1*> \brief \b ZQRT04 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE ZQRT04(M,N,NB,RESULT) 12* 13* .. Scalar Arguments .. 14* INTEGER M, N, NB, LDT 15* .. Return values .. 16* DOUBLE PRECISION RESULT(6) 17* 18* 19*> \par Purpose: 20* ============= 21*> 22*> \verbatim 23*> 24*> ZQRT04 tests ZGEQRT and ZGEMQRT. 25*> \endverbatim 26* 27* Arguments: 28* ========== 29* 30*> \param[in] M 31*> \verbatim 32*> M is INTEGER 33*> Number of rows in test matrix. 34*> \endverbatim 35*> 36*> \param[in] N 37*> \verbatim 38*> N is INTEGER 39*> Number of columns in test matrix. 40*> \endverbatim 41*> 42*> \param[in] NB 43*> \verbatim 44*> NB is INTEGER 45*> Block size of test matrix. NB <= Min(M,N). 46*> \endverbatim 47*> 48*> \param[out] RESULT 49*> \verbatim 50*> RESULT is DOUBLE PRECISION array, dimension (6) 51*> Results of each of the six tests below. 52*> 53*> RESULT(1) = | A - Q R | 54*> RESULT(2) = | I - Q^H Q | 55*> RESULT(3) = | Q C - Q C | 56*> RESULT(4) = | Q^H C - Q^H C | 57*> RESULT(5) = | C Q - C Q | 58*> RESULT(6) = | C Q^H - C Q^H | 59*> \endverbatim 60* 61* Authors: 62* ======== 63* 64*> \author Univ. of Tennessee 65*> \author Univ. of California Berkeley 66*> \author Univ. of Colorado Denver 67*> \author NAG Ltd. 68* 69*> \ingroup complex16_lin 70* 71* ===================================================================== 72 SUBROUTINE ZQRT04(M,N,NB,RESULT) 73 IMPLICIT NONE 74* 75* -- LAPACK test routine -- 76* -- LAPACK is a software package provided by Univ. of Tennessee, -- 77* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 78* 79* .. Scalar Arguments .. 80 INTEGER M, N, NB, LDT 81* .. Return values .. 82 DOUBLE PRECISION RESULT(6) 83* 84* ===================================================================== 85* 86* .. 87* .. Local allocatable arrays 88 COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:), 89 $ R(:,:), WORK( : ), T(:,:), 90 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) 91 DOUBLE PRECISION, ALLOCATABLE :: RWORK(:) 92* 93* .. Parameters .. 94 DOUBLE PRECISION ZERO 95 COMPLEX*16 ONE, CZERO 96 PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) ) 97* .. 98* .. Local Scalars .. 99 INTEGER INFO, J, K, L, LWORK 100 DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM 101* .. 102* .. Local Arrays .. 103 INTEGER ISEED( 4 ) 104* .. 105* .. External Functions .. 106 DOUBLE PRECISION DLAMCH 107 DOUBLE PRECISION ZLANGE, ZLANSY 108 LOGICAL LSAME 109 EXTERNAL DLAMCH, ZLANGE, ZLANSY, LSAME 110* .. 111* .. Intrinsic Functions .. 112 INTRINSIC MAX, MIN 113* .. 114* .. Data statements .. 115 DATA ISEED / 1988, 1989, 1990, 1991 / 116* 117 EPS = DLAMCH( 'Epsilon' ) 118 K = MIN(M,N) 119 L = MAX(M,N) 120 LWORK = MAX(2,L)*MAX(2,L)*NB 121* 122* Dynamically allocate local arrays 123* 124 ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 125 $ WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 126 $ D(N,M), DF(N,M) ) 127* 128* Put random numbers into A and copy to AF 129* 130 LDT=NB 131 DO J=1,N 132 CALL ZLARNV( 2, ISEED, M, A( 1, J ) ) 133 END DO 134 CALL ZLACPY( 'Full', M, N, A, M, AF, M ) 135* 136* Factor the matrix A in the array AF. 137* 138 CALL ZGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO ) 139* 140* Generate the m-by-m matrix Q 141* 