sstevd(3)

NAME

SSTEVD - compute all eigenvalues and, optionally, eigen

vectors 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, eigenvec

tors 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 assump

tions 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 hexadeci

mal 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 tridiago

nal 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 (LI

WORK)

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 ille

gal value
> 0: if INFO = i, the algorithm failed to con

verge; i off-diagonal elements of E did not converge to zero.

LAPACK version 3.0 15 June 2000

SSTEVD(3)