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*1

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored, and how B has been factorized. = '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 triangular 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 factorization 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 illegal value.