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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHERFSX 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHERFSX + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zherfsx.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zherfsx.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zherfsx.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHERFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV, 00022 * S, B, 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 * INTEGER IPIV( * ) 00034 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00035 * $ X( LDX, * ), WORK( * ) 00036 * DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ), RWORK( * ), 00037 * $ ERR_BNDS_NORM( NRHS, * ), 00038 * $ ERR_BNDS_COMP( NRHS, * ) 00039 * 00040 * 00041 *> \par Purpose: 00042 * ============= 00043 *> 00044 *> \verbatim 00045 *> 00046 *> ZHERFSX improves the computed solution to a system of linear 00047 *> equations when the coefficient matrix is Hermitian indefinite, and 00048 *> provides error bounds and backward error estimates for the 00049 *> solution. In addition to normwise error bound, the code provides 00050 *> maximum componentwise error bound if possible. See comments for 00051 *> ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds. 00052 *> 00053 *> The original system of linear equations may have been equilibrated 00054 *> before calling this routine, as described by arguments EQUED and S 00055 *> below. In this case, the solution and error bounds returned are 00056 *> for the original unequilibrated system. 00057 *> \endverbatim 00058 * 00059 * Arguments: 00060 * ========== 00061 * 00062 *> \verbatim 00063 *> Some optional parameters are bundled in the PARAMS array. These 00064 *> settings determine how refinement is performed, but often the 00065 *> defaults are acceptable. If the defaults are acceptable, users 00066 *> can pass NPARAMS = 0 which prevents the source code from accessing 00067 *> the PARAMS argument. 00068 *> \endverbatim 00069 *> 00070 *> \param[in] UPLO 00071 *> \verbatim 00072 *> UPLO is CHARACTER*1 00073 *> = 'U': Upper triangle of A is stored; 00074 *> = 'L': Lower triangle of A is stored. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] EQUED 00078 *> \verbatim 00079 *> EQUED is CHARACTER*1 00080 *> Specifies the form of equilibration that was done to A 00081 *> before calling this routine. This is needed to compute 00082 *> the solution and error bounds correctly. 00083 *> = 'N': No equilibration 00084 *> = 'Y': Both row and column equilibration, i.e., A has been 00085 *> replaced by diag(S) * A * diag(S). 00086 *> The right hand side B has been changed accordingly. 00087 *> \endverbatim 00088 *> 00089 *> \param[in] N 00090 *> \verbatim 00091 *> N is INTEGER 00092 *> The order of the matrix A. N >= 0. 00093 *> \endverbatim 00094 *> 00095 *> \param[in] NRHS 00096 *> \verbatim 00097 *> NRHS is INTEGER 00098 *> The number of right hand sides, i.e., the number of columns 00099 *> of the matrices B and X. NRHS >= 0. 00100 *> \endverbatim 00101 *> 00102 *> \param[in] A 00103 *> \verbatim 00104 *> A is COMPLEX*16 array, dimension (LDA,N) 00105 *> The symmetric matrix A. If UPLO = 'U', the leading N-by-N 00106 *> upper triangular part of A contains the upper triangular 00107 *> part of the matrix A, and the strictly lower triangular 00108 *> part of A is not referenced. If UPLO = 'L', the leading 00109 *> N-by-N lower triangular part of A contains the lower 00110 *> triangular part of the matrix A, and the strictly upper 00111 *> triangular part of A is not referenced. 00112 *> \endverbatim 00113 *> 00114 *> \param[in] LDA 00115 *> \verbatim 00116 *> LDA is INTEGER 00117 *> The leading dimension of the array A. LDA >= max(1,N). 00118 *> \endverbatim 00119 *> 00120 *> \param[in] AF 00121 *> \verbatim 00122 *> AF is COMPLEX*16 array, dimension (LDAF,N) 00123 *> The factored form of the matrix A. AF contains the block 00124 *> diagonal matrix D and the multipliers used to obtain the 00125 *> factor U or L from the factorization A = U*D*U**T or A = 00126 *> L*D*L**T as computed by DSYTRF. 00127 *> \endverbatim 00128 *> 00129 *> \param[in] LDAF 00130 *> \verbatim 00131 *> LDAF is INTEGER 00132 *> The leading dimension of the array AF. LDAF >= max(1,N). 00133 *> \endverbatim 00134 *> 00135 *> \param[in] IPIV 00136 *> \verbatim 00137 *> IPIV is INTEGER array, dimension (N) 00138 *> Details of the interchanges and the block structure of D 00139 *> as determined by DSYTRF. 00140 *> \endverbatim 00141 *> 00142 *> \param[in,out] S 00143 *> \verbatim 00144 *> S is DOUBLE PRECISION array, dimension (N) 00145 *> The scale factors for A. If EQUED = 'Y', A is multiplied on 00146 *> the left and right by diag(S). S is an input argument if FACT = 00147 *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED 00148 *> = 'Y', each element of S must be positive. If S is output, each 00149 *> element of S is a power of the radix. If S is input, each element 00150 *> of S should be a power of the radix to ensure a reliable solution 00151 *> and error estimates. Scaling by powers of the radix does not cause 00152 *> rounding errors unless the result underflows or overflows. 00153 *> Rounding errors during scaling lead to refining with a matrix that 00154 *> is not equivalent to the input matrix, producing error estimates 00155 *> that may not be reliable. 00156 *> \endverbatim 00157 *> 00158 *> \param[in] B 00159 *> \verbatim 00160 *> B is COMPLEX*16 array, dimension (LDB,NRHS) 00161 *> The right hand side matrix B. 00162 *> \endverbatim 00163 *> 00164 *> \param[in] LDB 00165 *> \verbatim 00166 *> LDB is INTEGER 00167 *> The leading dimension of the array B. LDB >= max(1,N). 00168 *> \endverbatim 00169 *> 00170 *> \param[in,out] X 00171 *> \verbatim 00172 *> X is COMPLEX*16 array, dimension (LDX,NRHS) 00173 *> On entry, the solution matrix X, as computed by DGETRS. 00174 *> On exit, the improved solution matrix X. 00175 *> \endverbatim 00176 *> 00177 *> \param[in] LDX 00178 *> \verbatim 00179 *> LDX is INTEGER 00180 *> The leading dimension of the array X. LDX >= max(1,N). 00181 *> \endverbatim 00182 *> 00183 *> \param[out] RCOND 00184 *> \verbatim 00185 *> RCOND is DOUBLE PRECISION 00186 *> Reciprocal scaled condition number. This is an estimate of the 00187 *> reciprocal Skeel condition number of the matrix A after 00188 *> equilibration (if done). If this is less than the machine 00189 *> precision (in particular, if it is zero), the matrix is singular 00190 *> to working precision. Note that the error may still be small even 00191 *> if this number is very small and the matrix appears ill- 00192 *> conditioned. 00193 *> \endverbatim 00194 *> 00195 *> \param[out] BERR 00196 *> \verbatim 00197 *> BERR is DOUBLE PRECISION array, dimension (NRHS) 00198 *> Componentwise relative backward error. This is the 00199 *> componentwise relative backward error of each solution vector X(j) 00200 *> (i.e., the smallest relative change in any element of A or B that 00201 *> makes X(j) an exact solution). 00202 *> \endverbatim 00203 *> 00204 *> \param[in] N_ERR_BNDS 00205 *> \verbatim 00206 *> N_ERR_BNDS is INTEGER 00207 *> Number of error bounds to return for each right hand side 00208 *> and each type (normwise or componentwise). See ERR_BNDS_NORM and 00209 *> ERR_BNDS_COMP below. 00210 *> \endverbatim 00211 *> 00212 *> \param[out] ERR_BNDS_NORM 00213 *> \verbatim 00214 *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) 00215 *> For each right-hand side, this array contains information about 00216 *> various error bounds and condition numbers corresponding to the 00217 *> normwise relative error, which is defined as follows: 00218 *> 00219 *> Normwise relative error in the ith solution vector: 00220 *> max_j (abs(XTRUE(j,i) - X(j,i))) 00221 *> ------------------------------ 00222 *> max_j abs(X(j,i)) 00223 *> 00224 *> The array is indexed by the type of error information as described 00225 *> below. There currently are up to three pieces of information 00226 *> returned. 