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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CGBRFSX 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CGBRFSX + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbrfsx.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbrfsx.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbrfsx.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB, 00022 * LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND, 00023 * BERR, N_ERR_BNDS, ERR_BNDS_NORM, 00024 * ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK, 00025 * INFO ) 00026 * 00027 * .. Scalar Arguments .. 00028 * CHARACTER TRANS, EQUED 00029 * INTEGER INFO, LDAB, LDAFB, LDB, LDX, N, KL, KU, NRHS, 00030 * $ NPARAMS, N_ERR_BNDS 00031 * REAL RCOND 00032 * .. 00033 * .. Array Arguments .. 00034 * INTEGER IPIV( * ) 00035 * COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), 00036 * $ X( LDX , * ),WORK( * ) 00037 * REAL R( * ), C( * ), PARAMS( * ), BERR( * ), 00038 * $ ERR_BNDS_NORM( NRHS, * ), 00039 * $ ERR_BNDS_COMP( NRHS, * ), RWORK( * ) 00040 * .. 00041 * 00042 * 00043 *> \par Purpose: 00044 * ============= 00045 *> 00046 *> \verbatim 00047 *> 00048 *> CGBRFSX improves the computed solution to a system of linear 00049 *> equations and provides error bounds and backward error estimates 00050 *> for the solution. In addition to normwise error bound, the code 00051 *> provides maximum componentwise error bound if possible. See 00052 *> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the 00053 *> error bounds. 00054 *> 00055 *> The original system of linear equations may have been equilibrated 00056 *> before calling this routine, as described by arguments EQUED, R 00057 *> and C below. In this case, the solution and error bounds returned 00058 *> are for the original unequilibrated system. 00059 *> \endverbatim 00060 * 00061 * Arguments: 00062 * ========== 00063 * 00064 *> \verbatim 00065 *> Some optional parameters are bundled in the PARAMS array. These 00066 *> settings determine how refinement is performed, but often the 00067 *> defaults are acceptable. If the defaults are acceptable, users 00068 *> can pass NPARAMS = 0 which prevents the source code from accessing 00069 *> the PARAMS argument. 00070 *> \endverbatim 00071 *> 00072 *> \param[in] TRANS 00073 *> \verbatim 00074 *> TRANS is CHARACTER*1 00075 *> Specifies the form of the system of equations: 00076 *> = 'N': A * X = B (No transpose) 00077 *> = 'T': A**T * X = B (Transpose) 00078 *> = 'C': A**H * X = B (Conjugate transpose = Transpose) 00079 *> \endverbatim 00080 *> 00081 *> \param[in] EQUED 00082 *> \verbatim 00083 *> EQUED is CHARACTER*1 00084 *> Specifies the form of equilibration that was done to A 00085 *> before calling this routine. This is needed to compute 00086 *> the solution and error bounds correctly. 00087 *> = 'N': No equilibration 00088 *> = 'R': Row equilibration, i.e., A has been premultiplied by 00089 *> diag(R). 00090 *> = 'C': Column equilibration, i.e., A has been postmultiplied 00091 *> by diag(C). 00092 *> = 'B': Both row and column equilibration, i.e., A has been 00093 *> replaced by diag(R) * A * diag(C). 00094 *> The right hand side B has been changed accordingly. 00095 *> \endverbatim 00096 *> 00097 *> \param[in] N 00098 *> \verbatim 00099 *> N is INTEGER 00100 *> The order of the matrix A. N >= 0. 00101 *> \endverbatim 00102 *> 00103 *> \param[in] KL 00104 *> \verbatim 00105 *> KL is INTEGER 00106 *> The number of subdiagonals within the band of A. KL >= 0. 00107 *> \endverbatim 00108 *> 00109 *> \param[in] KU 00110 *> \verbatim 00111 *> KU is INTEGER 00112 *> The number of superdiagonals within the band of A. KU >= 0. 00113 *> \endverbatim 00114 *> 00115 *> \param[in] NRHS 00116 *> \verbatim 00117 *> NRHS is INTEGER 00118 *> The number of right hand sides, i.e., the number of columns 00119 *> of the matrices B and X. NRHS >= 0. 00120 *> \endverbatim 00121 *> 00122 *> \param[in] AB 00123 *> \verbatim 00124 *> AB is DOUBLE PRECISION array, dimension (LDAB,N) 00125 *> The original band matrix A, stored in rows 1 to KL+KU+1. 