NAME

DSPEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

SYNOPSIS

SUBROUTINE DSPEV(
JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )

CHARACTER JOBZ, UPLO

INTEGER INFO, LDZ, N

DOUBLE PRECISION AP( ∗ ), W( ∗ ), WORK( ∗ ), Z( LDZ, ∗ )

PURPOSE

DSPEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. 
 

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.

AP      (input/output) DOUBLE PRECISION array, dimension (N∗(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array.  The j-th column of A is stored in the array AP as follows: if UPLO = ’U’, AP(i + (j-1)∗j/2) = A(i,j) for 1<=i<=j; if UPLO = ’L’, AP(i + (j-1)∗(2∗n-j)/2) = A(i,j) for j<=i<=n.
 
On exit, AP is overwritten by values generated during the reduction to tridiagonal form.  If UPLO = ’U’, the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = ’L’, the diagonal and first subdiagonal of T overwrite the corresponding elements of A.

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

Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = ’V’, then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = ’N’, then Z is not referenced.

LDZ     (input) INTEGER
The leading dimension of the array Z.  LDZ >= 1, and if JOBZ = ’V’, LDZ >= max(1,N).

WORK    (workspace) DOUBLE PRECISION array, dimension (3∗N)

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.

  —  LAPACK version 2.0  —  08 October 1994