00227 *> 00228 *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00229 *> right-hand side. 00230 *> 00231 *> The second index in ERR_BNDS_NORM(:,err) contains the following 00232 *> three fields: 00233 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00234 *> reciprocal condition number is less than the threshold 00235 *> sqrt(n) * dlamch('Epsilon'). 00236 *> 00237 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00238 *> almost certainly within a factor of 10 of the true error 00239 *> so long as the next entry is greater than the threshold 00240 *> sqrt(n) * dlamch('Epsilon'). This error bound should only 00241 *> be trusted if the previous boolean is true. 00242 *> 00243 *> err = 3 Reciprocal condition number: Estimated normwise 00244 *> reciprocal condition number. Compared with the threshold 00245 *> sqrt(n) * dlamch('Epsilon') to determine if the error 00246 *> estimate is "guaranteed". These reciprocal condition 00247 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00248 *> appropriately scaled matrix Z. 00249 *> Let Z = S*A, where S scales each row by a power of the 00250 *> radix so all absolute row sums of Z are approximately 1. 00251 *> 00252 *> See Lapack Working Note 165 for further details and extra 00253 *> cautions. 00254 *> \endverbatim 00255 *> 00256 *> \param[out] ERR_BNDS_COMP 00257 *> \verbatim 00258 *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) 00259 *> For each right-hand side, this array contains information about 00260 *> various error bounds and condition numbers corresponding to the 00261 *> componentwise relative error, which is defined as follows: 00262 *> 00263 *> Componentwise relative error in the ith solution vector: 00264 *> abs(XTRUE(j,i) - X(j,i)) 00265 *> max_j ---------------------- 00266 *> abs(X(j,i)) 00267 *> 00268 *> The array is indexed by the right-hand side i (on which the 00269 *> componentwise relative error depends), and the type of error 00270 *> information as described below. There currently are up to three 00271 *> pieces of information returned for each right-hand side. If 00272 *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00273 *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00274 *> the first (:,N_ERR_BNDS) entries are returned. 00275 *> 00276 *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00277 *> right-hand side. 00278 *> 00279 *> The second index in ERR_BNDS_COMP(:,err) contains the following 00280 *> three fields: 00281 *> err = 1 "Trust/don't trust" boolean. Trust the answer if the 00282 *> reciprocal condition number is less than the threshold 00283 *> sqrt(n) * dlamch('Epsilon'). 00284 *> 00285 *> err = 2 "Guaranteed" error bound: The estimated forward error, 00286 *> almost certainly within a factor of 10 of the true error 00287 *> so long as the next entry is greater than the threshold 00288 *> sqrt(n) * dlamch('Epsilon'). This error bound should only 00289 *> be trusted if the previous boolean is true. 00290 *> 00291 *> err = 3 Reciprocal condition number: Estimated componentwise 00292 *> reciprocal condition number. Compared with the threshold 00293 *> sqrt(n) * dlamch('Epsilon') to determine if the error 00294 *> estimate is "guaranteed". These reciprocal condition 00295 *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00296 *> appropriately scaled matrix Z. 00297 *> Let Z = S*(A*diag(x)), where x is the solution for the 00298 *> current right-hand side and S scales each row of 00299 *> A*diag(x) by a power of the radix so all absolute row 00300 *> sums of Z are approximately 1. 00301 *> 00302 *> See Lapack Working Note 165 for further details and extra 00303 *> cautions. 