ssbgv(3)

NAME

SSBGV - compute all the eigenvalues, and optionally, the

eigenvectors of a real generalized symmetric-definite banded

eigenproblem, of the form A*x=(lambda)*B*x

SYNOPSIS

SUBROUTINE SSBGV( JOBZ, UPLO, N, KA,  KB,  AB,  LDAB,  BB,
LDBB, W, Z, LDZ, WORK, INFO )
    CHARACTER     JOBZ, UPLO
    INTEGER       INFO, KA, KB, LDAB, LDBB, LDZ, N
    REAL           AB(  LDAB,  * ), BB( LDBB, * ), W( * ),
WORK( * ), Z( LDZ, * )

PURPOSE

SSBGV computes all the eigenvalues, and optionally, the

eigenvectors of a real generalized symmetric-definite banded

eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are as

sumed to be symmetric and banded, and B is also positive defi

nite.

ARGUMENTS

JOBZ (input) CHARACTER*1

= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.

UPLO (input) CHARACTER*1

= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.

N (input) INTEGER

The order of the matrices A and B. N >= 0.

KA (input) INTEGER

The number of superdiagonals of the matrix A if

UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.

KB (input) INTEGER

The number of superdiagonals of the matrix B if

UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j

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

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

On exit, the contents of AB are destroyed.

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >=

KA+1.

BB (input/output) REAL array, dimension (LDBB, N)

On entry, the upper or lower triangle of the sym

metric band matrix B, stored in the first kb+1 rows of the array.

The j-th column of B is stored in the j-th column of the array BB

as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j

kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for

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

On exit, the factor S from the split Cholesky fac

torization B = S**T*S, as returned by SPBSTF.

LDBB (input) INTEGER

The leading dimension of the array BB. LDBB >=

KB+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

matrix Z of eigenvectors, with the i-th column of Z holding the

eigenvector associated with W(i). The eigenvectors are normalized

so that Z**T*B*Z = 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 >= N.

WORK (workspace) REAL array, dimension (3*N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge: i off-di

agonal elements of an intermediate tridiagonal form did not con

verge to zero; > N: if INFO = N + i, for 1 <= i <= N, then SPB

STF
returned INFO = i: B is not positive definite.

The factorization of B could not be completed and no eigenvalues

or eigenvectors were computed.

LAPACK version 3.0 15 June 2000

SSBGV(3)