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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SLA_GBRFSX_EXTENDED 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SLA_GBRFSX_EXTENDED + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_gbrfsx_extended.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_gbrfsx_extended.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_gbrfsx_extended.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE SLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU, 00022 * NRHS, AB, LDAB, AFB, LDAFB, IPIV, 00023 * COLEQU, C, B, LDB, Y, LDY, 00024 * BERR_OUT, N_NORMS, ERR_BNDS_NORM, 00025 * ERR_BNDS_COMP, RES, AYB, DY, 00026 * Y_TAIL, RCOND, ITHRESH, RTHRESH, 00027 * DZ_UB, IGNORE_CWISE, INFO ) 00028 * 00029 * .. Scalar Arguments .. 00030 * INTEGER INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS, 00031 * $ PREC_TYPE, TRANS_TYPE, N_NORMS, ITHRESH 00032 * LOGICAL COLEQU, IGNORE_CWISE 00033 * REAL RTHRESH, DZ_UB 00034 * .. 00035 * .. Array Arguments .. 00036 * INTEGER IPIV( * ) 00037 * REAL AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), 00038 * $ Y( LDY, * ), RES(*), DY(*), Y_TAIL(*) 00039 * REAL C( * ), AYB(*), RCOND, BERR_OUT(*), 00040 * $ ERR_BNDS_NORM( NRHS, * ), 00041 * $ ERR_BNDS_COMP( NRHS, * ) 00042 * .. 00043 * 00044 * 00045 *> \par Purpose: 00046 * ============= 00047 *> 00048 *> \verbatim 00049 *> 00050 *> SLA_GBRFSX_EXTENDED improves the computed solution to a system of 00051 *> linear equations by performing extra-precise iterative refinement 00052 *> and provides error bounds and backward error estimates for the solution. 00053 *> This subroutine is called by SGBRFSX to perform iterative refinement. 00054 *> In addition to normwise error bound, the code provides maximum 00055 *> componentwise error bound if possible. See comments for ERR_BNDS_NORM 00056 *> and ERR_BNDS_COMP for details of the error bounds. Note that this 00057 *> subroutine is only resonsible for setting the second fields of 00058 *> ERR_BNDS_NORM and ERR_BNDS_COMP. 00059 *> \endverbatim 00060 * 00061 * Arguments: 00062 * ========== 00063 * 00064 *> \param[in] PREC_TYPE 00065 *> \verbatim 00066 *> PREC_TYPE is INTEGER 00067 *> Specifies the intermediate precision to be used in refinement. 00068 *> The value is defined by ILAPREC(P) where P is a CHARACTER and 00069 *> P = 'S': Single 00070 *> = 'D': Double 00071 *> = 'I': Indigenous 00072 *> = 'X', 'E': Extra 00073 *> \endverbatim 00074 *> 00075 *> \param[in] TRANS_TYPE 00076 *> \verbatim 00077 *> TRANS_TYPE is INTEGER 00078 *> Specifies the transposition operation on A. 00079 *> The value is defined by ILATRANS(T) where T is a CHARACTER and 00080 *> T = 'N': No transpose 00081 *> = 'T': Transpose 00082 *> = 'C': Conjugate transpose 00083 *> \endverbatim 00084 *> 00085 *> \param[in] N 00086 *> \verbatim 00087 *> N is INTEGER 00088 *> The number of linear equations, i.e., the order of the 00089 *> matrix A. N >= 0. 00090 *> \endverbatim 00091 *> 00092 *> \param[in] KL 00093 *> \verbatim 00094 *> KL is INTEGER 00095 *> The number of subdiagonals within the band of A. KL >= 0. 00096 *> \endverbatim 00097 *> 00098 *> \param[in] KU 00099 *> \verbatim 00100 *> KU is INTEGER 00101 *> The number of superdiagonals within the band of A. KU >= 0 00102 *> \endverbatim 00103 *> 00104 *> \param[in] NRHS 00105 *> \verbatim 00106 *> NRHS is INTEGER 00107 *> The number of right-hand-sides, i.e., the number of columns of the 00108 *> matrix B. 00109 *> \endverbatim 00110 *> 00111 *> \param[in] AB 00112 *> \verbatim 00113 *> AB is REAL array, dimension (LDAB,N) 00114 *> On entry, the N-by-N matrix AB. 00115 *> \endverbatim 00116 *> 00117 *> \param[in] LDAB 00118 *> \verbatim 00119 *> LDAB is INTEGER 00120 *> The leading dimension of the array AB. LDAB >= max(1,N). 