.TH DSBGST 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
DSBGST - a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
.SH SYNOPSIS
.TP 19
SUBROUTINE DSBGST(
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
DOUBLE
PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
X( LDX, * )
.SH PURPOSE
DSBGST 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 DPBSTF, 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDBB,N)
The banded factor S from the split Cholesky factorization of
B, as returned by DPBSTF, 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.