1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577
|
*> \brief \b CCHKTB
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
* NMAX, AB, AINV, B, X, XACT, WORK, RWORK, NOUT )
*
* .. Scalar Arguments ..
* LOGICAL TSTERR
* INTEGER NMAX, NN, NNS, NOUT
* REAL THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER NSVAL( * ), NVAL( * )
* REAL RWORK( * )
* COMPLEX AB( * ), AINV( * ), B( * ), WORK( * ), X( * ),
* $ XACT( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CCHKTB tests CTBTRS, -RFS, and -CON, and CLATBS.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] DOTYPE
*> \verbatim
*> DOTYPE is LOGICAL array, dimension (NTYPES)
*> The matrix types to be used for testing. Matrices of type j
*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
*> \endverbatim
*>
*> \param[in] NN
*> \verbatim
*> NN is INTEGER
*> The number of values of N contained in the vector NVAL.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NN)
*> The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NNS
*> \verbatim
*> NNS is INTEGER
*> The number of values of NRHS contained in the vector NSVAL.
*> \endverbatim
*>
*> \param[in] NSVAL
*> \verbatim
*> NSVAL is INTEGER array, dimension (NNS)
*> The values of the number of right hand sides NRHS.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> THRESH is REAL
*> The threshold value for the test ratios. A result is
*> included in the output file if RESULT >= THRESH. To have
*> every test ratio printed, use THRESH = 0.
*> \endverbatim
*>
*> \param[in] TSTERR
*> \verbatim
*> TSTERR is LOGICAL
*> Flag that indicates whether error exits are to be tested.
*> \endverbatim
*>
*> \param[in] NMAX
*> \verbatim
*> NMAX is INTEGER
*> The leading dimension of the work arrays.
*> NMAX >= the maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[out] AB
*> \verbatim
*> AB is COMPLEX array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] AINV
*> \verbatim
*> AINV is COMPLEX array, dimension (NMAX*NMAX)
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is COMPLEX array, dimension (NMAX*NSMAX)
*> where NSMAX is the largest entry in NSVAL.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is COMPLEX array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] XACT
*> \verbatim
*> XACT is COMPLEX array, dimension (NMAX*NSMAX)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension
*> (NMAX*max(3,NSMAX))
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension
*> (max(NMAX,2*NSMAX))
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
$ NMAX, AB, AINV, B, X, XACT, WORK, RWORK, NOUT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NMAX, NN, NNS, NOUT
REAL THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER NSVAL( * ), NVAL( * )
REAL RWORK( * )
COMPLEX AB( * ), AINV( * ), B( * ), WORK( * ), X( * ),
$ XACT( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTYPE1, NTYPES
PARAMETER ( NTYPE1 = 9, NTYPES = 17 )
INTEGER NTESTS
PARAMETER ( NTESTS = 8 )
INTEGER NTRAN
PARAMETER ( NTRAN = 3 )
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER I, IDIAG, IK, IMAT, IN, INFO, IRHS, ITRAN,
$ IUPLO, J, K, KD, LDA, LDAB, N, NERRS, NFAIL,
$ NIMAT, NIMAT2, NK, NRHS, NRUN
REAL AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO,
$ SCALE
* ..
* .. Local Arrays ..
CHARACTER TRANSS( NTRAN ), UPLOS( 2 )
INTEGER ISEED( 4 ), ISEEDY( 4 )
REAL RESULT( NTESTS )
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANTB, CLANTR
EXTERNAL LSAME, CLANTB, CLANTR
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASUM, CCOPY, CERRTR, CGET04,
$ CLACPY, CLARHS, CLASET, CLATBS, CLATTB, CTBCON,
$ CTBRFS, CTBSV, CTBT02, CTBT03, CTBT05, CTBT06,
$ CTBTRS
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MAX, MIN
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
DATA UPLOS / 'U', 'L' / , TRANSS / 'N', 'T', 'C' /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Complex precision'
PATH( 2: 3 ) = 'TB'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
*
* Test the error exits
*
IF( TSTERR )
$ CALL CERRTR( PATH, NOUT )
INFOT = 0
*
DO 140 IN = 1, NN
*
* Do for each value of N in NVAL
*
N = NVAL( IN )
LDA = MAX( 1, N )
XTYPE = 'N'
NIMAT = NTYPE1
NIMAT2 = NTYPES
IF( N.LE.0 ) THEN
NIMAT = 1
NIMAT2 = NTYPE1 + 1
END IF
*
NK = MIN( N+1, 4 )
DO 130 IK = 1, NK
*
* Do for KD = 0, N, (3N-1)/4, and (N+1)/4. This order makes
* it easier to skip redundant values for small values of N.
