*> \brief \b SORHR_COL01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SORHR_COL01( M, N, MB1, NB1, NB2, RESULT) * * .. Scalar Arguments .. * INTEGER M, N, MB1, NB1, NB2 * .. Return values .. * REAL RESULT(6) * * *> \par Purpose: * ============= *> *> \verbatim *> *> SORHR_COL01 tests SORHR_COL using SLATSQR, SGEMQRT and SORGTSQR. *> Therefore, SLATSQR (part of SGEQR), SGEMQRT (part SGEMQR), SORGTSQR *> have to be tested before this test. *> *> \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] MB1 *> \verbatim *> MB1 is INTEGER *> Number of row in row block in an input test matrix. *> \endverbatim *> *> \param[in] NB1 *> \verbatim *> NB1 is INTEGER *> Number of columns in column block an input test matrix. *> \endverbatim *> *> \param[in] NB2 *> \verbatim *> NB2 is INTEGER *> Number of columns in column block in an output test matrix. *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL array, dimension (6) *> Results of each of the six tests below. *> ( C is a M-by-N random matrix, D is a N-by-M random matrix ) *> *> RESULT(1) = | A - Q * R | / (eps * m * |A|) *> RESULT(2) = | I - (Q**H) * Q | / (eps * m ) *> RESULT(3) = | Q * C - Q * C | / (eps * m * |C|) *> RESULT(4) = | (Q**H) * C - (Q**H) * C | / (eps * m * |C|) *> RESULT(5) = | (D * Q) - D * Q | / (eps * m * |D|) *> RESULT(6) = | D * (Q**H) - D * (Q**H) | / (eps * m * |D|) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2019 * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SORHR_COL01( M, N, MB1, NB1, NB2, RESULT ) IMPLICIT NONE * * -- LAPACK test routine (version 3.9.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2019 * * .. Scalar Arguments .. INTEGER M, N, MB1, NB1, NB2 * .. Return values .. REAL RESULT(6) * * ===================================================================== * * .. * .. Local allocatable arrays REAL, ALLOCATABLE :: A(:,:), AF(:,:), Q(:,:), R(:,:), $ RWORK(:), WORK( : ), T1(:,:), T2(:,:), DIAG(:), $ C(:,:), CF(:,:), D(:,:), DF(:,:) * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL TESTZEROS INTEGER INFO, I, J, K, L, LWORK, NB1_UB, NB2_UB, NRB REAL ANORM, EPS, RESID, CNORM, DNORM * .. * .. Local Arrays .. INTEGER ISEED( 4 ) REAL WORKQUERY( 1 ) * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SLACPY, SLARNV, SLASET, SLATSQR, SORHR_COL, $ SORGTSQR, SSCAL, SGEMM, SGEMQRT, SSYRK * .. * .. Intrinsic Functions .. INTRINSIC CEILING, MAX, MIN, REAL * .. * .. Scalars in Common .. CHARACTER(LEN=32) SRNAMT * .. * .. Common blocks .. COMMON / SRMNAMC / SRNAMT * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * * TEST MATRICES WITH HALF OF MATRIX BEING ZEROS * TESTZEROS = .FALSE. * EPS = SLAMCH( 'Epsilon' ) K = MIN( M, N ) L = MAX( M, N, 1) * * Dynamically allocate local arrays * ALLOCATE ( A(M,N), AF(M,N), Q(L,L), R(M,L), RWORK(L), $ C(M,N), CF(M,N), $ D(N,M), DF(N,M) ) * * Put random numbers into A and copy to AF * DO J = 1, N CALL SLARNV( 2, ISEED, M, A( 1, J ) ) END DO IF( TESTZEROS ) THEN IF( M.GE.4 ) THEN DO J = 1, N CALL SLARNV( 2, ISEED, M/2, A( M/4, J ) ) END DO END IF END IF CALL SLACPY( 'Full', M, N, A, M, AF, M ) * * Number of row blocks in SLATSQR * NRB = MAX( 1, CEILING( REAL( M - N ) / REAL( MB1 - N ) ) ) * ALLOCATE ( T1( NB1, N * NRB ) ) ALLOCATE ( T2( NB2, N ) ) ALLOCATE ( DIAG( N ) ) * * Begin determine LWORK for the array WORK and allocate