NAME
DSTEQR2 - i a modified version of LAPACK routine DSTEQR
SYNOPSIS
SUBROUTINE DSTEQR2( COMPZ, N, D, E, Z, LDZ, NR, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N, NR
DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
PURPOSE
DSTEQR2 is a modified version of LAPACK routine DSTEQR. DSTEQR2
computes all eigenvalues and, optionally, eigenvectors of a symmetric
tridiagonal matrix using the implicit QL or QR method. DSTEQR2 is
modified from DSTEQR to allow each ScaLAPACK process running DSTEQR2 to
perform updates on a distributed matrix Q. Proper usage of DSTEQR2 can
be gleaned from examination of ScaLAPACK’s PDSYEV.
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
PDLASET or DLASET 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) DOUBLE PRECISION 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.