectors of a real (complex) general matrix. BISECT - - Compute eigenvalues of symmetric tridiagonal matrix given interval using Sturm sequencing. IMTQL1 - - Computes eigenvalues of symmetric tridiagonal matrix implicit QL method. IMTQL2 - - Computes eigenvalues and eigenvectors of symmetric tridiagonal matrix using implicit QL method. IMTQLV - - Computes eigenvalues of symmetric tridiagonal matrix by the implicit QL method. Eigenvectors may be computed later. RATQR - - Computes largest or smallest eigenvalues of symmetric tridiagonal matrix using rational QR method with Newton correction. RST - - Compute eigenvalues and, optionally, eigenvectors of real symmetric tridiagonal matrix. RT - - Compute eigenvalues and eigenvectors of a special real tridiagonal matrix. TQL1 - - Compute eigenvalues of symmetric tridiagonal matrix by QL method. TQL2 - - Compute eigenvalues and eigenvectors of symmetric tridiagonal matrix. TQLRAT - - Computes eigenvalues of symmetric tridiagonal matrix a rational variant of the QL method. TRIDIB - - Computes eigenvalues of symmetric tridiagonal matrix given interval using Sturm sequencing. TSTURM - - Computes eigenvalues of symmetric tridiagonal matrix given interval and eigenvectors by Sturm sequencing. This subroutine is a translation of the ALGOL procedure TRISTURM by Peters and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 418-439(1971). BQR - - Computes some of the eigenvalues of a real symmetric matrix using the QR method with shifts of origin. RSB - - Computes eigenvalues and, optionally, eigenvectors of symmetric band matrix. RSG - - Computes eigenvalues and, optionally, eigenvectors of symmetric generalized eigenproblem: A*X=(LAMBDA)*B*X RSGAB - - Computes eigenvalues and, optionally, eigenvectors of symmetric generalized eigenproblem: A*B*X=(LAMBDA)*X RSGBA - - Computes eigenvalues and, optionally, eigenvectors of symmetric generalized eigenproblem: B*A*X=(LAMBDA)*X RGG - - Computes eigenvalues and eigenvectors for real generalized eigenproblem: A*X=(LAMBDA)*B*X. BALANC - CBAL Balances a general real (complex) matrix and isolates eigenvalues whenever possible. BANDR - - Reduces real symmetric band matrix to symmetric tridiagonal matrix and, optionally, accumulates orthogonal similarity transformations. HTRID3 - - Reduces complex Hermitian (packed) matrix to real symmetric tridiagonal matrix by unitary similarity transformations. HTRIDI - - Reduces complex Hermitian matrix to real symmetric tridiagonal matrix using unitary similarity transformations. TRED1 - - Reduce real symmetric matrix to symmetric tridiagonal matrix using orthogonal similarity transformations. TRED2 - - Reduce real symmetric matrix to symmetric tridiagonal matrix using and accumulating orthogonal transformations. TRED3 - - Reduce symmetric matrix stored in packed form to symmetric tridiagonal matrix using orthogonal transformations. ELMHES - COMHES Reduces real (complex) general matrix to upper Hessenberg form using stabilized elementary similarity transformations. ORTHES - CORTH Reduces real (complex) general matrix to upper Hessenberg form orthogonal (unitary) similarity transformations. 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, QZ 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. FIGI - - Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix. FIGI2 - - Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix. REDUC - - Reduces generalized symmetric eigenproblem A*X=(LAMBDA)*B*X, to standard symmetric eigenproblem using Cholesky factorization. REDUC2 - - Reduces certain generalized symmetric eigenproblems standard symmetric eigenproblem, using Cholesky factorization. - - COMLR Computes eigenvalues of a complex upper Hessenberg matrix using the modified LR method. - - COMLR2 Computes eigenvalues and eigenvectors of complex upper Hessenberg matrix using modified LR method. HQR - COMQR Computes eigenvalues of a real (complex) upper Hessenberg matrix using the QR method. HQR2 - COMQR2 Computes eigenvalues and eigenvectors of real (complex) upper Hessenberg matrix using QR method. INVIT - CINVIT Computes eigenvectors of real (complex) Hessenberg matrix associated with specified eigenvalues by inverse iteration. QZVAL - - The third step of the QZ algorithm for generalized eigenproblems. Accepts a pair of real matrices, one 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. BANDV - - Forms eigenvectors of real symmetric band matrix associated with a set of ordered approximate eigenvalue by inverse iteration. 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, QZVAL. TINVIT - - Eigenvectors of symmetric tridiagonal matrix corresponding to some specified eigenvalues, using inverse iteration. BAKVEC - - Forms eigenvectors of certain real non-symmetric tridiagonal matrix from symmetric tridiagonal matrix output from FIGI. BALBAK - CBABK2 Forms eigenvectors of real (complex) general matrix from eigenvectors of matrix output from BALANC (CBAL). ELMBAK - COMBAK Forms eigenvectors of real (complex) general matrix from eigenvectors of upper Hessenberg matrix output from ELMHES (COMHES). ELTRAN - - Accumulates the stabilized elementary similarity transformations used in the reduction of a real general matrix to upper Hessenberg form by ELMHES. HTRIB3 - - Computes eigenvectors of complex Hermitian matrix from eigenvectors of real symmetric tridiagonal matrix output from HTRID3. HTRIBK - - Forms eigenvectors of complex Hermitian matrix from eigenvectors of real symmetric tridiagonal matrix output from HTRIDI. ORTBAK - CORTB Forms eigenvectors of general real (complex) matrix from eigenvectors of upper Hessenberg matrix output from ORTHES (CORTH). ORTRAN - - Accumulates orthogonal similarity transformations in reduction of real general matrix by ORTHES. REBAK - - Forms eigenvectors of generalized symmetric eigensystem from eigenvectors of derived matrix output from REDUC or REDUC2. REBAKB - - Forms eigenvectors of generalized symmetric eigensystem from eigenvectors of derived matrix output from REDUC2 TRBAK1 - - Forms the eigenvectors of real symmetric matrix from eigenvectors of symmetric tridiagonal matrix formed by TRED1. TRBAK3 - - Forms eigenvectors of real symmetric matrix from the eigenvectors of symmetric tridiagonal matrix formed by TRED3. MINFIT - - Compute Singular Value Decomposition of rectangular matrix and solve related Linear Least Squares problem.

REFERENCES
B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- system Routines - EISPACK Guide, Springer-Verlag, 1976.

ROUTINES CALLED
(NONE)

REVISION HISTORY (YYMMDD)
811101 DATE WRITTEN
861211 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900723 PURPOSE section revised. (WRB)
920501 Reformatted the REFERENCES section. (WRB)