1*> \brief \b SDRVPP 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 SDRVPP( 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*> SDRVPP tests the driver routines SPPSV 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 91*> (NMAX*(NMAX+1)/2) 92*> \endverbatim 93*> 94*> \param[out] AFAC 95*> \verbatim 96*> AFAC is REAL array, dimension 97*> (NMAX*(NMAX+1)/2) 98*> \endverbatim 99*> 100*> \param[out] ASAV 101*> \verbatim 102*> ASAV is REAL array, dimension 103*> (NMAX*(NMAX+1)/2) 104*> \endverbatim 105*> 106*> \param[out] B 107*> \verbatim 108*> B is REAL array, dimension (NMAX*NRHS) 109*> \endverbatim 110*> 111*> \param[out] BSAV 112*> \verbatim 113*> BSAV is REAL array, dimension (NMAX*NRHS) 114*> \endverbatim 115*> 116*> \param[out] X 117*> \verbatim 118*> X is REAL array, dimension (NMAX*NRHS) 119*> \endverbatim 120*> 121*> \param[out] XACT 122*> \verbatim 123*> XACT is REAL array, dimension (NMAX*NRHS) 124*> \endverbatim 125*> 126*> \param[out] S 127*> \verbatim 128*> S is REAL array, dimension (NMAX) 129*> \endverbatim 130*> 131*> \param[out] WORK 132*> \verbatim 133*> WORK is REAL array, dimension 134*> (NMAX*max(3,NRHS)) 135*> \endverbatim 136*> 137*> \param[out] RWORK 138*> \verbatim 139*> RWORK is REAL array, dimension (NMAX+2*NRHS) 140*> \endverbatim 141*> 142*> \param[out] IWORK 143*> \verbatim 144*> IWORK is INTEGER array, dimension (NMAX) 145*> \endverbatim 146*> 147*> \param[in] NOUT 148*> \verbatim 149*> NOUT is INTEGER 150*> The unit number for output. 151*> \endverbatim 152* 153* Authors: 154* ======== 155* 156*> \author Univ. of Tennessee 157*> \author Univ. of California Berkeley 158*> \author Univ. of Colorado Denver 159*> \author NAG Ltd. 160* 161*> \ingroup single_lin 162* 163* ===================================================================== 164 SUBROUTINE SDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, 165 $ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, 166 $ RWORK, IWORK, NOUT ) 167* 168* -- LAPACK test routine -- 169* -- LAPACK is a software package provided by Univ. of Tennessee, -- 170* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 171* 172* .. Scalar Arguments .. 173 LOGICAL TSTERR 174 INTEGER NMAX, NN, NOUT, NRHS 175 REAL THRESH 176* .. 177* .. Array Arguments .. 178 LOGICAL DOTYPE( * ) 179 INTEGER IWORK( * ), NVAL( * ) 180 REAL A( * ), AFAC( * ), ASAV( * ), B( * ), 181 $ BSAV( * ), RWORK( * ), S( * ), WORK( * ), 182 $ X( * ), XACT( * ) 183* .. 184* 185* ===================================================================== 186* 187* .. Parameters .. 188 REAL ONE, ZERO 189 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 190 INTEGER NTYPES 191 PARAMETER ( NTYPES = 9 ) 192 INTEGER NTESTS 193 PARAMETER ( NTESTS = 6 ) 194* .. 195* .. Local Scalars .. 196 LOGICAL EQUIL, NOFACT, PREFAC, ZEROT 197 CHARACTER DIST, EQUED, FACT, PACKIT, TYPE, UPLO, XTYPE 198 CHARACTER*3 PATH 199 INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO, 200 $ IZERO, K, K1, KL, KU, LDA, MODE, N, NERRS, 201 $ NFACT, NFAIL, NIMAT, NPP, NRUN, NT 202 REAL AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC, 203 $ ROLDC, SCOND 204* .. 205* .. Local Arrays .. 206 CHARACTER EQUEDS( 2 ), FACTS( 3 ), PACKS( 2 ), UPLOS( 2 ) 207 INTEGER ISEED( 4 ), ISEEDY( 4 ) 208 REAL RESULT( NTESTS ) 209* .. 