# dsygs2 (l) - Linux Man Pages

## NAME

DSYGS2 - reduces 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(Uaq)*A*inv(U) or inv(L)*A*inv(Laq) 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 Laq*A*L. B must have been previously factorized as Uaq*U or L*Laq by DPOTRF.

## ARGUMENTS

ITYPE (input) INTEGER
= 1: compute inv(Uaq)*A*inv(U) or inv(L)*A*inv(Laq);
= 2 or 3: compute U*A*Uaq or Laq*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. = aqUaq: Upper triangular
= aqLaq: 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 = aqUaq, 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 = aqLaq, 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.