1*> \brief \b CDRVSY 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 CDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, 12* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, 13* 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 RWORK( * ) 24* COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ), 25* $ WORK( * ), X( * ), XACT( * ) 26* .. 27* 28* 29*> \par Purpose: 30* ============= 31*> 32*> \verbatim 33*> 34*> CDRVSY tests the driver routines CSYSV 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 COMPLEX array, dimension (NMAX*NMAX) 91*> \endverbatim 92*> 93*> \param[out] AFAC 94*> \verbatim 95*> AFAC is COMPLEX array, dimension (NMAX*NMAX) 96*> \endverbatim 97*> 98*> \param[out] AINV 99*> \verbatim 100*> AINV is COMPLEX array, dimension (NMAX*NMAX) 101*> \endverbatim 102*> 103*> \param[out] B 104*> \verbatim 105*> B is COMPLEX array, dimension (NMAX*NRHS) 106*> \endverbatim 107*> 108*> \param[out] X 109*> \verbatim 110*> X is COMPLEX array, dimension (NMAX*NRHS) 111*> \endverbatim 112*> 113*> \param[out] XACT 114*> \verbatim 115*> XACT is COMPLEX array, dimension (NMAX*NRHS) 116*> \endverbatim 117*> 118*> \param[out] WORK 119*> \verbatim 120*> WORK is COMPLEX array, dimension 121*> (NMAX*max(2,NRHS)) 122*> \endverbatim 123*> 124*> \param[out] RWORK 125*> \verbatim 126*> RWORK is REAL array, dimension (NMAX+2*NRHS) 127*> \endverbatim 128*> 129*> \param[out] IWORK 130*> \verbatim 131*> IWORK is INTEGER array, dimension (NMAX) 132*> \endverbatim 133*> 134*> \param[in] NOUT 135*> \verbatim 136*> NOUT is INTEGER 137*> The unit number for output. 138*> \endverbatim 139* 140* Authors: 141* ======== 142* 143*> \author Univ. of Tennessee 144*> \author Univ. of California Berkeley 145*> \author Univ. of Colorado Denver 146*> \author NAG Ltd. 147* 148*> \date November 2011 149* 150*> \ingroup complex_lin 151* 152* ===================================================================== 153 SUBROUTINE CDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, 154 $ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, 155 $ NOUT ) 156* 157* -- LAPACK test routine (version 3.4.0) -- 158* -- LAPACK is a software package provided by Univ. of Tennessee, -- 159* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 160* November 2011 161* 162* .. Scalar Arguments .. 163 LOGICAL TSTERR 164 INTEGER NMAX, NN, NOUT, NRHS 165 REAL THRESH 166* .. 167* .. Array Arguments .. 168 LOGICAL DOTYPE( * ) 169 INTEGER IWORK( * ), NVAL( * ) 170 REAL RWORK( * ) 171 COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ), 172 $ WORK( * ), X( * ), XACT( * ) 173* .. 174* 175* ===================================================================== 176* 177* .. Parameters .. 178 REAL ONE, ZERO 179 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 180 INTEGER NTYPES, NTESTS 181 PARAMETER ( NTYPES = 11, NTESTS = 6 ) 182 INTEGER NFACT 183 PARAMETER ( NFACT = 2 ) 184* .. 185* .. Local Scalars .. 186 LOGICAL ZEROT 187 CHARACTER DIST, FACT, TYPE, UPLO, XTYPE 188 CHARACTER*3 PATH 189 INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO, 190 $ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N, 191 $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT 192 REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC 193* .. 194* .. Local Arrays .. 195 CHARACTER FACTS( NFACT ), UPLOS( 2 ) 196 INTEGER ISEED( 4 ), ISEEDY( 4 ) 197 REAL RESULT( NTESTS ) 198* .. 199* .. External Functions .. 200 REAL CLANSY, SGET06 201 EXTERNAL CLANSY, SGET06 202* .. 203* .. External Subroutines .. 204 EXTERNAL ALADHD, ALAERH, ALASVM, CERRVX, CGET04, CLACPY, 205 $ CLARHS, CLASET, CLATB4, CLATMS, CLATSY, CPOT05, 206 $ CSYSV, CSYSVX, CSYT01, CSYT02, CSYTRF, CSYTRI2, 207 $ XLAENV 208* .. 209* .. Scalars in Common .. 210 LOGICAL LERR, OK 211 CHARACTER*32 SRNAMT 212 INTEGER INFOT, NUNIT 213* .. 214* .. Common blocks .. 215 COMMON / INFOC / INFOT, NUNIT, OK, LERR 216 COMMON / SRNAMC / SRNAMT 217* .. 218* .. Intrinsic Functions .. 219 INTRINSIC CMPLX, MAX, MIN 220* .. 221* .. Data statements .. 222 DATA ISEEDY / 1988, 1989, 1990, 1991 / 223 DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' / 224* .. 225* .. Executable Statements .. 226* 227* Initialize constants and the random number seed. 228* 229 PATH( 1: 1 ) = 'Complex precision' 230 PATH( 2: 3 ) = 'SY' 231 NRUN = 0 232 NFAIL = 0 233 NERRS = 0 234 DO 10 I = 1, 4 235 ISEED( I ) = ISEEDY( I ) 236 10 CONTINUE 237 LWORK = MAX( 2*NMAX, NMAX*NRHS ) 238* 239* Test the error exits 240* 241 IF( TSTERR ) 242 $ CALL CERRVX( PATH, NOUT ) 243 INFOT = 0 244* 245* Set the block size and minimum block size for testing. 246* 247 NB = 1 248 NBMIN = 2 249 CALL XLAENV( 1, NB ) 250 CALL XLAENV( 2, NBMIN ) 251* 252* Do for each value of N in NVAL 253* 254 DO 180 IN = 1, NN 255 N = NVAL( IN ) 256 LDA = MAX( N, 1 ) 257 XTYPE = 'N' 258 NIMAT = NTYPES 259 IF( N.LE.0 ) 260 $ NIMAT = 1 261* 262 DO 170 IMAT = 1, NIMAT 263* 264* Do the tests only if DOTYPE( IMAT ) is true. 265* 266 IF( .NOT.DOTYPE( IMAT ) ) 267 $ GO TO 170 268* 269* Skip types 3, 4, 5, or 6 if the matrix size is too small. 270* 271 ZEROT = IMAT.GE.3 .AND. IMAT.LE.6 272 IF( ZEROT .AND. N.LT.IMAT-2 ) 273 $ GO TO 170 274* 275* Do first for UPLO = 'U', then for UPLO = 'L' 276* 277 DO 160 IUPLO = 1, 2 278 UPLO = UPLOS( IUPLO ) 279* 280 IF( IMAT.NE.NTYPES ) THEN 281* 282* Set up parameters with CLATB4 and generate a test 283* matrix with CLATMS. 284* 285 CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, 286 $ MODE, CNDNUM, DIST ) 287* 288 SRNAMT = 'CLATMS' 289 CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, 290 $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, 291 $ WORK, INFO ) 292* 293* Check error code from CLATMS. 294* 295 IF( INFO.NE.0 ) THEN 296 CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N, 297 $ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT ) 298 GO TO 160 299 END IF 300* 301* For types 3-6, zero one or more rows and columns of 302* the matrix to test that INFO is returned correctly. 303* 304 IF( ZEROT ) THEN 305 IF( IMAT.EQ.3 ) THEN 306 IZERO = 1 307 ELSE IF( IMAT.EQ.4 ) THEN 308 IZERO = N 309 ELSE 310 IZERO = N / 2 + 1 311 END IF 312* 313 IF( IMAT.LT.6 ) THEN 314* 315* Set row and column IZERO to zero. 316* 317 IF( IUPLO.EQ.1 ) THEN 318 IOFF = ( IZERO-1 )*LDA 319 DO 20 I = 1, IZERO - 1 320 A( IOFF+I ) = ZERO 321 20 CONTINUE 322 IOFF = IOFF + IZERO 323 DO 30 I = IZERO, N 324 A( IOFF ) = ZERO 325 IOFF = IOFF + LDA 326 30 CONTINUE 327 ELSE 328 IOFF = IZERO 329 DO 40 I = 1, IZERO - 1 330 A( IOFF ) = ZERO 331 IOFF = IOFF + LDA 332 40 CONTINUE 333 IOFF = IOFF - IZERO 334 DO 50 I = IZERO, N 335 A( IOFF+I ) = ZERO 336 50 CONTINUE 337 END IF 338 ELSE 339 IF( IUPLO.EQ.1 ) THEN 340* 341* Set the first IZERO rows to zero. 342* 343 IOFF = 0 344 DO 70 J = 1, N 345 I2 = MIN( J, IZERO ) 346 DO 60 I = 1, I2 347 A( IOFF+I ) = ZERO 348 60 CONTINUE 349 IOFF = IOFF + LDA 350 70 CONTINUE 351 ELSE 352* 353* Set the last IZERO rows to zero. 354* 355 IOFF = 0 356 DO 90 J = 1, N 357 I1 = MAX( J, IZERO ) 358 DO 80 I = I1, N 359 A( IOFF+I ) = ZERO 360 80 CONTINUE 361 IOFF = IOFF + LDA 362 90 CONTINUE 363 END IF 364 END IF 365 ELSE 366 IZERO = 0 367 END IF 368 ELSE 369* 370* IMAT = NTYPES: Use a special block diagonal matrix to 371* test alternate code for the 2-by-2 blocks. 372* 373 CALL CLATSY( UPLO, N, A, LDA, ISEED ) 374 END IF 375* 376 DO 150 IFACT = 1, NFACT 377* 378* Do first for FACT = 'F', then for other values. 379* 380 FACT = FACTS( IFACT ) 381* 382* Compute the condition number for comparison with 383* the value returned by CSYSVX. 384* 385 IF( ZEROT ) THEN 386 IF( IFACT.EQ.1 ) 387 $ GO TO 150 388 RCONDC = ZERO 389* 390 ELSE IF( IFACT.EQ.1 ) THEN 391* 392* Compute the 1-norm of A. 393* 394 ANORM = CLANSY( '1', UPLO, N, A, LDA, RWORK ) 395* 396* Factor the matrix A. 397* 398 CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) 399 CALL CSYTRF( UPLO, N, AFAC, LDA, IWORK, WORK, 400 $ LWORK, INFO ) 401* 402* Compute inv(A) and take its norm. 403* 404 CALL CLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA ) 405 LWORK = (N+NB+1)*(NB+3) 406 CALL CSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK, 407 $ LWORK, INFO ) 408 AINVNM = CLANSY( '1', UPLO, N, AINV, LDA, RWORK ) 409* 410* Compute the 1-norm condition number of A. 411* 412 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN 413 RCONDC = ONE 414 ELSE 415 RCONDC = ( ONE / ANORM ) / AINVNM 416 END IF 417 END IF 418* 419* Form an exact solution and set the right hand side. 420* 421 SRNAMT = 'CLARHS' 422 CALL CLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU, 423 $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED, 424 $ INFO ) 425 XTYPE = 'C' 426* 427* --- Test CSYSV --- 428* 429 IF( IFACT.EQ.2 ) THEN 430 CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) 431 CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) 432* 433* Factor the matrix and solve the system using CSYSV. 434* 435 SRNAMT = 'CSYSV ' 436 CALL CSYSV( UPLO, N, NRHS, AFAC, LDA, IWORK, X, 437 $ LDA, WORK, LWORK, INFO ) 438* 439* Adjust the expected value of INFO to account for 440* pivoting. 441* 442 K = IZERO 443 IF( K.GT.0 ) THEN 444 100 CONTINUE 445 IF( IWORK( K ).LT.0 ) THEN 446 IF( IWORK( K ).NE.-K ) THEN 447 K = -IWORK( K ) 448 GO TO 100 449 END IF 450 ELSE IF( IWORK( K ).NE.K ) THEN 451 K = IWORK( K ) 452 GO TO 100 453 END IF 454 END IF 455* 456* Check error code from CSYSV . 457* 458 IF( INFO.NE.K ) THEN 459 CALL ALAERH( PATH, 'CSYSV ', INFO, K, UPLO, N, 460 $ N, -1, -1, NRHS, IMAT, NFAIL, 461 $ NERRS, NOUT ) 462 GO TO 120 463 ELSE IF( INFO.NE.0 ) THEN 464 GO TO 120 465 END IF 466* 467* Reconstruct matrix from factors and compute 468* residual. 469* 470 CALL CSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK, 471 $ AINV, LDA, RWORK, RESULT( 1 ) ) 472* 473* Compute residual of the computed solution. 474* 475 CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) 476 CALL CSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK, 477 $ LDA, RWORK, RESULT( 2 ) ) 478* 479* Check solution from generated exact solution. 