1*> \brief \b SDRVPO 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 SDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, 12* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, 13* RWORK, IWORK, NOUT ) 14* 15* .. Scalar Arguments .. 16* LOGICAL TSTERR 17* INTEGER NMAX, NN, NOUT, NRHS 18* REAL THRESH 19* .. 20* .. Array Arguments .. 21* LOGICAL DOTYPE( * ) 22* INTEGER IWORK( * ), NVAL( * ) 23* REAL A( * ), AFAC( * ), ASAV( * ), B( * ), 24* $ BSAV( * ), RWORK( * ), S( * ), WORK( * ), 25* $ X( * ), XACT( * ) 26* .. 27* 28* 29*> \par Purpose: 30* ============= 31*> 32*> \verbatim 33*> 34*> SDRVPO tests the driver routines SPOSV and -SVX. 35*> \endverbatim 36* 37* Arguments: 38* ========== 39* 40*> \param[in] DOTYPE 41*> \verbatim 42*> DOTYPE is LOGICAL array, dimension (NTYPES) 43*> The matrix types to be used for testing. Matrices of type j 44*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = 45*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. 46*> \endverbatim 47*> 48*> \param[in] NN 49*> \verbatim 50*> NN is INTEGER 51*> The number of values of N contained in the vector NVAL. 52*> \endverbatim 53*> 54*> \param[in] NVAL 55*> \verbatim 56*> NVAL is INTEGER array, dimension (NN) 57*> The values of the matrix dimension N. 58*> \endverbatim 59*> 60*> \param[in] NRHS 61*> \verbatim 62*> NRHS is INTEGER 63*> The number of right hand side vectors to be generated for 64*> each linear system. 65*> \endverbatim 66*> 67*> \param[in] THRESH 68*> \verbatim 69*> THRESH is REAL 70*> The threshold value for the test ratios. A result is 71*> included in the output file if RESULT >= THRESH. To have 72*> every test ratio printed, use THRESH = 0. 73*> \endverbatim 74*> 75*> \param[in] TSTERR 76*> \verbatim 77*> TSTERR is LOGICAL 78*> Flag that indicates whether error exits are to be tested. 79*> \endverbatim 80*> 81*> \param[in] NMAX 82*> \verbatim 83*> NMAX is INTEGER 84*> The maximum value permitted for N, used in dimensioning the 85*> work arrays. 86*> \endverbatim 87*> 88*> \param[out] A 89*> \verbatim 90*> A is REAL array, dimension (NMAX*NMAX) 91*> \endverbatim 92*> 93*> \param[out] AFAC 94*> \verbatim 95*> AFAC is REAL array, dimension (NMAX*NMAX) 96*> \endverbatim 97*> 98*> \param[out] ASAV 99*> \verbatim 100*> ASAV is REAL array, dimension (NMAX*NMAX) 101*> \endverbatim 102*> 103*> \param[out] B 104*> \verbatim 105*> B is REAL array, dimension (NMAX*NRHS) 106*> \endverbatim 107*> 108*> \param[out] BSAV 109*> \verbatim 110*> BSAV is REAL array, dimension (NMAX*NRHS) 111*> \endverbatim 112*> 113*> \param[out] X 114*> \verbatim 115*> X is REAL array, dimension (NMAX*NRHS) 116*> \endverbatim 117*> 118*> \param[out] XACT 119*> \verbatim 120*> XACT is REAL array, dimension (NMAX*NRHS) 121*> \endverbatim 122*> 123*> \param[out] S 124*> \verbatim 125*> S is REAL array, dimension (NMAX) 126*> \endverbatim 127*> 128*> \param[out] WORK 129*> \verbatim 130*> WORK is REAL array, dimension 131*> (NMAX*max(3,NRHS)) 132*> \endverbatim 133*> 134*> \param[out] RWORK 135*> \verbatim 136*> RWORK is REAL array, dimension (NMAX+2*NRHS) 137*> \endverbatim 138*> 139*> \param[out] IWORK 140*> \verbatim 141*> IWORK is INTEGER array, dimension (NMAX) 142*> \endverbatim 143*> 144*> \param[in] NOUT 145*> \verbatim 146*> NOUT is INTEGER 147*> The unit number for output. 148*> \endverbatim 149* 150* Authors: 151* ======== 152* 153*> \author Univ. of Tennessee 154*> \author Univ. of California Berkeley 155*> \author Univ. of Colorado Denver 156*> \author NAG Ltd. 157* 158*> \ingroup single_lin 159* 160* ===================================================================== 161 SUBROUTINE SDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, 162 $ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, 163 $ RWORK, IWORK, NOUT ) 164* 165* -- LAPACK test routine -- 166* -- LAPACK is a software package provided by Univ. of Tennessee, -- 167* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 168* 169* .. Scalar Arguments .. 170 LOGICAL TSTERR 171 INTEGER NMAX, NN, NOUT, NRHS 172 REAL THRESH 173* .. 174* .. Array Arguments .. 175 LOGICAL DOTYPE( * ) 176 INTEGER IWORK( * ), NVAL( * ) 177 REAL A( * ), AFAC( * ), ASAV( * ), B( * ), 178 $ BSAV( * ), RWORK( * ), S( * ), WORK( * ), 179 $ X( * ), XACT( * ) 180* .. 181* 182* ===================================================================== 183* 184* .. Parameters .. 185 REAL ONE, ZERO 186 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 187 INTEGER NTYPES 188 PARAMETER ( NTYPES = 9 ) 189 INTEGER NTESTS 190 PARAMETER ( NTESTS = 6 ) 191* .. 192* .. Local Scalars .. 193 LOGICAL EQUIL, NOFACT, PREFAC, ZEROT 194 CHARACTER DIST, EQUED, FACT, TYPE, UPLO, XTYPE 195 CHARACTER*3 PATH 196 INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO, 197 $ IZERO, K, K1, KL, KU, LDA, MODE, N, NB, NBMIN, 198 $ NERRS, NFACT, NFAIL, NIMAT, NRUN, NT 199 REAL AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC, 200 $ ROLDC, SCOND 201* .. 202* .. Local Arrays .. 203 CHARACTER EQUEDS( 2 ), FACTS( 3 ), UPLOS( 2 ) 204 INTEGER ISEED( 4 ), ISEEDY( 4 ) 205 REAL RESULT( NTESTS ) 206* .. 207* .. External Functions .. 208 LOGICAL LSAME 209 REAL SGET06, SLANSY 210 EXTERNAL LSAME, SGET06, SLANSY 211* .. 212* .. External Subroutines .. 213 EXTERNAL ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY, 214 $ SLAQSY, SLARHS, SLASET, SLATB4, SLATMS, SPOEQU, 215 $ SPOSV, SPOSVX, SPOT01, SPOT02, SPOT05, SPOTRF, 216 $ SPOTRI, XLAENV 217* .. 218* .. Intrinsic Functions .. 219 INTRINSIC MAX 220* .. 221* .. Scalars in Common .. 222 LOGICAL LERR, OK 223 CHARACTER*32 SRNAMT 224 INTEGER INFOT, NUNIT 225* .. 226* .. Common blocks .. 227 COMMON / INFOC / INFOT, NUNIT, OK, LERR 228 COMMON / SRNAMC / SRNAMT 229* .. 230* .. Data statements .. 231 DATA ISEEDY / 1988, 1989, 1990, 1991 / 232 DATA UPLOS / 'U', 'L' / 233 DATA FACTS / 'F', 'N', 'E' / 234 DATA EQUEDS / 'N', 'Y' / 235* .. 236* .. Executable Statements .. 237* 238* Initialize constants and the random number seed. 239* 240 PATH( 1: 1 ) = 'Single precision' 241 PATH( 2: 3 ) = 'PO' 242 NRUN = 0 243 NFAIL = 0 244 NERRS = 0 245 DO 10 I = 1, 4 246 ISEED( I ) = ISEEDY( I ) 247 10 CONTINUE 248* 249* Test the error exits 250* 251 IF( TSTERR ) 252 $ CALL SERRVX( PATH, NOUT ) 253 INFOT = 0 254* 255* Set the block size and minimum block size for testing. 256* 257 NB = 1 258 NBMIN = 2 259 CALL XLAENV( 1, NB ) 260 CALL XLAENV( 2, NBMIN ) 261* 262* Do for each value of N in NVAL 263* 264 DO 130 IN = 1, NN 265 N = NVAL( IN ) 266 LDA = MAX( N, 1 ) 267 XTYPE = 'N' 268 NIMAT = NTYPES 269 IF( N.LE.0 ) 270 $ NIMAT = 1 271* 272 DO 120 IMAT = 1, NIMAT 273* 274* Do the tests only if DOTYPE( IMAT ) is true. 275* 276 IF( .NOT.DOTYPE( IMAT ) ) 277 $ GO TO 120 278* 279* Skip types 3, 4, or 5 if the matrix size is too small. 280* 281 ZEROT = IMAT.GE.3 .AND. IMAT.LE.5 282 IF( ZEROT .AND. N.LT.IMAT-2 ) 283 $ GO TO 120 284* 285* Do first for UPLO = 'U', then for UPLO = 'L' 286* 287 DO 110 IUPLO = 1, 2 288 UPLO = UPLOS( IUPLO ) 289* 290* Set up parameters with SLATB4 and generate a test matrix 291* with SLATMS. 292* 293 CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, 294 $ CNDNUM, DIST ) 295* 296 SRNAMT = 'SLATMS' 297 CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, 298 $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK, 299 $ INFO ) 300* 301* Check error code from SLATMS. 302* 303 IF( INFO.NE.0 ) THEN 304 CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1, 305 $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) 306 GO TO 110 307 END IF 308* 309* For types 3-5, zero one row and column of the matrix to 310* test that INFO is returned correctly. 311* 312 IF( ZEROT ) THEN 313 IF( IMAT.EQ.3 ) THEN 314 IZERO = 1 315 ELSE IF( IMAT.EQ.4 ) THEN 316 IZERO = N 317 ELSE 318 IZERO = N / 2 + 1 319 END IF 320 IOFF = ( IZERO-1 )*LDA 321* 322* Set row and column IZERO of A to 0. 323* 324 IF( IUPLO.EQ.1 ) THEN 325 DO 20 I = 1, IZERO - 1 326 A( IOFF+I ) = ZERO 327 20 CONTINUE 328 IOFF = IOFF + IZERO 329 DO 30 I = IZERO, N 330 A( IOFF ) = ZERO 331 IOFF = IOFF + LDA 332 30 CONTINUE 333 ELSE 334 IOFF = IZERO 335 DO 40 I = 1, IZERO - 1 336 A( IOFF ) = ZERO 337 IOFF = IOFF + LDA 338 40 CONTINUE 339 IOFF = IOFF - IZERO 340 DO 50 I = IZERO, N 341 A( IOFF+I ) = ZERO 342 50 CONTINUE 343 END IF 344 ELSE 345 IZERO = 0 346 END IF 347* 348* Save a copy of the matrix A in ASAV. 349* 350 CALL SLACPY( UPLO, N, N, A, LDA, ASAV, LDA ) 351* 352 DO 100 IEQUED = 1, 2 353 EQUED = EQUEDS( IEQUED ) 354 IF( IEQUED.EQ.1 ) THEN 355 NFACT = 3 356 ELSE 357 NFACT = 1 358 END IF 359* 360 DO 90 IFACT = 1, NFACT 361 FACT = FACTS( IFACT ) 362 PREFAC = LSAME( FACT, 'F' ) 363 NOFACT = LSAME( FACT, 'N' ) 364 EQUIL = LSAME( FACT, 'E' ) 365* 366 IF( ZEROT ) THEN 367 IF( PREFAC ) 368 $ GO TO 90 369 RCONDC = ZERO 370* 371 ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN 372* 373* Compute the condition number for comparison with 374* the value returned by SPOSVX (FACT = 'N' reuses 375* the condition number from the previous iteration 376* with FACT = 'F'). 377* 378 CALL SLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA ) 379 IF( EQUIL .OR. IEQUED.GT.1 ) THEN 380* 381* Compute row and column scale factors to 382* equilibrate the matrix A. 383* 384 CALL SPOEQU( N, AFAC, LDA, S, SCOND, AMAX, 385 $ INFO ) 386 IF( INFO.EQ.0 .AND. N.GT.0 ) THEN 387 IF( IEQUED.GT.1 ) 388 $ SCOND = ZERO 389* 390* Equilibrate the matrix. 391* 392 CALL SLAQSY( UPLO, N, AFAC, LDA, S, SCOND, 393 $ AMAX, EQUED ) 394 END IF 395 END IF 396* 397* Save the condition number of the 398* non-equilibrated system for use in SGET04. 399* 400 IF( EQUIL ) 401 $ ROLDC = RCONDC 402* 403* Compute the 1-norm of A. 404* 405 ANORM = SLANSY( '1', UPLO, N, AFAC, LDA, RWORK ) 406* 407* Factor the matrix A. 408* 409 CALL SPOTRF( UPLO, N, AFAC, LDA, INFO ) 410* 411* Form the inverse of A. 412* 413 CALL SLACPY( UPLO, N, N, AFAC, LDA, A, LDA ) 414 CALL SPOTRI( UPLO, N, A, LDA, INFO ) 415* 416* Compute the 1-norm condition number of A. 417* 418 AINVNM = SLANSY( '1', UPLO, N, A, LDA, RWORK ) 419 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN 420 RCONDC = ONE 421 ELSE 422 RCONDC = ( ONE / ANORM ) / AINVNM 423 END IF 424 END IF 425* 426* Restore the matrix A. 427* 428 CALL SLACPY( UPLO, N, N, ASAV, LDA, A, LDA ) 429* 430* Form an exact solution and set the right hand side. 431* 432 SRNAMT = 'SLARHS' 433 CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU, 434 $ NRHS, A, LDA, XACT, LDA, B, LDA, 435 $ ISEED, INFO ) 436 XTYPE = 'C' 437 CALL SLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) 438* 439 IF( NOFACT ) THEN 440* 441* --- Test SPOSV --- 442* 443* Compute the L*L' or U'*U factorization of the 444* matrix and solve the system. 445* 446 CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) 447 CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) 448* 449 SRNAMT = 'SPOSV ' 450 CALL SPOSV( UPLO, N, NRHS, AFAC, LDA, X, LDA, 451 $ INFO ) 452* 453* Check error code from SPOSV . 454* 455 IF( INFO.NE.IZERO ) THEN 456 CALL ALAERH( PATH, 'SPOSV ', INFO, IZERO, 457 $ UPLO, N, N, -1, -1, NRHS, IMAT, 458 $ NFAIL, NERRS, NOUT ) 459 GO TO 70 460 ELSE IF( INFO.NE.0 ) THEN 461 GO TO 70 462 END IF 463* 464* Reconstruct matrix from factors and compute 465* residual. 466* 467 CALL SPOT01( UPLO, N, A, LDA, AFAC, LDA, RWORK, 468 $ RESULT( 1 ) ) 469* 470* Compute residual of the computed solution. 471* 472 CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, 473 $ LDA ) 474 CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, 475 $ WORK, LDA, RWORK, RESULT( 2 ) ) 476* 477* Check solution from generated exact solution. 478* 479 CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, 480 $ RESULT( 3 ) ) 481 NT = 3 482* 483* Print information about the tests that did not 484* pass the threshold. 485* 486 DO 60 K = 1, NT 487 IF( RESULT( K ).GE.THRESH ) THEN 488 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 489 $ CALL ALADHD( NOUT, PATH ) 490 WRITE( NOUT, FMT = 9999 )'SPOSV ', UPLO, 491 $ N, IMAT, K, RESULT( K ) 492 NFAIL = NFAIL + 1 493 END IF 494 60 CONTINUE 495 NRUN = NRUN + NT 496 70 CONTINUE 497 END IF 498* 499* --- Test SPOSVX --- 500* 501 IF( .NOT.PREFAC ) 502 $ CALL SLASET( UPLO, N, N, ZERO, ZERO, AFAC, LDA ) 503 CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA ) 504 IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN 505* 506* Equilibrate the matrix if FACT='F' and 507* EQUED='Y'. 