• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

dstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration

SYNOPSIS

  SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, 
 *      IWORK, IFAIL, INFO)
  INTEGER N, M, LDZ, INFO
  INTEGER IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
  DOUBLE PRECISION D(*), E(*), W(*), Z(LDZ,*), WORK(*)

  SUBROUTINE DSTEIN_64( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, 
 *      IWORK, IFAIL, INFO)
  INTEGER*8 N, M, LDZ, INFO
  INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
  DOUBLE PRECISION D(*), E(*), W(*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE STEIN( [N], D, E, [M], W, IBLOCK, ISPLIT, Z, [LDZ], [WORK], 
 *       [IWORK], IFAIL, [INFO])
  INTEGER :: N, M, LDZ, INFO
  INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
  REAL(8), DIMENSION(:) :: D, E, W, WORK
  REAL(8), DIMENSION(:,:) :: Z

  SUBROUTINE STEIN_64( [N], D, E, [M], W, IBLOCK, ISPLIT, Z, [LDZ], 
 *       [WORK], [IWORK], IFAIL, [INFO])
  INTEGER(8) :: N, M, LDZ, INFO
  INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
  REAL(8), DIMENSION(:) :: D, E, W, WORK
  REAL(8), DIMENSION(:,:) :: Z

C INTERFACE

#include <sunperf.h>

void dstein(int n, double *d, double *e, int m, double *w, int *iblock, int *isplit, double *z, int ldz, int *ifail, int *info);

void dstein_64(long n, double *d, double *e, long m, double *w, long *iblock, long *isplit, double *z, long ldz, long *ifail, long *info);

PURPOSE

dstein computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration.

The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5).

ARGUMENTS

• N (input)
  The order of the matrix. N > = 0.

• D (input)
  The n diagonal elements of the tridiagonal matrix T.

• E (input)
  The (n-1) subdiagonal elements of the tridiagonal matrix T, in elements 1 to N-1. E(N) need not be set.

• M (input)
  The number of eigenvectors to be found. 0 < = M < = N.

• W (input)
  The first M elements of W contain the eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. ( The output array W from SSTEBZ with ORDER = 'B' is expected here. )

• IBLOCK (input)
  The submatrix indices associated with the corresponding eigenvalues in W; IBLOCK(i) =1 if eigenvalue W(i) belongs to the first submatrix from the top, =2 if W(i) belongs to the second submatrix, etc. ( The output array IBLOCK from SSTEBZ is expected here. )

• ISPLIT (input)
  The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ), etc. ( The output array ISPLIT from SSTEBZ is expected here. )

• Z (output)
  The computed eigenvectors. The eigenvector associated with the eigenvalue W(i) is stored in the i-th column of Z. Any vector which fails to converge is set to its current iterate after MAXITS iterations.

• LDZ (input)
  The leading dimension of the array Z. LDZ > = max(1,N).

• WORK (workspace)
  dimension(5*N)

• IWORK (workspace)
  dimension(N)

• IFAIL (output)
  On normal exit, all elements of IFAIL are zero. If one or more eigenvectors fail to converge after MAXITS iterations, then their indices are stored in array IFAIL.

• INFO (output)
  

   = 0: successful exit.

   < 0: if INFO  = -i, the i-th argument had an illegal value

   > 0: if INFO  = i, then i eigenvectors failed to converge
  in MAXITS iterations.  Their indices are stored in
  array IFAIL.