dsygv()

subroutine dsygv	(	integer	itype,
		character	jobz,
		character	uplo,
		integer	n,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		double precision, dimension( * )	w,
		double precision, dimension( * )	work,
		integer	lwork,
		integer	info )

DSYGV

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Purpose:

!>
!> DSYGV computes all the eigenvalues, and optionally, the eigenvectors
!> of a real generalized symmetric-definite eigenproblem, of the form
!> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
!> Here A and B are assumed to be symmetric and B is also
!> positive definite.
!> 

Parameters

[in]	ITYPE	!> ITYPE is INTEGER !> Specifies the problem type to be solved: !> = 1: A*x = (lambda)*B*x !> = 2: A*B*x = (lambda)*x !> = 3: B*A*x = (lambda)*x !>
[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,out]	A	!> A is DOUBLE PRECISION array, dimension (LDA, N) !> On entry, the symmetric matrix A. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A. !> !> On exit, if JOBZ = 'V', then if INFO = 0, A contains the !> matrix Z of eigenvectors. The eigenvectors are normalized !> as follows: !> if ITYPE = 1 or 2, Z**T*B*Z = I; !> if ITYPE = 3, Z**T*inv(B)*Z = I. !> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') !> or the lower triangle (if UPLO='L') of A, including the !> diagonal, is destroyed. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in,out]	B	!> B is DOUBLE PRECISION array, dimension (LDB, N) !> On entry, the symmetric positive definite matrix B. !> If UPLO = 'U', the leading N-by-N upper triangular part of B !> contains the upper triangular part of the matrix B. !> If UPLO = 'L', the leading N-by-N lower triangular part of B !> contains the lower triangular part of the matrix B. !> !> On exit, if INFO <= N, the part of B containing the matrix is !> overwritten by the triangular factor U or L from the Cholesky !> factorization B = U**T*U or B = L*L**T. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	W	!> W is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The length of the array WORK. LWORK >= max(1,3*N-1). !> For optimal efficiency, LWORK >= (NB+2)*N, !> where NB is the blocksize for DSYTRD returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: DPOTRF or DSYEV returned an error code: !> <= N: if INFO = i, DSYEV 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 the leading !> principal minor of order i of B is not positive. !> 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.