csteqr(3P) Sun Performance Library csteqr(3P)NAMEcsteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the implicit QL or QR method
SYNOPSIS
SUBROUTINE CSTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CHARACTER * 1 COMPZ
COMPLEX Z(LDZ,*)
INTEGER N, LDZ, INFO
REAL D(*), E(*), WORK(*)
SUBROUTINE CSTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CHARACTER * 1 COMPZ
COMPLEX Z(LDZ,*)
INTEGER*8 N, LDZ, INFO
REAL D(*), E(*), WORK(*)
F95 INTERFACE
SUBROUTINE STEQR(COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: COMPZ
COMPLEX, DIMENSION(:,:) :: Z
INTEGER :: N, LDZ, INFO
REAL, DIMENSION(:) :: D, E, WORK
SUBROUTINE STEQR_64(COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: COMPZ
COMPLEX, DIMENSION(:,:) :: Z
INTEGER(8) :: N, LDZ, INFO
REAL, DIMENSION(:) :: D, E, WORK
C INTERFACE
#include <sunperf.h>
void csteqr(char compz, int n, float *d, float *e, complex *z, int ldz,
int *info);
void csteqr_64(char compz, long n, float *d, float *e, complex *z, long
ldz, long *info);
PURPOSEcsteqr computes all eigenvalues and, optionally, eigenvectors of a sym‐
metric 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) 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 eigen‐
vectors 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 refer‐
enced.
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 ref‐
erenced.
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 ele‐
ments of a symmetric tridiagonal matrix which is unitarily
similar to the original matrix.
6 Mar 2009 csteqr(3P)
