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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

```NAME
LAPACK-3   -   reduces   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*1
= '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

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
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