dsygs2(3)

NAME

DSYGS2 - reduce a real symmetric-definite generalized

eigenproblem to standard form

SYNOPSIS

SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, ITYPE, LDA, LDB, N
    DOUBLE         PRECISION A( LDA, * ), B( LDB, * )

PURPOSE

DSYGS2 reduces a real symmetric-definite generalized

eigenproblem to standard form. If ITYPE = 1, the problem is A*x

= lambda*B*x,
and A is overwritten by inv(U')*A*inv(U) or

inv(L)*A*inv(L')

If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U` or

L'*A*L.

B must have been previously factorized as U'*U or L*L' by

DPOTRF.

ARGUMENTS

ITYPE (input) INTEGER

= 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
= 2 or 3: compute U*A*U' or L'*A*L.

UPLO (input) CHARACTER

Specifies whether the upper or lower triangular

part of the symmetric matrix A is stored, and how B has been fac

torized. = 'U': Upper triangular
= 'L': Lower triangular

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, and the strictly lower triangu

lar part of A is not referenced. If UPLO = 'L', the leading n by

n lower triangular part of A contains the lower triangular part

of the matrix A, and the strictly upper triangular part of A is

not referenced.

On exit, if INFO = 0, the transformed matrix,

stored in the same format as A.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

B (input) DOUBLE PRECISION array, dimension (LDB,N)

The triangular factor from the Cholesky factoriza

tion of B, as returned by DPOTRF.

LDB (input) INTEGER

The leading dimension of the array B. LDB >=

max(1,N).

INFO (output) INTEGER

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

gal value.

LAPACK version 3.0 15 June 2000

DSYGS2(3)