DSYEV(3f)

NAME
DSYEV - all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

SYNOPSIS

SUBROUTINE DSYEV(
    JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )

CHARACTER
    JOBZ, UPLO

INTEGER
    INFO, LDA, LWORK, N

DOUBLE
    PRECISION A( LDA, * ), W( * ), WORK( * )

PURPOSE
DSYEV computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

ARGUMENTS

JOBZ    (input) CHARACTER*1
    = 'N': Compute eigenvalues only;
    = 'V': Compute eigenvalues and eigenvectors.

UPLO    (input) CHARACTER*1
    = 'U': Upper triangle of A is stored;
    = 'L': Lower triangle of A is stored.

N       (input) INTEGER
    The order of the matrix A. N >= 0.

A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
    On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed.

LDA     (input) INTEGER
    The leading dimension of the array A. LDA >= max(1,N).

W       (output) DOUBLE PRECISION array, dimension (N)
    If INFO = 0, the eigenvalues in ascending order.

WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
    The length of the array WORK. LWORK >= max(1,3*N-1). For optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize for DSYTRD returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

INFO    (output) INTEGER
    = 0: successful exit
    < 0: if INFO = -i, the i-th argument had an illegal value
    > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.