numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/cdrvrf3.f | 13816B | -rw-r--r-- |
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416
*> \brief \b CDRVRF3 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, * + S_WORK_CLANGE, C_WORK_CGEQRF, TAU ) * * .. Scalar Arguments .. * INTEGER LDA, NN, NOUT * REAL THRESH * .. * .. Array Arguments .. * INTEGER NVAL( NN ) * REAL S_WORK_CLANGE( * ) * COMPLEX A( LDA, * ), ARF( * ), B1( LDA, * ), * + B2( LDA, * ) * COMPLEX C_WORK_CGEQRF( * ), TAU( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CDRVRF3 tests the LAPACK RFP routines: *> CTFSM *> \endverbatim * * Arguments: * ========== * *> \param[in] NOUT *> \verbatim *> NOUT is INTEGER *> The unit number for output. *> \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 dimension N. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is DOUBLE PRECISION *> 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[out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,NMAX) *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,NMAX). *> \endverbatim *> *> \param[out] ARF *> \verbatim *> ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2). *> \endverbatim *> *> \param[out] B1 *> \verbatim *> B1 is COMPLEX array, dimension (LDA,NMAX) *> \endverbatim *> *> \param[out] B2 *> \verbatim *> B2 is COMPLEX array, dimension (LDA,NMAX) *> \endverbatim *> *> \param[out] S_WORK_CLANGE *> \verbatim *> S_WORK_CLANGE is REAL array, dimension (NMAX) *> \endverbatim *> *> \param[out] C_WORK_CGEQRF *> \verbatim *> C_WORK_CGEQRF is COMPLEX array, dimension (NMAX) *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX array, dimension (NMAX) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, + S_WORK_CLANGE, C_WORK_CGEQRF, TAU ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER LDA, NN, NOUT REAL THRESH * .. * .. Array Arguments .. INTEGER NVAL( NN ) REAL S_WORK_CLANGE( * ) COMPLEX A( LDA, * ), ARF( * ), B1( LDA, * ), + B2( LDA, * ) COMPLEX C_WORK_CGEQRF( * ), TAU( * ) * .. * * ===================================================================== * .. * .. Parameters .. COMPLEX ZERO, ONE PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) , + ONE = ( 1.0E+0, 0.0E+0 ) ) INTEGER NTESTS PARAMETER ( NTESTS = 1 ) * .. * .. Local Scalars .. CHARACTER UPLO, CFORM, DIAG, TRANS, SIDE INTEGER I, IFORM, IIM, IIN, INFO, IUPLO, J, M, N, NA, + NFAIL, NRUN, ISIDE, IDIAG, IALPHA, ITRANS COMPLEX ALPHA REAL EPS * .. * .. Local Arrays .. CHARACTER UPLOS( 2 ), FORMS( 2 ), TRANSS( 2 ), + DIAGS( 2 ), SIDES( 2 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, CLANGE COMPLEX CLARND EXTERNAL SLAMCH, CLARND, CLANGE, LSAME * .. * .. External Subroutines .. EXTERNAL CTRTTF, CGEQRF, CGEQLF, CTFSM, CTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / DATA UPLOS / 'U', 'L' / DATA FORMS / 'N', 'C' / DATA SIDES / 'L', 'R' / DATA TRANSS / 'N', 'C' / DATA DIAGS / 'N', 'U' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * NRUN = 0 NFAIL = 0 INFO = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE EPS = SLAMCH( 'Precision' ) * DO 170 IIM = 1, NN * M = NVAL( IIM ) * DO 160 IIN = 1, NN * N = NVAL( IIN ) * DO 150 IFORM = 1, 2 * CFORM = FORMS( IFORM ) * DO 140 IUPLO = 1, 2 * UPLO = UPLOS( IUPLO ) * DO 130 ISIDE = 1, 2 * SIDE = SIDES( ISIDE ) * DO 120 ITRANS = 1, 2 * TRANS = TRANSS( ITRANS ) * DO 110 IDIAG = 1, 2 * DIAG = DIAGS( IDIAG ) * DO 100 IALPHA = 1, 3 * IF ( IALPHA.EQ.1 ) THEN ALPHA = ZERO ELSE IF ( IALPHA.EQ.2 ) THEN ALPHA = ONE ELSE ALPHA = CLARND( 