1*> \brief \b CDRVHE 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 CDRVHE( 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*> CDRVHE tests the driver routines CHESV 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 (NMAX*max(2,NRHS)) 121*> \endverbatim 122*> 123*> \param[out] RWORK 124*> \verbatim 125*> RWORK is REAL array, dimension (NMAX+2*NRHS) 126*> \endverbatim 127*> 128*> \param[out] IWORK 129*> \verbatim 130*> IWORK is INTEGER array, dimension (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*> \date November 2013 148* 149*> \ingroup complex_lin 150* 151* ===================================================================== 152 SUBROUTINE CDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, 153 $ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, 154 $ NOUT ) 155* 156* -- LAPACK test routine (version 3.5.0) -- 157* -- LAPACK is a software package provided by Univ. of Tennessee, -- 158* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 159* November 2013 160* 161* .. Scalar Arguments .. 162 LOGICAL TSTERR 163 INTEGER NMAX, NN, NOUT, NRHS 164 REAL THRESH 165* .. 166* .. Array Arguments .. 167 LOGICAL DOTYPE( * ) 168 INTEGER IWORK( * ), NVAL( * ) 169 REAL RWORK( * ) 170 COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ), 171 $ WORK( * ), X( * ), XACT( * ) 172* .. 173* 174* ===================================================================== 175* 176* .. Parameters .. 177 REAL ONE, ZERO 178 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 179 INTEGER NTYPES, NTESTS 180 PARAMETER ( NTYPES = 10, NTESTS = 6 ) 181 INTEGER NFACT 182 PARAMETER ( NFACT = 2 ) 183* .. 184* .. Local Scalars .. 185 LOGICAL ZEROT 186 CHARACTER DIST, FACT, TYPE, UPLO, XTYPE 187 CHARACTER*3 PATH 188 INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO, 189 $ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N, 190 $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT 191 REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC 192* .. 193* .. Local Arrays .. 194 CHARACTER FACTS( NFACT ), UPLOS( 2 ) 195 INTEGER ISEED( 4 ), ISEEDY( 4 ) 196 REAL RESULT( NTESTS ) 197* .. 198* .. External Functions .. 199 REAL CLANHE, SGET06 200 EXTERNAL CLANHE, SGET06 201* .. 202* .. External Subroutines .. 203 EXTERNAL ALADHD, ALAERH, ALASVM, CERRVX, CGET04, CHESV, 204 $ CHESVX, CHET01, CHETRF, CHETRI2, CLACPY, 205 $ CLAIPD, CLARHS, CLASET, CLATB4, CLATMS, CPOT02, 206 $ CPOT05, XLAENV 207* .. 208* .. Scalars in Common .. 209 LOGICAL LERR, OK 210 CHARACTER*32 SRNAMT 211 INTEGER INFOT, NUNIT 212* .. 213* .. Common blocks .. 214 COMMON / INFOC / INFOT, NUNIT, OK, LERR 215 COMMON / SRNAMC / SRNAMT 216* .. 217* .. Intrinsic Functions .. 218 INTRINSIC CMPLX, MAX, MIN 219* .. 220* .. Data statements .. 221 DATA ISEEDY / 1988, 1989, 1990, 1991 / 222 DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' / 223* .. 224* .. Executable Statements .. 225* 226* Initialize constants and the random number seed. 227* 228 PATH( 1: 1 ) = 'Complex precision' 229 PATH( 2: 3 ) = 'HE' 230 NRUN = 0 231 NFAIL = 0 232 NERRS = 0 233 DO 10 I = 1, 4 234 ISEED( I ) = ISEEDY( I ) 235 10 CONTINUE 236 LWORK = MAX( 2*NMAX, NMAX*NRHS ) 237* 238* Test the error exits 239* 240 IF( TSTERR ) 241 $ CALL CERRVX( PATH, NOUT ) 242 INFOT = 0 243* 244* Set the block size and minimum block size for testing. 245* 246 NB = 1 247 NBMIN = 2 248 CALL XLAENV( 1, NB ) 249 CALL XLAENV( 2, NBMIN ) 250* 251* Do for each value of N in NVAL 252* 253 DO 180 IN = 1, NN 254 N = NVAL( IN ) 255 LDA = MAX( N, 1 ) 256 XTYPE = 'N' 257 NIMAT = NTYPES 258 IF( N.LE.0 ) 259 $ NIMAT = 1 260* 261 DO 170 IMAT = 1, NIMAT 262* 263* Do the tests only if DOTYPE( IMAT ) is true. 264* 265 IF( .NOT.DOTYPE( IMAT ) ) 266 $ GO TO 170 267* 268* Skip types 3, 4, 5, or 6 if the matrix size is too small. 269* 270 ZEROT = IMAT.GE.3 .AND. IMAT.LE.6 271 IF( ZEROT .AND. N.LT.IMAT-2 ) 272 $ GO TO 170 273* 274* Do first for UPLO = 'U', then for UPLO = 'L' 275* 276 DO 160 IUPLO = 1, 2 277 UPLO = UPLOS( IUPLO ) 278* 279* Set up parameters with CLATB4 and generate a test matrix 280* with CLATMS. 281* 282 CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, 283 $ CNDNUM, DIST ) 284* 285 SRNAMT = 'CLATMS' 286 CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, 287 $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK, 288 $ INFO ) 289* 290* Check error code from CLATMS. 291* 292 IF( INFO.NE.0 ) THEN 293 CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N, -1, 294 $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) 295 GO TO 160 296 END IF 297* 298* For types 3-6, zero one or more rows and columns of the 299* matrix to test that INFO is returned correctly. 300* 301 IF( ZEROT ) THEN 302 IF( IMAT.EQ.3 ) THEN 303 IZERO = 1 304 ELSE IF( IMAT.EQ.4 ) THEN 305 IZERO = N 306 ELSE 307 IZERO = N / 2 + 1 308 END IF 309* 310 IF( IMAT.LT.6 ) THEN 311* 312* Set row and column IZERO to zero. 313* 314 IF( IUPLO.EQ.1 ) THEN 315 IOFF = ( IZERO-1 )*LDA 316 DO 20 I = 1, IZERO - 1 317 A( IOFF+I ) = ZERO 318 20 CONTINUE 319 IOFF = IOFF + IZERO 320 DO 30 I = IZERO, N 321 A( IOFF ) = ZERO 322 IOFF = IOFF + LDA 323 30 CONTINUE 324 ELSE 325 IOFF = IZERO 326 DO 40 I = 1, IZERO - 1 327 A( IOFF ) = ZERO 328 IOFF = IOFF + LDA 329 40 CONTINUE 330 IOFF = IOFF - IZERO 331 DO 50 I = IZERO, N 332 A( IOFF+I ) = ZERO 333 50 CONTINUE 334 END IF 335 ELSE 336 IOFF = 0 337 IF( IUPLO.EQ.1 ) THEN 338* 339* Set the first IZERO rows and columns to zero. 340* 341 DO 70 J = 1, N 342 I2 = MIN( J, IZERO ) 343 DO 60 I = 1, I2 344 A( IOFF+I ) = ZERO 345 60 CONTINUE 346 IOFF = IOFF + LDA 347 70 CONTINUE 348 ELSE 349* 350* Set the last IZERO rows and columns to zero. 351* 352 DO 90 J = 1, N 353 I1 = MAX( J, IZERO ) 354 DO 80 I = I1, N 355 A( IOFF+I ) = ZERO 356 80 CONTINUE 357 IOFF = IOFF + LDA 358 90 CONTINUE 359 END IF 360 END IF 361 ELSE 362 IZERO = 0 363 END IF 364* 365* Set the imaginary part of the diagonals. 366* 367 CALL CLAIPD( N, A, LDA+1, 0 ) 368* 369 DO 150 IFACT = 1, NFACT 370* 371* Do first for FACT = 'F', then for other values. 372* 373 FACT = FACTS( IFACT ) 374* 375* Compute the condition number for comparison with 376* the value returned by CHESVX. 377* 378 IF( ZEROT ) THEN 379 IF( IFACT.EQ.1 ) 380 $ GO TO 150 381 RCONDC = ZERO 382* 383 ELSE IF( IFACT.EQ.1 ) THEN 384* 385* Compute the 1-norm of A. 386* 387 ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK ) 388* 389* Factor the matrix A. 390* 391 CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) 392 CALL CHETRF( UPLO, N, AFAC, LDA, IWORK, WORK, 393 $ LWORK, INFO ) 394* 395* Compute inv(A) and take its norm. 396* 397 CALL CLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA ) 398 LWORK = (N+NB+1)*(NB+3) 399 CALL CHETRI2( UPLO, N, AINV, LDA, IWORK, WORK, 400 $ LWORK, INFO ) 401 AINVNM = CLANHE( '1', UPLO, N, AINV, LDA, RWORK ) 402* 403* Compute the 1-norm condition number of A. 404* 405 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN 406 RCONDC = ONE 407 ELSE 408 RCONDC = ( ONE / ANORM ) / AINVNM 409 END IF 410 END IF 411* 412* Form an exact solution and set the right hand side. 413* 414 SRNAMT = 'CLARHS' 415 CALL CLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU, 416 $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED, 417 $ INFO ) 418 XTYPE = 'C' 419* 420* --- Test CHESV --- 421* 422 IF( IFACT.EQ.2 ) THEN 423 CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) 424 CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) 425* 426* Factor the matrix and solve the system using CHESV. 427* 428 SRNAMT = 'CHESV ' 429 CALL CHESV( UPLO, N, NRHS, AFAC, LDA, IWORK, X, 430 $ LDA, WORK, LWORK, INFO ) 431* 432* Adjust the expected value of INFO to account for 433* pivoting. 434* 435 K = IZERO 436 IF( K.GT.0 ) THEN 437 100 CONTINUE 438 IF( IWORK( K ).LT.0 ) THEN 439 IF( IWORK( K ).NE.-K ) THEN 440 K = -IWORK( K ) 441 GO TO 100 442 END IF 443 ELSE IF( IWORK( K ).NE.K ) THEN 444 K = IWORK( K ) 445 GO TO 100 446 END IF 447 END IF 448* 449* Check error code from CHESV . 450* 451 IF( INFO.NE.K ) THEN 452 CALL ALAERH( PATH, 'CHESV ', INFO, K, UPLO, N, 453 $ N, -1, -1, NRHS, IMAT, NFAIL, 454 $ NERRS, NOUT ) 455 GO TO 120 456 ELSE IF( INFO.NE.0 ) THEN 457 GO TO 120 458 END IF 459* 460* Reconstruct matrix from factors and compute 461* residual. 462* 463 CALL CHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK, 464 $ AINV, LDA, RWORK, RESULT( 1 ) ) 465* 466* Compute residual of the computed solution. 467* 468 CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) 469 CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK, 470 $ LDA, RWORK, RESULT( 2 ) ) 471* 472* Check solution from generated exact solution. 473* 474 CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, 475 $ RESULT( 3 ) ) 476 NT = 3 477* 478* Print information about the tests that did not pass 479* the threshold. 480* 481 DO 110 K = 1, NT 482 IF( RESULT( K ).GE.THRESH ) THEN 483 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 484 $ CALL ALADHD( NOUT, PATH ) 485 WRITE( NOUT, FMT = 9999 )'CHESV ', UPLO, N, 486 $ IMAT, K, RESULT( K ) 487 NFAIL = NFAIL + 1 488 END IF 489 110 CONTINUE 490 NRUN = NRUN + NT 491 120 CONTINUE 492 END IF 493* 494* --- Test CHESVX --- 495* 496 IF( IFACT.EQ.2 ) 497 $ CALL CLASET( UPLO, N, N, CMPLX( ZERO ), 498 $ CMPLX( ZERO ), AFAC, LDA ) 499 CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ), 500 $ CMPLX( ZERO ), X, LDA ) 501* 502* Solve the system and compute the condition number and 503* error bounds using CHESVX. 504* 505 SRNAMT = 'CHESVX' 506 CALL CHESVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA, 507 $ IWORK, B, LDA, X, LDA, RCOND, RWORK, 508 $ RWORK( NRHS+1 ), WORK, LWORK, 509 $ RWORK( 2*NRHS+1 ), INFO ) 510* 511* Adjust the expected value of INFO to account for 512* pivoting. 513* 514 K = IZERO 515 IF( K.GT.0 ) THEN 516 130 CONTINUE 517 IF( IWORK( K ).LT.0 ) THEN 518 IF( IWORK( K ).NE.-K ) THEN 519 K = -IWORK( K ) 520 GO TO 130 521 END IF 522 ELSE IF( IWORK( K ).NE.K ) THEN 523 K = IWORK( K ) 524 GO TO 130 525 END IF 526 END IF 527* 528* Check the error code from CHESVX. 529* 530 IF( INFO.NE.K ) THEN 531 CALL ALAERH( PATH, 'CHESVX', INFO, K, FACT // UPLO, 532 $ N, N, -1, -1, NRHS, IMAT, NFAIL, 533 $ NERRS, NOUT ) 534 GO TO 150 535 END IF 536* 537 IF( INFO.EQ.0 ) THEN 538 IF( IFACT.GE.2 ) THEN 539* 540* Reconstruct matrix from factors and compute 541* residual. 542* 543 CALL CHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK, 544 $ AINV, LDA, RWORK( 2*NRHS+1 ), 545 $ RESULT( 1 ) ) 546 K1 = 1 547 ELSE 548 K1 = 2 549 END IF 550* 551* Compute residual of the computed solution. 552* 553 CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) 554 CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK, 555 $ LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) ) 556* 557* Check solution from generated exact solution. 558* 559 CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, 560 $ RESULT( 3 ) ) 561* 562* Check the error bounds from iterative refinement. 563* 564 CALL CPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA, 565 $ XACT, LDA, RWORK, RWORK( NRHS+1 ), 566 $ RESULT( 4 ) ) 567 ELSE 568 K1 = 6 569 END IF 570* 571* Compare RCOND from CHESVX with the computed value 572* in RCONDC. 573* 574 RESULT( 6 ) = SGET06( RCOND, RCONDC ) 575* 576* Print information about the tests that did not pass 577* the threshold. 578* 579 DO 140 K = K1, 6 580 IF( RESULT( K ).GE.THRESH ) THEN 581 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 582 $ CALL ALADHD( NOUT, PATH ) 583 WRITE( NOUT, FMT = 9998 )'CHESVX', FACT, UPLO, 584 $ N, IMAT, K, RESULT( K ) 585 NFAIL = NFAIL + 1 586 END IF 587 140 CONTINUE 588 NRUN = NRUN + 7 - K1 589* 590 150 CONTINUE 591* 592 160 CONTINUE 593 170 CONTINUE 594 180 CONTINUE 595* 596* Print a summary of the results. 597* 598 CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) 599* 600 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2, 601 $ ', test ', I2, ', ratio =', G12.5 ) 602 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5, 603 $ ', type ', I2, ', test ', I2, ', ratio =', G12.5 ) 604 RETURN 605* 606* End of CDRVHE 607* 608 END 609