NAME¶

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

SYNOPSIS¶

SUBROUTINE ZSTEQR(

COMPZ, N, D, E, Z, LDZ, WORK, INFO )

CHARACTER COMPZ INTEGER INFO, LDZ, N DOUBLE PRECISION D( * ), E( * ), WORK( * ) COMPLEX*16 Z( LDZ, * )

PURPOSE¶

ZSTEQR 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 ZHETRD or ZHPTRD or ZHBTRD 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) DOUBLE PRECISION 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) 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) COMPLEX*16 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) DOUBLE PRECISION 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.