.TH SSBGV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) " .SH 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 .SH SYNOPSIS .TP 18 SUBROUTINE SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO ) .TP 18 .ti +4 CHARACTER JOBZ, UPLO .TP 18 .ti +4 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N .TP 18 .ti +4 REAL AB( LDAB, * ), BB( LDBB, * ), W( * ), WORK( * ), Z( LDZ, * ) .SH 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. .br .SH ARGUMENTS .TP 8 JOBZ (input) CHARACTER*1 = \(aqN\(aq: Compute eigenvalues only; .br = \(aqV\(aq: Compute eigenvalues and eigenvectors. .TP 8 UPLO (input) CHARACTER*1 .br = \(aqU\(aq: Upper triangles of A and B are stored; .br = \(aqL\(aq: Lower triangles of A and B are stored. .TP 8 N (input) INTEGER The order of the matrices A and B. N >= 0. .TP 8 KA (input) INTEGER The number of superdiagonals of the matrix A if UPLO = \(aqU\(aq, or the number of subdiagonals if UPLO = \(aqL\(aq. KA >= 0. .TP 8 KB (input) INTEGER The number of superdiagonals of the matrix B if UPLO = \(aqU\(aq, or the number of subdiagonals if UPLO = \(aqL\(aq. KB >= 0. .TP 8 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 = \(aqU\(aq, AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = \(aqL\(aq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KA+1. .TP 8 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 = \(aqU\(aq, BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = \(aqL\(aq, 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. .TP 8 LDBB (input) INTEGER The leading dimension of the array BB. LDBB >= KB+1. .TP 8 W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. .TP 8 Z (output) REAL array, dimension (LDZ, N) If JOBZ = \(aqV\(aq, 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 = \(aqN\(aq, then Z is not referenced. .TP 8 LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = \(aqV\(aq, LDZ >= N. .TP 8 WORK (workspace) REAL array, dimension (3*N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: if INFO = i, and i is: .br <= 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 .br returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.