?sygs2/?hegs2

Reduces a symmetric/Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from ?potrf (unblocked algorithm).

Syntax

call ssygs2( itype, uplo, n, a, lda, b, ldb, info )

call dsygs2( itype, uplo, n, a, lda, b, ldb, info )

call chegs2( itype, uplo, n, a, lda, b, ldb, info )

call zhegs2( itype, uplo, n, a, lda, b, ldb, info )

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

The routine ?sygs2/?hegs2 reduces a real symmetric-definite or a complex Hermitian-definite generalized eigenproblem to standard form.

If itype = 1, the problem is

A*x = λ*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 = λ*x, or B*A*x = λ*x,

and A is overwritten by U*A*U' or L'*A*L. Here U'(L') is the transpose (conjugate transpose) of U (L).

B must be previously factorized as U'*U or L*L' by ?potrf.

Input Parameters

itype

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

CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix A is stored, and how B has been factorized.

= 'U': upper triangular

= 'L': lower triangular

n

INTEGER. The order of the matrices A and B. n ≥ 0.

a

REAL for ssygs2

DOUBLE PRECISION for dsygs2

COMPLEX for chegs2

COMPLEX*16 for zhegs2.

Array, DIMENSION (lda, n).

On entry, the symmetric/Hermitian 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.

lda

INTEGER.

The leading dimension of the array a. lda ≥ max(1,n).

b

REAL for ssygs2

DOUBLE PRECISION for dsygs2

COMPLEX for chegs2

COMPLEX*16 for zhegs2.

Array, DIMENSION (ldb, n).

The triangular factor from the Cholesky factorization of B as returned by ?potrf.

ldb

INTEGER. The leading dimension of the array b. ldb ≥ max(1,n).

Output Parameters

a

On exit, If info = 0, the transformed matrix, stored in the same format as A.

info

INTEGER.

= 0: successful exit.

< 0: if info = -i, the i-th argument had an illegal value.