1*> \brief \b ZDRVSY_ROOK 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 ZDRVSY_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, 12* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, 13* IWORK, NOUT ) 14* 15* .. Scalar Arguments .. 16* LOGICAL TSTERR 17* INTEGER NMAX, NN, NOUT, NRHS 18* DOUBLE PRECISION THRESH 19* .. 20* .. Array Arguments .. 21* LOGICAL DOTYPE( * ) 22* INTEGER IWORK( * ), NVAL( * ) 23* DOUBLE PRECISION RWORK( * ) 24* COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), 25* $ WORK( * ), X( * ), XACT( * ) 26* .. 27* 28* 29*> \par Purpose: 30* ============= 31*> 32*> \verbatim 33*> 34*> ZDRVSY_ROOK tests the driver routines ZSYSV_ROOK. 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 DOUBLE PRECISION 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*16 array, dimension (NMAX*NMAX) 91*> \endverbatim 92*> 93*> \param[out] AFAC 94*> \verbatim 95*> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX) 96*> \endverbatim 97*> 98*> \param[out] AINV 99*> \verbatim 100*> AINV is COMPLEX*16 array, dimension (NMAX*NMAX) 101*> \endverbatim 102*> 103*> \param[out] B 104*> \verbatim 105*> B is COMPLEX*16 array, dimension (NMAX*NRHS) 106*> \endverbatim 107*> 108*> \param[out] X 109*> \verbatim 110*> X is COMPLEX*16 array, dimension (NMAX*NRHS) 111*> \endverbatim 112*> 113*> \param[out] XACT 114*> \verbatim 115*> XACT is COMPLEX*16 array, dimension (NMAX*NRHS) 116*> \endverbatim 117*> 118*> \param[out] WORK 119*> \verbatim 120*> WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS)) 121*> \endverbatim 122*> 123*> \param[out] RWORK 124*> \verbatim 125*> RWORK is DOUBLE PRECISION 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*> \ingroup complex16_lin 148* 149* ===================================================================== 150 SUBROUTINE ZDRVSY_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, 151 $ NMAX, A, AFAC, AINV, B, X, XACT, WORK, 152 $ RWORK, IWORK, NOUT ) 153* 154* -- LAPACK test routine -- 155* -- LAPACK is a software package provided by Univ. of Tennessee, -- 156* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 157* 158* .. Scalar Arguments .. 159 LOGICAL TSTERR 160 INTEGER NMAX, NN, NOUT, NRHS 161 DOUBLE PRECISION THRESH 162* .. 163* .. Array Arguments .. 164 LOGICAL DOTYPE( * ) 165 INTEGER IWORK( * ), NVAL( * ) 166 DOUBLE PRECISION RWORK( * ) 167 COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), 168 $ WORK( * ), X( * ), XACT( * ) 169* .. 170* 171* ===================================================================== 172* 173* .. Parameters .. 174 DOUBLE PRECISION ONE, ZERO 175 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 176 INTEGER NTYPES, NTESTS 177 PARAMETER ( NTYPES = 11, NTESTS = 3 ) 178 INTEGER NFACT 179 PARAMETER ( NFACT = 2 ) 180* .. 181* .. Local Scalars .. 182 LOGICAL ZEROT 183 CHARACTER DIST, FACT, TYPE, UPLO, XTYPE 184 CHARACTER*3 MATPATH, PATH 185 INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO, 186 $ IZERO, J, K, KL, KU, LDA, LWORK, MODE, N, 187 $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT 188 DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC 189* .. 190* .. Local Arrays .. 191 CHARACTER FACTS( NFACT ), UPLOS( 2 ) 192 INTEGER ISEED( 4 ), ISEEDY( 4 ) 193 DOUBLE PRECISION RESULT( NTESTS ) 194 195* .. 196* .. External Functions .. 197 DOUBLE PRECISION ZLANSY 198 EXTERNAL ZLANSY 199* .. 200* .. External Subroutines .. 201 EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04, 202 $ ZLACPY, ZLARHS, ZLASET, ZLATB4, ZLATMS, ZLATSY, 203 $ ZPOT05, ZSYSV_ROOK, ZSYT01_ROOK, ZSYT02, 204 $ ZSYTRF_ROOK, ZSYTRI_ROOK 205* .. 206* .. Scalars in Common .. 207 LOGICAL LERR, OK 208 CHARACTER*32 SRNAMT 209 INTEGER INFOT, NUNIT 210* .. 211* .. Common blocks .. 