210* .. External Functions .. 211 LOGICAL LSAME 212 REAL SGET06, SLANSP 213 EXTERNAL LSAME, SGET06, SLANSP 214* .. 215* .. External Subroutines .. 216 EXTERNAL ALADHD, ALAERH, ALASVM, SCOPY, SERRVX, SGET04, 217 $ SLACPY, SLAQSP, SLARHS, SLASET, SLATB4, SLATMS, 218 $ SPPEQU, SPPSV, SPPSVX, SPPT01, SPPT02, SPPT05, 219 $ SPPTRF, SPPTRI 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* .. Intrinsic Functions .. 231 INTRINSIC MAX 232* .. 233* .. Data statements .. 234 DATA ISEEDY / 1988, 1989, 1990, 1991 / 235 DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N', 'E' / , 236 $ PACKS / 'C', 'R' / , EQUEDS / 'N', 'Y' / 237* .. 238* .. Executable Statements .. 239* 240* Initialize constants and the random number seed. 241* 242 PATH( 1: 1 ) = 'Single precision' 243 PATH( 2: 3 ) = 'PP' 244 NRUN = 0 245 NFAIL = 0 246 NERRS = 0 247 DO 10 I = 1, 4 248 ISEED( I ) = ISEEDY( I ) 249 10 CONTINUE 250* 251* Test the error exits 252* 253 IF( TSTERR ) 254 $ CALL SERRVX( PATH, NOUT ) 255 INFOT = 0 256* 257* Do for each value of N in NVAL 258* 259 DO 140 IN = 1, NN 260 N = NVAL( IN ) 261 LDA = MAX( N, 1 ) 262 NPP = N*( N+1 ) / 2 263 XTYPE = 'N' 264 NIMAT = NTYPES 265 IF( N.LE.0 ) 266 $ NIMAT = 1 267* 268 DO 130 IMAT = 1, NIMAT 269* 270* Do the tests only if DOTYPE( IMAT ) is true. 271* 272 IF( .NOT.DOTYPE( IMAT ) ) 273 $ GO TO 130 274* 275* Skip types 3, 4, or 5 if the matrix size is too small. 276* 277 ZEROT = IMAT.GE.3 .AND. IMAT.LE.5 278 IF( ZEROT .AND. N.LT.IMAT-2 ) 279 $ GO TO 130 280* 281* Do first for UPLO = 'U', then for UPLO = 'L' 282* 283 DO 120 IUPLO = 1, 2 284 UPLO = UPLOS( IUPLO ) 285 PACKIT = PACKS( IUPLO ) 286* 287* Set up parameters with SLATB4 and generate a test matrix 288* with SLATMS. 289* 290 CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, 291 $ CNDNUM, DIST ) 292 RCONDC = ONE / CNDNUM 293* 294 SRNAMT = 'SLATMS' 295 CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, 296 $ CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK, 297 $ INFO ) 298* 299* Check error code from SLATMS. 300* 301 IF( INFO.NE.0 ) THEN 302 CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1, 303 $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) 304 GO TO 120 305 END IF 306* 307* For types 3-5, zero one row and column of the matrix to 308* test that INFO is returned correctly. 309* 310 IF( ZEROT ) THEN 311 IF( IMAT.EQ.3 ) THEN 312 IZERO = 1 313 ELSE IF( IMAT.EQ.4 ) THEN 314 IZERO = N 315 ELSE 316 IZERO = N / 2 + 1 317 END IF 318* 319* Set row and column IZERO of A to 0. 320* 321 IF( IUPLO.EQ.1 ) THEN 322 IOFF = ( IZERO-1 )*IZERO / 2 323 DO 20 I = 1, IZERO - 1 324 A( IOFF+I ) = ZERO 325 20 CONTINUE 326 IOFF = IOFF + IZERO 327 DO 30 I = IZERO, N 328 A( IOFF ) = ZERO 329 IOFF = IOFF + I 330 30 CONTINUE 331 ELSE 332 IOFF = IZERO 333 DO 40 I = 1, IZERO - 1 334 A( IOFF ) = ZERO 335 IOFF = IOFF + N - I 336 40 CONTINUE 337 IOFF = IOFF - IZERO 338 DO 50 I = IZERO, N 339 A( IOFF+I ) = ZERO 340 50 CONTINUE 341 END IF 342 ELSE 343 IZERO = 0 344 END IF 345* 346* Save a copy of the matrix A in ASAV. 347* 348 CALL SCOPY( NPP, A, 1, ASAV, 1 ) 349* 350 DO 110 IEQUED = 1, 2 351 EQUED = EQUEDS( IEQUED ) 352 IF( IEQUED.EQ.1 ) THEN 353 NFACT = 3 354 ELSE 355 NFACT = 1 356 END IF 357* 358 DO 100 IFACT = 1, NFACT 359 FACT = FACTS( IFACT ) 360 PREFAC = LSAME( FACT, 'F' ) 361 NOFACT = LSAME( FACT, 'N' ) 362 EQUIL = LSAME( FACT, 'E' ) 363* 364 IF( ZEROT ) THEN 365 IF( PREFAC ) 366 $ GO TO 100 367 RCONDC = ZERO 368* 369 ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN 370* 371* Compute the condition number for comparison with 372* the value returned by SPPSVX (FACT = 'N' reuses 373* the condition number from the previous iteration 374* with FACT = 'F'). 375* 376 CALL SCOPY( NPP, ASAV, 1, AFAC, 1 ) 377 IF( EQUIL .OR. IEQUED.GT.1 ) THEN 378* 379* Compute row and column scale factors to 380* equilibrate the matrix A. 381* 382 CALL SPPEQU( UPLO, N, AFAC, S, SCOND, AMAX, 383 $ INFO ) 384 IF( INFO.EQ.0 .AND. N.GT.0 ) THEN 385 IF( IEQUED.GT.1 ) 386 $ SCOND = ZERO 387* 388* Equilibrate the matrix. 389* 390 CALL SLAQSP( UPLO, N, AFAC, S, SCOND, 391 $ AMAX, EQUED ) 392 END IF 393 END IF 394* 395* Save the condition number of the 396* non-equilibrated system for use in SGET04. 397* 398 IF( EQUIL ) 399 $ ROLDC = RCONDC 400* 401* Compute the 1-norm of A. 402* 403 ANORM = SLANSP( '1', UPLO, N, AFAC, RWORK ) 404* 405* Factor the matrix A. 406* 407 CALL SPPTRF( UPLO, N, AFAC, INFO ) 408* 409* Form the inverse of A. 410* 411 CALL SCOPY( NPP, AFAC, 1, A, 1 ) 412 CALL SPPTRI( UPLO, N, A, INFO ) 413* 414* Compute the 1-norm condition number of A. 415* 416 AINVNM = SLANSP( '1', UPLO, N, A, RWORK ) 417 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN 418 RCONDC = ONE 419 ELSE 420 RCONDC = ( ONE / ANORM ) / AINVNM 421 END IF 422 END IF 423* 424* Restore the matrix A. 425* 426 CALL SCOPY( NPP, ASAV, 1, A, 1 ) 427* 428* Form an exact solution and set the right hand side. 429* 430 SRNAMT = 'SLARHS' 431 CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU, 432 $ NRHS, A, LDA, XACT, LDA, B, LDA, 433 $ ISEED, INFO ) 434 XTYPE = 'C' 435 CALL SLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) 436* 437 IF( NOFACT ) THEN 438* 439* --- Test SPPSV --- 440* 441* Compute the L*L' or U'*U factorization of the 442* matrix and solve the system. 443* 444 CALL SCOPY( NPP, A, 1, AFAC, 1 ) 445 CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) 446* 447 SRNAMT = 'SPPSV ' 448 CALL SPPSV( UPLO, N, NRHS, AFAC, X, LDA, INFO ) 449* 450* Check error code from SPPSV . 451* 452 IF( INFO.NE.IZERO ) THEN 453 CALL ALAERH( PATH, 'SPPSV ', INFO, IZERO, 454 $ UPLO, N, N, -1, -1, NRHS, IMAT, 455 $ NFAIL, NERRS, NOUT ) 456 GO TO 70 457 ELSE IF( INFO.NE.0 ) THEN 458 GO TO 70 459 END IF 460* 461* Reconstruct matrix from factors and compute 462* residual. 463* 464 CALL SPPT01( UPLO, N, A, AFAC, RWORK, 465 $ RESULT( 1 ) ) 466* 467* Compute residual of the computed solution. 468* 469 CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, 470 $ LDA ) 471 CALL SPPT02( UPLO, N, NRHS, A, X, LDA, WORK, 472 $ LDA, RWORK, RESULT( 2 ) ) 473* 474* Check solution from generated exact solution. 475* 476 CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, 477 $ RESULT( 3 ) ) 478 NT = 3 479* 480* Print information about the tests that did not 481* pass the threshold. 