00121 *> \endverbatim 00122 *> 00123 *> \param[in] AFB 00124 *> \verbatim 00125 *> AFB is REAL array, dimension (LDAFB,N) 00126 *> The factors L and U from the factorization 00127 *> A = P*L*U as computed by SGBTRF. 00128 *> \endverbatim 00129 *> 00130 *> \param[in] LDAFB 00131 *> \verbatim 00132 *> LDAFB is INTEGER 00133 *> The leading dimension of the array AF. LDAFB >= max(1,N). 00134 *> \endverbatim 00135 *> 00136 *> \param[in] IPIV 00137 *> \verbatim 00138 *> IPIV is INTEGER array, dimension (N) 00139 *> The pivot indices from the factorization A = P*L*U 00140 *> as computed by SGBTRF; row i of the matrix was interchanged 00141 *> with row IPIV(i). 00142 *> \endverbatim 00143 *> 00144 *> \param[in] COLEQU 00145 *> \verbatim 00146 *> COLEQU is LOGICAL 00147 *> If .TRUE. then column equilibration was done to A before calling 00148 *> this routine. This is needed to compute the solution and error 00149 *> bounds correctly. 00150 *> \endverbatim 00151 *> 00152 *> \param[in] C 00153 *> \verbatim 00154 *> C is REAL array, dimension (N) 00155 *> The column scale factors for A. If COLEQU = .FALSE., C 00156 *> is not accessed. If C is input, each element of C should be a power 00157 *> of the radix to ensure a reliable solution and error estimates. 00158 *> Scaling by powers of the radix does not cause rounding errors unless 00159 *> the result underflows or overflows. Rounding errors during scaling 00160 *> lead to refining with a matrix that is not equivalent to the 00161 *> input matrix, producing error estimates that may not be 00162 *> reliable. 00163 *> \endverbatim 00164 *> 00165 *> \param[in] B 00166 *> \verbatim 00167 *> B is REAL array, dimension (LDB,NRHS) 00168 *> The right-hand-side matrix B. 00169 *> \endverbatim 00170 *> 00171 *> \param[in] LDB 00172 *> \verbatim 00173 *> LDB is INTEGER 00174 *> The leading dimension of the array B. LDB >= max(1,N). 00175 *> \endverbatim 00176 *> 00177 *> \param[in,out] Y 00178 *> \verbatim 00179 *> Y is REAL array, dimension (LDY,NRHS) 00180 *> On entry, the solution matrix X, as computed by SGBTRS. 00181 *> On exit, the improved solution matrix Y. 00182 *> \endverbatim 00183 *> 00184 *> \param[in] LDY 00185 *> \verbatim 00186 *> LDY is INTEGER 00187 *> The leading dimension of the array Y. LDY >= max(1,N). 00188 *> \endverbatim 00189 *> 00190 *> \param[out] BERR_OUT 00191 *> \verbatim 00192 *> BERR_OUT is REAL array, dimension (NRHS) 00193 *> On exit, BERR_OUT(j) contains the componentwise relative backward 00194 *> error for right-hand-side j from the formula 00195 *> max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00196 *> where abs(Z) is the componentwise absolute value of the matrix 00197 *> or vector Z. This is computed by SLA_LIN_BERR. 00198 *> \endverbatim 00199 *> 00200 *> \param[in] N_NORMS 00201 *> \verbatim 00202 *> N_NORMS is INTEGER 00203 *> Determines which error bounds to return (see ERR_BNDS_NORM 00204 *> and ERR_BNDS_COMP). 00205 *> If N_NORMS >= 1 return normwise error bounds. 00206 *> If N_NORMS >= 2 return componentwise error bounds. 00207 *> \endverbatim 00208 *> 00209 *> \param[in,out] ERR_BNDS_NORM 00210 *> \verbatim 00211 *> ERR_BNDS_NORM is REAL array, dimension 00212 *> (NRHS, N_ERR_BNDS) 00213 *> For each right-hand side, this array contains information about 00214 *> various error bounds and condition numbers corresponding to the 00215 *> normwise relative error, which is defined as follows: 00216 *> 00217 *> Normwise relative error in the ith solution vector: 00218 *> max_j (abs(XTRUE(j,i) - X(j,i))) 00219 *> ------------------------------ 00220 *> max_j abs(X(j,i)) 00221 *> 00222 *> The array is indexed by the type of error information as described 00223 *> below. There currently are up to three pieces of information 00224 *> returned. 00225 *> 00226 *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00227 *> right-hand side. 00228 *> 00229 *> The second index in ERR_BNDS_NORM(:,err) contains the following 00230 *> three fields: 00231 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00232 *> reciprocal condition number is less than the threshold 00233 *> sqrt(n) * slamch('Epsilon'). 00234 *> 00235 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00236 *> almost certainly within a factor of 10 of the true error 00237 *> so long as the next entry is greater than the threshold 00238 *> sqrt(n) * slamch('Epsilon'). This error bound should only 00239 *> be trusted if the previous boolean is true. 00240 *> 00241 *> err = 3 Reciprocal condition number: Estimated normwise 00242 *> reciprocal condition number. Compared with the threshold 00243 *> sqrt(n) * slamch('Epsilon') to determine if the error 00244 *> estimate is "guaranteed". These reciprocal condition 00245 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00246 *> appropriately scaled matrix Z. 00247 *> Let Z = S*A, where S scales each row by a power of the 00248 *> radix so all absolute row sums of Z are approximately 1. 00249 *> 00250 *> This subroutine is only responsible for setting the second field 00251 *> above. 00252 *> See Lapack Working Note 165 for further details and extra 00253 *> cautions. 00254 *> \endverbatim 00255 *> 00256 *> \param[in,out] ERR_BNDS_COMP 00257 *> \verbatim 00258 *> ERR_BNDS_COMP is REAL array, dimension 00259 *> (NRHS, N_ERR_BNDS) 00260 *> For each right-hand side, this array contains information about 00261 *> various error bounds and condition numbers corresponding to the 00262 *> componentwise relative error, which is defined as follows: 00263 *> 00264 *> Componentwise relative error in the ith solution vector: 00265 *> abs(XTRUE(j,i) - X(j,i)) 00266 *> max_j ---------------------- 00267 *> abs(X(j,i)) 00268 *> 00269 *> The array is indexed by the right-hand side i (on which the 00270 *> componentwise relative error depends), and the type of error 00271 *> information as described below. There currently are up to three 00272 *> pieces of information returned for each right-hand side. If 00273 *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00274 *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00275 *> the first (:,N_ERR_BNDS) entries are returned. 00276 *> 00277 *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00278 *> right-hand side. 00279 *> 00280 *> The second index in ERR_BNDS_COMP(:,err) contains the following 00281 *> three fields: 00282 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00283 *> reciprocal condition number is less than the threshold 00284 *> sqrt(n) * slamch('Epsilon'). 