---
name: "zhpgst.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/zhpgst.f"
---

# zhpgst.f(3)

## NAME

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **112** of file **zhpgst.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.