TESTING/EIG/shst01.f(3)

NAME
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

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