.TH SSBGST 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME SSBGST - a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, .SH SYNOPSIS .TP 19 SUBROUTINE SSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO, VECT .TP 19 .ti +4 INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N .TP 19 .ti +4 REAL AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * ) .SH PURPOSE SSBGST reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. .br B must have been previously factorized as S**T*S by SPBSTF, using a split Cholesky factorization. A is overwritten by C = X**T*A*X, where X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the bandwidth of A. .br .SH ARGUMENTS .TP 8 VECT (input) CHARACTER*1 = \(aqN\(aq: do not form the transformation matrix X; .br = \(aqV\(aq: form X. .TP 8 UPLO (input) CHARACTER*1 .br = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is 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. KA >= 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 transformed matrix X**T*A*X, stored in the same format as A. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KA+1. .TP 8 BB (input) REAL array, dimension (LDBB,N) The banded factor S from the split Cholesky factorization of B, as returned by SPBSTF, stored in the first KB+1 rows of the array. .TP 8 LDBB (input) INTEGER The leading dimension of the array BB. LDBB >= KB+1. .TP 8 X (output) REAL array, dimension (LDX,N) If VECT = \(aqV\(aq, the n-by-n matrix X. If VECT = \(aqN\(aq, the array X is not referenced. .TP 8 LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N) if VECT = \(aqV\(aq; LDX >= 1 otherwise. .TP 8 WORK (workspace) REAL array, dimension (2*N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value.