# ssygs2.f - Man Page

SRC/ssygs2.f

## Synopsis

### Functions/Subroutines

subroutine **ssygs2** (itype, uplo, n, a, lda, b, ldb, info)**SSYGS2** reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine ssygs2 (integer itype, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)

**SSYGS2** reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).

**Purpose:**

SSYGS2 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 SPOTRF.

**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 REAL 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 REAL array, dimension (LDB,N) The triangular factor from the Cholesky factorization of B, as returned by SPOTRF.

*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.

Definition at line **126** of file **ssygs2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ssygs2(3) is an alias of ssygs2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK