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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZPORFSX 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZPORFSX + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zporfsx.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zporfsx.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zporfsx.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B, 00022 * LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, 00023 * ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, 00024 * WORK, RWORK, INFO ) 00025 * 00026 * .. Scalar Arguments .. 00027 * CHARACTER UPLO, EQUED 00028 * INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, 00029 * $ N_ERR_BNDS 00030 * DOUBLE PRECISION RCOND 00031 * .. 00032 * .. Array Arguments .. 00033 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00034 * $ X( LDX, * ), WORK( * ) 00035 * DOUBLE PRECISION RWORK( * ), S( * ), PARAMS(*), BERR( * ), 00036 * $ ERR_BNDS_NORM( NRHS, * ), 00037 * $ ERR_BNDS_COMP( NRHS, * ) 00038 * .. 00039 * 00040 * 00041 *> \par Purpose: 00042 * ============= 00043 *> 00044 *> \verbatim 00045 *> 00046 *> ZPORFSX improves the computed solution to a system of linear 00047 *> equations when the coefficient matrix is symmetric positive 00048 *> definite, and provides error bounds and backward error estimates 00049 *> for the solution. In addition to normwise error bound, the code 00050 *> provides maximum componentwise error bound if possible. See 00051 *> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the 00052 *> error bounds. 00053 *> 00054 *> The original system of linear equations may have been equilibrated 00055 *> before calling this routine, as described by arguments EQUED and S 00056 *> below. In this case, the solution and error bounds returned are 00057 *> for the original unequilibrated system. 00058 *> \endverbatim 00059 * 00060 * Arguments: 00061 * ========== 00062 * 00063 *> \verbatim 00064 *> Some optional parameters are bundled in the PARAMS array. These 00065 *> settings determine how refinement is performed, but often the 00066 *> defaults are acceptable. If the defaults are acceptable, users 00067 *> can pass NPARAMS = 0 which prevents the source code from accessing 00068 *> the PARAMS argument. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] UPLO 00072 *> \verbatim 00073 *> UPLO is CHARACTER*1 00074 *> = 'U': Upper triangle of A is stored; 00075 *> = 'L': Lower triangle of A is stored. 00076 *> \endverbatim 00077 *> 00078 *> \param[in] EQUED 00079 *> \verbatim 00080 *> EQUED is CHARACTER*1 00081 *> Specifies the form of equilibration that was done to A 00082 *> before calling this routine. This is needed to compute 00083 *> the solution and error bounds correctly. 00084 *> = 'N': No equilibration 00085 *> = 'Y': Both row and column equilibration, i.e., A has been 00086 *> replaced by diag(S) * A * diag(S). 00087 *> The right hand side B has been changed accordingly. 00088 *> \endverbatim 00089 *> 00090 *> \param[in] N 00091 *> \verbatim 00092 *> N is INTEGER 00093 *> The order of the matrix A. N >= 0. 00094 *> \endverbatim 00095 *> 00096 *> \param[in] NRHS 00097 *> \verbatim 00098 *> NRHS is INTEGER 00099 *> The number of right hand sides, i.e., the number of columns 00100 *> of the matrices B and X. NRHS >= 0. 00101 *> \endverbatim 00102 *> 00103 *> \param[in] A 00104 *> \verbatim 00105 *> A is COMPLEX*16 array, dimension (LDA,N) 00106 *> The symmetric matrix A. If UPLO = 'U', the leading N-by-N 00107 *> upper triangular part of A contains the upper triangular part 00108 *> of the matrix A, and the strictly lower triangular part of A 00109 *> is not referenced. If UPLO = 'L', the leading N-by-N lower 00110 *> triangular part of A contains the lower triangular part of 00111 *> the matrix A, and the strictly upper triangular part of A is 00112 *> not referenced. 00113 *> \endverbatim 00114 *> 00115 *> \param[in] LDA 00116 *> \verbatim 00117 *> LDA is INTEGER 00118 *> The leading dimension of the array A. LDA >= max(1,N). 00119 *> \endverbatim 00120 *> 00121 *> \param[in] AF 00122 *> \verbatim 00123 *> AF is COMPLEX*16 array, dimension (LDAF,N) 00124 *> The triangular factor U or L from the Cholesky factorization 00125 *> A = U**T*U or A = L*L**T, as computed by DPOTRF. 00126 *> \endverbatim 00127 *> 00128 *> \param[in] LDAF 00129 *> \verbatim 00130 *> LDAF is INTEGER 00131 *> The leading dimension of the array AF. LDAF >= max(1,N). 