dsygv(3)

NAME

DSYGV - compute all the eigenvalues, and optionally, the

eigenvectors of a real generalized symmetric-definite eigenprob

lem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or

B*A*x=(lambda)*x

SYNOPSIS

SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
WORK, LWORK, INFO )
    CHARACTER     JOBZ, UPLO
    INTEGER       INFO, ITYPE, LDA, LDB, LWORK, N
    DOUBLE        PRECISION A( LDA, * ), B( LDB, * ), W( *
), WORK( * )

PURPOSE

DSYGV computes all the eigenvalues, and optionally, the

eigenvectors of a real generalized symmetric-definite eigenprob

lem, 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.

ARGUMENTS

ITYPE (input) 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

JOBZ (input) CHARACTER*1

= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.

UPLO (input) CHARACTER*1

= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.

N (input) INTEGER

The order of the matrices A and B. N >= 0.

A (input/output) 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 con

tains the matrix Z of eigenvectors. The eigenvectors are normal

ized 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 trian

gle (if UPLO='U') or the lower triangle (if UPLO='L') of A, in

cluding the diagonal, is destroyed.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

B (input/output) 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.

LDB (input) INTEGER

The leading dimension of the array B. LDB >=

max(1,N).

W (output) DOUBLE PRECISION array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

WORK (workspace/output) DOUBLE PRECISION array, dimen

sion (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) 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.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal 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 minor of order i of B is not positive definite. The

factorization of B could not be completed and no eigenvalues or

eigenvectors were computed.

LAPACK version 3.0 15 June 2000

DSYGV(3)