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.