# 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

Univ. of Colorado Denver

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