00285 *> 00286 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00287 *> almost certainly within a factor of 10 of the true error 00288 *> so long as the next entry is greater than the threshold 00289 *> sqrt(n) * slamch('Epsilon'). This error bound should only 00290 *> be trusted if the previous boolean is true. 00291 *> 00292 *> err = 3 Reciprocal condition number: Estimated componentwise 00293 *> reciprocal condition number. Compared with the threshold 00294 *> sqrt(n) * slamch('Epsilon') to determine if the error 00295 *> estimate is "guaranteed". These reciprocal condition 00296 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00297 *> appropriately scaled matrix Z. 00298 *> Let Z = S*(A*diag(x)), where x is the solution for the 00299 *> current right-hand side and S scales each row of 00300 *> A*diag(x) by a power of the radix so all absolute row 00301 *> sums of Z are approximately 1. 00302 *> 00303 *> This subroutine is only responsible for setting the second field 00304 *> above. 00305 *> See Lapack Working Note 165 for further details and extra 00306 *> cautions. 00307 *> \endverbatim 00308 *> 00309 *> \param[in] RES 00310 *> \verbatim 00311 *> RES is REAL array, dimension (N) 00312 *> Workspace to hold the intermediate residual. 00313 *> \endverbatim 00314 *> 00315 *> \param[in] AYB 00316 *> \verbatim 00317 *> AYB is REAL array, dimension (N) 00318 *> Workspace. This can be the same workspace passed for Y_TAIL. 00319 *> \endverbatim 00320 *> 00321 *> \param[in] DY 00322 *> \verbatim 00323 *> DY is REAL array, dimension (N) 00324 *> Workspace to hold the intermediate solution. 00325 *> \endverbatim 00326 *> 00327 *> \param[in] Y_TAIL 00328 *> \verbatim 00329 *> Y_TAIL is REAL array, dimension (N) 00330 *> Workspace to hold the trailing bits of the intermediate solution. 00331 *> \endverbatim 00332 *> 00333 *> \param[in] RCOND 00334 *> \verbatim 00335 *> RCOND is REAL 00336 *> Reciprocal scaled condition number. This is an estimate of the 00337 *> reciprocal Skeel condition number of the matrix A after 00338 *> equilibration (if done). If this is less than the machine 00339 *> precision (in particular, if it is zero), the matrix is singular 00340 *> to working precision. Note that the error may still be small even 00341 *> if this number is very small and the matrix appears ill- 00342 *> conditioned. 00343 *> \endverbatim 00344 *> 00345 *> \param[in] ITHRESH 00346 *> \verbatim 00347 *> ITHRESH is INTEGER 00348 *> The maximum number of residual computations allowed for 00349 *> refinement. The default is 10. For 'aggressive' set to 100 to 00350 *> permit convergence using approximate factorizations or 00351 *> factorizations other than LU. If the factorization uses a 00352 *> technique other than Gaussian elimination, the guarantees in 00353 *> ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00354 *> \endverbatim 00355 *> 00356 *> \param[in] RTHRESH 00357 *> \verbatim 00358 *> RTHRESH is REAL 00359 *> Determines when to stop refinement if the error estimate stops 00360 *> decreasing. Refinement will stop when the next solution no longer 00361 *> satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00362 *> the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00363 *> default value is 0.5. For 'aggressive' set to 0.9 to permit 00364 *> convergence on extremely ill-conditioned matrices. See LAWN 165 00365 *> for more details. 00366 *> \endverbatim 00367 *> 00368 *> \param[in] DZ_UB 00369 *> \verbatim 00370 *> DZ_UB is REAL 00371 *> Determines when to start considering componentwise convergence. 