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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SDRVLS 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE SDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, 00012 * NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, 00013 * COPYB, C, S, COPYS, WORK, IWORK, NOUT ) 00014 * 00015 * .. Scalar Arguments .. 00016 * LOGICAL TSTERR 00017 * INTEGER NM, NN, NNB, NNS, NOUT 00018 * REAL THRESH 00019 * .. 00020 * .. Array Arguments .. 00021 * LOGICAL DOTYPE( * ) 00022 * INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ), 00023 * $ NVAL( * ), NXVAL( * ) 00024 * REAL A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ), 00025 * $ COPYS( * ), S( * ), WORK( * ) 00026 * .. 00027 * 00028 * 00029 *> \par Purpose: 00030 * ============= 00031 *> 00032 *> \verbatim 00033 *> 00034 *> SDRVLS tests the least squares driver routines SGELS, SGELSS, SGELSX, 00035 *> SGELSY and SGELSD. 00036 *> \endverbatim 00037 * 00038 * Arguments: 00039 * ========== 00040 * 00041 *> \param[in] DOTYPE 00042 *> \verbatim 00043 *> DOTYPE is LOGICAL array, dimension (NTYPES) 00044 *> The matrix types to be used for testing. Matrices of type j 00045 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = 00046 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. 00047 *> The matrix of type j is generated as follows: 00048 *> j=1: A = U*D*V where U and V are random orthogonal matrices 00049 *> and D has random entries (> 0.1) taken from a uniform 00050 *> distribution (0,1). A is full rank. 00051 *> j=2: The same of 1, but A is scaled up. 00052 *> j=3: The same of 1, but A is scaled down. 00053 *> j=4: A = U*D*V where U and V are random orthogonal matrices 00054 *> and D has 3*min(M,N)/4 random entries (> 0.1) taken 00055 *> from a uniform distribution (0,1) and the remaining 00056 *> entries set to 0. A is rank-deficient. 00057 *> j=5: The same of 4, but A is scaled up. 00058 *> j=6: The same of 5, but A is scaled down. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] NM 00062 *> \verbatim 00063 *> NM is INTEGER 00064 *> The number of values of M contained in the vector MVAL. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] MVAL 00068 *> \verbatim 00069 *> MVAL is INTEGER array, dimension (NM) 00070 *> The values of the matrix row dimension M. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] NN 00074 *> \verbatim 00075 *> NN is INTEGER 00076 *> The number of values of N contained in the vector NVAL. 00077 *> \endverbatim 00078 *> 00079 *> \param[in] NVAL 00080 *> \verbatim 00081 *> NVAL is INTEGER array, dimension (NN) 00082 *> The values of the matrix column dimension N. 00083 *> \endverbatim 00084 *> 00085 *> \param[in] NNS 00086 *> \verbatim 00087 *> NNS is INTEGER 00088 *> The number of values of NRHS contained in the vector NSVAL. 00089 *> \endverbatim 00090 *> 00091 *> \param[in] NSVAL 00092 *> \verbatim 00093 *> NSVAL is INTEGER array, dimension (NNS) 00094 *> The values of the number of right hand sides NRHS. 00095 *> \endverbatim 00096 *> 00097 *> \param[in] NNB 00098 *> \verbatim 00099 *> NNB is INTEGER 00100 *> The number of values of NB and NX contained in the 00101 *> vectors NBVAL and NXVAL. The blocking parameters are used 00102 *> in pairs (NB,NX). 00103 *> \endverbatim 00104 *> 00105 *> \param[in] NBVAL 00106 *> \verbatim 00107 *> NBVAL is INTEGER array, dimension (NNB) 00108 *> The values of the blocksize NB. 00109 *> \endverbatim 00110 *> 00111 *> \param[in] NXVAL 00112 *> \verbatim 00113 *> NXVAL is INTEGER array, dimension (NNB) 00114 *> The values of the crossover point NX. 00115 *> \endverbatim 00116 *> 00117 *> \param[in] THRESH 00118 *> \verbatim 00119 *> THRESH is REAL 00120 *> The threshold value for the test ratios. A result is 00121 *> included in the output file if RESULT >= THRESH. To have 00122 *> every test ratio printed, use THRESH = 0. 00123 *> \endverbatim 00124 *> 00125 *> \param[in] TSTERR 00126 *> \verbatim 00127 *> TSTERR is LOGICAL 00128 *> Flag that indicates whether error exits are to be tested. 00129 *> \endverbatim 00130 *> 00131 *> \param[out] A 00132 *> \verbatim 00133 *> A is REAL array, dimension (MMAX*NMAX) 00134 *> where MMAX is the maximum value of M in MVAL and NMAX is the 00135 *> maximum value of N in NVAL. 00136 *> \endverbatim 00137 *> 00138 *> \param[out] COPYA 00139 *> \verbatim 00140 *> COPYA is REAL array, dimension (MMAX*NMAX) 00141 *> \endverbatim 00142 *> 00143 *> \param[out] B 00144 *> \verbatim 00145 *> B is REAL array, dimension (MMAX*NSMAX) 00146 *> where MMAX is the maximum value of M in MVAL and NSMAX is the 00147 *> maximum value of NRHS in NSVAL. 00148 *> \endverbatim 00149 *> 00150 *> \param[out] COPYB 00151 *> \verbatim 00152 *> COPYB is REAL array, dimension (MMAX*NSMAX) 00153 *> \endverbatim 00154 *> 00155 *> \param[out] C 00156 *> \verbatim 00157 *> C is REAL array, dimension (MMAX*NSMAX) 00158 *> \endverbatim 00159 *> 00160 *> \param[out] S 00161 *> \verbatim 00162 *> S is REAL array, dimension 00163 *> (min(MMAX,NMAX)) 00164 *> \endverbatim 00165 *> 00166 *> \param[out] COPYS 00167 *> \verbatim 00168 *> COPYS is REAL array, dimension 00169 *> (min(MMAX,NMAX)) 00170 *> \endverbatim 00171 *> 00172 *> \param[out] WORK 00173 *> \verbatim 00174 *> WORK is REAL array, 00175 *> dimension (MMAX*NMAX + 4*NMAX + MMAX). 00176 *> \endverbatim 00177 *> 00178 *> \param[out] IWORK 00179 *> \verbatim 00180 *> IWORK is INTEGER array, dimension (15*NMAX) 00181 *> \endverbatim 00182 *> 00183 *> \param[in] NOUT 00184 *> \verbatim 00185 *> NOUT is INTEGER 00186 *> The unit number for output. 00187 *> \endverbatim 00188 * 00189 * Authors: 00190 * ======== 00191 * 00192 *> \author Univ. of Tennessee 00193 *> \author Univ. of California Berkeley 00194 *> \author Univ. of Colorado Denver 00195 *> \author NAG Ltd. 00196 * 00197 *> \date November 2011 00198 * 00199 *> \ingroup single_lin 00200 * 00201 * ===================================================================== 00202 SUBROUTINE SDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, 00203 $ NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, 00204 $ COPYB, C, S, COPYS, WORK, IWORK, NOUT ) 00205 * 00206 * -- LAPACK test routine (version 3.4.0) -- 00207 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00208 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00209 * November 2011 00210 * 00211 * .. Scalar Arguments .. 00212 LOGICAL TSTERR 00213 INTEGER NM, NN, NNB, NNS, NOUT 00214 REAL THRESH 00215 * .. 00216 * .. Array Arguments .. 00217 LOGICAL DOTYPE( * ) 00218 INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ), 00219 $ NVAL( * ), NXVAL( * ) 00220 REAL A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ), 00221 $ COPYS( * ), S( * ), WORK( * ) 00222 * .. 00223 * 00224 * ===================================================================== 00225 * 00226 * .. Parameters .. 00227 INTEGER NTESTS 00228 PARAMETER ( NTESTS = 18 ) 00229 INTEGER SMLSIZ 00230 PARAMETER ( SMLSIZ = 25 ) 00231 REAL ONE, TWO, ZERO 00232 PARAMETER ( ONE = 1.0E0, TWO = 2.0E0, ZERO = 0.0E0 ) 00233 * .. 00234 * .. Local Scalars .. 00235 CHARACTER TRANS 00236 CHARACTER*3 PATH 00237 INTEGER CRANK, I, IM, IN, INB, INFO, INS, IRANK, 00238 $ ISCALE, ITRAN, ITYPE, J, K, LDA, LDB, LDWORK, 00239 $ LWLSY, LWORK, M, MNMIN, N, NB, NCOLS, NERRS, 00240 $ NFAIL, NLVL, NRHS, NROWS, NRUN, RANK 00241 REAL EPS, NORMA, NORMB, RCOND 00242 * .. 00243 * .. Local Arrays .. 00244 INTEGER ISEED( 4 ), ISEEDY( 4 ) 00245 REAL RESULT( NTESTS ) 00246 * .. 00247 * .. External Functions .. 00248 REAL SASUM, SLAMCH, SQRT12, SQRT14, SQRT17 00249 EXTERNAL SASUM, SLAMCH, SQRT12, SQRT14, SQRT17 00250 * .. 00251 * .. External Subroutines .. 00252 EXTERNAL ALAERH, ALAHD, ALASVM, SAXPY, SERRLS, SGELS, 00253 $ SGELSD, SGELSS, SGELSX, SGELSY, SGEMM, SLACPY, 00254 $ SLARNV, SQRT13, SQRT15, SQRT16, SSCAL, 00255 $ XLAENV 00256 * .. 00257 * .. Intrinsic Functions .. 00258 INTRINSIC INT, LOG, MAX, MIN, REAL, SQRT 00259 * .. 00260 * .. Scalars in Common .. 00261 LOGICAL LERR, OK 00262 CHARACTER*32 SRNAMT 00263 INTEGER INFOT, IOUNIT 00264 * .. 00265 * .. Common blocks .. 00266 COMMON / INFOC / INFOT, IOUNIT, OK, LERR 00267 COMMON / SRNAMC / SRNAMT 00268 * .. 00269 * .. Data statements .. 00270 DATA ISEEDY / 1988, 1989, 1990, 1991 / 00271 * .. 00272 * .. Executable Statements .. 00273 * 00274 * Initialize constants and the random number seed. 00275 * 00276 PATH( 1: 1 ) = 'Single precision' 00277 PATH( 2: 3 ) = 'LS' 00278 NRUN = 0 00279 NFAIL = 0 00280 NERRS = 0 00281 DO 10 I = 1, 4 00282 ISEED( I ) = ISEEDY( I ) 00283 10 CONTINUE 00284 EPS = SLAMCH( 'Epsilon' ) 00285 * 00286 * Threshold for rank estimation 00287 * 00288 RCOND = SQRT( EPS ) - ( SQRT( EPS )-EPS ) / 2 00289 * 00290 * Test the error exits 00291 * 00292 CALL XLAENV( 2, 2 ) 00293 CALL XLAENV( 9, SMLSIZ ) 00294 IF( TSTERR ) 00295 $ CALL SERRLS( PATH, NOUT ) 00296 * 00297 * Print the header if NM = 0 or NN = 0 and THRESH = 0. 00298 * 00299 IF( ( NM.EQ.0 .OR. NN.EQ.0 ) .AND. THRESH.EQ.ZERO ) 00300 $ CALL ALAHD( NOUT, PATH ) 00301 INFOT = 0 00302 * 00303 DO 150 IM = 1, NM 00304 M = MVAL( IM ) 00305 LDA = MAX( 1, M ) 00306 * 00307 DO 140 IN = 1, NN 00308 N = NVAL( IN ) 00309 MNMIN = MIN( M, N ) 00310 LDB = MAX( 1, M, N ) 00311 * 00312 DO 130 INS = 1, NNS 00313 NRHS = NSVAL( INS ) 00314 NLVL = MAX( INT( LOG( MAX( ONE, REAL( MNMIN ) ) / 00315 $ REAL( SMLSIZ+1 ) ) / LOG( TWO ) ) + 1, 0 ) 00316 LWORK = MAX( 1, ( M+NRHS )*( N+2 ), ( N+NRHS )*( M+2 ), 00317 $ M*N+4*MNMIN+MAX( M, N ), 12*MNMIN+2*MNMIN*SMLSIZ+ 00318 $ 8*MNMIN*NLVL+MNMIN*NRHS+(SMLSIZ+1)**2 ) 00319 * 00320 DO 120 IRANK = 1, 2 00321 DO 110 ISCALE = 1, 3 00322 ITYPE = ( IRANK-1 )*3 + ISCALE 00323 IF( .NOT.DOTYPE( ITYPE ) ) 00324 $ GO TO 110 00325 * 00326 IF( IRANK.EQ.1 ) THEN 00327 * 00328 * Test SGELS 00329 * 00330 * Generate a matrix of scaling type ISCALE 00331 * 00332 CALL SQRT13( ISCALE, M, N, COPYA, LDA, NORMA, 00333 $ ISEED ) 00334 DO 40 INB = 1, NNB 00335 NB = NBVAL( INB ) 00336 CALL XLAENV( 1, NB ) 00337 CALL XLAENV( 3, NXVAL( INB ) ) 00338 * 00339 DO 30 ITRAN = 1, 2 00340 IF( ITRAN.EQ.1 ) THEN 00341 TRANS = 'N' 00342 NROWS = M 00343 NCOLS = N 00344 ELSE 00345 TRANS = 'T' 00346 NROWS = N 00347 NCOLS = M 00348 END IF 00349 LDWORK = MAX( 1, NCOLS ) 00350 * 00351 * Set up a consistent rhs 00352 * 00353 IF( NCOLS.GT.0 ) THEN 00354 CALL SLARNV( 2, ISEED, NCOLS*NRHS, 00355 $ WORK ) 00356 CALL SSCAL( NCOLS*NRHS, 00357 $ ONE / REAL( NCOLS ), WORK, 00358 $ 1 ) 00359 END IF 00360 CALL SGEMM( TRANS, 'No transpose', NROWS, 00361 $ NRHS, NCOLS, ONE, COPYA, LDA, 00362 $ WORK, LDWORK, ZERO, B, LDB ) 00363 CALL SLACPY( 'Full', NROWS, NRHS, B, LDB, 00364 $ COPYB, LDB ) 00365 * 00366 * Solve LS or overdetermined system 00367 * 00368 IF( M.GT.0 .AND. N.GT.0 ) THEN 00369 CALL SLACPY( 'Full', M, N, COPYA, LDA, 00370 $ A, LDA ) 00371 CALL SLACPY( 'Full', NROWS, NRHS, 00372 $ COPYB, LDB, B, LDB ) 00373 END IF 00374 SRNAMT = 'SGELS ' 00375 CALL SGELS( TRANS, M, N, NRHS, A, LDA, B, 00376 $ LDB, WORK, LWORK, INFO ) 00377 IF( INFO.NE.0 ) 00378 $ CALL ALAERH( PATH, 'SGELS ', INFO, 0, 00379 $ TRANS, M, N, NRHS, -1, NB, 00380 $ ITYPE, NFAIL, NERRS, 00381 $ NOUT ) 00382 * 00383 * Check correctness of results 00384 * 00385 LDWORK = MAX( 1, NROWS ) 00386 IF( NROWS.GT.0 .AND. NRHS.GT.0 ) 00387 $ CALL SLACPY( 'Full', NROWS, NRHS, 00388 $ COPYB, LDB, C, LDB ) 00389 CALL SQRT16( TRANS, M, N, NRHS, COPYA, 00390 $ LDA, B, LDB, C, LDB, WORK, 00391 $ RESULT( 1 ) ) 00392 * 00393 IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR. 00394 $ ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN 00395 * 00396 * Solving LS system 00397 * 00398 RESULT( 2 ) = SQRT17( TRANS, 1, M, N, 00399 $ NRHS, COPYA, LDA, B, LDB, 00400 $ COPYB, LDB, C, WORK, 00401 $ LWORK ) 00402 ELSE 00403 * 00404 * Solving overdetermined system 00405 * 00406 RESULT( 2 ) = SQRT14( TRANS, M, N, 00407 $ NRHS, COPYA, LDA, B, LDB, 00408 $ WORK, LWORK ) 00409 END IF 00410 * 00411 * Print information about the tests that 00412 * did not pass the threshold. 