1*> \brief \b SCHKQ3 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 SCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, 12* THRESH, A, COPYA, S, TAU, WORK, IWORK, 13* NOUT ) 14* 15* .. Scalar Arguments .. 16* INTEGER NM, NN, NNB, NOUT 17* REAL THRESH 18* .. 19* .. Array Arguments .. 20* LOGICAL DOTYPE( * ) 21* INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ), 22* $ NXVAL( * ) 23* REAL A( * ), COPYA( * ), S( * ), 24* $ TAU( * ), WORK( * ) 25* .. 26* 27* 28*> \par Purpose: 29* ============= 30*> 31*> \verbatim 32*> 33*> SCHKQ3 tests SGEQP3. 34*> \endverbatim 35* 36* Arguments: 37* ========== 38* 39*> \param[in] DOTYPE 40*> \verbatim 41*> DOTYPE is LOGICAL array, dimension (NTYPES) 42*> The matrix types to be used for testing. Matrices of type j 43*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = 44*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. 45*> \endverbatim 46*> 47*> \param[in] NM 48*> \verbatim 49*> NM is INTEGER 50*> The number of values of M contained in the vector MVAL. 51*> \endverbatim 52*> 53*> \param[in] MVAL 54*> \verbatim 55*> MVAL is INTEGER array, dimension (NM) 56*> The values of the matrix row dimension M. 57*> \endverbatim 58*> 59*> \param[in] NN 60*> \verbatim 61*> NN is INTEGER 62*> The number of values of N contained in the vector NVAL. 63*> \endverbatim 64*> 65*> \param[in] NVAL 66*> \verbatim 67*> NVAL is INTEGER array, dimension (NN) 68*> The values of the matrix column dimension N. 69*> \endverbatim 70*> 71*> \param[in] NNB 72*> \verbatim 73*> NNB is INTEGER 74*> The number of values of NB and NX contained in the 75*> vectors NBVAL and NXVAL. The blocking parameters are used 76*> in pairs (NB,NX). 77*> \endverbatim 78*> 79*> \param[in] NBVAL 80*> \verbatim 81*> NBVAL is INTEGER array, dimension (NNB) 82*> The values of the blocksize NB. 83*> \endverbatim 84*> 85*> \param[in] NXVAL 86*> \verbatim 87*> NXVAL is INTEGER array, dimension (NNB) 88*> The values of the crossover point NX. 89*> \endverbatim 90*> 91*> \param[in] THRESH 92*> \verbatim 93*> THRESH is REAL 94*> The threshold value for the test ratios. A result is 95*> included in the output file if RESULT >= THRESH. To have 96*> every test ratio printed, use THRESH = 0. 97*> \endverbatim 98*> 99*> \param[out] A 100*> \verbatim 101*> A is REAL array, dimension (MMAX*NMAX) 102*> where MMAX is the maximum value of M in MVAL and NMAX is the 103*> maximum value of N in NVAL. 104*> \endverbatim 105*> 106*> \param[out] COPYA 107*> \verbatim 108*> COPYA is REAL array, dimension (MMAX*NMAX) 109*> \endverbatim 110*> 111*> \param[out] S 112*> \verbatim 113*> S is REAL array, dimension 114*> (min(MMAX,NMAX)) 115*> \endverbatim 116*> 117*> \param[out] TAU 118*> \verbatim 119*> TAU is REAL array, dimension (MMAX) 120*> \endverbatim 121*> 122*> \param[out] WORK 123*> \verbatim 124*> WORK is REAL array, dimension 125*> (MMAX*NMAX + 4*NMAX + MMAX) 126*> \endverbatim 127*> 128*> \param[out] IWORK 129*> \verbatim 130*> IWORK is INTEGER array, dimension (2*NMAX) 131*> \endverbatim 132*> 133*> \param[in] NOUT 134*> \verbatim 135*> NOUT is INTEGER 136*> The unit number for output. 137*> \endverbatim 138* 139* Authors: 140* ======== 141* 142*> \author Univ. of Tennessee 143*> \author Univ. of California Berkeley 144*> \author Univ. of Colorado Denver 145*> \author NAG Ltd. 146* 147*> \ingroup single_lin 148* 149* ===================================================================== 150 SUBROUTINE SCHKQ3( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, 151 $ THRESH, A, COPYA, S, TAU, WORK, IWORK, 152 $ NOUT ) 153* 154* -- LAPACK test routine -- 155* -- LAPACK is a software package provided by Univ. of Tennessee, -- 156* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 157* 158* .. Scalar Arguments .. 159 INTEGER NM, NN, NNB, NOUT 160 REAL THRESH 161* .. 162* .. Array Arguments .. 163 LOGICAL DOTYPE( * ) 164 INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ), 165 $ NXVAL( * ) 166 REAL A( * ), COPYA( * ), S( * ), 167 $ TAU( * ), WORK( * ) 168* .. 169* 170* ===================================================================== 171* 172* .. Parameters .. 173 INTEGER NTYPES 174 PARAMETER ( NTYPES = 6 ) 175 INTEGER NTESTS 176 PARAMETER ( NTESTS = 3 ) 177 REAL ONE, ZERO 178 PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 ) 179* .. 180* .. Local Scalars .. 181 CHARACTER*3 PATH 182 INTEGER I, IHIGH, ILOW, IM, IMODE, IN, INB, INFO, 183 $ ISTEP, K, LDA, LW, LWORK, M, MNMIN, MODE, N, 184 $ NB, NERRS, NFAIL, NRUN, NX 185 REAL EPS 186* .. 187* .. Local Arrays .. 188 INTEGER ISEED( 4 ), ISEEDY( 4 ) 189 REAL RESULT( NTESTS ) 190* .. 191* .. External Functions .. 192 REAL SLAMCH, SQPT01, SQRT11, SQRT12 193 EXTERNAL SLAMCH, SQPT01, SQRT11, SQRT12 194* .. 195* .. External Subroutines .. 196 EXTERNAL ALAHD, ALASUM, ICOPY, SGEQP3, SLACPY, SLAORD, 197 $ SLASET, SLATMS, XLAENV 198* .. 199* .. Intrinsic Functions .. 200 INTRINSIC MAX, MIN 201* .. 202* .. Scalars in Common .. 203 LOGICAL LERR, OK 204 CHARACTER*32 SRNAMT 205 INTEGER INFOT, IOUNIT 206* .. 207* .. Common blocks .. 208 COMMON / INFOC / INFOT, IOUNIT, OK, LERR 209 COMMON / SRNAMC / SRNAMT 210* .. 211* .. Data statements .. 212 DATA ISEEDY / 1988, 1989, 1990, 1991 / 213* .. 214* .. Executable Statements .. 215* 216* Initialize constants and the random number seed. 217* 218 PATH( 1: 1 ) = 'Single precision' 219 PATH( 2: 3 ) = 'Q3' 220 NRUN = 0 221 NFAIL = 0 222 NERRS = 0 223 DO 10 I = 1, 4 224 ISEED( I ) = ISEEDY( I ) 225 10 CONTINUE 226 EPS = SLAMCH( 'Epsilon' ) 227 INFOT = 0 228* 229 DO 90 IM = 1, NM 230* 231* Do for each value of M in MVAL. 232* 233 M = MVAL( IM ) 234 LDA = MAX( 1, M ) 235* 236 DO 80 IN = 1, NN 237* 238* Do for each value of N in NVAL. 239* 240 N = NVAL( IN ) 241 MNMIN = MIN( M, N ) 242 LWORK = MAX( 1, M*MAX( M, N )+4*MNMIN+MAX( M, N ), 243 $ M*N + 2*MNMIN + 4*N ) 244* 245 DO 70 IMODE = 1, NTYPES 246 IF( .NOT.DOTYPE( IMODE ) ) 247 $ GO TO 70 248* 249* Do for each type of matrix 250* 1: zero matrix 251* 2: one small singular value 252* 3: geometric distribution of singular values 253* 4: first n/2 columns fixed 254* 5: last n/2 columns fixed 255* 6: every second column fixed 256* 257 MODE = IMODE 258 IF( IMODE.GT.3 ) 259 $ MODE = 1 260* 261* Generate test matrix of size m by n using 262* singular value distribution indicated by `mode'. 263* 264 DO 20 I = 1, N 265 IWORK( I ) = 0 266 20 CONTINUE 267 IF( IMODE.EQ.1 ) THEN 268 CALL SLASET( 'Full', M, N, ZERO, ZERO, COPYA, LDA ) 269 DO 30 I = 1, MNMIN 270 S( I ) = ZERO 271 30 CONTINUE 272 ELSE 273 CALL SLATMS( M, N, 'Uniform', ISEED, 'Nonsymm', S, 274 $ MODE, ONE / EPS, ONE, M, N, 'No packing', 275 $ COPYA, LDA, WORK, INFO ) 276 IF( IMODE.GE.4 ) THEN 277 IF( IMODE.EQ.4 ) THEN 278 ILOW = 1 279 ISTEP = 1 280 IHIGH = MAX( 1, N / 2 ) 281 ELSE IF( IMODE.EQ.5 ) THEN 282 ILOW = MAX( 1, N / 2 ) 283 ISTEP = 1 284 IHIGH = N 285 ELSE IF( IMODE.EQ.6 ) THEN 286 ILOW = 1 287 ISTEP = 2 288 IHIGH = N 289 END IF 290 DO 40 I = ILOW, IHIGH, ISTEP 291 IWORK( I ) = 1 292 40 CONTINUE 293 END IF 294 CALL SLAORD( 'Decreasing', MNMIN, S, 1 ) 295 END IF 296* 297 DO 60 INB = 1, NNB 298* 299* Do for each pair of values (NB,NX) in NBVAL and NXVAL. 300* 301 NB = NBVAL( INB ) 302 CALL XLAENV( 1, NB ) 303 NX = NXVAL( INB ) 304 CALL XLAENV( 3, NX ) 305* 306* Get a working copy of COPYA into A and a copy of 307* vector IWORK. 308* 309 CALL SLACPY( 'All', M, N, COPYA, LDA, A, LDA ) 310 CALL ICOPY( N, IWORK( 1 ), 1, IWORK( N+1 ), 1 ) 311* 312* Compute the QR factorization with pivoting of A 313* 314 LW = MAX( 1, 2*N+NB*( N+1 ) ) 315* 316* Compute the QP3 factorization of A 317* 318 SRNAMT = 'SGEQP3' 319 CALL SGEQP3( M, N, A, LDA, IWORK( N+1 ), TAU, WORK, 320 $ LW, INFO ) 321* 322* Compute norm(svd(a) - svd(r)) 323* 324 RESULT( 1 ) = SQRT12( M, N, A, LDA, S, WORK, 325 $ LWORK ) 326* 327* Compute norm( A*P - Q*R ) 328* 329 RESULT( 2 ) = SQPT01( M, N, MNMIN, COPYA, A, LDA, TAU, 330 $ IWORK( N+1 ), WORK, LWORK ) 331* 332* Compute Q'*Q 333* 334 RESULT( 3 ) = SQRT11( M, MNMIN, A, LDA, TAU, WORK, 335 $ LWORK ) 336* 337* Print information about the tests that did not pass 338* the threshold. 339* 340 DO 50 K = 1, NTESTS 341 IF( RESULT( K ).GE.THRESH ) THEN 342 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 343 $ CALL ALAHD( NOUT, PATH ) 344 WRITE( NOUT, FMT = 9999 )'SGEQP3', M, N, NB, 345 $ IMODE, K, RESULT( K ) 346 NFAIL = NFAIL + 1 347 END IF 348 50 CONTINUE 349 NRUN = NRUN + NTESTS 350* 351 60 CONTINUE 352 70 CONTINUE 353 80 CONTINUE 354 90 CONTINUE 355* 356* Print a summary of the results. 357* 358 CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) 359* 360 9999 FORMAT( 1X, A, ' M =', I5, ', N =', I5, ', NB =', I4, ', type ', 361 $ I2, ', test ', I2, ', ratio =', G12.5 ) 362* 363* End of SCHKQ3 364* 365 END 366