man zhegs2 (Fonctions bibliothèques) - reduce a complex Hermitian-definite generalized eigenproblem to standard form

NAME

ZHEGS2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form

SYNOPSIS

SUBROUTINE ZHEGS2(
ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, ITYPE, LDA, LDB, N
COMPLEX*16 A( LDA, * ), B( LDB, * )

PURPOSE

ZHEGS2 reduces a complex Hermitian-definite generalized eigenproblem to standard form. If ITYPE = 1, the problem is A*x = lambda*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 = lambda*x or

B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.

B must have been previously factorized as U'*U or L*L' by ZPOTRF.

ARGUMENTS

ITYPE (input) 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 (input) CHARACTER
Specifies whether the upper or lower triangular part of the Hermitian 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) COMPLEX*16 array, dimension (LDA,N)
On entry, the 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.

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) COMPLEX*16 array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B, as returned by ZPOTRF.
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.