00132 *> \endverbatim 00133 *> 00134 *> \param[in,out] S 00135 *> \verbatim 00136 *> S is DOUBLE PRECISION array, dimension (N) 00137 *> The row scale factors for A. If EQUED = 'Y', A is multiplied on 00138 *> the left and right by diag(S). S is an input argument if FACT = 00139 *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED 00140 *> = 'Y', each element of S must be positive. If S is output, each 00141 *> element of S is a power of the radix. If S is input, each element 00142 *> of S should be a power of the radix to ensure a reliable solution 00143 *> and error estimates. Scaling by powers of the radix does not cause 00144 *> rounding errors unless the result underflows or overflows. 00145 *> Rounding errors during scaling lead to refining with a matrix that 00146 *> is not equivalent to the input matrix, producing error estimates 00147 *> that may not be reliable. 00148 *> \endverbatim 00149 *> 00150 *> \param[in] B 00151 *> \verbatim 00152 *> B is COMPLEX*16 array, dimension (LDB,NRHS) 00153 *> The right hand side matrix B. 00154 *> \endverbatim 00155 *> 00156 *> \param[in] LDB 00157 *> \verbatim 00158 *> LDB is INTEGER 00159 *> The leading dimension of the array B. LDB >= max(1,N). 00160 *> \endverbatim 00161 *> 00162 *> \param[in,out] X 00163 *> \verbatim 00164 *> X is COMPLEX*16 array, dimension (LDX,NRHS) 00165 *> On entry, the solution matrix X, as computed by DGETRS. 00166 *> On exit, the improved solution matrix X. 00167 *> \endverbatim 00168 *> 00169 *> \param[in] LDX 00170 *> \verbatim 00171 *> LDX is INTEGER 00172 *> The leading dimension of the array X. LDX >= max(1,N). 00173 *> \endverbatim 00174 *> 00175 *> \param[out] RCOND 00176 *> \verbatim 00177 *> RCOND is DOUBLE PRECISION 00178 *> Reciprocal scaled condition number. This is an estimate of the 00179 *> reciprocal Skeel condition number of the matrix A after 00180 *> equilibration (if done). If this is less than the machine 00181 *> precision (in particular, if it is zero), the matrix is singular 00182 *> to working precision. Note that the error may still be small even 00183 *> if this number is very small and the matrix appears ill- 00184 *> conditioned. 00185 *> \endverbatim 00186 *> 00187 *> \param[out] BERR 00188 *> \verbatim 00189 *> BERR is DOUBLE PRECISION array, dimension (NRHS) 00190 *> Componentwise relative backward error. This is the 00191 *> componentwise relative backward error of each solution vector X(j) 00192 *> (i.e., the smallest relative change in any element of A or B that 00193 *> makes X(j) an exact solution). 00194 *> \endverbatim 00195 *> 00196 *> \param[in] N_ERR_BNDS 00197 *> \verbatim 00198 *> N_ERR_BNDS is INTEGER 00199 *> Number of error bounds to return for each right hand side 00200 *> and each type (normwise or componentwise). See ERR_BNDS_NORM and 00201 *> ERR_BNDS_COMP below. 00202 *> \endverbatim 00203 *> 00204 *> \param[out] ERR_BNDS_NORM 00205 *> \verbatim 00206 *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) 00207 *> For each right-hand side, this array contains information about 00208 *> various error bounds and condition numbers corresponding to the 00209 *> normwise relative error, which is defined as follows: 00210 *> 00211 *> Normwise relative error in the ith solution vector: 00212 *> max_j (abs(XTRUE(j,i) - X(j,i))) 00213 *> ------------------------------ 00214 *> max_j abs(X(j,i)) 00215 *> 00216 *> The array is indexed by the type of error information as described 00217 *> below. There currently are up to three pieces of information 00218 *> returned. 00219 *> 00220 *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00221 *> right-hand side. 00222 *> 00223 *> The second index in ERR_BNDS_NORM(:,err) contains the following 00224 *> three fields: 00225 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00226 *> reciprocal condition number is less than the threshold 00227 *> sqrt(n) * dlamch('Epsilon'). 