---
name: "zhst01.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/zhst01.f"
---

# zhst01.f(3)

## NAME

TESTING/EIG/zhst01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zhst01** (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork, rwork, result)\
 **ZHST01**

## Function/Subroutine Documentation

### subroutine zhst01 (integer n, integer ilo, integer ihi, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldh, \* ) h, integer ldh, complex\*16, dimension( ldq, \* ) q, integer ldq, complex\*16, dimension( lwork ) work, integer lwork, double precision, dimension( \* ) rwork, double precision, dimension( 2 ) result)

**ZHST01**

**Purpose:**

```
!>
!> ZHST01 tests the reduction of a general matrix A to upper Hessenberg
!> form:  A = Q*H*Q'.  Two test ratios are computed;
!>
!> RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
!> RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
!>
!> The matrix Q is assumed to be given explicitly as it would be
!> following ZGEHRD + ZUNGHR.
!>
!> In this version, ILO and IHI are not used, but they could be used
!> to save some work if this is desired.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
```

*ILO*

```
!>          ILO is INTEGER
!>
```

*IHI*

```
!>          IHI is INTEGER
!>
!>          A is assumed to be upper triangular in rows and columns
!>          1:ILO-1 and IHI+1:N, so Q differs from the identity only in
!>          rows and columns ILO+1:IHI.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The original n by n matrix A.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*H*

```
!>          H is COMPLEX*16 array, dimension (LDH,N)
!>          The upper Hessenberg matrix H from the reduction A = Q*H*Q'
!>          as computed by ZGEHRD.  H is assumed to be zero below the
!>          first subdiagonal.
!>
```

*LDH*

```
!>          LDH is INTEGER
!>          The leading dimension of the array H.  LDH >= max(1,N).
!>
```

*Q*

```
!>          Q is COMPLEX*16 array, dimension (LDQ,N)
!>          The orthogonal matrix Q from the reduction A = Q*H*Q' as
!>          computed by ZGEHRD + ZUNGHR.
!>
```

*LDQ*

```
!>          LDQ is INTEGER
!>          The leading dimension of the array Q.  LDQ >= max(1,N).
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The length of the array WORK.  LWORK >= 2*N*N.
!>
```

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (N)
!>
```

*RESULT*

```
!>          RESULT is DOUBLE PRECISION array, dimension (2)
!>          RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
!>          RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **138** of file **zhst01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.