00126 *> The j-th column of A is stored in the j-th column of the 00127 *> array AB as follows: 00128 *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). 00129 *> \endverbatim 00130 *> 00131 *> \param[in] LDAB 00132 *> \verbatim 00133 *> LDAB is INTEGER 00134 *> The leading dimension of the array AB. LDAB >= KL+KU+1. 00135 *> \endverbatim 00136 *> 00137 *> \param[in] AFB 00138 *> \verbatim 00139 *> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) 00140 *> Details of the LU factorization of the band matrix A, as 00141 *> computed by DGBTRF. U is stored as an upper triangular band 00142 *> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and 00143 *> the multipliers used during the factorization are stored in 00144 *> rows KL+KU+2 to 2*KL+KU+1. 00145 *> \endverbatim 00146 *> 00147 *> \param[in] LDAFB 00148 *> \verbatim 00149 *> LDAFB is INTEGER 00150 *> The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. 00151 *> \endverbatim 00152 *> 00153 *> \param[in] IPIV 00154 *> \verbatim 00155 *> IPIV is INTEGER array, dimension (N) 00156 *> The pivot indices from SGETRF; for 1<=i<=N, row i of the 00157 *> matrix was interchanged with row IPIV(i). 00158 *> \endverbatim 00159 *> 00160 *> \param[in,out] R 00161 *> \verbatim 00162 *> R is REAL array, dimension (N) 00163 *> The row scale factors for A. If EQUED = 'R' or 'B', A is 00164 *> multiplied on the left by diag(R); if EQUED = 'N' or 'C', R 00165 *> is not accessed. R is an input argument if FACT = 'F'; 00166 *> otherwise, R is an output argument. If FACT = 'F' and 00167 *> EQUED = 'R' or 'B', each element of R must be positive. 00168 *> If R is output, each element of R is a power of the radix. 00169 *> If R is input, each element of R should be a power of the radix 00170 *> to ensure a reliable solution and error estimates. Scaling by 00171 *> powers of the radix does not cause rounding errors unless the 00172 *> result underflows or overflows. Rounding errors during scaling 00173 *> lead to refining with a matrix that is not equivalent to the 00174 *> input matrix, producing error estimates that may not be 00175 *> reliable. 00176 *> \endverbatim 00177 *> 00178 *> \param[in,out] C 00179 *> \verbatim 00180 *> C is REAL array, dimension (N) 00181 *> The column scale factors for A. If EQUED = 'C' or 'B', A is 00182 *> multiplied on the right by diag(C); if EQUED = 'N' or 'R', C 00183 *> is not accessed. C is an input argument if FACT = 'F'; 00184 *> otherwise, C is an output argument. If FACT = 'F' and 00185 *> EQUED = 'C' or 'B', each element of C must be positive. 00186 *> If C is output, each element of C is a power of the radix. 00187 *> If C is input, each element of C should be a power of the radix 00188 *> to ensure a reliable solution and error estimates. Scaling by 00189 *> powers of the radix does not cause rounding errors unless the 00190 *> result underflows or overflows. Rounding errors during scaling 00191 *> lead to refining with a matrix that is not equivalent to the 00192 *> input matrix, producing error estimates that may not be 00193 *> reliable. 00194 *> \endverbatim 00195 *> 00196 *> \param[in] B 00197 *> \verbatim 00198 *> B is REAL array, dimension (LDB,NRHS) 00199 *> The right hand side matrix B. 00200 *> \endverbatim 00201 *> 00202 *> \param[in] LDB 00203 *> \verbatim 00204 *> LDB is INTEGER 00205 *> The leading dimension of the array B. LDB >= max(1,N). 00206 *> \endverbatim 00207 *> 00208 *> \param[in,out] X 00209 *> \verbatim 00210 *> X is REAL array, dimension (LDX,NRHS) 00211 *> On entry, the solution matrix X, as computed by SGETRS. 00212 *> On exit, the improved solution matrix X. 00213 *> \endverbatim 00214 *> 00215 *> \param[in] LDX 00216 *> \verbatim 00217 *> LDX is INTEGER 00218 *> The leading dimension of the array X. LDX >= max(1,N). 00219 *> \endverbatim 00220 *> 00221 *> \param[out] RCOND 00222 *> \verbatim 00223 *> RCOND is REAL 00224 *> Reciprocal scaled condition number. This is an estimate of the 00225 *> reciprocal Skeel condition number of the matrix A after 00226 *> equilibration (if done). If this is less than the machine 00227 *> precision (in particular, if it is zero), the matrix is singular 00228 *> to working precision. Note that the error may still be small even 00229 *> if this number is very small and the matrix appears ill- 00230 *> conditioned. 