00228 *> 00229 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00230 *> almost certainly within a factor of 10 of the true error 00231 *> so long as the next entry is greater than the threshold 00232 *> sqrt(n) * dlamch('Epsilon'). This error bound should only 00233 *> be trusted if the previous boolean is true. 00234 *> 00235 *> err = 3 Reciprocal condition number: Estimated normwise 00236 *> reciprocal condition number. Compared with the threshold 00237 *> sqrt(n) * dlamch('Epsilon') to determine if the error 00238 *> estimate is "guaranteed". These reciprocal condition 00239 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00240 *> appropriately scaled matrix Z. 00241 *> Let Z = S*A, where S scales each row by a power of the 00242 *> radix so all absolute row sums of Z are approximately 1. 00243 *> 00244 *> See Lapack Working Note 165 for further details and extra 00245 *> cautions. 00246 *> \endverbatim 00247 *> 00248 *> \param[out] ERR_BNDS_COMP 00249 *> \verbatim 00250 *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) 00251 *> For each right-hand side, this array contains information about 00252 *> various error bounds and condition numbers corresponding to the 00253 *> componentwise relative error, which is defined as follows: 00254 *> 00255 *> Componentwise relative error in the ith solution vector: 00256 *> abs(XTRUE(j,i) - X(j,i)) 00257 *> max_j ---------------------- 00258 *> abs(X(j,i)) 00259 *> 00260 *> The array is indexed by the right-hand side i (on which the 00261 *> componentwise relative error depends), and the type of error 00262 *> information as described below. There currently are up to three 00263 *> pieces of information returned for each right-hand side. If 00264 *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00265 *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00266 *> the first (:,N_ERR_BNDS) entries are returned. 00267 *> 00268 *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00269 *> right-hand side. 00270 *> 00271 *> The second index in ERR_BNDS_COMP(:,err) contains the following 00272 *> three fields: 00273 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00274 *> reciprocal condition number is less than the threshold 00275 *> sqrt(n) * dlamch('Epsilon'). 00276 *> 00277 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00278 *> almost certainly within a factor of 10 of the true error 00279 *> so long as the next entry is greater than the threshold 00280 *> sqrt(n) * dlamch('Epsilon'). This error bound should only 00281 *> be trusted if the previous boolean is true. 00282 *> 00283 *> err = 3 Reciprocal condition number: Estimated componentwise 00284 *> reciprocal condition number. Compared with the threshold 00285 *> sqrt(n) * dlamch('Epsilon') to determine if the error 00286 *> estimate is "guaranteed". These reciprocal condition 00287 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00288 *> appropriately scaled matrix Z. 00289 *> Let Z = S*(A*diag(x)), where x is the solution for the 00290 *> current right-hand side and S scales each row of 00291 *> A*diag(x) by a power of the radix so all absolute row 00292 *> sums of Z are approximately 1. 00293 *> 00294 *> See Lapack Working Note 165 for further details and extra 00295 *> cautions. 00296 *> \endverbatim 00297 *> 00298 *> \param[in] NPARAMS 00299 *> \verbatim 00300 *> NPARAMS is INTEGER 00301 *> Specifies the number of parameters set in PARAMS. If .LE. 0, the 00302 *> PARAMS array is never referenced and default values are used. 00303 *> \endverbatim 00304 *> 00305 *> \param[in,out] PARAMS 00306 *> \verbatim 00307 *> PARAMS is / output) DOUBLE PRECISION array, dimension NPARAMS 00308 *> Specifies algorithm parameters. If an entry is .LT. 0.0, then 00309 *> that entry will be filled with default value used for that 00310 *> parameter. Only positions up to NPARAMS are accessed; defaults 00311 *> are used for higher-numbered parameters. 00312 *> 00313 *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative 00314 *> refinement or not. 00315 *> Default: 1.0D+0 00316 *> = 0.0 : No refinement is performed, and no error bounds are 00317 *> computed. 00318 *> = 1.0 : Use the double-precision refinement algorithm, 00319 *> possibly with doubled-single computations if the 00320 *> compilation environment does not support DOUBLE 00321 *> PRECISION. 00322 *> (other values are reserved for future use) 00323 *> 00324 *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual 00325 *> computations allowed for refinement. 00326 *> Default: 10 00327 *> Aggressive: Set to 100 to permit convergence using approximate 00328 *> factorizations or factorizations other than LU. If 00329 *> the factorization uses a technique other than 00330 *> Gaussian elimination, the guarantees in 00331 *> err_bnds_norm and err_bnds_comp may no longer be 00332 *> trustworthy. 