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 COMPZ

INTEGER INFO, LDZ, N

DOUBLE PRECISION D( ∗ ), E( ∗ ), WORK( ∗ )

COMPLEX∗16 Z( LDZ, ∗ )

#include <sunperf.h>

void zsteqr(char compz, int n, double ∗d, double ∗e, doublecomplex ∗zz, int ldz, int ∗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 ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to tridiagonal form. 
 

ARGUMENTS

COMPZ (input) CHARACTER∗1
= ’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) INTEGER
The order of the matrix.  N >= 0.

D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.

E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

Z (input/output) COMPLEX∗16 array, dimension (LDZ, N)
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) INTEGER
The leading dimension of the array Z.  LDZ >= 1, and if eigenvectors are desired, then  LDZ >= max(1,N).

WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2∗N-2))
If COMPZ = ’N’, then WORK is not referenced.

INFO (output) INTEGER
= 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.

SunOS 5.0  —  Last change: 10 Dec 1998