00304 *> \endverbatim 00305 *> 00306 *> \param[in] NPARAMS 00307 *> \verbatim 00308 *> NPARAMS is INTEGER 00309 *> Specifies the number of parameters set in PARAMS. If .LE. 0, the 00310 *> PARAMS array is never referenced and default values are used. 00311 *> \endverbatim 00312 *> 00313 *> \param[in,out] PARAMS 00314 *> \verbatim 00315 *> PARAMS is DOUBLE PRECISION array, dimension NPARAMS 00316 *> Specifies algorithm parameters. If an entry is .LT. 0.0, then 00317 *> that entry will be filled with default value used for that 00318 *> parameter. Only positions up to NPARAMS are accessed; defaults 00319 *> are used for higher-numbered parameters. 00320 *> 00321 *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative 00322 *> refinement or not. 00323 *> Default: 1.0D+0 00324 *> = 0.0 : No refinement is performed, and no error bounds are 00325 *> computed. 00326 *> = 1.0 : Use the double-precision refinement algorithm, 00327 *> possibly with doubled-single computations if the 00328 *> compilation environment does not support DOUBLE 00329 *> PRECISION. 00330 *> (other values are reserved for future use) 00331 *> 00332 *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual 00333 *> computations allowed for refinement. 00334 *> Default: 10 00335 *> Aggressive: Set to 100 to permit convergence using approximate 00336 *> factorizations or factorizations other than LU. If 00337 *> the factorization uses a technique other than 00338 *> Gaussian elimination, the guarantees in 00339 *> err_bnds_norm and err_bnds_comp may no longer be 00340 *> trustworthy. 00341 *> 00342 *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code 00343 *> will attempt to find a solution with small componentwise 00344 *> relative error in the double-precision algorithm. Positive 00345 *> is true, 0.0 is false. 00346 *> Default: 1.0 (attempt componentwise convergence) 00347 *> \endverbatim 00348 *> 00349 *> \param[out] WORK 00350 *> \verbatim 00351 *> WORK is COMPLEX*16 array, dimension (2*N) 00352 *> \endverbatim 00353 *> 00354 *> \param[out] RWORK 00355 *> \verbatim 00356 *> RWORK is DOUBLE PRECISION array, dimension (2*N) 00357 *> \endverbatim 00358 *> 00359 *> \param[out] INFO 00360 *> \verbatim 00361 *> INFO is INTEGER 00362 *> = 0: Successful exit. The solution to every right-hand side is 00363 *> guaranteed. 00364 *> < 0: If INFO = -i, the i-th argument had an illegal value 00365 *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization 00366 *> has been completed, but the factor U is exactly singular, so 00367 *> the solution and error bounds could not be computed. RCOND = 0 00368 *> is returned. 00369 *> = N+J: The solution corresponding to the Jth right-hand side is 00370 *> not guaranteed. The solutions corresponding to other right- 00371 *> hand sides K with K > J may not be guaranteed as well, but 00372 *> only the first such right-hand side is reported. If a small 00373 *> componentwise error is not requested (PARAMS(3) = 0.0) then 00374 *> the Jth right-hand side is the first with a normwise error 00375 *> bound that is not guaranteed (the smallest J such 00376 *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) 00377 *> the Jth right-hand side is the first with either a normwise or 00378 *> componentwise error bound that is not guaranteed (the smallest 00379 *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or 00380 *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of 00381 *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information 00382 *> about all of the right-hand sides check ERR_BNDS_NORM or 00383 *> ERR_BNDS_COMP. 00384 *> \endverbatim 00385 * 00386 * Authors: 00387 * ======== 00388 * 00389 *> \author Univ. of Tennessee 00390 *> \author Univ. of California Berkeley 00391 *> \author Univ. of Colorado Denver 00392 *> \author NAG Ltd. 00393 * 00394 *> \date April 2012 00395 * 00396 *> \ingroup complex16HEcomputational 00397 * 00398 * ===================================================================== 00399 SUBROUTINE ZHERFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV, 00400 $ S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, 00401 $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, 00402 $ WORK, RWORK, INFO ) 00403 * 00404 * -- LAPACK computational routine (version 3.4.1) -- 00405 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00406 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00407 * April 2012 00408 * 00409 * .. Scalar Arguments .. 