00372 *> Componentwise convergence is only considered after each component 00373 *> of the solution Y is stable, which we definte as the relative 00374 *> change in each component being less than DZ_UB. The default value 00375 *> is 0.25, requiring the first bit to be stable. See LAWN 165 for 00376 *> more details. 00377 *> \endverbatim 00378 *> 00379 *> \param[in] IGNORE_CWISE 00380 *> \verbatim 00381 *> IGNORE_CWISE is LOGICAL 00382 *> If .TRUE. then ignore componentwise convergence. Default value 00383 *> is .FALSE.. 00384 *> \endverbatim 00385 *> 00386 *> \param[out] INFO 00387 *> \verbatim 00388 *> INFO is INTEGER 00389 *> = 0: Successful exit. 00390 *> < 0: if INFO = -i, the ith argument to SGBTRS had an illegal 00391 *> value 00392 *> \endverbatim 00393 * 00394 * Authors: 00395 * ======== 00396 * 00397 *> \author Univ. of Tennessee 00398 *> \author Univ. of California Berkeley 00399 *> \author Univ. of Colorado Denver 00400 *> \author NAG Ltd. 00401 * 00402 *> \date November 2011 00403 * 00404 *> \ingroup realGBcomputational 00405 * 00406 * ===================================================================== 00407 SUBROUTINE SLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU, 00408 $ NRHS, AB, LDAB, AFB, LDAFB, IPIV, 00409 $ COLEQU, C, B, LDB, Y, LDY, 00410 $ BERR_OUT, N_NORMS, ERR_BNDS_NORM, 00411 $ ERR_BNDS_COMP, RES, AYB, DY, 00412 $ Y_TAIL, RCOND, ITHRESH, RTHRESH, 00413 $ DZ_UB, IGNORE_CWISE, INFO ) 00414 * 00415 * -- LAPACK computational routine (version 3.4.0) -- 00416 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00417 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00418 * November 2011 00419 * 00420 * .. Scalar Arguments .. 00421 INTEGER INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS, 00422 $ PREC_TYPE, TRANS_TYPE, N_NORMS, ITHRESH 00423 LOGICAL COLEQU, IGNORE_CWISE 00424 REAL RTHRESH, DZ_UB 00425 * .. 00426 * .. Array Arguments .. 00427 INTEGER IPIV( * ) 00428 REAL AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), 00429 $ Y( LDY, * ), RES(*), DY(*), Y_TAIL(*) 00430 REAL C( * ), AYB(*), RCOND, BERR_OUT(*), 00431 $ ERR_BNDS_NORM( NRHS, * ), 00432 $ ERR_BNDS_COMP( NRHS, * ) 00433 * .. 00434 * 00435 * ===================================================================== 00436 * 00437 * .. Local Scalars .. 00438 CHARACTER TRANS 00439 INTEGER CNT, I, J, M, X_STATE, Z_STATE, Y_PREC_STATE 00440 REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00441 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00442 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00443 $ EPS, HUGEVAL, INCR_THRESH 00444 LOGICAL INCR_PREC 00445 * .. 00446 * .. Parameters .. 00447 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00448 $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL, 00449 $ EXTRA_Y 00450 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00451 $ CONV_STATE = 2, NOPROG_STATE = 3 ) 00452 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00453 $ EXTRA_Y = 2 ) 00454 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00455 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00456 INTEGER CMP_ERR_I, PIV_GROWTH_I 00457 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00458 $ BERR_I = 3 ) 00459 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00460 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00461 $ PIV_GROWTH_I = 9 ) 00462 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00463 $ LA_LINRX_CWISE_I 00464 PARAMETER ( LA_LINRX_ITREF_I = 1, 00465 $ LA_LINRX_ITHRESH_I = 2 ) 00466 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00467 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00468 $ LA_LINRX_RCOND_I 00469 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00470 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00471 * .. 