142 CALL ZLASET( 'Full', M, M, CZERO, ONE, Q, M ) 143 CALL ZGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 144 $ WORK, INFO ) 145* 146* Copy R 147* 148 CALL ZLASET( 'Full', M, N, CZERO, CZERO, R, M ) 149 CALL ZLACPY( 'Upper', M, N, AF, M, R, M ) 150* 151* Compute |R - Q'*A| / |A| and store in RESULT(1) 152* 153 CALL ZGEMM( 'C', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M ) 154 ANORM = ZLANGE( '1', M, N, A, M, RWORK ) 155 RESID = ZLANGE( '1', M, N, R, M, RWORK ) 156 IF( ANORM.GT.ZERO ) THEN 157 RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM) 158 ELSE 159 RESULT( 1 ) = ZERO 160 END IF 161* 162* Compute |I - Q'*Q| and store in RESULT(2) 163* 164 CALL ZLASET( 'Full', M, M, CZERO, ONE, R, M ) 165 CALL ZHERK( 'U', 'C', M, M, DREAL(-ONE), Q, M, DREAL(ONE), R, M ) 166 RESID = ZLANSY( '1', 'Upper', M, R, M, RWORK ) 167 RESULT( 2 ) = RESID / (EPS*MAX(1,M)) 168* 169* Generate random m-by-n matrix C and a copy CF 170* 171 DO J=1,N 172 CALL ZLARNV( 2, ISEED, M, C( 1, J ) ) 173 END DO 174 CNORM = ZLANGE( '1', M, N, C, M, RWORK) 175 CALL ZLACPY( 'Full', M, N, C, M, CF, M ) 176* 177* Apply Q to C as Q*C 178* 179 CALL ZGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 180 $ WORK, INFO) 181* 182* Compute |Q*C - Q*C| / |C| 183* 184 CALL ZGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 185 RESID = ZLANGE( '1', M, N, CF, M, RWORK ) 186 IF( CNORM.GT.ZERO ) THEN 187 RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM) 188 ELSE 189 RESULT( 3 ) = ZERO 190 END IF 191* 192* Copy C into CF again 193* 194 CALL ZLACPY( 'Full', M, N, C, M, CF, M ) 195* 196* Apply Q to C as QT*C 197* 198 CALL ZGEMQRT( 'L', 'C', M, N, K, NB, AF, M, T, NB, CF, M, 199 $ WORK, INFO) 200* 201* Compute |QT*C - QT*C| / |C| 202* 203 CALL ZGEMM( 'C', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 204 RESID = ZLANGE( '1', M, N, CF, M, RWORK ) 205 IF( CNORM.GT.ZERO ) THEN 206 RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM) 207 ELSE 208 RESULT( 4 ) = ZERO 209 END IF 210* 211* Generate random n-by-m matrix D and a copy DF 212* 213 DO J=1,M 214 CALL ZLARNV( 2, ISEED, N, D( 1, J ) ) 215 END DO 216 DNORM = ZLANGE( '1', N, M, D, N, RWORK) 217 CALL ZLACPY( 'Full', N, M, D, N, DF, N ) 218* 219* Apply Q to D as D*Q 220* 221 CALL ZGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 222 $ WORK, INFO) 223* 224* Compute |D*Q - D*Q| / |D| 225* 226 CALL ZGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 227 RESID = ZLANGE( '1', N, M, DF, N, RWORK ) 228 IF( CNORM.GT.ZERO ) THEN 229 RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM) 230 ELSE 231 RESULT( 5 ) = ZERO 232 END IF 233* 234* Copy D into DF again 235* 236 CALL ZLACPY( 'Full', N, M, D, N, DF, N ) 237* 238* Apply Q to D as D*QT 239* 240 CALL ZGEMQRT( 'R', 'C', N, M, K, NB, AF, M, T, NB, DF, N, 241 $ WORK, INFO) 242* 243* Compute |D*QT - D*QT| / |D| 244* 245 CALL ZGEMM( 'N', 'C', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 246 RESID = ZLANGE( '1', N, M, DF, N, RWORK ) 247 IF( CNORM.GT.ZERO ) THEN 248 RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM) 249 ELSE 250 RESULT( 6 ) = ZERO 251 END IF 252* 253* Deallocate all arrays 254* 255 DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) 256* 257 RETURN 258 END 259 260