261 lines
6.5 KiB
Fortran
261 lines
6.5 KiB
Fortran
*> \brief \b SQRT04
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SQRT04(M,N,NB,RESULT)
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*
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* .. Scalar Arguments ..
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* INTEGER M, N, NB, LDT
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* .. Return values ..
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* REAL RESULT(6)
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SQRT04 tests SGEQRT and SGEMQRT.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> Number of rows in test matrix.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> Number of columns in test matrix.
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*> \endverbatim
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*>
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*> \param[in] NB
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*> \verbatim
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*> NB is INTEGER
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*> Block size of test matrix. NB <= Min(M,N).
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL array, dimension (6)
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*> Results of each of the six tests below.
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*>
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*> RESULT(1) = | A - Q R |
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*> RESULT(2) = | I - Q^H Q |
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*> RESULT(3) = | Q C - Q C |
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*> RESULT(4) = | Q^H C - Q^H C |
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*> RESULT(5) = | C Q - C Q |
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*> RESULT(6) = | C Q^H - C Q^H |
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SQRT04(M,N,NB,RESULT)
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IMPLICIT NONE
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER M, N, NB, LDT
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* .. Return values ..
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REAL RESULT(6)
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*
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* =====================================================================
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*
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* ..
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* .. Local allocatable arrays
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REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
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$ R(:,:), RWORK(:), WORK( : ), T(:,:),
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$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER( ZERO = 0.0, ONE = 1.0 )
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* ..
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* .. Local Scalars ..
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INTEGER INFO, J, K, L, LWORK
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REAL ANORM, EPS, RESID, CNORM, DNORM
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* ..
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* .. Local Arrays ..
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INTEGER ISEED( 4 )
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* ..
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* .. External Subroutine ..
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EXTERNAL SGEMM, SLACPY, SLARNV, SGEMQRT, SLASET, SGEQRT, SSYRK
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* ..
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* .. External Functions ..
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REAL SLAMCH
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REAL SLANGE, SLANSY
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LOGICAL LSAME
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EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Data statements ..
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DATA ISEED / 1988, 1989, 1990, 1991 /
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*
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EPS = SLAMCH( 'Epsilon' )
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K = MIN(M,N)
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L = MAX(M,N)
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LWORK = MAX(2,L)*MAX(2,L)*NB
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*
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* Dynamically allocate local arrays
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*
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ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L),
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$ WORK(LWORK), T(NB,N), C(M,N), CF(M,N),
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$ D(N,M), DF(N,M) )
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*
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* Put random numbers into A and copy to AF
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*
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LDT=NB
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DO J=1,N
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CALL SLARNV( 2, ISEED, M, A( 1, J ) )
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END DO
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CALL SLACPY( 'Full', M, N, A, M, AF, M )
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*
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* Factor the matrix A in the array AF.
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*
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CALL SGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
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*
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* Generate the m-by-m matrix Q
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*
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CALL SLASET( 'Full', M, M, ZERO, ONE, Q, M )
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CALL SGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M,
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$ WORK, INFO )
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*
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* Copy R
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*
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CALL SLASET( 'Full', M, N, ZERO, ZERO, R, M )
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CALL SLACPY( 'Upper', M, N, AF, M, R, M )
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*
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* Compute |R - Q'*A| / |A| and store in RESULT(1)
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*
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CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
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ANORM = SLANGE( '1', M, N, A, M, RWORK )
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RESID = SLANGE( '1', M, N, R, M, RWORK )
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IF( ANORM.GT.ZERO ) THEN
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RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
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ELSE
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RESULT( 1 ) = ZERO
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END IF
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*
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* Compute |I - Q'*Q| and store in RESULT(2)
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*
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CALL SLASET( 'Full', M, M, ZERO, ONE, R, M )
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CALL SSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M )
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RESID = SLANSY( '1', 'Upper', M, R, M, RWORK )
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RESULT( 2 ) = RESID / (EPS*MAX(1,M))
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*
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* Generate random m-by-n matrix C and a copy CF
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*
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DO J=1,N
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CALL SLARNV( 2, ISEED, M, C( 1, J ) )
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END DO
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CNORM = SLANGE( '1', M, N, C, M, RWORK)
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CALL SLACPY( 'Full', M, N, C, M, CF, M )
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*
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* Apply Q to C as Q*C
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*
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CALL SGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M,
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$ WORK, INFO)
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*
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* Compute |Q*C - Q*C| / |C|
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*
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CALL SGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
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RESID = SLANGE( '1', M, N, CF, M, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
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ELSE
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RESULT( 3 ) = ZERO
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END IF
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*
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* Copy C into CF again
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*
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CALL SLACPY( 'Full', M, N, C, M, CF, M )
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*
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* Apply Q to C as QT*C
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*
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CALL SGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M,
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$ WORK, INFO)
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*
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* Compute |QT*C - QT*C| / |C|
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*
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CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
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RESID = SLANGE( '1', M, N, CF, M, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
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ELSE
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RESULT( 4 ) = ZERO
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END IF
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*
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* Generate random n-by-m matrix D and a copy DF
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*
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DO J=1,M
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CALL SLARNV( 2, ISEED, N, D( 1, J ) )
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END DO
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DNORM = SLANGE( '1', N, M, D, N, RWORK)
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CALL SLACPY( 'Full', N, M, D, N, DF, N )
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*
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* Apply Q to D as D*Q
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*
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CALL SGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N,
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$ WORK, INFO)
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*
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* Compute |D*Q - D*Q| / |D|
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*
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CALL SGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
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RESID = SLANGE( '1', N, M, DF, N, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
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ELSE
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RESULT( 5 ) = ZERO
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END IF
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*
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* Copy D into DF again
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*
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CALL SLACPY( 'Full', N, M, D, N, DF, N )
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*
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* Apply Q to D as D*QT
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*
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CALL SGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N,
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$ WORK, INFO)
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*
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* Compute |D*QT - D*QT| / |D|
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*
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CALL SGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
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RESID = SLANGE( '1', N, M, DF, N, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
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ELSE
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RESULT( 6 ) = ZERO
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END IF
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*
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* Deallocate all arrays
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*
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DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
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*
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RETURN
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END
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