man zhpgst (Fonctions bibliothèques) - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

NAME

ZHPGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

SYNOPSIS

SUBROUTINE ZHPGST(
ITYPE, UPLO, N, AP, BP, INFO )
CHARACTER UPLO
INTEGER INFO, ITYPE, N
COMPLEX*16 AP( * ), BP( * )

PURPOSE

ZHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. If ITYPE = 1, the problem is A*x = lambda*B*x,

and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)

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**H or L**H*A*L.

B must have been previously factorized as U**H*U or L*L**H by ZPPTRF.

ARGUMENTS

ITYPE (input) INTEGER
= 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);

= 2 or 3: compute U*A*U**H or L**H*A*L.
UPLO (input) CHARACTER


= 'U': Upper triangle of A is stored and B is factored as U**H*U; = 'L': Lower triangle of A is stored and B is factored as L*L**H.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, if INFO = 0, the transformed matrix, stored in the same format as A.

BP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by ZPPTRF.
INFO (output) INTEGER
= 0: successful exit

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