00231 *> \endverbatim 00232 *> 00233 *> \param[out] BERR 00234 *> \verbatim 00235 *> BERR is REAL array, dimension (NRHS) 00236 *> Componentwise relative backward error. This is the 00237 *> componentwise relative backward error of each solution vector X(j) 00238 *> (i.e., the smallest relative change in any element of A or B that 00239 *> makes X(j) an exact solution). 00240 *> \endverbatim 00241 *> 00242 *> \param[in] N_ERR_BNDS 00243 *> \verbatim 00244 *> N_ERR_BNDS is INTEGER 00245 *> Number of error bounds to return for each right hand side 00246 *> and each type (normwise or componentwise). See ERR_BNDS_NORM and 00247 *> ERR_BNDS_COMP below. 00248 *> \endverbatim 00249 *> 00250 *> \param[out] ERR_BNDS_NORM 00251 *> \verbatim 00252 *> ERR_BNDS_NORM is REAL array, dimension (NRHS, N_ERR_BNDS) 00253 *> For each right-hand side, this array contains information about 00254 *> various error bounds and condition numbers corresponding to the 00255 *> normwise relative error, which is defined as follows: 00256 *> 00257 *> Normwise relative error in the ith solution vector: 00258 *> max_j (abs(XTRUE(j,i) - X(j,i))) 00259 *> ------------------------------ 00260 *> max_j abs(X(j,i)) 00261 *> 00262 *> The array is indexed by the type of error information as described 00263 *> below. There currently are up to three pieces of information 00264 *> returned. 00265 *> 00266 *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00267 *> right-hand side. 00268 *> 00269 *> The second index in ERR_BNDS_NORM(:,err) contains the following 00270 *> three fields: 00271 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00272 *> reciprocal condition number is less than the threshold 00273 *> sqrt(n) * slamch('Epsilon'). 00274 *> 00275 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00276 *> almost certainly within a factor of 10 of the true error 00277 *> so long as the next entry is greater than the threshold 00278 *> sqrt(n) * slamch('Epsilon'). This error bound should only 00279 *> be trusted if the previous boolean is true. 00280 *> 00281 *> err = 3 Reciprocal condition number: Estimated normwise 00282 *> reciprocal condition number. Compared with the threshold 00283 *> sqrt(n) * slamch('Epsilon') to determine if the error 00284 *> estimate is "guaranteed". These reciprocal condition 00285 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00286 *> appropriately scaled matrix Z. 00287 *> Let Z = S*A, where S scales each row by a power of the 00288 *> radix so all absolute row sums of Z are approximately 1. 00289 *> 00290 *> See Lapack Working Note 165 for further details and extra 00291 *> cautions. 00292 *> \endverbatim 00293 *> 00294 *> \param[out] ERR_BNDS_COMP 00295 *> \verbatim 00296 *> ERR_BNDS_COMP is REAL array, dimension (NRHS, N_ERR_BNDS) 00297 *> For each right-hand side, this array contains information about 00298 *> various error bounds and condition numbers corresponding to the 00299 *> componentwise relative error, which is defined as follows: 00300 *> 00301 *> Componentwise relative error in the ith solution vector: 00302 *> abs(XTRUE(j,i) - X(j,i)) 00303 *> max_j ---------------------- 00304 *> abs(X(j,i)) 00305 *> 00306 *> The array is indexed by the right-hand side i (on which the 00307 *> componentwise relative error depends), and the type of error 00308 *> information as described below. There currently are up to three 00309 *> pieces of information returned for each right-hand side. If 00310 *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00311 *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00312 *> the first (:,N_ERR_BNDS) entries are returned. 00313 *> 00314 *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00315 *> right-hand side. 00316 *> 00317 *> The second index in ERR_BNDS_COMP(:,err) contains the following 00318 *> three fields: 00319 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00320 *> reciprocal condition number is less than the threshold 00321 *> sqrt(n) * slamch('Epsilon'). 00322 *> 00323 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00324 *> almost certainly within a factor of 10 of the true error 00325 *> so long as the next entry is greater than the threshold 00326 *> sqrt(n) * slamch('Epsilon'). This error bound should only 00327 *> be trusted if the previous boolean is true. 00328 *> 00329 *> err = 3 Reciprocal condition number: Estimated componentwise 00330 *> reciprocal condition number. Compared with the threshold 00331 *> sqrt(n) * slamch('Epsilon') to determine if the error 00332 *> estimate is "guaranteed". These reciprocal condition 00333 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00334 *> appropriately scaled matrix Z. 00335 *> Let Z = S*(A*diag(x)), where x is the solution for the 00336 *> current right-hand side and S scales each row of 00337 *> A*diag(x) by a power of the radix so all absolute row 00338 *> sums of Z are approximately 1. 00339 *> 00340 *> See Lapack Working Note 165 for further details and extra 00341 *> cautions. 00342 *> \endverbatim 00343 *> 00344 *> \param[in] NPARAMS 00345 *> \verbatim 00346 *> NPARAMS is INTEGER 00347 *> Specifies the number of parameters set in PARAMS. If .LE. 0, the 00348 *> PARAMS array is never referenced and default values are used. 00349 *> \endverbatim 00350 *> 00351 *> \param[in,out] PARAMS 00352 *> \verbatim 00353 *> PARAMS is / output) REAL array, dimension NPARAMS 00354 *> Specifies algorithm parameters. If an entry is .LT. 0.0, then 00355 *> that entry will be filled with default value used for that 00356 *> parameter. Only positions up to NPARAMS are accessed; defaults 00357 *> are used for higher-numbered parameters. 00358 *> 00359 *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative 00360 *> refinement or not. 00361 *> Default: 1.0 00362 *> = 0.0 : No refinement is performed, and no error bounds are 00363 *> computed. 00364 *> = 1.0 : Use the double-precision refinement algorithm, 00365 *> possibly with doubled-single computations if the 00366 *> compilation environment does not support DOUBLE 00367 *> PRECISION. 00368 *> (other values are reserved for future use) 00369 *> 00370 *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual 00371 *> computations allowed for refinement. 00372 *> Default: 10 00373 *> Aggressive: Set to 100 to permit convergence using approximate 00374 *> factorizations or factorizations other than LU. If 00375 *> the factorization uses a technique other than 00376 *> Gaussian elimination, the guarantees in 00377 *> err_bnds_norm and err_bnds_comp may no longer be 00378 *> trustworthy. 00379 *> 00380 *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code 00381 *> will attempt to find a solution with small componentwise 00382 *> relative error in the double-precision algorithm. Positive 00383 *> is true, 0.0 is false. 00384 *> Default: 1.0 (attempt componentwise convergence) 00385 *> \endverbatim 00386 *> 00387 *> \param[out] WORK 00388 *> \verbatim 00389 *> WORK is COMPLEX array, dimension (2*N) 00390 *> \endverbatim 00391 *> 00392 *> \param[out] RWORK 00393 *> \verbatim 00394 *> RWORK is REAL array, dimension (2*N) 00395 *> \endverbatim 00396 *> 00397 *> \param[out] INFO 00398 *> \verbatim 00399 *> INFO is INTEGER 00400 *> = 0: Successful exit. The solution to every right-hand side is 00401 *> guaranteed. 00402 *> < 0: If INFO = -i, the i-th argument had an illegal value 00403 *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization 00404 *> has been completed, but the factor U is exactly singular, so 00405 *> the solution and error bounds could not be computed. RCOND = 0 00406 *> is returned. 