00333 *> 00334 *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code 00335 *> will attempt to find a solution with small componentwise 00336 *> relative error in the double-precision algorithm. Positive 00337 *> is true, 0.0 is false. 00338 *> Default: 1.0 (attempt componentwise convergence) 00339 *> \endverbatim 00340 *> 00341 *> \param[out] WORK 00342 *> \verbatim 00343 *> WORK is COMPLEX*16 array, dimension (2*N) 00344 *> \endverbatim 00345 *> 00346 *> \param[out] RWORK 00347 *> \verbatim 00348 *> RWORK is DOUBLE PRECISION array, dimension (2*N) 00349 *> \endverbatim 00350 *> 00351 *> \param[out] INFO 00352 *> \verbatim 00353 *> INFO is INTEGER 00354 *> = 0: Successful exit. The solution to every right-hand side is 00355 *> guaranteed. 00356 *> < 0: If INFO = -i, the i-th argument had an illegal value 00357 *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization 00358 *> has been completed, but the factor U is exactly singular, so 00359 *> the solution and error bounds could not be computed. RCOND = 0 00360 *> is returned. 00361 *> = N+J: The solution corresponding to the Jth right-hand side is 00362 *> not guaranteed. The solutions corresponding to other right- 00363 *> hand sides K with K > J may not be guaranteed as well, but 00364 *> only the first such right-hand side is reported. If a small 00365 *> componentwise error is not requested (PARAMS(3) = 0.0) then 00366 *> the Jth right-hand side is the first with a normwise error 00367 *> bound that is not guaranteed (the smallest J such 00368 *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) 00369 *> the Jth right-hand side is the first with either a normwise or 00370 *> componentwise error bound that is not guaranteed (the smallest 00371 *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or 00372 *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of 00373 *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information 00374 *> about all of the right-hand sides check ERR_BNDS_NORM or 00375 *> ERR_BNDS_COMP. 00376 *> \endverbatim 00377 * 00378 * Authors: 00379 * ======== 00380 * 00381 *> \author Univ. of Tennessee 00382 *> \author Univ. of California Berkeley 00383 *> \author Univ. of Colorado Denver 00384 *> \author NAG Ltd. 00385 * 00386 *> \date April 2012 00387 * 00388 *> \ingroup complex16POcomputational 00389 * 00390 * ===================================================================== 00391 SUBROUTINE ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B, 00392 $ LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, 00393 $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, 00394 $ WORK, RWORK, INFO ) 00395 * 00396 * -- LAPACK computational routine (version 3.4.1) -- 00397 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00398 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00399 * April 2012 00400 * 00401 * .. Scalar Arguments .. 00402 CHARACTER UPLO, EQUED 00403 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, 00404 $ N_ERR_BNDS 00405 DOUBLE PRECISION RCOND 00406 * .. 00407 * .. Array Arguments .. 00408 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00409 $ X( LDX, * ), WORK( * ) 00410 DOUBLE PRECISION RWORK( * ), S( * ), PARAMS(*), BERR( * ), 00411 $ ERR_BNDS_NORM( NRHS, * ), 00412 $ ERR_BNDS_COMP( NRHS, * ) 00413 * .. 00414 * 00415 * ================================================================== 00416 * 00417 * .. Parameters .. 00418 DOUBLE PRECISION ZERO, ONE 00419 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00420 DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT 00421 DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT 00422 DOUBLE PRECISION DZTHRESH_DEFAULT 00423 PARAMETER ( ITREF_DEFAULT = 1.0D+0 ) 00424 PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 ) 00425 PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 ) 00426 PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 ) 00427 PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 ) 00428 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00429 $ LA_LINRX_CWISE_I 00430 PARAMETER ( LA_LINRX_ITREF_I = 1, 00431 $ LA_LINRX_ITHRESH_I = 2 ) 00432 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00433 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00434 $ LA_LINRX_RCOND_I 00435 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00436 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00437 * .. 