dsbgst()

subroutine dsbgst	(	character	vect,
		character	uplo,
		integer	n,
		integer	ka,
		integer	kb,
		double precision, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( ldbb, * )	bb,
		integer	ldbb,
		double precision, dimension( ldx, * )	x,
		integer	ldx,
		double precision, dimension( * )	work,
		integer	info )

DSBGST

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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.
!>
!> 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.
!> 

Parameters

[in]	VECT	!> VECT is CHARACTER*1 !> = 'N': do not form the transformation matrix X; !> = 'V': form X. !>
[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrices A and B. N >= 0. !>
[in]	KA	!> KA is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KA >= 0. !>
[in]	KB	!> KB is INTEGER !> The number of superdiagonals of the matrix B if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. !>
[in,out]	AB	!> AB is 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. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KA+1. !>
[in]	BB	!> BB is 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. !>
[in]	LDBB	!> LDBB is INTEGER !> The leading dimension of the array BB. LDBB >= KB+1. !>
[out]	X	!> X is DOUBLE PRECISION array, dimension (LDX,N) !> If VECT = 'V', the n-by-n matrix X. !> If VECT = 'N', the array X is not referenced. !>
[in]	LDX	!> LDX is INTEGER !> The leading dimension of the array X. !> LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (2*N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.