spteqr(3P) Sun Performance Library spteqr(3P)NAMEspteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first factoring the
matrix using SPTTRF, and then calling SBDSQR to compute the singular
values of the bidiagonal factor
SYNOPSIS
SUBROUTINE SPTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CHARACTER * 1 COMPZ
INTEGER N, LDZ, INFO
REAL D(*), E(*), Z(LDZ,*), WORK(*)
SUBROUTINE SPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CHARACTER * 1 COMPZ
INTEGER*8 N, LDZ, INFO
REAL D(*), E(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE PTEQR(COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: COMPZ
INTEGER :: N, LDZ, INFO
REAL, DIMENSION(:) :: D, E, WORK
REAL, DIMENSION(:,:) :: Z
SUBROUTINE PTEQR_64(COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: COMPZ
INTEGER(8) :: N, LDZ, INFO
REAL, DIMENSION(:) :: D, E, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void spteqr(char compz, int n, float *d, float *e, float *z, int ldz,
int *info);
void spteqr_64(char compz, long n, float *d, float *e, float *z, long
ldz, long *info);
PURPOSEspteqr computes all eigenvalues and, optionally, eigenvectors of a sym‐
metric positive definite tridiagonal matrix by first factoring the
matrix using SPTTRF, and then calling SBDSQR to compute the singular
values of the bidiagonal factor.
This routine computes the eigenvalues of the positive definite tridiag‐
onal matrix to high relative accuracy. This means that if the eigen‐
values range over many orders of magnitude in size, then the small ei‐
genvalues and corresponding eigenvectors will be computed more accu‐
rately than, for example, with the standard QR method.
The eigenvectors of a full or band symmetric positive definite matrix
can also be found if SSYTRD, SSPTRD, or SSBTRD has been used to reduce
this matrix to tridiagonal form. (The reduction to tridiagonal form,
however, may preclude the possibility of obtaining high relative accu‐
racy in the small eigenvalues of the original matrix, if these eigen‐
values range over many orders of magnitude.)
ARGUMENTS
COMPZ (input)
= 'N': Compute eigenvalues only.
= 'V': Compute eigenvectors of original symmetric matrix
also. Array Z contains the orthogonal matrix used to reduce
the original matrix to tridiagonal form. = 'I': Compute
eigenvectors of tridiagonal matrix also.
N (input) The order of the matrix. N >= 0.
D (input/output)
On entry, the n diagonal elements of the tridiagonal matrix.
On normal exit, D contains the eigenvalues, in descending
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', the orthogonal matrix used in the
reduction to tridiagonal form. On exit, if COMPZ = 'V', the
orthonormal eigenvectors of the original symmetric matrix; if
COMPZ = 'I', the orthonormal eigenvectors of the tridiagonal
matrix. If INFO > 0 on exit, Z contains the eigenvectors
associated with only the stored eigenvalues. If COMPZ =
'N', then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if COMPZ
= 'V' or 'I', LDZ >= max(1,N).
WORK (workspace)
dimension(4*N)
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, and i is: <= N the Cholesky factorization
of the matrix could not be performed because the i-th princi‐
pal minor was not positive definite. > N the SVD algorithm
failed to converge; if INFO = N+i, i off-diagonal elements of
the bidiagonal factor did not converge to zero.
6 Mar 2009 spteqr(3P)