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SUBROUTINE SHST01( N, ILO, IHI, A, LDA, H, LDH, Q, LDQ, WORK,
$ LWORK, RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
INTEGER IHI, ILO, LDA, LDH, LDQ, LWORK, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), H( LDH, * ), Q( LDQ, * ),
$ RESULT( 2 ), WORK( LWORK )
* ..
*
* 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.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* ILO (input) INTEGER
* IHI (input) 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 (input) REAL array, dimension (LDA,N)
* The original n by n matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* H (input) 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 (input) INTEGER
* The leading dimension of the array H. LDH >= max(1,N).
*
* Q (input) REAL array, dimension (LDQ,N)
* The orthogonal matrix Q from the reduction A = Q*H*Q' as
* computed by SGEHRD + SORGHR.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= max(1,N).
*
* WORK (workspace) REAL array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The length of the array WORK. LWORK >= 2*N*N.
*
* RESULT (output) REAL array, dimension (2)
* RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
* RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER LDWORK
REAL ANORM, EPS, OVFL, SMLNUM, UNFL, WNORM
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE
EXTERNAL SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLABAD, SLACPY, SORT01
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
RETURN
END IF
*
UNFL = SLAMCH( 'Safe minimum' )
EPS = SLAMCH( 'Precision' )
OVFL = ONE / UNFL
CALL SLABAD( UNFL, OVFL )
SMLNUM = UNFL*N / EPS
*
* Test 1: Compute norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
*
* Copy A to WORK
*
LDWORK = MAX( 1, N )
CALL SLACPY( ' ', N, N, A, LDA, WORK, LDWORK )
*
* Compute Q*H
*
CALL SGEMM( 'No transpose', 'No transpose', N, N, N, ONE, Q, LDQ,
$ H, LDH, ZERO, WORK( LDWORK*N+1 ), LDWORK )
*
* Compute A - Q*H*Q'
*
CALL SGEMM( 'No transpose', 'Transpose', N, N, N, -ONE,
$ WORK( LDWORK*N+1 ), LDWORK, Q, LDQ, ONE, WORK,
$ LDWORK )
*
ANORM = MAX( SLANGE( '1', N, N, A, LDA, WORK( LDWORK*N+1 ) ),
$ UNFL )
WNORM = SLANGE( '1', N, N, WORK, LDWORK, WORK( LDWORK*N+1 ) )
*
* Note that RESULT(1) cannot overflow and is bounded by 1/(N*EPS)
*
RESULT( 1 ) = MIN( WNORM, ANORM ) / MAX( SMLNUM, ANORM*EPS ) / N
*
* Test 2: Compute norm( I - Q'*Q ) / ( N * EPS )
*
CALL SORT01( 'Columns', N, N, Q, LDQ, WORK, LWORK, RESULT( 2 ) )
*
RETURN
*
* End of SHST01
*
END
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