00410 CHARACTER UPLO, EQUED 00411 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, 00412 $ N_ERR_BNDS 00413 DOUBLE PRECISION RCOND 00414 * .. 00415 * .. Array Arguments .. 00416 INTEGER IPIV( * ) 00417 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00418 $ X( LDX, * ), WORK( * ) 00419 DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ), RWORK( * ), 00420 $ ERR_BNDS_NORM( NRHS, * ), 00421 $ ERR_BNDS_COMP( NRHS, * ) 00422 * 00423 * ================================================================== 00424 * 00425 * .. Parameters .. 00426 DOUBLE PRECISION ZERO, ONE 00427 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00428 DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT 00429 DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT 00430 DOUBLE PRECISION DZTHRESH_DEFAULT 00431 PARAMETER ( ITREF_DEFAULT = 1.0D+0 ) 00432 PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 ) 00433 PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 ) 00434 PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 ) 00435 PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 ) 00436 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00437 $ LA_LINRX_CWISE_I 00438 PARAMETER ( LA_LINRX_ITREF_I = 1, 00439 $ LA_LINRX_ITHRESH_I = 2 ) 00440 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00441 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00442 $ LA_LINRX_RCOND_I 00443 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00444 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00445 * .. 00446 * .. Local Scalars .. 00447 CHARACTER(1) NORM 00448 LOGICAL RCEQU 00449 INTEGER J, PREC_TYPE, REF_TYPE 00450 INTEGER N_NORMS 00451 DOUBLE PRECISION ANORM, RCOND_TMP 00452 DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG 00453 LOGICAL IGNORE_CWISE 00454 INTEGER ITHRESH 00455 DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH 00456 * .. 00457 * .. External Subroutines .. 00458 EXTERNAL XERBLA, ZHECON, ZLA_HERFSX_EXTENDED 00459 * .. 00460 * .. Intrinsic Functions .. 00461 INTRINSIC MAX, SQRT, TRANSFER 00462 * .. 00463 * .. External Functions .. 00464 EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC 00465 EXTERNAL DLAMCH, ZLANHE, ZLA_HERCOND_X, ZLA_HERCOND_C 00466 DOUBLE PRECISION DLAMCH, ZLANHE, ZLA_HERCOND_X, ZLA_HERCOND_C 00467 LOGICAL LSAME 00468 INTEGER BLAS_FPINFO_X 00469 INTEGER ILATRANS, ILAPREC 00470 * .. 00471 * .. Executable Statements .. 00472 * 00473 * Check the input parameters. 00474 * 00475 INFO = 0 00476 REF_TYPE = INT( ITREF_DEFAULT ) 00477 IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN 00478 IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN 00479 PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT 00480 ELSE 00481 REF_TYPE = PARAMS( LA_LINRX_ITREF_I ) 00482 END IF 00483 END IF 00484 * 00485 * Set default parameters. 00486 * 00487 ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' ) 00488 ITHRESH = INT( ITHRESH_DEFAULT ) 00489 RTHRESH = RTHRESH_DEFAULT 00490 UNSTABLE_THRESH = DZTHRESH_DEFAULT 00491 IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0 00492 * 00493 IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN 00494 IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN 00495 PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH 00496 ELSE 00497 ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) ) 00498 END IF 00499 END IF 00500 IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN 00501 IF ( PARAMS(LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN 00502 IF ( IGNORE_CWISE ) THEN 00503 PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0 00504 ELSE 00505 PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0 00506 END IF 00507 ELSE 00508 IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0 00509 END IF 00510 END IF 00511 IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN 00512 N_NORMS = 0 00513 ELSE IF ( IGNORE_CWISE ) THEN 00514 N_NORMS = 1 00515 ELSE 00516 N_NORMS = 2 00517 END IF 00518 * 00519 RCEQU = LSAME( EQUED, 'Y' ) 00520 * 00521 * Test input parameters. 