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

NAME

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

SYNOPSIS

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

  SUBROUTINE ZSTEIN_64( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, 
 *      IWORK, IFAIL, INFO)
  DOUBLE COMPLEX Z(LDZ,*)
  INTEGER*8 N, M, LDZ, INFO
  INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
  DOUBLE PRECISION D(*), E(*), W(*), WORK(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

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

void zstein_64(long n, double *d, double *e, long m, double *w, long *iblock, long *isplit, doublecomplex *z, long ldz, long *ifail, long *info);

PURPOSE

zstein 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).

Although the eigenvectors are real, they are stored in a complex array, which may be passed to CUNMTR or CUPMTR for back

transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form.

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, stored 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. The imaginary parts of the eigenvectors are set to zero.

• 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.