*
IF( IK.EQ.1 ) THEN
KD = 0
ELSE IF( IK.EQ.2 ) THEN
KD = MAX( N, 0 )
ELSE IF( IK.EQ.3 ) THEN
KD = ( 3*N-1 ) / 4
ELSE IF( IK.EQ.4 ) THEN
KD = ( N+1 ) / 4
END IF
LDAB = KD + 1
*
DO 90 IMAT = 1, NIMAT
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 90
*
DO 80 IUPLO = 1, 2
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
UPLO = UPLOS( IUPLO )
*
* Call CLATTB to generate a triangular test matrix.
*
SRNAMT = 'CLATTB'
CALL CLATTB( IMAT, UPLO, 'No transpose', DIAG, ISEED,
$ N, KD, AB, LDAB, X, WORK, RWORK, INFO )
*
* Set IDIAG = 1 for non-unit matrices, 2 for unit.
*
IF( LSAME( DIAG, 'N' ) ) THEN
IDIAG = 1
ELSE
IDIAG = 2
END IF
*
* Form the inverse of A so we can get a good estimate
* of RCONDC = 1/(norm(A) * norm(inv(A))).
*
CALL CLASET( 'Full', N, N, CMPLX( ZERO ),
$ CMPLX( ONE ), AINV, LDA )
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
CALL CTBSV( UPLO, 'No transpose', DIAG, J, KD,
$ AB, LDAB, AINV( ( J-1 )*LDA+1 ), 1 )
20 CONTINUE
ELSE
DO 30 J = 1, N
CALL CTBSV( UPLO, 'No transpose', DIAG, N-J+1,
$ KD, AB( ( J-1 )*LDAB+1 ), LDAB,
$ AINV( ( J-1 )*LDA+J ), 1 )
30 CONTINUE
END IF
*
* Compute the 1-norm condition number of A.
*
ANORM = CLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB,
$ RWORK )
AINVNM = CLANTR( '1', UPLO, DIAG, N, N, AINV, LDA,
$ RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDO = ONE
ELSE
RCONDO = ( ONE / ANORM ) / AINVNM
END IF
*
* Compute the infinity-norm condition number of A.
*
ANORM = CLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB,
$ RWORK )
AINVNM = CLANTR( 'I', UPLO, DIAG, N, N, AINV, LDA,
$ RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCONDI = ONE
ELSE
RCONDI = ( ONE / ANORM ) / AINVNM
END IF
*
DO 60 IRHS = 1, NNS
NRHS = NSVAL( IRHS )
XTYPE = 'N'
*
DO 50 ITRAN = 1, NTRAN
*
* Do for op(A) = A, A**T, or A**H.
*
TRANS = TRANSS( ITRAN )
IF( ITRAN.EQ.1 ) THEN
NORM = 'O'
RCONDC = RCONDO
ELSE
NORM = 'I'
RCONDC = RCONDI
END IF
*
*+ TEST 1
* Solve and compute residual for op(A)*x = b.
*
SRNAMT = 'CLARHS'
CALL CLARHS( PATH, XTYPE, UPLO, TRANS, N, N, KD,
$ IDIAG, NRHS, AB, LDAB, XACT, LDA,
$ B, LDA, ISEED, INFO )
XTYPE = 'C'
CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
*
SRNAMT = 'CTBTRS'
CALL CTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, X, LDA, INFO )
*
* Check error code from CTBTRS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'CTBTRS', INFO, 0,
$ UPLO // TRANS // DIAG, N, N, KD,
$ KD, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, X, LDA, B, LDA, WORK, RWORK,
$ RESULT( 1 ) )
*
*+ TEST 2
* Check solution from generated exact solution.
*
CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 2 ) )
*
*+ TESTS 3, 4, and 5
* Use iterative refinement to improve the solution
* and compute error bounds.
*
SRNAMT = 'CTBRFS'
CALL CTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, B, LDA, X, LDA, RWORK,
$ RWORK( NRHS+1 ), WORK,
$ RWORK( 2*NRHS+1 ), INFO )
*
* Check error code from CTBRFS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'CTBRFS', INFO, 0,
$ UPLO // TRANS // DIAG, N, N, KD,
$ KD, NRHS, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
$ RESULT( 3 ) )
CALL CTBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
$ LDAB, B, LDA, X, LDA, XACT, LDA,
$ RWORK, RWORK( NRHS+1 ),
$ RESULT( 4 ) )
*
* Print information about the tests that did not
* pass the threshold.
