1*> \brief \b SLQT03 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 SLQT03( 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* REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ), 19* $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), 20* $ WORK( LWORK ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> SLQT03 tests SORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'. 30*> 31*> SLQT03 compares the results of a call to SORMLQ with the results of 32*> forming Q explicitly by a call to SORGLQ and then performing matrix 33*> multiplication by a call to SGEMM. 34*> \endverbatim 35* 36* Arguments: 37* ========== 38* 39*> \param[in] M 40*> \verbatim 41*> M is INTEGER 42*> The number of rows or columns of the matrix C; C is n-by-m if 43*> Q is applied from the left, or m-by-n if Q is applied from 44*> the right. M >= 0. 45*> \endverbatim 46*> 47*> \param[in] N 48*> \verbatim 49*> N is INTEGER 50*> The order of the orthogonal matrix Q. 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. N >= K >= 0. 58*> \endverbatim 59*> 60*> \param[in] AF 61*> \verbatim 62*> AF is REAL array, dimension (LDA,N) 63*> Details of the LQ factorization of an m-by-n matrix, as 64*> returned by SGELQF. See SGELQF for further details. 65*> \endverbatim 66*> 67*> \param[out] C 68*> \verbatim 69*> C is REAL array, dimension (LDA,N) 70*> \endverbatim 71*> 72*> \param[out] CC 73*> \verbatim 74*> CC is REAL array, dimension (LDA,N) 75*> \endverbatim 76*> 77*> \param[out] Q 78*> \verbatim 79*> Q is REAL array, dimension (LDA,N) 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 REAL array, dimension (min(M,N)) 91*> The scalar factors of the elementary reflectors corresponding 92*> to the LQ factorization in AF. 93*> \endverbatim 94*> 95*> \param[out] WORK 96*> \verbatim 97*> WORK is REAL 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 REAL array, dimension (M) 110*> \endverbatim 111*> 112*> \param[out] RESULT 113*> \verbatim 114*> RESULT is REAL array, dimension (4) 115*> The test ratios compare two techniques for multiplying a 116*> random matrix C by an n-by-n orthogonal matrix Q. 117*> RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS ) 118*> RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS ) 119*> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) 120*> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * 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 November 2011 132* 133*> \ingroup single_lin 134* 135* ===================================================================== 136 SUBROUTINE SLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, 137 $ RWORK, RESULT ) 138* 139* -- LAPACK test routine (version 3.4.0) -- 140* -- LAPACK is a software package provided by Univ. of Tennessee, -- 141* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 142* November 2011 143* 144* .. Scalar Arguments .. 145 INTEGER K, LDA, LWORK, M, N 146* .. 147* .. Array Arguments .. 148 REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ), 149 $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), 150 $ WORK( LWORK ) 151* .. 152* 153* ===================================================================== 154* 155* .. Parameters .. 156 REAL ONE 157 PARAMETER ( ONE = 1.0E0 ) 158 REAL ROGUE 159 PARAMETER ( ROGUE = -1.0E+10 ) 160* .. 161* .. Local Scalars .. 162 CHARACTER SIDE, TRANS 163 INTEGER INFO, ISIDE, ITRANS, J, MC, NC 164 REAL CNORM, EPS, RESID 165* .. 166* .. External Functions .. 167 LOGICAL LSAME 168 REAL SLAMCH, SLANGE 169 EXTERNAL LSAME, SLAMCH, SLANGE 170* .. 171* .. External Subroutines .. 172 EXTERNAL SGEMM, SLACPY, SLARNV, SLASET, SORGLQ, SORMLQ 173* .. 174* .. Local Arrays .. 175 INTEGER ISEED( 4 ) 176* .. 177* .. Intrinsic Functions .. 178 INTRINSIC MAX, REAL 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 = SLAMCH( 'Epsilon' ) 192* 193* Copy the first k rows of the factorization to the array Q 194* 195 CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) 196 CALL SLACPY( 'Upper', K, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA ) 197* 198* Generate the n-by-n matrix Q 199* 200 SRNAMT = 'SORGLQ' 201 CALL SORGLQ( N, N, K, Q, LDA, TAU, WORK, LWORK, INFO ) 202* 203 DO 30 ISIDE = 1, 2 204 IF( ISIDE.EQ.1 ) THEN 205 SIDE = 'L' 206 MC = N 207 NC = M 208 ELSE 209 SIDE = 'R' 210 MC = M 211 NC = N 212 END IF 213* 214* Generate MC by NC matrix C 215* 216 DO 10 J = 1, NC 217 CALL SLARNV( 2, ISEED, MC, C( 1, J ) ) 218 10 CONTINUE 219 CNORM = SLANGE( '1', MC, NC, C, LDA, RWORK ) 220 IF( CNORM.EQ.0.0 ) 221 $ CNORM = ONE 222* 223 DO 20 ITRANS = 1, 2 224 IF( ITRANS.EQ.1 ) THEN 225 TRANS = 'N' 226 ELSE 227 TRANS = 'T' 228 END IF 229* 230* Copy C 231* 232 CALL SLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) 233* 234* Apply Q or Q' to C 235* 236 SRNAMT = 'SORMLQ' 237 CALL SORMLQ( SIDE, TRANS, MC, NC, K, AF, LDA, TAU, CC, LDA, 238 $ WORK, LWORK, INFO ) 239* 240* Form explicit product and subtract 241* 242 IF( LSAME( SIDE, 'L' ) ) THEN 243 CALL SGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q, 244 $ LDA, C, LDA, ONE, CC, LDA ) 245 ELSE 246 CALL SGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C, 247 $ LDA, Q, LDA, ONE, CC, LDA ) 248 END IF 249* 250* Compute error in the difference 251* 252 RESID = SLANGE( '1', MC, NC, CC, LDA, RWORK ) 253 RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / 254 $ ( REAL( MAX( 1, N ) )*CNORM*EPS ) 255* 256 20 CONTINUE 257 30 CONTINUE 258* 259 RETURN 260* 261* End of SLQT03 262* 263 END 264