1*> \brief \b CQRT04 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 CQRT04(M,N,NB,RESULT) 12* 13* .. Scalar Arguments .. 14* INTEGER M, N, NB, LDT 15* .. Return values .. 16* REAL RESULT(6) 17* 18* 19*> \par Purpose: 20* ============= 21*> 22*> \verbatim 23*> 24*> CQRT04 tests CGEQRT and CGEMQRT. 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 REAL 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*> \date April 2012 70* 71*> \ingroup complex_lin 72* 73* ===================================================================== 74 SUBROUTINE CQRT04(M,N,NB,RESULT) 75 IMPLICIT NONE 76* 77* -- LAPACK test routine (version 3.4.1) -- 78* -- LAPACK is a software package provided by Univ. of Tennessee, -- 79* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 80* April 2012 81* 82* .. Scalar Arguments .. 83 INTEGER M, N, NB, LDT 84* .. Return values .. 85 REAL RESULT(6) 86* 87* ===================================================================== 88* 89* .. 90* .. Local allocatable arrays 91 COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:), 92 $ R(:,:), RWORK(:), WORK( : ), T(:,:), 93 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) 94* 95* .. Parameters .. 96 REAL ZERO 97 COMPLEX ONE, CZERO 98 PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) ) 99* .. 100* .. Local Scalars .. 101 INTEGER INFO, J, K, L, LWORK 102 REAL ANORM, EPS, RESID, CNORM, DNORM 103* .. 104* .. Local Arrays .. 105 INTEGER ISEED( 4 ) 106* .. 107* .. External Functions .. 108 REAL SLAMCH 109 REAL CLANGE, CLANSY 110 LOGICAL LSAME 111 EXTERNAL SLAMCH, CLANGE, CLANSY, LSAME 112* .. 113* .. Intrinsic Functions .. 114 INTRINSIC MAX, MIN 115* .. 116* .. Data statements .. 117 DATA ISEED / 1988, 1989, 1990, 1991 / 118* 119 EPS = SLAMCH( 'Epsilon' ) 120 K = MIN(M,N) 121 L = MAX(M,N) 122 LWORK = MAX(2,L)*MAX(2,L)*NB 123* 124* Dynamically allocate local arrays 125* 126 ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 127 $ WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 128 $ D(N,M), DF(N,M) ) 129* 130* Put random numbers into A and copy to AF 131* 132 LDT=NB 133 DO J=1,N 134 CALL CLARNV( 2, ISEED, M, A( 1, J ) ) 135 END DO 136 CALL CLACPY( 'Full', M, N, A, M, AF, M ) 137* 138* Factor the matrix A in the array AF. 139* 140 CALL CGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO ) 141* 142* Generate the m-by-m matrix Q 143* 144 CALL CLASET( 'Full', M, M, CZERO, ONE, Q, M ) 145 CALL CGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 146 $ WORK, INFO ) 147* 148* Copy R 149* 150 CALL CLASET( 'Full', M, N, CZERO, CZERO, R, M ) 151 CALL CLACPY( 'Upper', M, N, AF, M, R, M ) 152* 153* Compute |R - Q'*A| / |A| and store in RESULT(1) 154* 155 CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M ) 156 ANORM = CLANGE( '1', M, N, A, M, RWORK ) 157 RESID = CLANGE( '1', M, N, R, M, RWORK ) 158 IF( ANORM.GT.ZERO ) THEN 159 RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM) 160 ELSE 161 RESULT( 1 ) = ZERO 162 END IF 163* 164* Compute |I - Q'*Q| and store in RESULT(2) 165* 166 CALL CLASET( 'Full', M, M, CZERO, ONE, R, M ) 167 CALL CHERK( 'U', 'C', M, M, REAL(-ONE), Q, M, REAL(ONE), R, M ) 168 RESID = CLANSY( '1', 'Upper', M, R, M, RWORK ) 169 RESULT( 2 ) = RESID / (EPS*MAX(1,M)) 170* 171* Generate random m-by-n matrix C and a copy CF 172* 173 DO J=1,N 174 CALL CLARNV( 2, ISEED, M, C( 1, J ) ) 175 END DO 176 CNORM = CLANGE( '1', M, N, C, M, RWORK) 177 CALL CLACPY( 'Full', M, N, C, M, CF, M ) 178* 179* Apply Q to C as Q*C 180* 181 CALL CGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 182 $ WORK, INFO) 183* 184* Compute |Q*C - Q*C| / |C| 185* 186 CALL CGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 187 RESID = CLANGE( '1', M, N, CF, M, RWORK ) 188 IF( CNORM.GT.ZERO ) THEN 189 RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM) 190 ELSE 191 RESULT( 3 ) = ZERO 192 END IF 193* 194* Copy C into CF again 195* 196 CALL CLACPY( 'Full', M, N, C, M, CF, M ) 197* 198* Apply Q to C as QT*C 199* 200 CALL CGEMQRT( 'L', 'C', M, N, K, NB, AF, M, T, NB, CF, M, 201 $ WORK, INFO) 202* 203* Compute |QT*C - QT*C| / |C| 204* 205 CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 206 RESID = CLANGE( '1', M, N, CF, M, RWORK ) 207 IF( CNORM.GT.ZERO ) THEN 208 RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM) 209 ELSE 210 RESULT( 4 ) = ZERO 211 END IF 212* 213* Generate random n-by-m matrix D and a copy DF 214* 215 DO J=1,M 216 CALL CLARNV( 2, ISEED, N, D( 1, J ) ) 217 END DO 218 DNORM = CLANGE( '1', N, M, D, N, RWORK) 219 CALL CLACPY( 'Full', N, M, D, N, DF, N ) 220* 221* Apply Q to D as D*Q 222* 223 CALL CGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 224 $ WORK, INFO) 225* 226* Compute |D*Q - D*Q| / |D| 227* 228 CALL CGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 229 RESID = CLANGE( '1', N, M, DF, N, RWORK ) 230 IF( CNORM.GT.ZERO ) THEN 231 RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM) 232 ELSE 233 RESULT( 5 ) = ZERO 234 END IF 235* 236* Copy D into DF again 237* 238 CALL CLACPY( 'Full', N, M, D, N, DF, N ) 239* 240* Apply Q to D as D*QT 241* 242 CALL CGEMQRT( 'R', 'C', N, M, K, NB, AF, M, T, NB, DF, N, 243 $ WORK, INFO) 244* 245* Compute |D*QT - D*QT| / |D| 246* 247 CALL CGEMM( 'N', 'C', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 248 RESID = CLANGE( '1', N, M, DF, N, RWORK ) 249 IF( CNORM.GT.ZERO ) THEN 250 RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM) 251 ELSE 252 RESULT( 6 ) = ZERO 253 END IF 254* 255* Deallocate all arrays 256* 257 DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) 258* 259 RETURN 260 END 261 262