# shst01.f - Man Page

TESTING/EIG/shst01.f

## Synopsis

### Functions/Subroutines

subroutine shst01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork, result)
SHST01

## Function/Subroutine Documentation

### subroutine shst01 (integer n, integer ilo, integer ihi, real, dimension( lda, * ) a, integer lda, real, dimension( ldh, * ) h, integer ldh, real, dimension( ldq, * ) q, integer ldq, real, dimension( lwork ) work, integer lwork, real, dimension( 2 ) result)

SHST01

Purpose:

``` SHST01 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 SGEHRD + SORGHR.

In this version, ILO and IHI are not used and are assumed to be 1 and
N, respectively.```
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 REAL 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 REAL array, dimension (LDH,N)
The upper Hessenberg matrix H from the reduction A = Q*H*Q'
as computed by SGEHRD.  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 REAL array, dimension (LDQ,N)
The orthogonal matrix Q from the reduction A = Q*H*Q' as
computed by SGEHRD + SORGHR.```

LDQ

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

WORK

`          WORK is REAL array, dimension (LWORK)`

LWORK

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

RESULT

```          RESULT is REAL 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

NAG Ltd.

Definition at line 132 of file shst01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page shst01(3) is an alias of shst01.f(3).

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