# zhpgst.f - Man Page

SRC/zhpgst.f

## Synopsis

### Functions/Subroutines

subroutine zhpgst (itype, uplo, n, ap, bp, info)
ZHPGST

## Function/Subroutine Documentation

### subroutine zhpgst (integer itype, character uplo, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, integer info)

ZHPGST

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.```
Parameters

ITYPE

```          ITYPE is 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

```          UPLO is 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

```          N is INTEGER
The order of the matrices A and B.  N >= 0.```

AP

```          AP is 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

```          BP is 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

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 112 of file zhpgst.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhpgst(3) is an alias of zhpgst.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK