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*> \ingroup single_lin 132* 133* ===================================================================== 134 SUBROUTINE SLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, 135 $ RWORK, RESULT ) 136* 137* -- LAPACK test routine -- 138* -- LAPACK is a software package provided by Univ. of Tennessee, -- 139* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 140* 141* .. Scalar Arguments .. 142 INTEGER K, LDA, LWORK, M, N 143* .. 144* .. Array Arguments .. 145 REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ), 146 $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), 147 $ WORK( LWORK ) 148* .. 149* 150* ===================================================================== 151* 152* .. Parameters .. 153 REAL ONE 154 PARAMETER ( ONE = 1.0E0 ) 155 REAL ROGUE 156 PARAMETER ( ROGUE = -1.0E+10 ) 157* .. 158* .. Local Scalars .. 159 CHARACTER SIDE, TRANS 160 INTEGER INFO, ISIDE, ITRANS, J, MC, NC 161 REAL CNORM, EPS, RESID 162* .. 163* .. External Functions .. 164 LOGICAL LSAME 165 REAL SLAMCH, SLANGE 166 EXTERNAL LSAME, SLAMCH, SLANGE 167* .. 168* .. External Subroutines .. 169 EXTERNAL SGEMM, SLACPY, SLARNV, SLASET, SORGLQ, SORMLQ 170* .. 171* .. Local Arrays .. 172 INTEGER ISEED( 4 ) 173* .. 174* .. Intrinsic Functions .. 175 INTRINSIC MAX, REAL 176* .. 177* .. Scalars in Common .. 178 CHARACTER*32 SRNAMT 179* .. 180* .. Common blocks .. 181 COMMON / SRNAMC / SRNAMT 182* .. 183* .. Data statements .. 184 DATA ISEED / 1988, 1989, 1990, 1991 / 185* .. 186* .. Executable Statements .. 187* 188 EPS = SLAMCH( 'Epsilon' ) 189* 190* Copy the first k rows of the factorization to the array Q 191* 192 CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) 193 CALL SLACPY( 'Upper', K, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA ) 194* 195* Generate the n-by-n matrix Q 196* 197 SRNAMT = 'SORGLQ' 198 CALL SORGLQ( N, N, K, Q, LDA, TAU, WORK, LWORK, INFO ) 199* 200 DO 30 ISIDE = 1, 2 201 IF( ISIDE.EQ.1 ) THEN 202 SIDE = 'L' 203 MC = N 204 NC = M 205 ELSE 206 SIDE = 'R' 207 MC = M 208 NC = N 209 END IF 210* 211* Generate MC by NC matrix C 212* 213 DO 10 J = 1, NC 214 CALL SLARNV( 2, ISEED, MC, C( 1, J ) ) 215 10 CONTINUE 216 CNORM = SLANGE( '1', MC, NC, C, LDA, RWORK ) 217 IF( CNORM.EQ.0.0 ) 218 $ CNORM = ONE 219* 220 DO 20 ITRANS = 1, 2 221 IF( ITRANS.EQ.1 ) THEN 222 TRANS = 'N' 223 ELSE 224 TRANS = 'T' 225 END IF 226* 227* Copy C 228* 229 CALL SLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) 230* 231* Apply Q or Q' to C 232* 233 SRNAMT = 'SORMLQ' 234 CALL SORMLQ( SIDE, TRANS, MC, NC, K, AF, LDA, TAU, CC, LDA, 235 $ WORK, LWORK, INFO ) 236* 237* Form explicit product and subtract 238* 239 IF( LSAME( SIDE, 'L' ) ) THEN 240 CALL SGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q, 241 $ LDA, C, LDA, ONE, CC, LDA ) 242 ELSE 243 CALL SGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C, 244 $ LDA, Q, LDA, ONE, CC, LDA ) 245 END IF 246* 247* Compute error in the difference 248* 249 RESID = SLANGE( '1', MC, NC, CC, LDA, RWORK ) 250 RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / 251 $ ( REAL( MAX( 1, N ) )*CNORM*EPS ) 252* 253 20 CONTINUE 254 30 CONTINUE 255* 256 RETURN 257* 258* End of SLQT03 259* 260 END 261