00438 * .. Local Scalars .. 00439 CHARACTER(1) NORM 00440 LOGICAL RCEQU 00441 INTEGER J, PREC_TYPE, REF_TYPE 00442 INTEGER N_NORMS 00443 DOUBLE PRECISION ANORM, RCOND_TMP 00444 DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG 00445 LOGICAL IGNORE_CWISE 00446 INTEGER ITHRESH 00447 DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH 00448 * .. 00449 * .. External Subroutines .. 00450 EXTERNAL XERBLA, ZPOCON, ZLA_PORFSX_EXTENDED 00451 * .. 00452 * .. Intrinsic Functions .. 00453 INTRINSIC MAX, SQRT, TRANSFER 00454 * .. 00455 * .. External Functions .. 00456 EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC 00457 EXTERNAL DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C 00458 DOUBLE PRECISION DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C 00459 LOGICAL LSAME 00460 INTEGER BLAS_FPINFO_X 00461 INTEGER ILATRANS, ILAPREC 00462 * .. 00463 * .. Executable Statements .. 00464 * 00465 * Check the input parameters. 00466 * 00467 INFO = 0 00468 REF_TYPE = INT( ITREF_DEFAULT ) 00469 IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN 00470 IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN 00471 PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT 00472 ELSE 00473 REF_TYPE = PARAMS( LA_LINRX_ITREF_I ) 00474 END IF 00475 END IF 00476 * 00477 * Set default parameters. 00478 * 00479 ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' ) 00480 ITHRESH = INT( ITHRESH_DEFAULT ) 00481 RTHRESH = RTHRESH_DEFAULT 00482 UNSTABLE_THRESH = DZTHRESH_DEFAULT 00483 IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0 00484 * 00485 IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN 00486 IF ( PARAMS(LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN 00487 PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH 00488 ELSE 00489 ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) ) 00490 END IF 00491 END IF 00492 IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN 00493 IF ( PARAMS(LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN 00494 IF ( IGNORE_CWISE ) THEN 00495 PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0 00496 ELSE 00497 PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0 00498 END IF 00499 ELSE 00500 IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0 00501 END IF 00502 END IF 00503 IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN 00504 N_NORMS = 0 00505 ELSE IF ( IGNORE_CWISE ) THEN 00506 N_NORMS = 1 00507 ELSE 00508 N_NORMS = 2 00509 END IF 00510 * 00511 RCEQU = LSAME( EQUED, 'Y' ) 00512 * 00513 * Test input parameters. 00514 * 00515 IF (.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00516 INFO = -1 00517 ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN 00518 INFO = -2 00519 ELSE IF( N.LT.0 ) THEN 00520 INFO = -3 00521 ELSE IF( NRHS.LT.0 ) THEN 00522 INFO = -4 00523 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00524 INFO = -6 00525 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00526 INFO = -8 00527 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00528 INFO = -11 00529 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN 00530 INFO = -13 00531 END IF 00532 IF( INFO.NE.0 ) THEN 00533 CALL XERBLA( 'ZPORFSX', -INFO ) 00534 RETURN 00535 END IF 00536 * 00537 * Quick return if possible. 00538 * 00539 IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN 00540 RCOND = 1.0D+0 00541 DO J = 1, NRHS 00542 BERR( J ) = 0.0D+0 00543 IF ( N_ERR_BNDS .GE. 1 ) THEN 00544 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00545 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00546 END IF 00547 IF ( N_ERR_BNDS .GE. 2 ) THEN 00548 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0 00549 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0 00550 END IF 00551 IF ( N_ERR_BNDS .GE. 3 ) THEN 00552 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0 00553 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0 00554 END IF 00555 END DO 00556 RETURN 00557 END IF 00558 * 00559 * Default to failure. 