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Man Pages


Manual Reference Pages  -  ZSTEQR2 (l)

NAME

ZSTEQR2 - i a modified version of LAPACK routine ZSTEQR

CONTENTS

Synopsis
Purpose
Arguments

SYNOPSIS

SUBROUTINE ZSTEQR2( COMPZ, N, D, E, Z, LDZ, NR, WORK, INFO )
    CHARACTER COMPZ
    INTEGER INFO, LDZ, N, NR
    DOUBLE PRECISION D( * ), E( * ), WORK( * )
    COMPLEX*16 Z( LDZ, * )

PURPOSE

ZSTEQR2 is a modified version of LAPACK routine ZSTEQR. ZSTEQR2 computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. ZSTEQR2 is modified from ZSTEQR to allow each ScaLAPACK process running ZSTEQR2 to perform updates on a distributed matrix Q. Proper usage of ZSTEQR2 can be gleaned from
examination of ScaLAPACK’s * PZHEEV.
ZSTEQR2 incorporates changes attributed to Greg Henry.

ARGUMENTS

COMPZ (input) CHARACTER*1
  = ’N’: Compute eigenvalues only.
= ’I’: Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z must be initialized to the identity matrix by PZLASET or ZLASET prior to entering this subroutine.
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 (local input/local output) COMPLEX*16 array, global
  dimension (N, N), local dimension (LDZ, NR). 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) INTEGER
  The leading dimension of the array Z. LDZ >= 1, and if eigenvectors are desired, then LDZ >= max(1,N).
NR (input) INTEGER
  NR = MAX(1, NUMROC( N, NB, MYPROW, 0, NPROCS ) ). If COMPZ = ’N’, then NR is not referenced.
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 orthogonally similar to the original matrix.
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ScaLAPACK version 1.7 ZSTEQR2 (l) 13 August 2001

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