482* 483 DO 60 K = 1, NT 484 IF( RESULT( K ).GE.THRESH ) THEN 485 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 486 $ CALL ALADHD( NOUT, PATH ) 487 WRITE( NOUT, FMT = 9999 )'SPPSV ', UPLO, 488 $ N, IMAT, K, RESULT( K ) 489 NFAIL = NFAIL + 1 490 END IF 491 60 CONTINUE 492 NRUN = NRUN + NT 493 70 CONTINUE 494 END IF 495* 496* --- Test SPPSVX --- 497* 498 IF( .NOT.PREFAC .AND. NPP.GT.0 ) 499 $ CALL SLASET( 'Full', NPP, 1, ZERO, ZERO, AFAC, 500 $ NPP ) 501 CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA ) 502 IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN 503* 504* Equilibrate the matrix if FACT='F' and 505* EQUED='Y'. 506* 507 CALL SLAQSP( UPLO, N, A, S, SCOND, AMAX, EQUED ) 508 END IF 509* 510* Solve the system and compute the condition number 511* and error bounds using SPPSVX. 512* 513 SRNAMT = 'SPPSVX' 514 CALL SPPSVX( FACT, UPLO, N, NRHS, A, AFAC, EQUED, 515 $ S, B, LDA, X, LDA, RCOND, RWORK, 516 $ RWORK( NRHS+1 ), WORK, IWORK, INFO ) 517* 518* Check the error code from SPPSVX. 519* 520 IF( INFO.NE.IZERO ) THEN 521 CALL ALAERH( PATH, 'SPPSVX', INFO, IZERO, 522 $ FACT // UPLO, N, N, -1, -1, NRHS, 523 $ IMAT, NFAIL, NERRS, NOUT ) 524 GO TO 90 525 END IF 526* 527 IF( INFO.EQ.0 ) THEN 528 IF( .NOT.PREFAC ) THEN 529* 530* Reconstruct matrix from factors and compute 531* residual. 532* 533 CALL SPPT01( UPLO, N, A, AFAC, 534 $ RWORK( 2*NRHS+1 ), RESULT( 1 ) ) 535 K1 = 1 536 ELSE 537 K1 = 2 538 END IF 539* 540* Compute residual of the computed solution. 541* 542 CALL SLACPY( 'Full', N, NRHS, BSAV, LDA, WORK, 543 $ LDA ) 544 CALL SPPT02( UPLO, N, NRHS, ASAV, X, LDA, WORK, 545 $ LDA, RWORK( 2*NRHS+1 ), 546 $ RESULT( 2 ) ) 547* 548* Check solution from generated exact solution. 549* 550 IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED, 551 $ 'N' ) ) ) THEN 552 CALL SGET04( N, NRHS, X, LDA, XACT, LDA, 553 $ RCONDC, RESULT( 3 ) ) 554 ELSE 555 CALL SGET04( N, NRHS, X, LDA, XACT, LDA, 556 $ ROLDC, RESULT( 3 ) ) 557 END IF 558* 559* Check the error bounds from iterative 560* refinement. 561* 562 CALL SPPT05( UPLO, N, NRHS, ASAV, B, LDA, X, 563 $ LDA, XACT, LDA, RWORK, 564 $ RWORK( NRHS+1 ), RESULT( 4 ) ) 565 ELSE 566 K1 = 6 567 END IF 568* 569* Compare RCOND from SPPSVX with the computed value 570* in RCONDC. 571* 572 RESULT( 6 ) = SGET06( RCOND, RCONDC ) 573* 574* Print information about the tests that did not pass 575* the threshold. 576* 577 DO 80 K = K1, 6 578 IF( RESULT( K ).GE.THRESH ) THEN 579 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 580 $ CALL ALADHD( NOUT, PATH ) 581 IF( PREFAC ) THEN 582 WRITE( NOUT, FMT = 9997 )'SPPSVX', FACT, 583 $ UPLO, N, EQUED, IMAT, K, RESULT( K ) 584 ELSE 585 WRITE( NOUT, FMT = 9998 )'SPPSVX', FACT, 586 $ UPLO, N, IMAT, K, RESULT( K ) 587 END IF 588 NFAIL = NFAIL + 1 589 END IF 590 80 CONTINUE 591 NRUN = NRUN + 7 - K1 592 90 CONTINUE 593 100 CONTINUE 594 110 CONTINUE 595 120 CONTINUE 596 130 CONTINUE 597 140 CONTINUE 598* 599* Print a summary of the results. 600* 601 CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) 602* 603 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1, 604 $ ', test(', I1, ')=', G12.5 ) 605 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5, 606 $ ', type ', I1, ', test(', I1, ')=', G12.5 ) 607 9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5, 608 $ ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ')=', 609 $ G12.5 ) 610 RETURN 611* 612* End of SDRVPP 613* 614 END 615