SSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix

SUBROUTINE SSTEVD(

JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )

CHARACTER JOBZ

INTEGER INFO, LDZ, LIWORK, LWORK, N

INTEGER IWORK( * )

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

SSTEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

JOBZ (input) CHARACTER*1

= 'N': Compute eigenvalues only;

= 'V': Compute eigenvalues and eigenvectors.

N (input) INTEGER

The order of the matrix. N >= 0.

D (input/output) REAL array, dimension (N)

On entry, the n diagonal elements of the tridiagonal matrix A. On exit, if INFO = 0, the eigenvalues in ascending order.

E (input/output) REAL array, dimension (N)

On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A, stored in elements 1 to N-1 of E; E(N) need not be set, but is used by the routine. On exit, the contents of E are destroyed.

Z (output) REAL 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 D(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/output) REAL array,

dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. If JOBZ = 'N' or N <= 1 then LWORK must be at least 1. If JOBZ = 'V' and N > 1 then LWORK must be at least ( 1 + 4*N + N**2 ).

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.

IWORK (workspace/output) INTEGER array, dimension (LIWORK)

On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK (input) INTEGER

The dimension of the array IWORK. If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1. If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK 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 E did not converge to zero.