dsbgv()

subroutine dsbgv	(	character	jobz,
		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( * )	w,
		double precision, dimension( ldz, * )	z,
		integer	ldz,
		double precision, dimension( * )	work,
		integer	info )

DSBGV

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Purpose:

!>
!> DSBGV 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.
!> 

Parameters

[in]	JOBZ	!> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !>
[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangles of A and B are stored; !> = 'L': Lower triangles of A and B are 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'. 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 contents of AB are destroyed. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KA+1. !>
[in,out]	BB	!> BB is DOUBLE PRECISION 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 = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; !> if UPLO = 'L', 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 DPBSTF. !>
[in]	LDBB	!> LDBB is INTEGER !> The leading dimension of the array BB. LDBB >= KB+1. !>
[out]	W	!> W is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !>
[out]	Z	!> Z is DOUBLE PRECISION array, dimension (LDZ, N) !> If JOBZ = 'V', 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 = 'N', then Z is not referenced. !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> JOBZ = 'V', LDZ >= N. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (3*N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, and i is: !> <= 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 DPBSTF !> returned INFO = i: B is not positive definite. !> The factorization of B could not be completed and !> no eigenvalues or eigenvectors were computed. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.