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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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 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 April 2012 00070 * 00071 *> \ingroup double_lin 00072 * 00073 * ===================================================================== 00074 SUBROUTINE DQRT04(M,N,NB,RESULT) 00075 IMPLICIT NONE 00076 * 00077 * -- LAPACK test routine (version 3.4.1) -- 00078 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00079 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00080 * April 2012 00081 * 00082 * .. Scalar Arguments .. 00083 INTEGER M, N, NB, LDT 00084 * .. Return values .. 00085 DOUBLE PRECISION RESULT(6) 00086 * 00087 * ===================================================================== 00088 * 00089 * .. 00090 * .. Local allocatable arrays 00091 DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:), 00092 $ R(:,:), RWORK(:), WORK( : ), T(:,:), 00093 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) 00094 * 00095 * .. Parameters .. 00096 DOUBLE PRECISION ONE, ZERO 00097 PARAMETER( ZERO = 0.0, ONE = 1.0 ) 00098 * .. 00099 * .. Local Scalars .. 00100 INTEGER INFO, J, K, L, LWORK 00101 DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM 00102 * .. 00103 * .. Local Arrays .. 00104 INTEGER ISEED( 4 ) 00105 * .. 00106 * .. External Functions .. 00107 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY 00108 LOGICAL LSAME 00109 EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME 00110 * .. 00111 * .. Intrinsic Functions .. 00112 INTRINSIC MAX, MIN 00113 * .. 00114 * .. Data statements .. 00115 DATA ISEED / 1988, 1989, 1990, 1991 / 00116 * 00117 EPS = DLAMCH( 'Epsilon' ) 00118 K = MIN(M,N) 00119 L = MAX(M,N) 00120 LWORK = MAX(2,L)*MAX(2,L)*NB 00121 * 00122 * Dynamically allocate local arrays 00123 * 00124 ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 00125 $ WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 00126 $ D(N,M), DF(N,M) ) 00127 * 00128 * Put random numbers into A and copy to AF 00129 * 00130 LDT=NB 00131 DO J=1,N 00132 CALL DLARNV( 2, ISEED, M, A( 1, J ) ) 00133 END DO 00134 CALL DLACPY( 'Full', M, N, A, M, AF, M ) 00135 * 00136 * Factor the matrix A in the array AF. 00137 * 00138 CALL DGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO ) 00139 * 00140 * Generate the m-by-m matrix Q 00141 * 00142 CALL DLASET( 'Full', M, M, ZERO, ONE, Q, M ) 00143 CALL DGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 00144 $ WORK, INFO ) 00145 * 00146 * Copy R 00147 * 00148 CALL DLASET( 'Full', M, N, ZERO, ZERO, R, M ) 00149 CALL DLACPY( 'Upper', M, N, AF, M, R, M ) 00150 * 00151 * Compute |R - Q'*A| / |A| and store in RESULT(1) 00152 * 00153 CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M ) 00154 ANORM = DLANGE( '1', M, N, A, M, RWORK ) 00155 RESID = DLANGE( '1', M, N, R, M, RWORK ) 00156 IF( ANORM.GT.ZERO ) THEN 00157 RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM) 00158 ELSE 00159 RESULT( 1 ) = ZERO 00160 END IF 00161 * 00162 * Compute |I - Q'*Q| and store in RESULT(2) 00163 * 00164 CALL DLASET( 'Full', M, M, ZERO, ONE, R, M ) 00165 CALL DSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M ) 00166 RESID = DLANSY( '1', 'Upper', M, R, M, RWORK ) 00167 RESULT( 2 ) = RESID / (EPS*MAX(1,M)) 00168 * 00169 * Generate random m-by-n matrix C and a copy CF 00170 * 00171 DO J=1,N 00172 CALL DLARNV( 2, ISEED, M, C( 1, J ) ) 00173 END DO 00174 CNORM = DLANGE( '1', M, N, C, M, RWORK) 00175 CALL DLACPY( 'Full', M, N, C, M, CF, M ) 00176 * 00177 * Apply Q to C as Q*C 00178 * 00179 CALL DGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 00180 $ WORK, INFO) 00181 * 00182 * Compute |Q*C - Q*C| / |C| 00183 * 00184 CALL DGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 00185 RESID = DLANGE( '1', M, N, CF, M, RWORK ) 00186 IF( CNORM.GT.ZERO ) THEN 00187 RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM) 00188 ELSE 00189 RESULT( 3 ) = ZERO 00190 END IF 00191 * 00192 * Copy C into CF again 00193 * 00194 CALL DLACPY( 'Full', M, N, C, M, CF, M ) 00195 * 00196 * Apply Q to C as QT*C 00197 * 00198 CALL DGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M, 00199 $ WORK, INFO) 00200 * 00201 * Compute |QT*C - QT*C| / |C| 00202 * 00203 CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 00204 RESID = DLANGE( '1', M, N, CF, M, RWORK ) 00205 IF( CNORM.GT.ZERO ) THEN 00206 RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM) 00207 ELSE 00208 RESULT( 4 ) = ZERO 00209 END IF 00210 * 00211 * Generate random n-by-m matrix D and a copy DF 00212 * 00213 DO J=1,M 00214 CALL DLARNV( 2, ISEED, N, D( 1, J ) ) 00215 END DO 00216 DNORM = DLANGE( '1', N, M, D, N, RWORK) 00217 CALL DLACPY( 'Full', N, M, D, N, DF, N ) 00218 * 00219 * Apply Q to D as D*Q 00220 * 00221 CALL DGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 00222 $ WORK, INFO) 00223 * 00224 * Compute |D*Q - D*Q| / |D| 00225 * 00226 CALL DGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 00227 RESID = DLANGE( '1', N, M, DF, N, RWORK ) 00228 IF( CNORM.GT.ZERO ) THEN 00229 RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM) 00230 ELSE 00231 RESULT( 5 ) = ZERO 00232 END IF 00233 * 00234 * Copy D into DF again 00235 * 00236 CALL DLACPY( 'Full', N, M, D, N, DF, N ) 00237 * 00238 * Apply Q to D as D*QT 00239 * 00240 CALL DGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N, 00241 $ WORK, INFO) 00242 * 00243 * Compute |D*QT - D*QT| / |D| 00244 * 00245 CALL DGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 00246 RESID = DLANGE( '1', N, M, DF, N, RWORK ) 00247 IF( CNORM.GT.ZERO ) THEN 00248 RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM) 00249 ELSE 00250 RESULT( 6 ) = ZERO 00251 END IF 00252 * 00253 * Deallocate all arrays 00254 * 00255 DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) 00256 * 00257 RETURN 00258 END 00259