DSBGST(l) ) DSBGST(l)NAME
DSBGST - reduce a real symmetric-definite banded generalized eigenprob‐
lem A*x = lambda*B*x to standard form C*y = lambda*y,
SYNOPSIS
SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX,
WORK, INFO )
CHARACTER UPLO, VECT
INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N
DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
X( LDX, * )
PURPOSE
DSBGST reduces a real symmetric-definite banded generalized eigenprob‐
lem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has
the same bandwidth as A.
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 band‐
width of A.
ARGUMENTS
VECT (input) CHARACTER*1
= 'N': do not form the transformation matrix X;
= 'V': form X.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is 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'. KA >= KB >= 0.
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 = '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 transformed matrix X**T*A*X, stored in the same
format as A.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KA+1.
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.
LDBB (input) INTEGER
The leading dimension of the array BB. LDBB >= KB+1.
X (output) DOUBLE PRECISION array, dimension (LDX,N)
If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X
is not referenced.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N) if VECT
= 'V'; LDX >= 1 otherwise.
WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
LAPACK version 3.0 15 June 2000 DSBGST(l)
