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00001 *> \brief \b DQRT04
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE DQRT04(M,N,NB,RESULT)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER LWORK, M, N, NB, LDT
00015 *       .. Return values ..
00016 *       DOUBLE PRECISION RESULT(6)
00017 *  
00018 *
00019 *> \par Purpose:
00020 *  =============
00021 *>
00022 *> \verbatim
00023 *>
00024 *> DQRT04 tests DGEQRT and DGEMQRT.
00025 *> \endverbatim
00026 *
00027 *  Arguments:
00028 *  ==========
00029 *
00030 *> \param[in] M
00031 *> \verbatim
00032 *>          M is INTEGER
00033 *>          Number of rows in test matrix.
00034 *> \endverbatim
00035 *>
00036 *> \param[in] N
00037 *> \verbatim
00038 *>          N is INTEGER
00039 *>          Number of columns in test matrix.
00040 *> \endverbatim
00041 *>
00042 *> \param[in] NB
00043 *> \verbatim
00044 *>          NB is INTEGER
00045 *>          Block size of test matrix.  NB <= Min(M,N).
00046 *> \endverbatim
00047 *>
00048 *> \param[out] RESULT
00049 *> \verbatim
00050 *>          RESULT is DOUBLE PRECISION array, dimension (6)
00051 *>          Results of each of the six tests below.
00052 *>
00053 *>          RESULT(1) = | A - Q R |
00054 *>          RESULT(2) = | I - Q^H Q |
00055 *>          RESULT(3) = | Q C - Q C |
00056 *>          RESULT(4) = | Q^H C - Q^H C |
00057 *>          RESULT(5) = | C Q - C Q | 
00058 *>          RESULT(6) = | C Q^H - C Q^H |
00059 *> \endverbatim
00060 *
00061 *  Authors:
00062 *  ========
00063 *
00064 *> \author Univ. of Tennessee 
00065 *> \author Univ. of California Berkeley 
00066 *> \author Univ. of Colorado Denver 
00067 *> \author NAG Ltd. 
00068 *
00069 *> \date November 2011
00070 *
00071 *> \ingroup double_lin
00072 *
00073 *  =====================================================================
00074       SUBROUTINE DQRT04(M,N,NB,RESULT)
00075 *
00076 *  -- LAPACK test routine (version 3.4.0) --
00077 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00078 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00079 *     November 2011
00080 *
00081 *     .. Scalar Arguments ..
00082       INTEGER LWORK, M, N, NB, LDT
00083 *     .. Return values ..
00084       DOUBLE PRECISION RESULT(6)
00085 *
00086 *  =====================================================================
00087 *
00088 *     ..
00089 *     .. Local allocatable arrays 
00090       DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
00091      $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
00092      $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
00093 *
00094 *     .. Parameters ..
00095       DOUBLE PRECISION ONE, ZERO
00096       PARAMETER( ZERO = 0.0, ONE = 1.0 )
00097 *     ..
00098 *     .. Local Scalars ..
00099       INTEGER INFO, J, K, L
00100       DOUBLE PRECISION   ANORM, EPS, RESID, CNORM, DNORM
00101 *     ..
00102 *     .. Local Arrays ..
00103       INTEGER            ISEED( 4 )
00104 *     ..
00105 *     .. External Functions ..
00106       DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
00107       LOGICAL  LSAME
00108       EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME
00109 *     ..
00110 *     .. Intrinsic Functions ..
00111       INTRINSIC  MAX, MIN      
00112 *     ..
00113 *     .. Data statements ..
00114       DATA ISEED / 1988, 1989, 1990, 1991 /      
00115 *      
00116       EPS = DLAMCH( 'Epsilon' )
00117       K = MIN(M,N)
00118       L = MAX(M,N)
00119       LWORK = MAX(2,L)*MAX(2,L)*NB
00120 *
00121 *     Dynamically allocate local arrays
00122 *
00123       ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 
00124      $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 
00125      $           D(N,M), DF(N,M) )
00126 *
00127 *     Put random numbers into A and copy to AF
00128 *
00129       LDT=NB
00130       DO J=1,N
00131          CALL DLARNV( 2, ISEED, M, A( 1, J ) )
00132       END DO
00133       CALL DLACPY( 'Full', M, N, A, M, AF, M )
00134 *
00135 *     Factor the matrix A in the array AF.
