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

NAME

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

SYNOPSIS

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

  SUBROUTINE ZSTEQR_64( COMPZ, N, D, E, Z, LDZ, WORK, INFO)
  CHARACTER * 1 COMPZ
  DOUBLE COMPLEX Z(LDZ,*)
  INTEGER*8 N, LDZ, INFO
  DOUBLE PRECISION D(*), E(*), WORK(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

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

void zsteqr_64(char compz, long n, double *d, double *e, doublecomplex *z, long ldz, long *info);

PURPOSE

zsteqr 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 complex Hermitian matrix can also be found if CHETRD or CHPTRD or CHBTRD 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
  Hermitian matrix.  On entry, Z must contain the
  unitary 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 unitary 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 Hermitian 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 unitarily similar to the original
  matrix.