1*> \brief \b ZQLT03 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 ZQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, 12* RWORK, RESULT ) 13* 14* .. Scalar Arguments .. 15* INTEGER K, LDA, LWORK, M, N 16* .. 17* .. Array Arguments .. 18* DOUBLE PRECISION RESULT( * ), RWORK( * ) 19* COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ), 20* $ Q( LDA, * ), TAU( * ), WORK( LWORK ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> ZQLT03 tests ZUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'. 30*> 31*> ZQLT03 compares the results of a call to ZUNMQL with the results of 32*> forming Q explicitly by a call to ZUNGQL and then performing matrix 33*> multiplication by a call to ZGEMM. 34*> \endverbatim 35* 36* Arguments: 37* ========== 38* 39*> \param[in] M 40*> \verbatim 41*> M is INTEGER 42*> The order of the orthogonal matrix Q. M >= 0. 43*> \endverbatim 44*> 45*> \param[in] N 46*> \verbatim 47*> N is INTEGER 48*> The number of rows or columns of the matrix C; C is m-by-n if 49*> Q is applied from the left, or n-by-m if Q is applied from 50*> the right. N >= 0. 51*> \endverbatim 52*> 53*> \param[in] K 54*> \verbatim 55*> K is INTEGER 56*> The number of elementary reflectors whose product defines the 57*> orthogonal matrix Q. M >= K >= 0. 58*> \endverbatim 59*> 60*> \param[in] AF 61*> \verbatim 62*> AF is COMPLEX*16 array, dimension (LDA,N) 63*> Details of the QL factorization of an m-by-n matrix, as 64*> returned by ZGEQLF. See CGEQLF for further details. 65*> \endverbatim 66*> 67*> \param[out] C 68*> \verbatim 69*> C is COMPLEX*16 array, dimension (LDA,N) 70*> \endverbatim 71*> 72*> \param[out] CC 73*> \verbatim 74*> CC is COMPLEX*16 array, dimension (LDA,N) 75*> \endverbatim 76*> 77*> \param[out] Q 78*> \verbatim 79*> Q is COMPLEX*16 array, dimension (LDA,M) 80*> \endverbatim 81*> 82*> \param[in] LDA 83*> \verbatim 84*> LDA is INTEGER 85*> The leading dimension of the arrays AF, C, CC, and Q. 86*> \endverbatim 87*> 88*> \param[in] TAU 89*> \verbatim 90*> TAU is COMPLEX*16 array, dimension (min(M,N)) 91*> The scalar factors of the elementary reflectors corresponding 92*> to the QL factorization in AF. 93*> \endverbatim 94*> 95*> \param[out] WORK 96*> \verbatim 97*> WORK is COMPLEX*16 array, dimension (LWORK) 98*> \endverbatim 99*> 100*> \param[in] LWORK 101*> \verbatim 102*> LWORK is INTEGER 103*> The length of WORK. LWORK must be at least M, and should be 104*> M*NB, where NB is the blocksize for this environment. 105*> \endverbatim 106*> 107*> \param[out] RWORK 108*> \verbatim 109*> RWORK is DOUBLE PRECISION array, dimension (M) 110*> \endverbatim 111*> 112*> \param[out] RESULT 113*> \verbatim 114*> RESULT is DOUBLE PRECISION array, dimension (4) 115*> The test ratios compare two techniques for multiplying a 116*> random matrix C by an m-by-m orthogonal matrix Q. 117*> RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS ) 118*> RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS ) 119*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS ) 120*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS ) 121*> \endverbatim 122* 123* Authors: 124* ======== 125* 126*> \author Univ. of Tennessee 127*> \author Univ. of California Berkeley 128*> \author Univ. of Colorado Denver 129*> \author NAG Ltd. 130* 131*> \date December 2016 132* 133*> \ingroup complex16_lin 134* 135* ===================================================================== 136 SUBROUTINE ZQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, 137 $ RWORK, RESULT ) 138* 139* -- LAPACK test routine (version 3.7.0) -- 140* -- LAPACK is a software package provided by Univ. of Tennessee, -- 141* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 142* December 2016 143* 144* .. Scalar Arguments .. 