*DECK EISDOC 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 C***FIRST EXECUTABLE STATEMENT EISDOC RETURN END