*> \brief \b SQRT05 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SQRT05(M,N,L,NB,RESULT) * * .. Scalar Arguments .. * INTEGER LWORK, M, N, L, NB, LDT * .. Return values .. * REAL RESULT(6) * * *> \par Purpose: * ============= *> *> \verbatim *> *> SQRT05 tests STPQRT and STPMQRT. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> Number of rows in lower part of the test matrix. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> Number of columns in test matrix. *> \endverbatim *> *> \param[in] L *> \verbatim *> L is INTEGER *> The number of rows of the upper trapezoidal part the *> lower test matrix. 0 <= L <= M. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> Block size of test matrix. NB <= 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 SQRT05(M,N,L,NB,RESULT) IMPLICIT NONE * * -- LAPACK test routine (version 3.7.0) -- * -- 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 LWORK, M, N, L, 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 ZERO, ONE PARAMETER( ZERO = 0.0, ONE = 1.0 ) * .. * .. Local Scalars .. INTEGER INFO, J, K, M2, NP1 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 * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * EPS = SLAMCH( 'Epsilon' ) K = N M2 = M+N IF( M.GT.0 ) THEN NP1 = N+1 ELSE NP1 = 1 END IF LWORK = M2*M2*NB * * Dynamically allocate all arrays * ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2), $ WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), $ D(N,M2),DF(N,M2) ) * * Put random stuff into A * LDT=NB CALL SLASET( 'Full', M2, N, ZERO, ZERO, A, M2 ) CALL SLASET( 'Full', NB, N, ZERO, ZERO, T, NB ) DO J=1,N CALL SLARNV( 2, ISEED, J, A( 1, J ) ) END DO IF( M.GT.0 ) THEN DO J=1,N CALL SLARNV( 2, ISEED, M-L, A( N+1, J ) ) END DO END IF IF( L.GT.0 ) THEN DO J=1,N CALL SLARNV( 2, ISEED, MIN(J,L), A( N+M-L+1, J ) ) END DO END IF * * Copy the matrix A to the array AF. * CALL SLACPY( 'Full', M2, N, A, M2, AF, M2 ) * * Factor the matrix A in the array AF. * CALL STPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO) * * Generate the (M+N)-by-(M+N) matrix Q by applying H to I * CALL SLASET( 'Full', M2, M2, ZERO, ONE, Q, M2 ) CALL SGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2, $ WORK, INFO ) * * Copy R * CALL SLASET( 'Full', M2, N, ZERO, ZERO, R, M2 ) CALL SLACPY( 'Upper', M2, N, AF, M2, R, M2 ) * * Compute |R - Q'*A| / |A| and store in RESULT(1) * CALL SGEMM( 'T', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 ) ANORM = SLANGE( '1', M2, N, A, M2, RWORK ) RESID = SLANGE( '1', M2, N, R, M2, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2)) ELSE RESULT( 1 ) = ZERO END IF * * Compute |I - Q'*Q| and store in RESULT(2) * CALL SLASET( 'Full', M2, M2, ZERO, ONE, R, M2 ) CALL SSYRK( 'U', 'C', M2, M2, -ONE, Q, M2, ONE, $ R, M2 ) RESID = SLANSY( '1', 'Upper', M2, R, M2, RWORK ) RESULT( 2 ) = RESID / (EPS*MAX(1,M2)) * * Generate random m-by-n matrix C and a copy CF * DO J=1,N CALL SLARNV( 2, ISEED, M2, C( 1, J ) ) END DO CNORM = SLANGE( '1', M2, N, C, M2, RWORK) CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 ) * * Apply Q to C as Q*C * CALL STPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF, $ M2,CF(NP1,1),M2,WORK,INFO) * * Compute |Q*C - Q*C| / |C| * CALL SGEMM( 'N', 'N', M2, N, M2, -ONE, Q,M2,C,M2,ONE,CF,M2) RESID = SLANGE( '1', M2, N, CF, M2, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM) ELSE RESULT( 3 ) = ZERO END IF * * Copy C into CF again * CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 ) * * Apply Q to C as QT*C * CALL STPMQRT('L','T',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2, $ CF(NP1,1),M2,WORK,INFO) * * Compute |QT*C - QT*C| / |C| * CALL SGEMM('T','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2) RESID = SLANGE( '1', M2, N, CF, M2, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM) ELSE RESULT( 4 ) = ZERO END IF * * Generate random n-by-m matrix D and a copy DF * DO J=1,M2 CALL SLARNV( 2, ISEED, N, D( 1, J ) ) END DO DNORM = SLANGE( '1', N, M2, D, N, RWORK) CALL SLACPY( 'Full', N, M2, D, N, DF, N ) * * Apply Q to D as D*Q * CALL STPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, $ DF(1,NP1),N,WORK,INFO) * * Compute |D*Q - D*Q| / |D| * CALL SGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N) RESID = SLANGE('1',N, M2,DF,N,RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM) ELSE RESULT( 5 ) = ZERO END IF * * Copy D into DF again * CALL SLACPY('Full',N,M2,D,N,DF,N ) * * Apply Q to D as D*QT * CALL STPMQRT('R','T',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, $ DF(1,NP1),N,WORK,INFO) * * Compute |D*QT - D*QT| / |D| * CALL SGEMM( 'N', 'T', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N ) RESID = SLANGE( '1', N, M2, DF, N, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM) ELSE RESULT( 6 ) = ZERO END IF * * Deallocate all arrays * DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) RETURN END