*
DO 40 K = 1, 5
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )UPLO, TRANS,
$ DIAG, N, KD, NRHS, IMAT, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
40 CONTINUE
NRUN = NRUN + 5
50 CONTINUE
60 CONTINUE
*
*+ TEST 6
* Get an estimate of RCOND = 1/CNDNUM.
*
DO 70 ITRAN = 1, 2
IF( ITRAN.EQ.1 ) THEN
NORM = 'O'
RCONDC = RCONDO
ELSE
NORM = 'I'
RCONDC = RCONDI
END IF
SRNAMT = 'CTBCON'
CALL CTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB,
$ RCOND, WORK, RWORK, INFO )
*
* Check error code from CTBCON.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'CTBCON', INFO, 0,
$ NORM // UPLO // DIAG, N, N, KD, KD,
$ -1, IMAT, NFAIL, NERRS, NOUT )
*
CALL CTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB,
$ LDAB, RWORK, RESULT( 6 ) )
*
* Print the test ratio if it is .GE. THRESH.
*
IF( RESULT( 6 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 ) 'CTBCON', NORM, UPLO,
$ DIAG, N, KD, IMAT, 6, RESULT( 6 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 1
70 CONTINUE
80 CONTINUE
90 CONTINUE
*
* Use pathological test matrices to test CLATBS.
*
DO 120 IMAT = NTYPE1 + 1, NIMAT2
*
* Do the tests only if DOTYPE( IMAT ) is true.
*
IF( .NOT.DOTYPE( IMAT ) )
$ GO TO 120
*
DO 110 IUPLO = 1, 2
*
* Do first for UPLO = 'U', then for UPLO = 'L'
*
UPLO = UPLOS( IUPLO )
DO 100 ITRAN = 1, NTRAN
*
* Do for op(A) = A, A**T, and A**H.
*
TRANS = TRANSS( ITRAN )
*
* Call CLATTB to generate a triangular test matrix.
*
SRNAMT = 'CLATTB'
CALL CLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD,
$ AB, LDAB, X, WORK, RWORK, INFO )
*
*+ TEST 7
* Solve the system op(A)*x = b
*
SRNAMT = 'CLATBS'
CALL CCOPY( N, X, 1, B, 1 )
CALL CLATBS( UPLO, TRANS, DIAG, 'N', N, KD, AB,
$ LDAB, B, SCALE, RWORK, INFO )
*
* Check error code from CLATBS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'CLATBS', INFO, 0,
$ UPLO // TRANS // DIAG // 'N', N, N,
$ KD, KD, -1, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL CTBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
$ SCALE, RWORK, ONE, B, LDA, X, LDA,
$ WORK, RESULT( 7 ) )
*
*+ TEST 8
* Solve op(A)*x = b again with NORMIN = 'Y'.
*
CALL CCOPY( N, X, 1, B, 1 )
CALL CLATBS( UPLO, TRANS, DIAG, 'Y', N, KD, AB,
$ LDAB, B, SCALE, RWORK, INFO )
*
* Check error code from CLATBS.
*
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'CLATBS', INFO, 0,
$ UPLO // TRANS // DIAG // 'Y', N, N,
$ KD, KD, -1, IMAT, NFAIL, NERRS,
$ NOUT )
*
CALL CTBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
$ SCALE, RWORK, ONE, B, LDA, X, LDA,
$ WORK, RESULT( 8 ) )
*
* Print information about the tests that did not pass
* the threshold.
*
IF( RESULT( 7 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )'CLATBS', UPLO, TRANS,
$ DIAG, 'N', N, KD, IMAT, 7, RESULT( 7 )
NFAIL = NFAIL + 1
END IF
IF( RESULT( 8 ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9997 )'CLATBS', UPLO, TRANS,
$ DIAG, 'Y', N, KD, IMAT, 8, RESULT( 8 )
NFAIL = NFAIL + 1
END IF
NRUN = NRUN + 2
100 CONTINUE
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
*
* Print a summary of the results.
*
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''',
$ DIAG=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I5,
$ ', type ', I2, ', test(', I2, ')=', G12.5 )
9998 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''',',
$ I5, ',', I5, ', ... ), type ', I2, ', test(', I2, ')=',
$ G12.5 )
9997 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
$ A1, ''',', I5, ',', I5, ', ... ), type ', I2, ', test(',
$ I1, ')=', G12.5 )
RETURN
*
* End of CCHKTB
*
END
|