00413 * 00414 DO 20 K = 1, 2 00415 IF( RESULT( K ).GE.THRESH ) THEN 00416 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 00417 $ CALL ALAHD( NOUT, PATH ) 00418 WRITE( NOUT, FMT = 9999 )TRANS, M, 00419 $ N, NRHS, NB, ITYPE, K, 00420 $ RESULT( K ) 00421 NFAIL = NFAIL + 1 00422 END IF 00423 20 CONTINUE 00424 NRUN = NRUN + 2 00425 30 CONTINUE 00426 40 CONTINUE 00427 END IF 00428 * 00429 * Generate a matrix of scaling type ISCALE and rank 00430 * type IRANK. 00431 * 00432 CALL SQRT15( ISCALE, IRANK, M, N, NRHS, COPYA, LDA, 00433 $ COPYB, LDB, COPYS, RANK, NORMA, NORMB, 00434 $ ISEED, WORK, LWORK ) 00435 * 00436 * workspace used: MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M) 00437 * 00438 * Initialize vector IWORK. 00439 * 00440 DO 50 J = 1, N 00441 IWORK( J ) = 0 00442 50 CONTINUE 00443 LDWORK = MAX( 1, M ) 00444 * 00445 * Test SGELSX 00446 * 00447 * SGELSX: Compute the minimum-norm solution X 00448 * to min( norm( A * X - B ) ) using a complete 00449 * orthogonal factorization. 00450 * 00451 CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA ) 00452 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B, LDB ) 00453 * 00454 SRNAMT = 'SGELSX' 00455 CALL SGELSX( M, N, NRHS, A, LDA, B, LDB, IWORK, 00456 $ RCOND, CRANK, WORK, INFO ) 00457 IF( INFO.NE.0 ) 00458 $ CALL ALAERH( PATH, 'SGELSX', INFO, 0, ' ', M, N, 00459 $ NRHS, -1, NB, ITYPE, NFAIL, NERRS, 00460 $ NOUT ) 00461 * 00462 * workspace used: MAX( MNMIN+3*N, 2*MNMIN+NRHS ) 00463 * 00464 * Test 3: Compute relative error in svd 00465 * workspace: M*N + 4*MIN(M,N) + MAX(M,N) 00466 * 00467 RESULT( 3 ) = SQRT12( CRANK, CRANK, A, LDA, COPYS, 00468 $ WORK, LWORK ) 00469 * 00470 * Test 4: Compute error in solution 00471 * workspace: M*NRHS + M 00472 * 00473 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK, 00474 $ LDWORK ) 00475 CALL SQRT16( 'No transpose', M, N, NRHS, COPYA, 00476 $ LDA, B, LDB, WORK, LDWORK, 00477 $ WORK( M*NRHS+1 ), RESULT( 4 ) ) 00478 * 00479 * Test 5: Check norm of r'*A 00480 * workspace: NRHS*(M+N) 00481 * 00482 RESULT( 5 ) = ZERO 00483 IF( M.GT.CRANK ) 00484 $ RESULT( 5 ) = SQRT17( 'No transpose', 1, M, N, 00485 $ NRHS, COPYA, LDA, B, LDB, COPYB, 00486 $ LDB, C, WORK, LWORK ) 00487 * 00488 * Test 6: Check if x is in the rowspace of A 00489 * workspace: (M+NRHS)*(N+2) 00490 * 00491 RESULT( 6 ) = ZERO 00492 * 00493 IF( N.GT.CRANK ) 00494 $ RESULT( 6 ) = SQRT14( 'No transpose', M, N, 00495 $ NRHS, COPYA, LDA, B, LDB, WORK, 00496 $ LWORK ) 00497 * 00498 * Print information about the tests that did not 00499 * pass the threshold. 00500 * 00501 DO 60 K = 3, 6 00502 IF( RESULT( K ).GE.THRESH ) THEN 00503 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 00504 $ CALL ALAHD( NOUT, PATH ) 00505 WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB, 00506 $ ITYPE, K, RESULT( K ) 00507 NFAIL = NFAIL + 1 00508 END IF 00509 60 CONTINUE 00510 NRUN = NRUN + 4 00511 * 00512 * Loop for testing different block sizes. 00513 * 00514 DO 100 INB = 1, NNB 00515 NB = NBVAL( INB ) 00516 CALL XLAENV( 1, NB ) 00517 CALL XLAENV( 3, NXVAL( INB ) ) 00518 * 00519 * Test SGELSY 00520 * 00521 * SGELSY: Compute the minimum-norm solution X 00522 * to min( norm( A * X - B ) ) 00523 * using the rank-revealing orthogonal 00524 * factorization. 