212 COMMON / INFOC / INFOT, NUNIT, OK, LERR 213 COMMON / SRNAMC / SRNAMT 214* .. 215* .. Intrinsic Functions .. 216 INTRINSIC MAX, MIN 217* .. 218* .. Data statements .. 219 DATA ISEEDY / 1988, 1989, 1990, 1991 / 220 DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' / 221* .. 222* .. Executable Statements .. 223* 224* Initialize constants and the random number seed. 225* 226* Test path 227* 228 PATH( 1: 1 ) = 'Zomplex precision' 229 PATH( 2: 3 ) = 'SR' 230* 231* Path to generate matrices 232* 233 MATPATH( 1: 1 ) = 'Zomplex precision' 234 MATPATH( 2: 3 ) = 'SY' 235* 236 NRUN = 0 237 NFAIL = 0 238 NERRS = 0 239 DO 10 I = 1, 4 240 ISEED( I ) = ISEEDY( I ) 241 10 CONTINUE 242 LWORK = MAX( 2*NMAX, NMAX*NRHS ) 243* 244* Test the error exits 245* 246 IF( TSTERR ) 247 $ CALL ZERRVX( PATH, NOUT ) 248 INFOT = 0 249* 250* Set the block size and minimum block size for which the block 251* routine should be used, which will be later returned by ILAENV. 252* 253 NB = 1 254 NBMIN = 2 255 CALL XLAENV( 1, NB ) 256 CALL XLAENV( 2, NBMIN ) 257* 258* Do for each value of N in NVAL 259* 260 DO 180 IN = 1, NN 261 N = NVAL( IN ) 262 LDA = MAX( N, 1 ) 263 XTYPE = 'N' 264 NIMAT = NTYPES 265 IF( N.LE.0 ) 266 $ NIMAT = 1 267* 268 DO 170 IMAT = 1, NIMAT 269* 270* Do the tests only if DOTYPE( IMAT ) is true. 271* 272 IF( .NOT.DOTYPE( IMAT ) ) 273 $ GO TO 170 274* 275* Skip types 3, 4, 5, or 6 if the matrix size is too small. 276* 277 ZEROT = IMAT.GE.3 .AND. IMAT.LE.6 278 IF( ZEROT .AND. N.LT.IMAT-2 ) 279 $ GO TO 170 280* 281* Do first for UPLO = 'U', then for UPLO = 'L' 282* 283 DO 160 IUPLO = 1, 2 284 UPLO = UPLOS( IUPLO ) 285* 286 IF( IMAT.NE.NTYPES ) THEN 287* 288* Begin generate the test matrix A. 289* 290* Set up parameters with ZLATB4 for the matrix generator 291* based on the type of matrix to be generated. 292* 293 CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM, 294 $ MODE, CNDNUM, DIST ) 295* 296* Generate a matrix with ZLATMS. 297* 298 SRNAMT = 'ZLATMS' 299 CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, 300 $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, 301 $ WORK, INFO ) 302* 303* Check error code from DLATMS and handle error. 304* 305 IF( INFO.NE.0 ) THEN 306 CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, 307 $ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT ) 308 GO TO 160 309 END IF 310* 311* For types 3-6, zero one or more rows and columns of 312* the matrix to test that INFO is returned correctly. 313* 314 IF( ZEROT ) THEN 315 IF( IMAT.EQ.3 ) THEN 316 IZERO = 1 317 ELSE IF( IMAT.EQ.4 ) THEN 318 IZERO = N 319 ELSE 320 IZERO = N / 2 + 1 321 END IF 322* 323 IF( IMAT.LT.6 ) THEN 324* 325* Set row and column IZERO to zero. 326* 327 IF( IUPLO.EQ.1 ) THEN 328 IOFF = ( IZERO-1 )*LDA 329 DO 20 I = 1, IZERO - 1 330 A( IOFF+I ) = ZERO 331 20 CONTINUE 332 IOFF = IOFF + IZERO 333 DO 30 I = IZERO, N 334 A( IOFF ) = ZERO 335 IOFF = IOFF + LDA 336 30 CONTINUE 337 ELSE 338 IOFF = IZERO 339 DO 40 I = 1, IZERO - 1 340 A( IOFF ) = ZERO 341 IOFF = IOFF + LDA 342 40 CONTINUE 343 IOFF = IOFF - IZERO 344 DO 50 I = IZERO, N 345 A( IOFF+I ) = ZERO 346 50 CONTINUE 347 END IF 348 ELSE 349 IF( IUPLO.EQ.1 ) THEN 350* 351* Set the first IZERO rows and columns to zero. 352* 353 IOFF = 0 354 DO 70 J = 1, N 355 I2 = MIN( J, IZERO ) 356 DO 60 I = 1, I2 357 A( IOFF+I ) = ZERO 358 60 CONTINUE 359 IOFF = IOFF + LDA 360 70 CONTINUE 361 ELSE 362* 363* Set the first IZERO rows and columns to zero. 364* 365 IOFF = 0 366 DO 90 J = 1, N 367 I1 = MAX( J, IZERO ) 368 DO 80 I = I1, N 369 A( IOFF+I ) = ZERO 370 80 CONTINUE 371 IOFF = IOFF + LDA 372 90 CONTINUE 373 END IF 374 END IF 375 ELSE 376 IZERO = 0 377 END IF 378 ELSE 379* 380* IMAT = NTYPES: Use a special block diagonal matrix to 381* test alternate code for the 2-by-2 blocks. 382* 383 CALL ZLATSY( UPLO, N, A, LDA, ISEED ) 384 END IF 385* 386 DO 150 IFACT = 1, NFACT 387* 388* Do first for FACT = 'F', then for other values. 389* 390 FACT = FACTS( IFACT ) 391* 392* Compute the condition number for comparison with 393* the value returned by ZSYSVX_ROOK. 394* 395 IF( ZEROT ) THEN 396 IF( IFACT.EQ.1 ) 397 $ GO TO 150 398 RCONDC = ZERO 399* 400 ELSE IF( IFACT.EQ.1 ) THEN 401* 402* Compute the 1-norm of A. 403* 404 ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK ) 405* 406* Factor the matrix A. 407* 408 409 CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) 410 CALL ZSYTRF_ROOK( UPLO, N, AFAC, LDA, IWORK, WORK, 411 $ LWORK, INFO ) 412* 413* Compute inv(A) and take its norm. 414* 415 CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA ) 416 LWORK = (N+NB+1)*(NB+3) 417 CALL ZSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK, 418 $ WORK, INFO ) 419 AINVNM = ZLANSY( '1', UPLO, N, AINV, LDA, RWORK ) 420* 421* Compute the 1-norm condition number of A. 422* 423 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN 424 RCONDC = ONE 425 ELSE 426 RCONDC = ( ONE / ANORM ) / AINVNM 427 END IF 428 END IF 429* 430* Form an exact solution and set the right hand side. 431* 432 SRNAMT = 'ZLARHS' 433 CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU, 434 $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED, 435 $ INFO ) 436 XTYPE = 'C' 437* 438* --- Test ZSYSV_ROOK --- 439* 440 IF( IFACT.EQ.2 ) THEN 441 CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA ) 442 CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) 443* 444* Factor the matrix and solve the system using 445* ZSYSV_ROOK. 446* 447 SRNAMT = 'ZSYSV_ROOK' 448 CALL ZSYSV_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK, 449 $ X, LDA, WORK, LWORK, INFO ) 450* 451* Adjust the expected value of INFO to account for 452* pivoting. 453* 454 K = IZERO 455 IF( K.GT.0 ) THEN 456 100 CONTINUE 457 IF( IWORK( K ).LT.0 ) THEN 458 IF( IWORK( K ).NE.-K ) THEN 459 K = -IWORK( K ) 460 GO TO 100 461 END IF 462 ELSE IF( IWORK( K ).NE.K ) THEN 463 K = IWORK( K ) 464 GO TO 100 465 END IF 466 END IF 467* 468* Check error code from ZSYSV_ROOK and handle error. 469* 470 IF( INFO.NE.K ) THEN 471 CALL ALAERH( PATH, 'ZSYSV_ROOK', INFO, K, UPLO, 472 $ N, N, -1, -1, NRHS, IMAT, NFAIL, 473 $ NERRS, NOUT ) 474 GO TO 120 475 ELSE IF( INFO.NE.0 ) THEN 476 GO TO 120 477 END IF 478* 479*+ TEST 1 Reconstruct matrix from factors and compute 480* residual. 481* 482 CALL ZSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA, 483 $ IWORK, AINV, LDA, RWORK, 484 $ RESULT( 1 ) ) 485* 486*+ TEST 2 Compute residual of the computed solution. 487* 488 CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) 489 CALL ZSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK, 490 $ LDA, RWORK, RESULT( 2 ) ) 491* 492*+ TEST 3 493* Check solution from generated exact solution. 494* 495 CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, 496 $ RESULT( 3 ) ) 497 NT = 3 498* 499* Print information about the tests that did not pass 500* the threshold. 501* 502 DO 110 K = 1, NT 503 IF( RESULT( K ).GE.THRESH ) THEN 504 IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) 505 $ CALL ALADHD( NOUT, PATH ) 506 WRITE( NOUT, FMT = 9999 )'ZSYSV_ROOK', UPLO, 507 $ N, IMAT, K, RESULT( K ) 508 NFAIL = NFAIL + 1 509 END IF 510 110 CONTINUE 511 NRUN = NRUN + NT 512 120 CONTINUE 513 END IF 514* 515 150 CONTINUE 516* 517 160 CONTINUE 518 170 CONTINUE 519 180 CONTINUE 520* 521* Print a summary of the results. 522* 523 CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) 524* 525 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2, 526 $ ', test ', I2, ', ratio =', G12.5 ) 527 RETURN 528* 529* End of ZDRVSY_ROOK 530* 531 END 532