00472 * .. External Subroutines .. 00473 EXTERNAL SAXPY, SCOPY, SGBTRS, SGBMV, BLAS_SGBMV_X, 00474 $ BLAS_SGBMV2_X, SLA_GBAMV, SLA_WWADDW, SLAMCH, 00475 $ CHLA_TRANSTYPE, SLA_LIN_BERR 00476 REAL SLAMCH 00477 CHARACTER CHLA_TRANSTYPE 00478 * .. 00479 * .. Intrinsic Functions .. 00480 INTRINSIC ABS, MAX, MIN 00481 * .. 00482 * .. Executable Statements .. 00483 * 00484 IF (INFO.NE.0) RETURN 00485 TRANS = CHLA_TRANSTYPE(TRANS_TYPE) 00486 EPS = SLAMCH( 'Epsilon' ) 00487 HUGEVAL = SLAMCH( 'Overflow' ) 00488 * Force HUGEVAL to Inf 00489 HUGEVAL = HUGEVAL * HUGEVAL 00490 * Using HUGEVAL may lead to spurious underflows. 00491 INCR_THRESH = REAL( N ) * EPS 00492 M = KL+KU+1 00493 00494 DO J = 1, NRHS 00495 Y_PREC_STATE = EXTRA_RESIDUAL 00496 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00497 DO I = 1, N 00498 Y_TAIL( I ) = 0.0 00499 END DO 00500 END IF 00501 00502 DXRAT = 0.0 00503 DXRATMAX = 0.0 00504 DZRAT = 0.0 00505 DZRATMAX = 0.0 00506 FINAL_DX_X = HUGEVAL 00507 FINAL_DZ_Z = HUGEVAL 00508 PREVNORMDX = HUGEVAL 00509 PREV_DZ_Z = HUGEVAL 00510 DZ_Z = HUGEVAL 00511 DX_X = HUGEVAL 00512 00513 X_STATE = WORKING_STATE 00514 Z_STATE = UNSTABLE_STATE 00515 INCR_PREC = .FALSE. 00516 00517 DO CNT = 1, ITHRESH 00518 * 00519 * Compute residual RES = B_s - op(A_s) * Y, 00520 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00521 * 00522 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00523 IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN 00524 CALL SGBMV( TRANS, M, N, KL, KU, -1.0, AB, LDAB, 00525 $ Y( 1, J ), 1, 1.0, RES, 1 ) 00526 ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN 00527 CALL BLAS_SGBMV_X( TRANS_TYPE, N, N, KL, KU, 00528 $ -1.0, AB, LDAB, Y( 1, J ), 1, 1.0, RES, 1, 00529 $ PREC_TYPE ) 00530 ELSE 00531 CALL BLAS_SGBMV2_X( TRANS_TYPE, N, N, KL, KU, -1.0, 00532 $ AB, LDAB, Y( 1, J ), Y_TAIL, 1, 1.0, RES, 1, 00533 $ PREC_TYPE ) 00534 END IF 00535 00536 ! XXX: RES is no longer needed. 00537 CALL SCOPY( N, RES, 1, DY, 1 ) 00538 CALL SGBTRS( TRANS, N, KL, KU, 1, AFB, LDAFB, IPIV, DY, N, 00539 $ INFO ) 00540 * 00541 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00542 * 00543 NORMX = 0.0 00544 NORMY = 0.0 00545 NORMDX = 0.0 00546 DZ_Z = 0.0 00547 YMIN = HUGEVAL 00548 00549 DO I = 1, N 00550 YK = ABS( Y( I, J ) ) 00551 DYK = ABS( DY( I ) ) 00552 00553 IF ( YK .NE. 0.0 ) THEN 00554 DZ_Z = MAX( DZ_Z, DYK / YK ) 00555 ELSE IF ( DYK .NE. 0.0 ) THEN 00556 DZ_Z = HUGEVAL 00557 END IF 00558 00559 YMIN = MIN( YMIN, YK ) 00560 00561 NORMY = MAX( NORMY, YK ) 00562 00563 IF ( COLEQU ) THEN 00564 NORMX = MAX( NORMX, YK * C( I ) ) 00565 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00566 ELSE 00567 NORMX = NORMY 00568 NORMDX = MAX( NORMDX, DYK ) 00569 END IF 00570 END DO 00571 00572 IF ( NORMX .NE. 0.0 ) THEN 00573 DX_X = NORMDX / NORMX 00574 ELSE IF ( NORMDX .EQ. 0.0 ) THEN 00575 DX_X = 0.0 00576 ELSE 00577 DX_X = HUGEVAL 00578 END IF 00579 00580 DXRAT = NORMDX / PREVNORMDX 00581 DZRAT = DZ_Z / PREV_DZ_Z 00582 * 00583 * Check termination criteria. 