memory. * * SLATSQR requires NB1 to be bounded by N. * NB1_UB = MIN( NB1, N) * * SGEMQRT requires NB2 to be bounded by N. * NB2_UB = MIN( NB2, N) * CALL SLATSQR( M, N, MB1, NB1_UB, AF, M, T1, NB1, $ WORKQUERY, -1, INFO ) LWORK = INT( WORKQUERY( 1 ) ) CALL SORGTSQR( M, N, MB1, NB1, AF, M, T1, NB1, WORKQUERY, -1, $ INFO ) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) * * In SGEMQRT, WORK is N*NB2_UB if SIDE = 'L', * or M*NB2_UB if SIDE = 'R'. * LWORK = MAX( LWORK, NB2_UB * N, NB2_UB * M ) * ALLOCATE ( WORK( LWORK ) ) * * End allocate memory for WORK. * * * Begin Householder reconstruction routines * * Factor the matrix A in the array AF. * SRNAMT = 'SLATSQR' CALL SLATSQR( M, N, MB1, NB1_UB, AF, M, T1, NB1, WORK, LWORK, $ INFO ) * * Copy the factor R into the array R. * SRNAMT = 'SLACPY' CALL SLACPY( 'U', N, N, AF, M, R, M ) * * Reconstruct the orthogonal matrix Q. * SRNAMT = 'SORGTSQR' CALL SORGTSQR( M, N, MB1, NB1, AF, M, T1, NB1, WORK, LWORK, $ INFO ) * * Perform the Householder reconstruction, the result is stored * the arrays AF and T2. * SRNAMT = 'SORHR_COL' CALL SORHR_COL( M, N, NB2, AF, M, T2, NB2, DIAG, INFO ) * * Compute the factor R_hr corresponding to the Householder * reconstructed Q_hr and place it in the upper triangle of AF to * match the Q storage format in DGEQRT. R_hr = R_tsqr * S, * this means changing the sign of I-th row of the matrix R_tsqr * according to sign of of I-th diagonal element DIAG(I) of the * matrix S. * SRNAMT = 'SLACPY' CALL SLACPY( 'U', N, N, R, M, AF, M ) * DO I = 1, N IF( DIAG( I ).EQ.-ONE ) THEN CALL SSCAL( N+1-I, -ONE, AF( I, I ), M ) END IF END DO * * End Householder reconstruction routines. * * * Generate the m-by-m matrix Q * CALL SLASET( 'Full', M, M, ZERO, ONE, Q, M ) * SRNAMT = 'SGEMQRT' CALL SGEMQRT( 'L', 'N', M, M, K, NB2_UB, AF, M, T2, NB2, Q, M, $ WORK, INFO ) * * Copy R * CALL SLASET( 'Full', M, N, ZERO, ZERO, R, M ) * CALL SLACPY( 'Upper', M, N, AF, M, R, M ) * * TEST 1 * Compute |R - (Q**T)*A| / ( eps * m * |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 * * TEST 2 * Compute |I - (Q**T)*Q| / ( eps * m ) and store in RESULT(2) * CALL SLASET( 'Full', M, M, ZERO, ONE, R, M ) CALL SSYRK( 'U', 'T', 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 * 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 = CF * SRNAMT = 'SGEMQRT' CALL SGEMQRT( 'L', 'N', M, N, K, NB2_UB, AF, M, T2, NB2, CF, M, $ WORK, INFO ) * * TEST 3 * Compute |CF - Q*C| / ( eps * m * |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 (Q**T)*C = CF * SRNAMT = 'SGEMQRT' CALL SGEMQRT( 'L', 'T', M, N, K, NB2_UB, AF, M, T2, NB2, CF, M, $ WORK, INFO ) * * TEST 4 * Compute |CF - (Q**T)*C| / ( eps * m * |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 = DF * SRNAMT = 'SGEMQRT' CALL SGEMQRT( 'R', 'N', N, M, K, NB2_UB, AF, M, T2, NB2, DF, N, $ WORK, INFO ) * * TEST 5 * Compute |DF - D*Q| / ( eps * m * |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( DNORM.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 = DF * SRNAMT = 'SGEMQRT' CALL SGEMQRT( 'R', 'T', N, M, K, NB2_UB, AF, M, T2, NB2, DF, N, $ WORK, INFO ) * * TEST 6 * Compute |DF - D*(Q**T)| / ( eps * m * |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( DNORM.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, T1, T2, DIAG, $ C, D, CF, DF ) * RETURN * * End of SORHR_COL01 * END