DPTEQR(l) ) DPTEQR(l)NAME
DPTEQR - compute all eigenvalues and, optionally, eigenvectors of a
symmetric positive definite tridiagonal matrix by first factoring the
matrix using DPTTRF, and then calling DBDSQR to compute the singular
values of the bidiagonal factor
SYNOPSIS
SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N
DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
PURPOSE
DPTEQR computes all eigenvalues and, optionally, eigenvectors of a sym‐
metric positive definite tridiagonal matrix by first factoring the
matrix using DPTTRF, and then calling DBDSQR 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 DSYTRD, DSPTRD, or DSBTRD 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) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'V': Compute eigenvectors of original symmetric matrix also.
Array Z contains the orthogonal matrix used to reduce the orig‐
inal matrix to tridiagonal form. = 'I': Compute eigenvectors
of tridiagonal matrix also.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix.
On normal exit, D contains the eigenvalues, in descending
order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix. On exit, E has been destroyed.
Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
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 asso‐
ciated with only the stored eigenvalues. If COMPZ = 'N', then
Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if COMPZ =
'V' or 'I', LDZ >= max(1,N).
WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
INFO (output) INTEGER
= 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.
LAPACK version 3.0 15 June 2000 DPTEQR(l)
