cpteqr(3P) Sun Performance Library cpteqr(3P)NAMEcpteqr - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first factoring the
matrix using SPTTRF and then calling CBDSQR to compute the singular
values of the bidiagonal factor
SYNOPSIS
SUBROUTINE CPTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CHARACTER * 1 COMPZ
COMPLEX Z(LDZ,*)
INTEGER N, LDZ, INFO
REAL D(*), E(*), WORK(*)
SUBROUTINE CPTEQR_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 PTEQR(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 PTEQR_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 cpteqr(char compz, int n, float *d, float *e, complex *z, int ldz,
int *info);
void cpteqr_64(char compz, long n, float *d, float *e, complex *z, long
ldz, long *info);
PURPOSEcpteqr computes all eigenvalues and, optionally, eigenvectors of a sym‐
metric positive definite tridiagonal matrix by first factoring the
matrix using SPTTRF and then calling CBDSQR 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 positive definite Hermitian matrix
can also be found if CHETRD, CHPTRD, or CHBTRD 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 Hermitian matrix
also. Array Z contains the unitary matrix used to reduce the
original matrix to tridiagonal form. = 'I': Compute eigen‐
vectors 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 unitary matrix used in the
reduction to tridiagonal form. On exit, if COMPZ = 'V', the
orthonormal eigenvectors of the original Hermitian 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 cpteqr(3P)
