dpteqr - 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
SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER * 1 COMPZ INTEGER N, LDZ, INFO DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)
SUBROUTINE DPTEQR_64( COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER * 1 COMPZ INTEGER*8 N, LDZ, INFO DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*)
SUBROUTINE PTEQR( COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO]) CHARACTER(LEN=1) :: COMPZ INTEGER :: N, LDZ, INFO REAL(8), DIMENSION(:) :: D, E, WORK REAL(8), DIMENSION(:,:) :: Z
SUBROUTINE PTEQR_64( COMPZ, [N], D, E, Z, [LDZ], [WORK], [INFO]) CHARACTER(LEN=1) :: COMPZ INTEGER(8) :: N, LDZ, INFO REAL(8), DIMENSION(:) :: D, E, WORK REAL(8), DIMENSION(:,:) :: Z
#include <sunperf.h>
void dpteqr(char compz, int n, double *d, double *e, double *z, int ldz, int *info);
void dpteqr_64(char compz, long n, double *d, double *e, double *z, long ldz, long *info);
dpteqr computes 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.
This routine computes the eigenvalues of the positive definite tridiagonal matrix to high relative accuracy. This means that if the eigenvalues range over many orders of magnitude in size, then the small eigenvalues and corresponding eigenvectors will be computed more accurately 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 accuracy in the small eigenvalues of the original matrix, if these eigenvalues range over many orders of magnitude.)
= '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.
dimension(4*N)
= 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 principal 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.