00560 * 00561 RCOND = 0.0D+0 00562 DO J = 1, NRHS 00563 BERR( J ) = 1.0D+0 00564 IF ( N_ERR_BNDS .GE. 1 ) THEN 00565 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00566 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00567 END IF 00568 IF ( N_ERR_BNDS .GE. 2 ) THEN 00569 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00570 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00571 END IF 00572 IF ( N_ERR_BNDS .GE. 3 ) THEN 00573 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0 00574 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0 00575 END IF 00576 END DO 00577 * 00578 * Compute the norm of A and the reciprocal of the condition 00579 * number of A. 00580 * 00581 NORM = 'I' 00582 ANORM = ZLANHE( NORM, UPLO, N, A, LDA, RWORK ) 00583 CALL ZPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK, RWORK, 00584 $ INFO ) 00585 * 00586 * Perform refinement on each right-hand side 00587 * 00588 IF ( REF_TYPE .NE. 0 ) THEN 00589 00590 PREC_TYPE = ILAPREC( 'E' ) 00591 00592 CALL ZLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, 00593 $ NRHS, A, LDA, AF, LDAF, RCEQU, S, B, 00594 $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP, 00595 $ WORK, RWORK, WORK(N+1), 00596 $ TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), RCOND, 00597 $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE, 00598 $ INFO ) 00599 END IF 00600 00601 ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' ) 00602 IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN 00603 * 00604 * Compute scaled normwise condition number cond(A*C). 00605 * 00606 IF ( RCEQU ) THEN 00607 RCOND_TMP = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, 00608 $ S, .TRUE., INFO, WORK, RWORK ) 00609 ELSE 00610 RCOND_TMP = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, 00611 $ S, .FALSE., INFO, WORK, RWORK ) 00612 END IF 00613 DO J = 1, NRHS 00614 * 00615 * Cap the error at 1.0. 00616 * 00617 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I 00618 $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 ) 00619 $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00620 * 00621 * Threshold the error (see LAWN). 00622 * 00623 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN 00624 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00625 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0 00626 IF ( INFO .LE. N ) INFO = N + J 00627 ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND ) 00628 $ THEN 00629 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND 00630 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00631 END IF 00632 * 00633 * Save the condition number. 00634 * 00635 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN 00636 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00637 END IF 00638 00639 END DO 00640 END IF 00641 00642 IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2) THEN 00643 * 00644 * Compute componentwise condition number cond(A*diag(Y(:,J))) for 00645 * each right-hand side using the current solution as an estimate of 00646 * the true solution. If the componentwise error estimate is too 00647 * large, then the solution is a lousy estimate of truth and the 00648 * estimated RCOND may be too optimistic. To avoid misleading users, 00649 * the inverse condition number is set to 0.0 when the estimated 00650 * cwise error is at least CWISE_WRONG. 00651 * 00652 CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) ) 00653 DO J = 1, NRHS 00654 IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG ) 00655 $ THEN 00656 RCOND_TMP = ZLA_PORCOND_X( UPLO, N, A, LDA, AF, LDAF, 00657 $ X(1,J), INFO, WORK, RWORK ) 00658 ELSE 00659 RCOND_TMP = 0.0D+0 00660 END IF 00661 * 00662 * Cap the error at 1.0. 00663 * 00664 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I 00665 $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 ) 00666 $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00667 * 00668 * Threshold the error (see LAWN). 00669 * 00670 IF (RCOND_TMP .LT. ILLRCOND_THRESH) THEN 00671 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00672 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0 00673 IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0 00674 $ .AND. INFO.LT.N + J ) INFO = N + J 00675 ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) 00676 $ .LT. ERR_LBND ) THEN 00677 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND 00678 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00679 END IF 00680 * 00681 * Save the condition number. 00682 * 00683 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN 00684 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00685 END IF 00686 00687 END DO 00688 END IF 00689 * 00690 RETURN 00691 * 00692 * End of ZPORFSX 00693 * 00694 END