480* 481 CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, 482 $ RESULT( 3 ) ) 483 NT = 3 484* 485* Print information about the tests that did not pass 486* the threshold. 487* 488 DO 110 K = 1, NT 489 IF( RESULT( K ).GE.THRESH ) THEN 490 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 491 $ CALL ALADHD( NOUT, PATH ) 492 WRITE( NOUT, FMT = 9999 )'CSYSV ', UPLO, N, 493 $ IMAT, K, RESULT( K ) 494 NFAIL = NFAIL + 1 495 END IF 496 110 CONTINUE 497 NRUN = NRUN + NT 498 120 CONTINUE 499 END IF 500* 501* --- Test CSYSVX --- 502* 503 IF( IFACT.EQ.2 ) 504 $ CALL CLASET( UPLO, N, N, CMPLX( ZERO ), 505 $ CMPLX( ZERO ), AFAC, LDA ) 506 CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ), 507 $ CMPLX( ZERO ), X, LDA ) 508* 509* Solve the system and compute the condition number and 510* error bounds using CSYSVX. 511* 512 SRNAMT = 'CSYSVX' 513 CALL CSYSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA, 514 $ IWORK, B, LDA, X, LDA, RCOND, RWORK, 515 $ RWORK( NRHS+1 ), WORK, LWORK, 516 $ RWORK( 2*NRHS+1 ), INFO ) 517* 518* Adjust the expected value of INFO to account for 519* pivoting. 520* 521 K = IZERO 522 IF( K.GT.0 ) THEN 523 130 CONTINUE 524 IF( IWORK( K ).LT.0 ) THEN 525 IF( IWORK( K ).NE.-K ) THEN 526 K = -IWORK( K ) 527 GO TO 130 528 END IF 529 ELSE IF( IWORK( K ).NE.K ) THEN 530 K = IWORK( K ) 531 GO TO 130 532 END IF 533 END IF 534* 535* Check the error code from CSYSVX. 536* 537 IF( INFO.NE.K ) THEN 538 CALL ALAERH( PATH, 'CSYSVX', INFO, K, FACT // UPLO, 539 $ N, N, -1, -1, NRHS, IMAT, NFAIL, 540 $ NERRS, NOUT ) 541 GO TO 150 542 END IF 543* 544 IF( INFO.EQ.0 ) THEN 545 IF( IFACT.GE.2 ) THEN 546* 547* Reconstruct matrix from factors and compute 548* residual. 549* 550 CALL CSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK, 551 $ AINV, LDA, RWORK( 2*NRHS+1 ), 552 $ RESULT( 1 ) ) 553 K1 = 1 554 ELSE 555 K1 = 2 556 END IF 557* 558* Compute residual of the computed solution. 559* 560 CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) 561 CALL CSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK, 562 $ LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) ) 563* 564* Check solution from generated exact solution. 565* 566 CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, 567 $ RESULT( 3 ) ) 568* 569* Check the error bounds from iterative refinement. 570* 571 CALL CPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA, 572 $ XACT, LDA, RWORK, RWORK( NRHS+1 ), 573 $ RESULT( 4 ) ) 574 ELSE 575 K1 = 6 576 END IF 577* 578* Compare RCOND from CSYSVX with the computed value 579* in RCONDC. 580* 581 RESULT( 6 ) = SGET06( RCOND, RCONDC ) 582* 583* Print information about the tests that did not pass 584* the threshold. 585* 586 DO 140 K = K1, 6 587 IF( RESULT( K ).GE.THRESH ) THEN 588 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 589 $ CALL ALADHD( NOUT, PATH ) 590 WRITE( NOUT, FMT = 9998 )'CSYSVX', FACT, UPLO, 591 $ N, IMAT, K, RESULT( K ) 592 NFAIL = NFAIL + 1 593 END IF 594 140 CONTINUE 595 NRUN = NRUN + 7 - K1 596* 597 150 CONTINUE 598* 599 160 CONTINUE 600 170 CONTINUE 601 180 CONTINUE 602* 603* Print a summary of the results. 604* 605 CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) 606* 607 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2, 608 $ ', test ', I2, ', ratio =', G12.5 ) 609 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5, 610 $ ', type ', I2, ', test ', I2, ', ratio =', G12.5 ) 611 RETURN 612* 613* End of CDRVSY 614* 615 END 616