|
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 |
SUBROUTINE CCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
$ A, D, E, B, X, XACT, WORK, RWORK, NOUT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL TSTERR INTEGER NN, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER NSVAL( * ), NVAL( * ) REAL D( * ), RWORK( * ) COMPLEX A( * ), B( * ), E( * ), WORK( * ), X( * ), $ XACT( * ) * .. * * Purpose * ======= * * CCHKPT tests CPTTRF, -TRS, -RFS, and -CON * * Arguments * ========= * * DOTYPE (input) 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. * * NN (input) INTEGER * The number of values of N contained in the vector NVAL. * * NVAL (input) INTEGER array, dimension (NN) * The values of the matrix dimension N. * * NNS (input) INTEGER * The number of values of NRHS contained in the vector NSVAL. * * NSVAL (input) INTEGER array, dimension (NNS) * The values of the number of right hand sides NRHS. * * THRESH (input) 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. * * TSTERR (input) LOGICAL * Flag that indicates whether error exits are to be tested. * * A (workspace) COMPLEX array, dimension (NMAX*2) * * D (workspace) REAL array, dimension (NMAX*2) * * E (workspace) COMPLEX array, dimension (NMAX*2) * * B (workspace) COMPLEX array, dimension (NMAX*NSMAX) * where NSMAX is the largest entry in NSVAL. * * X (workspace) COMPLEX array, dimension (NMAX*NSMAX) * * XACT (workspace) COMPLEX array, dimension (NMAX*NSMAX) * * WORK (workspace) COMPLEX array, dimension * (NMAX*max(3,NSMAX)) * * RWORK (workspace) REAL array, dimension * (max(NMAX,2*NSMAX)) * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 12 ) INTEGER NTESTS PARAMETER ( NTESTS = 7 ) * .. * .. Local Scalars .. LOGICAL ZEROT CHARACTER DIST, TYPE, UPLO CHARACTER*3 PATH INTEGER I, IA, IMAT, IN, INFO, IRHS, IUPLO, IX, IZERO, $ J, K, KL, KU, LDA, MODE, N, NERRS, NFAIL, $ NIMAT, NRHS, NRUN REAL AINVNM, ANORM, COND, DMAX, RCOND, RCONDC * .. * .. Local Arrays .. CHARACTER UPLOS( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ) COMPLEX Z( 3 ) * .. * .. External Functions .. INTEGER ISAMAX REAL CLANHT, SCASUM, SGET06 EXTERNAL ISAMAX, CLANHT, SCASUM, SGET06 * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, CCOPY, CERRGT, CGET04, $ CLACPY, CLAPTM, CLARNV, CLATB4, CLATMS, CPTCON, $ CPTRFS, CPTT01, CPTT02, CPTT05, CPTTRF, CPTTRS, $ CSSCAL, SCOPY, SLARNV, SSCAL * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, REAL * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, NUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, NUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 0, 0, 0, 1 / , UPLOS / 'U', 'L' / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Complex precision' PATH( 2: 3 ) = 'PT' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL CERRGT( PATH, NOUT ) INFOT = 0 * DO 120 IN = 1, NN * * Do for each value of N in NVAL. * N = NVAL( IN ) LDA = MAX( 1, N ) NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 110 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) ) $ GO TO 110 * * Set up parameters with CLATB4. * CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, $ COND, DIST ) * ZEROT = IMAT.GE.8 .AND. IMAT.LE.10 IF( IMAT.LE.6 ) THEN * * Type 1-6: generate a Hermitian tridiagonal matrix of * known condition number in lower triangular band storage. * SRNAMT = 'CLATMS' CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND, $ ANORM, KL, KU, 'B', A, 2, WORK, INFO ) * * Check the error code from CLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', N, N, KL, $ KU, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 110 END IF IZERO = 0 * * Copy the matrix to D and E. * IA = 1 DO 20 I = 1, N - 1 D( I ) = REAL( A( IA ) ) E( I ) = A( IA+1 ) IA = IA + 2 20 CONTINUE IF( N.GT.0 ) $ D( N ) = REAL( A( IA ) ) ELSE * * Type 7-12: generate a diagonally dominant matrix with * unknown condition number in the vectors D and E. * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN * * Let E be complex, D real, with values from [-1,1]. * CALL SLARNV( 2, ISEED, N, D ) CALL CLARNV( 2, ISEED, N-1, E ) * * Make the tridiagonal matrix diagonally dominant. * IF( N.EQ.1 ) THEN D( 1 ) = ABS( D( 1 ) ) ELSE D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) ) D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) ) DO 30 I = 2, N - 1 D( I ) = ABS( D( I ) ) + ABS( E( I ) ) + $ ABS( E( I-1 ) ) 30 CONTINUE END IF * * Scale D and E so the maximum element is ANORM. * IX = ISAMAX( N, D, 1 ) DMAX = D( IX ) CALL SSCAL( N, ANORM / DMAX, D, 1 ) CALL CSSCAL( N-1, ANORM / DMAX, E, 1 ) * ELSE IF( IZERO.GT.0 ) THEN * * Reuse the last matrix by copying back the zeroed out * elements. * IF( IZERO.EQ.1 ) THEN D( 1 ) = Z( 2 ) IF( N.GT.1 ) $ E( 1 ) = Z( 3 ) ELSE IF( IZERO.EQ.N ) THEN E( N-1 ) = Z( 1 ) D( N ) = Z( 2 ) ELSE E( IZERO-1 ) = Z( 1 ) D( IZERO ) = Z( 2 ) E( IZERO ) = Z( 3 ) END IF END IF * * For types 8-10, set one row and column of the matrix to * zero. * IZERO = 0 IF( IMAT.EQ.8 ) THEN IZERO = 1 Z( 2 ) = D( 1 ) D( 1 ) = ZERO IF( N.GT.1 ) THEN Z( 3 ) = E( 1 ) E( 1 ) = ZERO END IF ELSE IF( IMAT.EQ.9 ) THEN IZERO = N IF( N.GT.1 ) THEN Z( 1 ) = E( N-1 ) E( N-1 ) = ZERO END IF Z( 2 ) = D( N ) D( N ) = ZERO ELSE IF( IMAT.EQ.10 ) THEN IZERO = ( N+1 ) / 2 IF( IZERO.GT.1 ) THEN Z( 1 ) = E( IZERO-1 ) Z( 3 ) = E( IZERO ) E( IZERO-1 ) = ZERO E( IZERO ) = ZERO END IF Z( 2 ) = D( IZERO ) D( IZERO ) = ZERO END IF END IF * CALL SCOPY( N, D, 1, D( N+1 ), 1 ) IF( N.GT.1 ) $ CALL CCOPY( N-1, E, 1, E( N+1 ), 1 ) * *+ TEST 1 * Factor A as L*D*L' and compute the ratio * norm(L*D*L' - A) / (n * norm(A) * EPS ) * CALL CPTTRF( N, D( N+1 ), E( N+1 ), INFO ) * * Check error code from CPTTRF. * IF( INFO.NE.IZERO ) THEN CALL ALAERH( PATH, 'CPTTRF', INFO, IZERO, ' ', N, N, -1, $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 110 END IF * IF( INFO.GT.0 ) THEN RCONDC = ZERO GO TO 100 END IF * CALL CPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK, $ RESULT( 1 ) ) * * Print the test ratio if greater than or equal to THRESH. * IF( RESULT( 1 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )N, IMAT, 1, RESULT( 1 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 * * Compute RCONDC = 1 / (norm(A) * norm(inv(A)) * * Compute norm(A). * ANORM = CLANHT( '1', N, D, E ) * * Use CPTTRS to solve for one column at a time of inv(A), * computing the maximum column sum as we go. * AINVNM = ZERO DO 50 I = 1, N DO 40 J = 1, N X( J ) = ZERO 40 CONTINUE X( I ) = ONE CALL CPTTRS( 'Lower', N, 1, D( N+1 ), E( N+1 ), X, LDA, $ INFO ) AINVNM = MAX( AINVNM, SCASUM( N, X, 1 ) ) 50 CONTINUE RCONDC = ONE / MAX( ONE, ANORM*AINVNM ) * DO 90 IRHS = 1, NNS NRHS = NSVAL( IRHS ) * * Generate NRHS random solution vectors. * IX = 1 DO 60 J = 1, NRHS CALL CLARNV( 2, ISEED, N, XACT( IX ) ) IX = IX + LDA 60 CONTINUE * DO 80 IUPLO = 1, 2 * * Do first for UPLO = 'U', then for UPLO = 'L'. * UPLO = UPLOS( IUPLO ) * * Set the right hand side. * CALL CLAPTM( UPLO, N, NRHS, ONE, D, E, XACT, LDA, $ ZERO, B, LDA ) * *+ TEST 2 * Solve A*x = b and compute the residual. * CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) CALL CPTTRS( UPLO, N, NRHS, D( N+1 ), E( N+1 ), X, $ LDA, INFO ) * * Check error code from CPTTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CPTTRS', INFO, 0, UPLO, N, N, $ -1, -1, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) CALL CPTT02( UPLO, N, NRHS, D, E, X, LDA, WORK, LDA, $ RESULT( 2 ) ) * *+ TEST 3 * Check solution from generated exact solution. * CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) * *+ TESTS 4, 5, and 6 * Use iterative refinement to improve the solution. * SRNAMT = 'CPTRFS' CALL CPTRFS( UPLO, N, NRHS, D, E, D( N+1 ), E( N+1 ), $ B, LDA, X, LDA, RWORK, RWORK( NRHS+1 ), $ WORK, RWORK( 2*NRHS+1 ), INFO ) * * Check error code from CPTRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CPTRFS', INFO, 0, UPLO, N, N, $ -1, -1, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 4 ) ) CALL CPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA, $ RWORK, RWORK( NRHS+1 ), RESULT( 5 ) ) * * Print information about the tests that did not pass the * threshold. * DO 70 K = 2, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS, IMAT, $ K, RESULT( K ) NFAIL = NFAIL + 1 END IF 70 CONTINUE NRUN = NRUN + 5 * 80 CONTINUE 90 CONTINUE * *+ TEST 7 * Estimate the reciprocal of the condition number of the * matrix. * 100 CONTINUE SRNAMT = 'CPTCON' CALL CPTCON( N, D( N+1 ), E( N+1 ), ANORM, RCOND, RWORK, $ INFO ) * * Check error code from CPTCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'CPTCON', INFO, 0, ' ', N, N, -1, -1, $ -1, IMAT, NFAIL, NERRS, NOUT ) * RESULT( 7 ) = SGET06( RCOND, RCONDC ) * * Print the test ratio if greater than or equal to THRESH. * IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )N, IMAT, 7, RESULT( 7 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 110 CONTINUE 120 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( ' N =', I5, ', type ', I2, ', test ', I2, ', ratio = ', $ G12.5 ) 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS =', I3, $ ', type ', I2, ', test ', I2, ', ratio = ', G12.5 ) RETURN * * End of CCHKPT * END |