00407 *> = N+J: The solution corresponding to the Jth right-hand side is 00408 *> not guaranteed. The solutions corresponding to other right- 00409 *> hand sides K with K > J may not be guaranteed as well, but 00410 *> only the first such right-hand side is reported. If a small 00411 *> componentwise error is not requested (PARAMS(3) = 0.0) then 00412 *> the Jth right-hand side is the first with a normwise error 00413 *> bound that is not guaranteed (the smallest J such 00414 *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) 00415 *> the Jth right-hand side is the first with either a normwise or 00416 *> componentwise error bound that is not guaranteed (the smallest 00417 *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or 00418 *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of 00419 *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information 00420 *> about all of the right-hand sides check ERR_BNDS_NORM or 00421 *> ERR_BNDS_COMP. 00422 *> \endverbatim 00423 * 00424 * Authors: 00425 * ======== 00426 * 00427 *> \author Univ. of Tennessee 00428 *> \author Univ. of California Berkeley 00429 *> \author Univ. of Colorado Denver 00430 *> \author NAG Ltd. 00431 * 00432 *> \date April 2012 00433 * 00434 *> \ingroup complexGBcomputational 00435 * 00436 * ===================================================================== 00437 SUBROUTINE CGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB, 00438 $ LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND, 00439 $ BERR, N_ERR_BNDS, ERR_BNDS_NORM, 00440 $ ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK, 00441 $ INFO ) 00442 * 00443 * -- LAPACK computational routine (version 3.4.1) -- 00444 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00445 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00446 * April 2012 00447 * 00448 * .. Scalar Arguments .. 00449 CHARACTER TRANS, EQUED 00450 INTEGER INFO, LDAB, LDAFB, LDB, LDX, N, KL, KU, NRHS, 00451 $ NPARAMS, N_ERR_BNDS 00452 REAL RCOND 00453 * .. 00454 * .. Array Arguments .. 00455 INTEGER IPIV( * ) 00456 COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), 00457 $ X( LDX , * ),WORK( * ) 00458 REAL R( * ), C( * ), PARAMS( * ), BERR( * ), 00459 $ ERR_BNDS_NORM( NRHS, * ), 00460 $ ERR_BNDS_COMP( NRHS, * ), RWORK( * ) 00461 * .. 00462 * 00463 * ================================================================== 00464 * 00465 * .. Parameters .. 00466 REAL ZERO, ONE 00467 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00468 REAL ITREF_DEFAULT, ITHRESH_DEFAULT, 00469 $ COMPONENTWISE_DEFAULT 00470 REAL RTHRESH_DEFAULT, DZTHRESH_DEFAULT 00471 PARAMETER ( ITREF_DEFAULT = 1.0 ) 00472 PARAMETER ( ITHRESH_DEFAULT = 10.0 ) 00473 PARAMETER ( COMPONENTWISE_DEFAULT = 1.0 ) 00474 PARAMETER ( RTHRESH_DEFAULT = 0.5 ) 00475 PARAMETER ( DZTHRESH_DEFAULT = 0.25 ) 00476 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00477 $ LA_LINRX_CWISE_I 00478 PARAMETER ( LA_LINRX_ITREF_I = 1, 00479 $ LA_LINRX_ITHRESH_I = 2 ) 00480 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00481 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00482 $ LA_LINRX_RCOND_I 00483 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00484 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00485 * .. 00486 * .. Local Scalars .. 00487 CHARACTER(1) NORM 00488 LOGICAL ROWEQU, COLEQU, NOTRAN, IGNORE_CWISE 00489 INTEGER J, TRANS_TYPE, PREC_TYPE, REF_TYPE, N_NORMS, 00490 $ ITHRESH 00491 REAL ANORM, RCOND_TMP, ILLRCOND_THRESH, ERR_LBND, 00492 $ CWISE_WRONG, RTHRESH, UNSTABLE_THRESH 00493 * .. 00494 * .. External Subroutines .. 00495 EXTERNAL XERBLA, CGBCON, CLA_GBRFSX_EXTENDED 00496 * .. 00497 * .. Intrinsic Functions .. 00498 INTRINSIC MAX, SQRT, TRANSFER 00499 * .. 00500 * .. External Functions .. 00501 EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC 00502 EXTERNAL SLAMCH, CLANGB, CLA_GBRCOND_X, CLA_GBRCOND_C 00503 REAL SLAMCH, CLANGB, CLA_GBRCOND_X, CLA_GBRCOND_C 00504 LOGICAL LSAME 00505 INTEGER BLAS_FPINFO_X 00506 INTEGER ILATRANS, ILAPREC 00507 * .. 00508 * .. Executable Statements .. 00509 * 00510 * Check the input parameters. 00511 * 00512 INFO = 0 00513 TRANS_TYPE = ILATRANS( TRANS ) 00514 REF_TYPE = INT( ITREF_DEFAULT ) 00515 IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN 00516 IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0 ) THEN 00517 PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT 00518 ELSE 00519 REF_TYPE = PARAMS( LA_LINRX_ITREF_I ) 00520 END IF 00521 END IF 00522 * 00523 * Set default parameters. 