508* 509 CALL SLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, 510 $ EQUED ) 511 END IF 512* 513* Solve the system and compute the condition number 514* and error bounds using SPOSVX. 515* 516 SRNAMT = 'SPOSVX' 517 CALL SPOSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, 518 $ LDA, EQUED, S, B, LDA, X, LDA, RCOND, 519 $ RWORK, RWORK( NRHS+1 ), WORK, IWORK, 520 $ INFO ) 521* 522* Check the error code from SPOSVX. 523* 524 IF( INFO.NE.IZERO ) THEN 525 CALL ALAERH( PATH, 'SPOSVX', INFO, IZERO, 526 $ FACT // UPLO, N, N, -1, -1, NRHS, 527 $ IMAT, NFAIL, NERRS, NOUT ) 528 GO TO 90 529 END IF 530* 531 IF( INFO.EQ.0 ) THEN 532 IF( .NOT.PREFAC ) THEN 533* 534* Reconstruct matrix from factors and compute 535* residual. 536* 537 CALL SPOT01( UPLO, N, A, LDA, AFAC, LDA, 538 $ RWORK( 2*NRHS+1 ), RESULT( 1 ) ) 539 K1 = 1 540 ELSE 541 K1 = 2 542 END IF 543* 544* Compute residual of the computed solution. 545* 546 CALL SLACPY( 'Full', N, NRHS, BSAV, LDA, WORK, 547 $ LDA ) 548 CALL SPOT02( UPLO, N, NRHS, ASAV, LDA, X, LDA, 549 $ WORK, LDA, RWORK( 2*NRHS+1 ), 550 $ RESULT( 2 ) ) 551* 552* Check solution from generated exact solution. 553* 554 IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED, 555 $ 'N' ) ) ) THEN 556 CALL SGET04( N, NRHS, X, LDA, XACT, LDA, 557 $ RCONDC, RESULT( 3 ) ) 558 ELSE 559 CALL SGET04( N, NRHS, X, LDA, XACT, LDA, 560 $ ROLDC, RESULT( 3 ) ) 561 END IF 562* 563* Check the error bounds from iterative 564* refinement. 565* 566 CALL SPOT05( UPLO, N, NRHS, ASAV, LDA, B, LDA, 567 $ X, LDA, XACT, LDA, RWORK, 568 $ RWORK( NRHS+1 ), RESULT( 4 ) ) 569 ELSE 570 K1 = 6 571 END IF 572* 573* Compare RCOND from SPOSVX with the computed value 574* in RCONDC. 575* 576 RESULT( 6 ) = SGET06( RCOND, RCONDC ) 577* 578* Print information about the tests that did not pass 579* the threshold. 580* 581 DO 80 K = K1, 6 582 IF( RESULT( K ).GE.THRESH ) THEN 583 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 584 $ CALL ALADHD( NOUT, PATH ) 585 IF( PREFAC ) THEN 586 WRITE( NOUT, FMT = 9997 )'SPOSVX', FACT, 587 $ UPLO, N, EQUED, IMAT, K, RESULT( K ) 588 ELSE 589 WRITE( NOUT, FMT = 9998 )'SPOSVX', FACT, 590 $ UPLO, N, IMAT, K, RESULT( K ) 591 END IF 592 NFAIL = NFAIL + 1 593 END IF 594 80 CONTINUE 595 NRUN = NRUN + 7 - K1 596 90 CONTINUE 597 100 CONTINUE 598 110 CONTINUE 599 120 CONTINUE 600 130 CONTINUE 601* 602* Print a summary of the results. 603* 604 CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) 605* 606 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1, 607 $ ', test(', I1, ')=', G12.5 ) 608 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5, 609 $ ', type ', I1, ', test(', I1, ')=', G12.5 ) 610 9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5, 611 $ ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ') =', 612 $ G12.5 ) 613 RETURN 614* 615* End of SDRVPO 616* 617 END 618