Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3 - 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(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.

```

#### ARGUMENTS

```        ITYPE   (input) 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    (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.

LAPACK routine (version 3.3.1)             April 2011                            DSYGS2(3lapack)
```