00524 * 00525 ILLRCOND_THRESH = REAL( N ) * SLAMCH( 'Epsilon' ) 00526 ITHRESH = INT( ITHRESH_DEFAULT ) 00527 RTHRESH = RTHRESH_DEFAULT 00528 UNSTABLE_THRESH = DZTHRESH_DEFAULT 00529 IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0 00530 * 00531 IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN 00532 IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0 ) THEN 00533 PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH 00534 ELSE 00535 ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) ) 00536 END IF 00537 END IF 00538 IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN 00539 IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0 ) THEN 00540 IF ( IGNORE_CWISE ) THEN 00541 PARAMS( LA_LINRX_CWISE_I ) = 0.0 00542 ELSE 00543 PARAMS( LA_LINRX_CWISE_I ) = 1.0 00544 END IF 00545 ELSE 00546 IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0 00547 END IF 00548 END IF 00549 IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN 00550 N_NORMS = 0 00551 ELSE IF ( IGNORE_CWISE ) THEN 00552 N_NORMS = 1 00553 ELSE 00554 N_NORMS = 2 00555 END IF 00556 * 00557 NOTRAN = LSAME( TRANS, 'N' ) 00558 ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' ) 00559 COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' ) 00560 * 00561 * Test input parameters. 00562 * 00563 IF( TRANS_TYPE.EQ.-1 ) THEN 00564 INFO = -1 00565 ELSE IF( .NOT.ROWEQU .AND. .NOT.COLEQU .AND. 00566 $ .NOT.LSAME( EQUED, 'N' ) ) THEN 00567 INFO = -2 00568 ELSE IF( N.LT.0 ) THEN 00569 INFO = -3 00570 ELSE IF( KL.LT.0 ) THEN 00571 INFO = -4 00572 ELSE IF( KU.LT.0 ) THEN 00573 INFO = -5 00574 ELSE IF( NRHS.LT.0 ) THEN 00575 INFO = -6 00576 ELSE IF( LDAB.LT.KL+KU+1 ) THEN 00577 INFO = -8 00578 ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN 00579 INFO = -10 00580 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00581 INFO = -13 00582 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN 00583 INFO = -15 00584 END IF 00585 IF( INFO.NE.0 ) THEN 00586 CALL XERBLA( 'CGBRFSX', -INFO ) 00587 RETURN 00588 END IF 00589 * 00590 * Quick return if possible. 00591 * 00592 IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN 00593 RCOND = 1.0 00594 DO J = 1, NRHS 00595 BERR( J ) = 0.0 00596 IF ( N_ERR_BNDS .GE. 1 ) THEN 00597 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0 00598 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0 00599 END IF 00600 IF ( N_ERR_BNDS .GE. 2 ) THEN 00601 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0 00602 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0 00603 END IF 00604 IF ( N_ERR_BNDS .GE. 3 ) THEN 00605 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0 00606 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0 00607 END IF 00608 END DO 00609 RETURN 00610 END IF 00611 * 00612 * Default to failure. 00613 * 00614 RCOND = 0.0 00615 DO J = 1, NRHS 00616 BERR( J ) = 1.0 00617 IF ( N_ERR_BNDS .GE. 1 ) THEN 00618 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0 00619 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0 00620 END IF 00621 IF ( N_ERR_BNDS .GE. 2 ) THEN 00622 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0 00623 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0 00624 END IF 00625 IF ( N_ERR_BNDS .GE. 3 ) THEN 00626 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0 00627 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0 00628 END IF 00629 END DO 00630 * 00631 * Compute the norm of A and the reciprocal of the condition 00632 * number of A. 00633 * 00634 IF( NOTRAN ) THEN 00635 NORM = 'I' 00636 ELSE 00637 NORM = '1' 00638 END IF 00639 ANORM = CLANGB( NORM, N, KL, KU, AB, LDAB, RWORK ) 00640 CALL CGBCON( NORM, N, KL, KU, AFB, LDAFB, IPIV, ANORM, RCOND, 00641 $ WORK, RWORK, INFO ) 00642 * 00643 * Perform refinement on each right-hand side 00644 * 00645 IF ( REF_TYPE .NE. 0 ) THEN 00646 00647 PREC_TYPE = ILAPREC( 'D' ) 00648 00649 IF ( NOTRAN ) THEN 00650 CALL CLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU, 00651 $ NRHS, AB, LDAB, AFB, LDAFB, IPIV, COLEQU, C, B, 00652 $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, 00653 $ ERR_BNDS_COMP, WORK, RWORK, WORK(N+1), 00654 $ TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), 00655 $ RCOND, ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE, 00656 $ INFO ) 00657 ELSE 00658 CALL CLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU, 00659 $ NRHS, AB, LDAB, AFB, LDAFB, IPIV, ROWEQU, R, B, 00660 $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, 00661 $ ERR_BNDS_COMP, WORK, RWORK, WORK(N+1), 00662 $ TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), 00663 $ RCOND, ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE, 00664 $ INFO ) 00665 END IF 00666 END IF 00667 00668 ERR_LBND = MAX( 10.0, SQRT( REAL( N ) ) ) * SLAMCH( 'Epsilon' ) 00669 IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1) THEN 00670 * 00671 * Compute scaled normwise condition number cond(A*C). 00672 * 00673 IF ( COLEQU .AND. NOTRAN ) THEN 00674 RCOND_TMP = CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB, 00675 $ LDAFB, IPIV, C, .TRUE., INFO, WORK, RWORK ) 00676 ELSE IF ( ROWEQU .AND. .NOT. NOTRAN ) THEN 00677 RCOND_TMP = CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB, 00678 $ LDAFB, IPIV, R, .TRUE., INFO, WORK, RWORK ) 00679 ELSE 00680 RCOND_TMP = CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB, 00681 $ LDAFB, IPIV, C, .FALSE., INFO, WORK, RWORK ) 00682 END IF 00683 DO J = 1, NRHS 00684 * 00685 * Cap the error at 1.0. 00686 * 00687 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I 00688 $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0) 00689 $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0 00690 * 00691 * Threshold the error (see LAWN). 00692 * 00693 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN 00694 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0 00695 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0 00696 IF ( INFO .LE. N ) INFO = N + J 00697 ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND ) 00698 $ THEN 00699 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND 00700 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0 00701 END IF 00702 * 00703 * Save the condition number. 00704 * 00705 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN 00706 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00707 END IF 00708 00709 END DO 00710 END IF 00711 00712 IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2) THEN 00713 * 00714 * Compute componentwise condition number cond(A*diag(Y(:,J))) for 00715 * each right-hand side using the current solution as an estimate of 00716 * the true solution. If the componentwise error estimate is too 00717 * large, then the solution is a lousy estimate of truth and the 00718 * estimated RCOND may be too optimistic. To avoid misleading users, 00719 * the inverse condition number is set to 0.0 when the estimated 00720 * cwise error is at least CWISE_WRONG. 00721 * 00722 CWISE_WRONG = SQRT( SLAMCH( 'Epsilon' ) ) 00723 DO J = 1, NRHS 00724 IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG ) 00725 $ THEN 00726 RCOND_TMP = CLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, 00727 $ AFB, LDAFB, IPIV, X( 1, J ), INFO, WORK, RWORK ) 00728 ELSE 00729 RCOND_TMP = 0.0 00730 END IF 00731 * 00732 * Cap the error at 1.0. 00733 * 00734 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I 00735 $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0 ) 00736 $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0 00737 * 00738 * Threshold the error (see LAWN). 00739 * 00740 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN 00741 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0 00742 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0 00743 IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0 00744 $ .AND. INFO.LT.N + J ) INFO = N + J 00745 ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) 00746 $ .LT. ERR_LBND ) THEN 00747 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND 00748 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0 00749 END IF 00750 * 00751 * Save the condition number. 00752 * 00753 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN 00754 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00755 END IF 00756 00757 END DO 00758 END IF 00759 * 00760 RETURN 00761 * 00762 * End of CGBRFSX 00763 * 00764 END