shst01.f - Man Page

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

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.