00584 * 00585 IF ( .NOT.IGNORE_CWISE 00586 $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY 00587 $ .AND. Y_PREC_STATE .LT. EXTRA_Y ) 00588 $ INCR_PREC = .TRUE. 00589 00590 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00591 $ X_STATE = WORKING_STATE 00592 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00593 IF ( DX_X .LE. EPS ) THEN 00594 X_STATE = CONV_STATE 00595 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00596 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00597 INCR_PREC = .TRUE. 00598 ELSE 00599 X_STATE = NOPROG_STATE 00600 END IF 00601 ELSE 00602 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00603 END IF 00604 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00605 END IF 00606 00607 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00608 $ Z_STATE = WORKING_STATE 00609 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00610 $ Z_STATE = WORKING_STATE 00611 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00612 IF ( DZ_Z .LE. EPS ) THEN 00613 Z_STATE = CONV_STATE 00614 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00615 Z_STATE = UNSTABLE_STATE 00616 DZRATMAX = 0.0 00617 FINAL_DZ_Z = HUGEVAL 00618 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00619 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00620 INCR_PREC = .TRUE. 00621 ELSE 00622 Z_STATE = NOPROG_STATE 00623 END IF 00624 ELSE 00625 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00626 END IF 00627 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00628 END IF 00629 * 00630 * Exit if both normwise and componentwise stopped working, 00631 * but if componentwise is unstable, let it go at least two 00632 * iterations. 00633 * 00634 IF ( X_STATE.NE.WORKING_STATE ) THEN 00635 IF ( IGNORE_CWISE ) GOTO 666 00636 IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE ) 00637 $ GOTO 666 00638 IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666 00639 END IF 00640 00641 IF ( INCR_PREC ) THEN 00642 INCR_PREC = .FALSE. 00643 Y_PREC_STATE = Y_PREC_STATE + 1 00644 DO I = 1, N 00645 Y_TAIL( I ) = 0.0 00646 END DO 00647 END IF 00648 00649 PREVNORMDX = NORMDX 00650 PREV_DZ_Z = DZ_Z 00651 * 00652 * Update soluton. 00653 * 00654 IF (Y_PREC_STATE .LT. EXTRA_Y) THEN 00655 CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 ) 00656 ELSE 00657 CALL SLA_WWADDW( N, Y(1,J), Y_TAIL, DY ) 00658 END IF 00659 00660 END DO 00661 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00662 666 CONTINUE 00663 * 00664 * Set final_* when cnt hits ithresh. 00665 * 00666 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00667 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00668 * 00669 * Compute error bounds. 00670 * 00671 IF ( N_NORMS .GE. 1 ) THEN 00672 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 00673 $ FINAL_DX_X / (1 - DXRATMAX) 00674 END IF 00675 IF (N_NORMS .GE. 2) THEN 00676 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 00677 $ FINAL_DZ_Z / (1 - DZRATMAX) 00678 END IF 00679 * 00680 * Compute componentwise relative backward error from formula 00681 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00682 * where abs(Z) is the componentwise absolute value of the matrix 00683 * or vector Z. 00684 * 00685 * Compute residual RES = B_s - op(A_s) * Y, 00686 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00687 * 00688 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00689 CALL SGBMV(TRANS, N, N, KL, KU, -1.0, AB, LDAB, Y(1,J), 00690 $ 1, 1.0, RES, 1 ) 00691 00692 DO I = 1, N 00693 AYB( I ) = ABS( B( I, J ) ) 00694 END DO 00695 * 00696 * Compute abs(op(A_s))*abs(Y) + abs(B_s). 00697 * 00698 CALL SLA_GBAMV( TRANS_TYPE, N, N, KL, KU, 1.0, 00699 $ AB, LDAB, Y(1, J), 1, 1.0, AYB, 1 ) 00700 00701 CALL SLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) ) 00702 * 00703 * End of loop for each RHS 00704 * 00705 END DO 00706 * 00707 RETURN 00708 END