NAME

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

SYNOPSIS

SUBROUTINE CHPGST(
ITYPE, UPLO, N, AP, BP, INFO )

CHARACTER UPLO

INTEGER INFO, ITYPE, N

COMPLEX AP( ∗ ), BP( ∗ )

PURPOSE

CHPGST 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 CPPTRF.
 

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 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 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 CPPTRF.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

SunSoft, Inc.  —  Last change: 27 Jun 1995