145 INTEGER K, LDA, LWORK, M, N 146* .. 147* .. Array Arguments .. 148 DOUBLE PRECISION RESULT( * ), RWORK( * ) 149 COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ), 150 $ Q( LDA, * ), TAU( * ), WORK( LWORK ) 151* .. 152* 153* ===================================================================== 154* 155* .. Parameters .. 156 DOUBLE PRECISION ZERO, ONE 157 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 158 COMPLEX*16 ROGUE 159 PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) ) 160* .. 161* .. Local Scalars .. 162 CHARACTER SIDE, TRANS 163 INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC 164 DOUBLE PRECISION CNORM, EPS, RESID 165* .. 166* .. External Functions .. 167 LOGICAL LSAME 168 DOUBLE PRECISION DLAMCH, ZLANGE 169 EXTERNAL LSAME, DLAMCH, ZLANGE 170* .. 171* .. External Subroutines .. 172 EXTERNAL ZGEMM, ZLACPY, ZLARNV, ZLASET, ZUNGQL, ZUNMQL 173* .. 174* .. Local Arrays .. 175 INTEGER ISEED( 4 ) 176* .. 177* .. Intrinsic Functions .. 178 INTRINSIC DBLE, DCMPLX, MAX, MIN 179* .. 180* .. Scalars in Common .. 181 CHARACTER*32 SRNAMT 182* .. 183* .. Common blocks .. 184 COMMON / SRNAMC / SRNAMT 185* .. 186* .. Data statements .. 187 DATA ISEED / 1988, 1989, 1990, 1991 / 188* .. 189* .. Executable Statements .. 190* 191 EPS = DLAMCH( 'Epsilon' ) 192 MINMN = MIN( M, N ) 193* 194* Quick return if possible 195* 196 IF( MINMN.EQ.0 ) THEN 197 RESULT( 1 ) = ZERO 198 RESULT( 2 ) = ZERO 199 RESULT( 3 ) = ZERO 200 RESULT( 4 ) = ZERO 201 RETURN 202 END IF 203* 204* Copy the last k columns of the factorization to the array Q 205* 206 CALL ZLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) 207 IF( K.GT.0 .AND. M.GT.K ) 208 $ CALL ZLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA, 209 $ Q( 1, M-K+1 ), LDA ) 210 IF( K.GT.1 ) 211 $ CALL ZLACPY( 'Upper', K-1, K-1, AF( M-K+1, N-K+2 ), LDA, 212 $ Q( M-K+1, M-K+2 ), LDA ) 213* 214* Generate the m-by-m matrix Q 215* 216 SRNAMT = 'ZUNGQL' 217 CALL ZUNGQL( M, M, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK, 218 $ INFO ) 219* 220 DO 30 ISIDE = 1, 2 221 IF( ISIDE.EQ.1 ) THEN 222 SIDE = 'L' 223 MC = M 224 NC = N 225 ELSE 226 SIDE = 'R' 227 MC = N 228 NC = M 229 END IF 230* 231* Generate MC by NC matrix C 232* 233 DO 10 J = 1, NC 234 CALL ZLARNV( 2, ISEED, MC, C( 1, J ) ) 235 10 CONTINUE 236 CNORM = ZLANGE( '1', MC, NC, C, LDA, RWORK ) 237 IF( CNORM.EQ.ZERO ) 238 $ CNORM = ONE 239* 240 DO 20 ITRANS = 1, 2 241 IF( ITRANS.EQ.1 ) THEN 242 TRANS = 'N' 243 ELSE 244 TRANS = 'C' 245 END IF 246* 247* Copy C 248* 249 CALL ZLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) 250* 251* Apply Q or Q' to C 252* 253 SRNAMT = 'ZUNMQL' 254 IF( K.GT.0 ) 255 $ CALL ZUNMQL( SIDE, TRANS, MC, NC, K, AF( 1, N-K+1 ), LDA, 256 $ TAU( MINMN-K+1 ), CC, LDA, WORK, LWORK, 257 $ INFO ) 258* 259* Form explicit product and subtract 260* 261 IF( LSAME( SIDE, 'L' ) ) THEN 262 CALL ZGEMM( TRANS, 'No transpose', MC, NC, MC, 263 $ DCMPLX( -ONE ), Q, LDA, C, LDA, 264 $ DCMPLX( ONE ), CC, LDA ) 265 ELSE 266 CALL ZGEMM( 'No transpose', TRANS, MC, NC, NC, 267 $ DCMPLX( -ONE ), C, LDA, Q, LDA, 268 $ DCMPLX( ONE ), CC, LDA ) 269 END IF 270* 271* Compute error in the difference 272* 273 RESID = ZLANGE( '1', MC, NC, CC, LDA, RWORK ) 274 RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / 275 $ ( DBLE( MAX( 1, M ) )*CNORM*EPS ) 276* 277 20 CONTINUE 278 30 CONTINUE 279* 280 RETURN 281* 282* End of ZQLT03 283* 284 END 285