00525 * 00526 * Initialize vector IWORK. 00527 * 00528 DO 70 J = 1, N 00529 IWORK( J ) = 0 00530 70 CONTINUE 00531 * 00532 * Set LWLSY to the adequate value. 00533 * 00534 LWLSY = MAX( 1, MNMIN+2*N+NB*( N+1 ), 00535 $ 2*MNMIN+NB*NRHS ) 00536 * 00537 CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA ) 00538 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B, 00539 $ LDB ) 00540 * 00541 SRNAMT = 'SGELSY' 00542 CALL SGELSY( M, N, NRHS, A, LDA, B, LDB, IWORK, 00543 $ RCOND, CRANK, WORK, LWLSY, INFO ) 00544 IF( INFO.NE.0 ) 00545 $ CALL ALAERH( PATH, 'SGELSY', INFO, 0, ' ', M, 00546 $ N, NRHS, -1, NB, ITYPE, NFAIL, 00547 $ NERRS, NOUT ) 00548 * 00549 * Test 7: Compute relative error in svd 00550 * workspace: M*N + 4*MIN(M,N) + MAX(M,N) 00551 * 00552 RESULT( 7 ) = SQRT12( CRANK, CRANK, A, LDA, 00553 $ COPYS, WORK, LWORK ) 00554 * 00555 * Test 8: Compute error in solution 00556 * workspace: M*NRHS + M 00557 * 00558 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK, 00559 $ LDWORK ) 00560 CALL SQRT16( 'No transpose', M, N, NRHS, COPYA, 00561 $ LDA, B, LDB, WORK, LDWORK, 00562 $ WORK( M*NRHS+1 ), RESULT( 8 ) ) 00563 * 00564 * Test 9: Check norm of r'*A 00565 * workspace: NRHS*(M+N) 00566 * 00567 RESULT( 9 ) = ZERO 00568 IF( M.GT.CRANK ) 00569 $ RESULT( 9 ) = SQRT17( 'No transpose', 1, M, 00570 $ N, NRHS, COPYA, LDA, B, LDB, 00571 $ COPYB, LDB, C, WORK, LWORK ) 00572 * 00573 * Test 10: Check if x is in the rowspace of A 00574 * workspace: (M+NRHS)*(N+2) 00575 * 00576 RESULT( 10 ) = ZERO 00577 * 00578 IF( N.GT.CRANK ) 00579 $ RESULT( 10 ) = SQRT14( 'No transpose', M, N, 00580 $ NRHS, COPYA, LDA, B, LDB, 00581 $ WORK, LWORK ) 00582 * 00583 * Test SGELSS 00584 * 00585 * SGELSS: Compute the minimum-norm solution X 00586 * to min( norm( A * X - B ) ) 00587 * using the SVD. 00588 * 00589 CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA ) 00590 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B, 00591 $ LDB ) 00592 SRNAMT = 'SGELSS' 00593 CALL SGELSS( M, N, NRHS, A, LDA, B, LDB, S, 00594 $ RCOND, CRANK, WORK, LWORK, INFO ) 00595 IF( INFO.NE.0 ) 00596 $ CALL ALAERH( PATH, 'SGELSS', INFO, 0, ' ', M, 00597 $ N, NRHS, -1, NB, ITYPE, NFAIL, 00598 $ NERRS, NOUT ) 00599 * 00600 * workspace used: 3*min(m,n) + 00601 * max(2*min(m,n),nrhs,max(m,n)) 00602 * 00603 * Test 11: Compute relative error in svd 00604 * 00605 IF( RANK.GT.0 ) THEN 00606 CALL SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 ) 00607 RESULT( 11 ) = SASUM( MNMIN, S, 1 ) / 00608 $ SASUM( MNMIN, COPYS, 1 ) / 00609 $ ( EPS*REAL( MNMIN ) ) 00610 ELSE 00611 RESULT( 11 ) = ZERO 00612 END IF 00613 * 00614 * Test 12: Compute error in solution 00615 * 00616 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK, 00617 $ LDWORK ) 00618 CALL SQRT16( 'No transpose', M, N, NRHS, COPYA, 00619 $ LDA, B, LDB, WORK, LDWORK, 00620 $ WORK( M*NRHS+1 ), RESULT( 12 ) ) 00621 * 00622 * Test 13: Check norm of r'*A 00623 * 00624 RESULT( 13 ) = ZERO 00625 IF( M.GT.CRANK ) 00626 $ RESULT( 13 ) = SQRT17( 'No transpose', 1, M, 00627 $ N, NRHS, COPYA, LDA, B, LDB, 00628 $ COPYB, LDB, C, WORK, LWORK ) 00629 * 00630 * Test 14: Check if x is in the rowspace of A 00631 * 00632 RESULT( 14 ) = ZERO 00633 IF( N.GT.CRANK ) 00634 $ RESULT( 14 ) = SQRT14( 'No transpose', M, N, 00635 $ NRHS, COPYA, LDA, B, LDB, 00636 $ WORK, LWORK ) 00637 * 00638 * Test SGELSD 00639 * 00640 * SGELSD: Compute the minimum-norm solution X 00641 * to min( norm( A * X - B ) ) using a 00642 * divide and conquer SVD. 00643 * 00644 * Initialize vector IWORK. 00645 * 00646 DO 80 J = 1, N 00647 IWORK( J ) = 0 00648 80 CONTINUE 00649 * 00650 CALL SLACPY( 'Full', M, N, COPYA, LDA, A, LDA ) 00651 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, B, 00652 $ LDB ) 00653 * 00654 SRNAMT = 'SGELSD' 00655 CALL SGELSD( M, N, NRHS, A, LDA, B, LDB, S, 00656 $ RCOND, CRANK, WORK, LWORK, IWORK, 00657 $ INFO ) 00658 IF( INFO.NE.0 ) 00659 $ CALL ALAERH( PATH, 'SGELSD', INFO, 0, ' ', M, 00660 $ N, NRHS, -1, NB, ITYPE, NFAIL, 00661 $ NERRS, NOUT ) 00662 * 00663 * Test 15: Compute relative error in svd 00664 * 00665 IF( RANK.GT.0 ) THEN 00666 CALL SAXPY( MNMIN, -ONE, COPYS, 1, S, 1 ) 00667 RESULT( 15 ) = SASUM( MNMIN, S, 1 ) / 00668 $ SASUM( MNMIN, COPYS, 1 ) / 00669 $ ( EPS*REAL( MNMIN ) ) 00670 ELSE 00671 RESULT( 15 ) = ZERO 00672 END IF 00673 * 00674 * Test 16: Compute error in solution 00675 * 00676 CALL SLACPY( 'Full', M, NRHS, COPYB, LDB, WORK, 00677 $ LDWORK ) 00678 CALL SQRT16( 'No transpose', M, N, NRHS, COPYA, 00679 $ LDA, B, LDB, WORK, LDWORK, 00680 $ WORK( M*NRHS+1 ), RESULT( 16 ) ) 00681 * 00682 * Test 17: Check norm of r'*A 00683 * 00684 RESULT( 17 ) = ZERO 00685 IF( M.GT.CRANK ) 00686 $ RESULT( 17 ) = SQRT17( 'No transpose', 1, M, 00687 $ N, NRHS, COPYA, LDA, B, LDB, 00688 $ COPYB, LDB, C, WORK, LWORK ) 00689 * 00690 * Test 18: Check if x is in the rowspace of A 00691 * 00692 RESULT( 18 ) = ZERO 00693 IF( N.GT.CRANK ) 00694 $ RESULT( 18 ) = SQRT14( 'No transpose', M, N, 00695 $ NRHS, COPYA, LDA, B, LDB, 00696 $ WORK, LWORK ) 00697 * 00698 * Print information about the tests that did not 00699 * pass the threshold. 00700 * 00701 DO 90 K = 7, NTESTS 00702 IF( RESULT( K ).GE.THRESH ) THEN 00703 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 00704 $ CALL ALAHD( NOUT, PATH ) 00705 WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB, 00706 $ ITYPE, K, RESULT( K ) 00707 NFAIL = NFAIL + 1 00708 END IF 00709 90 CONTINUE 00710 NRUN = NRUN + 12 00711 * 00712 100 CONTINUE 00713 110 CONTINUE 00714 120 CONTINUE 00715 130 CONTINUE 00716 140 CONTINUE 00717 150 CONTINUE 00718 * 00719 * Print a summary of the results. 00720 * 00721 CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) 00722 * 00723 9999 FORMAT( ' TRANS=''', A1, ''', M=', I5, ', N=', I5, ', NRHS=', I4, 00724 $ ', NB=', I4, ', type', I2, ', test(', I2, ')=', G12.5 ) 00725 9998 FORMAT( ' M=', I5, ', N=', I5, ', NRHS=', I4, ', NB=', I4, 00726 $ ', type', I2, ', test(', I2, ')=', G12.5 ) 00727 RETURN 00728 * 00729 * End of SDRVLS 00730 * 00731 END