ssbev(3)

NAME

SSBEV - compute all the eigenvalues and, optionally,

eigenvectors of a real symmetric band matrix A

SYNOPSIS

SUBROUTINE  SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
WORK, INFO )
    CHARACTER     JOBZ, UPLO
    INTEGER       INFO, KD, LDAB, LDZ, N
    REAL          AB( LDAB, * ), W( * ),  WORK(  *  ),  Z(
LDZ, * )

PURPOSE

SSBEV computes all the eigenvalues and, optionally, eigen

vectors of a real symmetric band matrix A.

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.

KD (input) INTEGER

The number of superdiagonals of the matrix A if

UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >=

0.

AB (input/output) REAL array, dimension (LDAB, N)

On entry, the upper or lower triangle of the sym

metric band matrix A, stored in the first KD+1 rows of the array.

The j-th column of A is stored in the j-th column of the array AB

as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j

kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for

j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated

during the reduction to tridiagonal form. If UPLO = 'U', the

first superdiagonal and the diagonal of the tridiagonal matrix T

are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the

diagonal and first subdiagonal of T are returned in the first two

rows of AB.

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >= KD

+ 1.

W (output) REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

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 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) REAL array, dimension (max(1,3*N-2))

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 an intermediate tridiagonal

form did not converge to zero.

LAPACK version 3.0 15 June 2000

SSBEV(3)