4, ISEED ) END IF * * All the parameters are set: * CFORM, SIDE, UPLO, TRANS, DIAG, M, N, * and ALPHA * READY TO TEST! * NRUN = NRUN + 1 * IF ( ISIDE.EQ.1 ) THEN * * The case ISIDE.EQ.1 is when SIDE.EQ.'L' * -> A is M-by-M ( B is M-by-N ) * NA = M * ELSE * * The case ISIDE.EQ.2 is when SIDE.EQ.'R' * -> A is N-by-N ( B is M-by-N ) * NA = N * END IF * * Generate A our NA--by--NA triangular * matrix. * Our test is based on forward error so we * do want A to be well conditioned! To get * a well-conditioned triangular matrix, we * take the R factor of the QR/LQ factorization * of a random matrix. * DO J = 1, NA DO I = 1, NA A( I, J ) = CLARND( 4, ISEED ) END DO END DO * IF ( IUPLO.EQ.1 ) THEN * * The case IUPLO.EQ.1 is when SIDE.EQ.'U' * -> QR factorization. * SRNAMT = 'CGEQRF' CALL CGEQRF( NA, NA, A, LDA, TAU, + C_WORK_CGEQRF, LDA, + INFO ) * * Forcing main diagonal of test matrix to * be unit makes it ill-conditioned for * some test cases * IF ( LSAME( DIAG, 'U' ) ) THEN DO J = 1, NA DO I = 1, J A( I, J ) = A( I, J ) / + ( 2.0 * A( J, J ) ) END DO END DO END IF * ELSE * * The case IUPLO.EQ.2 is when SIDE.EQ.'L' * -> QL factorization. * SRNAMT = 'CGELQF' CALL CGELQF( NA, NA, A, LDA, TAU, + C_WORK_CGEQRF, LDA, + INFO ) * * Forcing main diagonal of test matrix to * be unit makes it ill-conditioned for * some test cases * IF ( LSAME( DIAG, 'U' ) ) THEN DO I = 1, NA DO J = 1, I A( I, J ) = A( I, J ) / + ( 2.0 * A( I, I ) ) END DO END DO END IF * END IF * * After the QR factorization, the diagonal * of A is made of real numbers, we multiply * by a random complex number of absolute * value 1.0E+00. * DO J = 1, NA A( J, J ) = A( J, J ) * + CLARND( 5, ISEED ) END DO * * Store a copy of A in RFP format (in ARF). * SRNAMT = 'CTRTTF' CALL CTRTTF( CFORM, UPLO, NA, A, LDA, ARF, + INFO ) * * Generate B1 our M--by--N right-hand side * and store a copy in B2. * DO J = 1, N DO I = 1, M B1( I, J ) = CLARND( 4, ISEED ) B2( I, J ) = B1( I, J ) END DO END DO * * Solve op( A ) X = B or X op( A ) = B * with CTRSM * SRNAMT = 'CTRSM' CALL CTRSM( SIDE, UPLO, TRANS, DIAG, M, N, + ALPHA, A, LDA, B1, LDA ) * * Solve op( A ) X = B or X op( A ) = B * with CTFSM * SRNAMT = 'CTFSM' CALL CTFSM( CFORM, SIDE, UPLO, TRANS, + DIAG, M, N, ALPHA, ARF, B2, + LDA ) * * Check that the result agrees. * DO J = 1, N DO I = 1, M B1( I, J ) = B2( I, J ) - B1( I, J ) END DO END DO * RESULT( 1 ) = CLANGE( 'I', M, N, B1, LDA, + S_WORK_CLANGE ) * RESULT( 1 ) = RESULT( 1 ) / SQRT( EPS ) + / MAX ( MAX( M, N ), 1 ) * IF( RESULT( 1 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 ) THEN WRITE( NOUT, * ) WRITE( NOUT, FMT = 9999 ) END IF WRITE( NOUT, FMT = 9997 ) 'CTFSM', + CFORM, SIDE, UPLO, TRANS, DIAG, M, + N, RESULT( 1 ) NFAIL = NFAIL + 1 END IF * 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE 150 CONTINUE 160 CONTINUE 170 CONTINUE * * Print a summary of the results. * IF ( NFAIL.EQ.0 ) THEN WRITE( NOUT, FMT = 9996 ) 'CTFSM', NRUN ELSE WRITE( NOUT, FMT = 9995 ) 'CTFSM', NFAIL, NRUN END IF * 9999 FORMAT( 1X, ' *** Error(s) or Failure(s) while testing CTFSM + ***') 9997 FORMAT( 1X, ' Failure in ',A5,', CFORM=''',A1,''',', + ' SIDE=''',A1,''',',' UPLO=''',A1,''',',' TRANS=''',A1,''',', + ' DIAG=''',A1,''',',' M=',I3,', N =', I3,', test=',G12.5) 9996 FORMAT( 1X, 'All tests for ',A5,' auxiliary routine passed the ', + 'threshold ( ',I5,' tests run)') 9995 FORMAT( 1X, A6, ' auxiliary routine: ',I5,' out of ',I5, + ' tests failed to pass the threshold') * RETURN * * End of CDRVRF3 * END