NAME

dsteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

SYNOPSIS

  SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO)
  CHARACTER * 1 COMPZ
  INTEGER N, LDZ, INFO
  DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)

  SUBROUTINE DSTEQR_64( COMPZ, N, D, E, Z, LDZ, WORK, INFO)
  CHARACTER * 1 COMPZ
  INTEGER*8 N, LDZ, INFO
  DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE STEQR( COMPZ, N, D, E, Z, [LDZ], [WORK], [INFO])
  CHARACTER(LEN=1) :: COMPZ
  INTEGER :: N, LDZ, INFO
  REAL(8), DIMENSION(:) :: D, E, WORK
  REAL(8), DIMENSION(:,:) :: Z

  SUBROUTINE STEQR_64( COMPZ, N, D, E, Z, [LDZ], [WORK], [INFO])
  CHARACTER(LEN=1) :: COMPZ
  INTEGER(8) :: N, LDZ, INFO
  REAL(8), DIMENSION(:) :: D, E, WORK
  REAL(8), DIMENSION(:,:) :: Z

C INTERFACE

#include <sunperf.h>

void dsteqr(char compz, int n, double *d, double *e, double *z, int ldz, int *info);

void dsteqr_64(char compz, long n, double *d, double *e, double *z, long ldz, long *info);

PURPOSE

dsteqr computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to tridiagonal form.

ARGUMENTS

COMPZ (input)

 = 'N':  Compute eigenvalues only.

 = 'V':  Compute eigenvalues and eigenvectors of the original
symmetric matrix.  On entry, Z must contain the
orthogonal matrix used to reduce the original matrix
to tridiagonal form.
 = 'I':  Compute eigenvalues and eigenvectors of the
tridiagonal matrix.  Z is initialized to the identity
matrix.

N (input)
The order of the matrix. N > = 0.
D (input/output)
On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output)
On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
Z (input/output)
On entry, if COMPZ = 'V', then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = 'N', then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ > = 1, and if eigenvectors are desired, then LDZ > = max(1,N).
WORK (workspace)
dimension(max(1,2*N-2)) If COMPZ = 'N', then WORK is not referenced.

INFO (output)

 = 0:  successful exit

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

 > 0:  the algorithm has failed to find all the eigenvalues in
a total of 30*N iterations; if INFO  = i, then i
elements of E have not converged to zero; on exit, D
and E contain the elements of a symmetric tridiagonal
matrix which is orthogonally similar to the original
matrix.