Contents
dpteqr - compute all eigenvalues and, optionally, eigenvec-
tors 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 fac-
tor
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(*)
F95 INTERFACE
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
C INTERFACE
#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 bidiag-
onal factor.
This routine computes the eigenvalues of the positive defin-
ite tridiagonal matrix to high relative accuracy. This
means that if the eigenvalues range over many orders of mag-
nitude 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 defin-
ite 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 eigen-
values range over many orders of magnitude.)
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 tri-
diagonal 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 tridiago-
nal matrix. On normal exit, D contains the eigen-
values, in descending order.
E (input/output)
On entry, the (n-1) subdiagonal elements of the
tridiagonal matrix. On exit, E has been des-
troyed.
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 ille-
gal 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 con-
verge; if INFO = N+i, i off-diagonal elements of
the bidiagonal factor did not converge to zero.