SSBGV(3f)

NAME
SSBGV - 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 assumed to be symmetric and banded, and B is also positive definite.

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 symmetric 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 symmetric 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 factorization 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 illegal value
    > 0: if INFO = i, and i is:
    <= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF
    returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.