00136 *
00137       CALL DGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
00138 *
00139 *     Generate the m-by-m matrix Q
00140 *
00141       CALL DLASET( 'Full', M, M, ZERO, ONE, Q, M )
00142       CALL DGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 
00143      $              WORK, INFO )
00144 *
00145 *     Copy R
00146 *
00147       CALL DLASET( 'Full', M, N, ZERO, ZERO, R, M )
00148       CALL DLACPY( 'Upper', M, N, AF, M, R, M )
00149 *
00150 *     Compute |R - Q'*A| / |A| and store in RESULT(1)
00151 *
00152       CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
00153       ANORM = DLANGE( '1', M, N, A, M, RWORK )
00154       RESID = DLANGE( '1', M, N, R, M, RWORK )
00155       IF( ANORM.GT.ZERO ) THEN
00156          RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
00157       ELSE
00158          RESULT( 1 ) = ZERO
00159       END IF
00160 *
00161 *     Compute |I - Q'*Q| and store in RESULT(2)
00162 *
00163       CALL DLASET( 'Full', M, M, ZERO, ONE, R, M )
00164       CALL DSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M )
00165       RESID = DLANSY( '1', 'Upper', M, R, M, RWORK )
00166       RESULT( 2 ) = RESID / (EPS*MAX(1,M))
00167 *
00168 *     Generate random m-by-n matrix C and a copy CF
00169 *
00170       DO J=1,N
00171          CALL DLARNV( 2, ISEED, M, C( 1, J ) )
00172       END DO
00173       CNORM = DLANGE( '1', M, N, C, M, RWORK)
00174       CALL DLACPY( 'Full', M, N, C, M, CF, M )
00175 *
00176 *     Apply Q to C as Q*C
00177 *
00178       CALL DGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 
00179      $             WORK, LWORK, INFO)
00180 *
00181 *     Compute |Q*C - Q*C| / |C|
00182 *
00183       CALL DGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
00184       RESID = DLANGE( '1', M, N, CF, M, RWORK )
00185       IF( CNORM.GT.ZERO ) THEN
00186          RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
00187       ELSE
00188          RESULT( 3 ) = ZERO
00189       END IF
00190 *
00191 *     Copy C into CF again
00192 *
00193       CALL DLACPY( 'Full', M, N, C, M, CF, M )
00194 *
00195 *     Apply Q to C as QT*C
00196 *
00197       CALL DGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M, 
00198      $             WORK, LWORK, INFO)
00199 *
00200 *     Compute |QT*C - QT*C| / |C|
00201 *
00202       CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
00203       RESID = DLANGE( '1', M, N, CF, M, RWORK )
00204       IF( CNORM.GT.ZERO ) THEN
00205          RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
00206       ELSE
00207          RESULT( 4 ) = ZERO
00208       END IF     
00209 *
00210 *     Generate random n-by-m matrix D and a copy DF
00211 *
00212       DO J=1,M
00213          CALL DLARNV( 2, ISEED, N, D( 1, J ) )
00214       END DO
00215       DNORM = DLANGE( '1', N, M, D, N, RWORK)
00216       CALL DLACPY( 'Full', N, M, D, N, DF, N )
00217 *
00218 *     Apply Q to D as D*Q
00219 *
00220       CALL DGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 
00221      $             WORK, LWORK, INFO)      
00222 *
00223 *     Compute |D*Q - D*Q| / |D|
00224 *
00225       CALL DGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
00226       RESID = DLANGE( '1', N, M, DF, N, RWORK )
00227       IF( CNORM.GT.ZERO ) THEN
00228          RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
00229       ELSE
00230          RESULT( 5 ) = ZERO
00231       END IF
00232 *
00233 *     Copy D into DF again
00234 *
00235       CALL DLACPY( 'Full', N, M, D, N, DF, N )
00236 *
00237 *     Apply Q to D as D*QT
00238 *
00239       CALL DGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N, 
00240      $             WORK, LWORK, INFO)      
00241 *
00242 *     Compute |D*QT - D*QT| / |D|
00243 *
00244       CALL DGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
00245       RESID = DLANGE( '1', N, M, DF, N, RWORK )
00246       IF( CNORM.GT.ZERO ) THEN
00247          RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
00248       ELSE
00249          RESULT( 6 ) = ZERO
00250       END IF
00251 *
00252 *     Deallocate all arrays
00253 *
00254       DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
00255 *
00256       RETURN
00257       END
00258