# dsygs2.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dsygs2** (ITYPE, UPLO, **N**, A, **LDA**, B, **LDB**, INFO)**DSYGS2** reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine dsygs2 (integer ITYPE, character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, integer INFO)

**DSYGS2** reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).

**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**T)*A*inv(U) or inv(L)*A*inv(L**T) 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**T or L**T *A*L. B must have been previously factorized as U**T *U or L*L**T by DPOTRF.

**Parameters:***ITYPE*ITYPE is INTEGER = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); = 2 or 3: compute U*A*U**T or L**T *A*L.

*UPLO*UPLO is 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*N is INTEGER The order of the matrices A and B. N >= 0.

*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, 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*B*B is DOUBLE PRECISION array, dimension (LDB,N) The triangular factor from the Cholesky factorization of B, as returned by DPOTRF.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*INFO*INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 129 of file dsygs2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dsygs2(3) is an alias of dsygs2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK