SSTEQR(3f)

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

SYNOPSIS

SUBROUTINE SSTEQR(
    COMPZ, N, D, E, Z, LDZ, WORK, INFO )

CHARACTER
    COMPZ

INTEGER
    INFO, LDZ, N

REAL
    D( * ), E( * ), WORK( * ), Z( LDZ, * )

PURPOSE
SSTEQR 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 symmetric matrix can also be found if SSYTRD or SSPTRD or SSBTRD 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 symmetric matrix. On entry, Z must contain the orthogonal 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) REAL array, dimension (LDZ, N)
    On entry, if COMPZ = 'V', then Z contains the orthogonal 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 symmetric 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 orthogonally similar to the original matrix.