NAME

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

SYNOPSIS

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, ∗ )

PURPOSE

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.
 

ARGUMENTS

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 LWORK > 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 + 3∗N + 2∗N∗lg N + 2∗N∗∗2 ), where lg( N ) = smallest integer k such that 2∗∗k >= N.

IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 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 2+5∗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 E did not converge to zero.

  —  LAPACK version 2.0  —  08 October 1994