man csteqr (Fonctions bibliothèques) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

NAME

CSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

SYNOPSIS

SUBROUTINE CSTEQR(
COMPZ, N, D, E, Z, LDZ, WORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, N
REAL D( * ), E( * ), WORK( * )
COMPLEX Z( LDZ, * )

PURPOSE

CSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band complex Hermitian matrix can also be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix to tridiagonal form.

ARGUMENTS

COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.

= 'V': Compute eigenvalues and eigenvectors of the original Hermitian matrix. On entry, Z must contain the unitary matrix used to reduce the original matrix to tridiagonal form. = 'I': Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z is initialized to the identity matrix.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
Z (input/output) COMPLEX array, dimension (LDZ, N)
On entry, if COMPZ = 'V', then Z contains the unitary matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original Hermitian matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if eigenvectors are desired, then LDZ >= max(1,N).
WORK (workspace) REAL array, dimension (max(1,2*N-2))
If COMPZ = 'N', then WORK is not referenced.
INFO (output) INTEGER
= 0: successful exit

< 0: if INFO = -i, the i-th argument had an illegal value

> 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if INFO = i, then i elements of E have not converged to zero; on exit, D and E contain the elements of a symmetric tridiagonal matrix which is unitarily similar to the original matrix.