*> \brief \b SQRT04 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SQRT04(M,N,NB,RESULT) * * .. Scalar Arguments .. * INTEGER M, N, NB, LDT * .. Return values .. * REAL RESULT(6) * * *> \par Purpose: * ============= *> *> \verbatim *> *> SQRT04 tests SGEQRT and SGEMQRT. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> Number of rows in test matrix. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> Number of columns in test matrix. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> Block size of test matrix. NB <= Min(M,N). *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL array, dimension (6) *> Results of each of the six tests below. *> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | *> RESULT(4) = | Q^H C - Q^H C | *> RESULT(5) = | C Q - C Q | *> RESULT(6) = | C Q^H - C Q^H | *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date April 2012 * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SQRT04(M,N,NB,RESULT) IMPLICIT NONE * * -- LAPACK test routine (version 3.4.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * April 2012 * * .. Scalar Arguments .. INTEGER M, N, NB, LDT * .. Return values .. REAL RESULT(6) * * ===================================================================== * * .. * .. Local allocatable arrays REAL, ALLOCATABLE :: AF(:,:), Q(:,:), $ R(:,:), RWORK(:), WORK( : ), T(:,:), $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) * * .. Parameters .. REAL ONE, ZERO PARAMETER( ZERO = 0.0, ONE = 1.0 ) * .. * .. Local Scalars .. INTEGER INFO, J, K, L, LWORK REAL ANORM, EPS, RESID, CNORM, DNORM * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. External Functions .. REAL SLAMCH REAL SLANGE, SLANSY LOGICAL LSAME EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * EPS = SLAMCH( 'Epsilon' ) K = MIN(M,N) L = MAX(M,N) LWORK = MAX(2,L)*MAX(2,L)*NB * * Dynamically allocate local arrays * ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), $ WORK(LWORK), T(NB,N), C(M,N), CF(M,N), $ D(N,M), DF(N,M) ) * * Put random numbers into A and copy to AF * LDT=NB DO J=1,N CALL SLARNV( 2, ISEED, M, A( 1, J ) ) END DO CALL SLACPY( 'Full', M, N, A, M, AF, M ) * * Factor the matrix A in the array AF. * CALL SGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO ) * * Generate the m-by-m matrix Q * CALL SLASET( 'Full', M, M, ZERO, ONE, Q, M ) CALL SGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, $ WORK, INFO ) * * Copy R * CALL SLASET( 'Full', M, N, ZERO, ZERO, R, M ) CALL SLACPY( 'Upper', M, N, AF, M, R, M ) * * Compute |R - Q'*A| / |A| and store in RESULT(1) * CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M ) ANORM = SLANGE( '1', M, N, A, M, RWORK ) RESID = SLANGE( '1', M, N, R, M, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM) ELSE RESULT( 1 ) = ZERO END IF * * Compute |I - Q'*Q| and store in RESULT(2) * CALL SLASET( 'Full', M, M, ZERO, ONE, R, M ) CALL SSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M ) RESID = SLANSY( '1', 'Upper', M, R, M, RWORK ) RESULT( 2 ) = RESID / (EPS*MAX(1,M)) * * Generate random m-by-n matrix C and a copy CF * DO J=1,N CALL SLARNV( 2, ISEED, M, C( 1, J ) ) END DO CNORM = SLANGE( '1', M, N, C, M, RWORK) CALL SLACPY( 'Full', M, N, C, M, CF, M ) * * Apply Q to C as Q*C * CALL SGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, $ WORK, INFO) * * Compute |Q*C - Q*C| / |C| * CALL SGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) RESID = SLANGE( '1', M, N, CF, M, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM) ELSE RESULT( 3 ) = ZERO END IF * * Copy C into CF again * CALL SLACPY( 'Full', M, N, C, M, CF, M ) * * Apply Q to C as QT*C * CALL SGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M, $ WORK, INFO) * * Compute |QT*C - QT*C| / |C| * CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) RESID = SLANGE( '1', M, N, CF, M, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM) ELSE RESULT( 4 ) = ZERO END IF * * Generate random n-by-m matrix D and a copy DF * DO J=1,M CALL SLARNV( 2, ISEED, N, D( 1, J ) ) END DO DNORM = SLANGE( '1', N, M, D, N, RWORK) CALL SLACPY( 'Full', N, M, D, N, DF, N ) * * Apply Q to D as D*Q * CALL SGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, $ WORK, INFO) * * Compute |D*Q - D*Q| / |D| * CALL SGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) RESID = SLANGE( '1', N, M, DF, N, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM) ELSE RESULT( 5 ) = ZERO END IF * * Copy D into DF again * CALL SLACPY( 'Full', N, M, D, N, DF, N ) * * Apply Q to D as D*QT * CALL SGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N, $ WORK, INFO) * * Compute |D*QT - D*QT| / |D| * CALL SGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) RESID = SLANGE( '1', N, M, DF, N, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM) ELSE RESULT( 6 ) = ZERO END IF * * Deallocate all arrays * DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) * RETURN END