00522 * 00523 IF (.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00524 INFO = -1 00525 ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN 00526 INFO = -2 00527 ELSE IF( N.LT.0 ) THEN 00528 INFO = -3 00529 ELSE IF( NRHS.LT.0 ) THEN 00530 INFO = -4 00531 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00532 INFO = -6 00533 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00534 INFO = -8 00535 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00536 INFO = -12 00537 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN 00538 INFO = -14 00539 END IF 00540 IF( INFO.NE.0 ) THEN 00541 CALL XERBLA( 'ZHERFSX', -INFO ) 00542 RETURN 00543 END IF 00544 * 00545 * Quick return if possible. 00546 * 00547 IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN 00548 RCOND = 1.0D+0 00549 DO J = 1, NRHS 00550 BERR( J ) = 0.0D+0 00551 IF ( N_ERR_BNDS .GE. 1 ) THEN 00552 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00553 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00554 END IF 00555 IF ( N_ERR_BNDS .GE. 2 ) THEN 00556 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0 00557 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0 00558 END IF 00559 IF ( N_ERR_BNDS .GE. 3 ) THEN 00560 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0 00561 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0 00562 END IF 00563 END DO 00564 RETURN 00565 END IF 00566 * 00567 * Default to failure. 00568 * 00569 RCOND = 0.0D+0 00570 DO J = 1, NRHS 00571 BERR( J ) = 1.0D+0 00572 IF ( N_ERR_BNDS .GE. 1 ) THEN 00573 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00574 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00575 END IF 00576 IF ( N_ERR_BNDS .GE. 2 ) THEN 00577 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00578 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00579 END IF 00580 IF ( N_ERR_BNDS .GE. 3 ) THEN 00581 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0 00582 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0 00583 END IF 00584 END DO 00585 * 00586 * Compute the norm of A and the reciprocal of the condition 00587 * number of A. 00588 * 00589 NORM = 'I' 00590 ANORM = ZLANHE( NORM, UPLO, N, A, LDA, RWORK ) 00591 CALL ZHECON( UPLO, N, AF, LDAF, IPIV, ANORM, RCOND, WORK, 00592 $ INFO ) 00593 * 00594 * Perform refinement on each right-hand side 00595 * 00596 IF ( REF_TYPE .NE. 0 ) THEN 00597 00598 PREC_TYPE = ILAPREC( 'E' ) 00599 00600 CALL ZLA_HERFSX_EXTENDED( PREC_TYPE, UPLO, N, 00601 $ NRHS, A, LDA, AF, LDAF, IPIV, RCEQU, S, B, 00602 $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP, 00603 $ WORK, RWORK, WORK(N+1), 00604 $ TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), RCOND, 00605 $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE, 00606 $ INFO ) 00607 END IF 00608 00609 ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' ) 00610 IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN 00611 * 00612 * Compute scaled normwise condition number cond(A*C). 00613 * 00614 IF ( RCEQU ) THEN 00615 RCOND_TMP = ZLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, 00616 $ S, .TRUE., INFO, WORK, RWORK ) 00617 ELSE 00618 RCOND_TMP = ZLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, 00619 $ S, .FALSE., INFO, WORK, RWORK ) 00620 END IF 00621 DO J = 1, NRHS 00622 * 00623 * Cap the error at 1.0. 00624 * 00625 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I 00626 $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 ) 00627 $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00628 * 00629 * Threshold the error (see LAWN). 00630 * 00631 IF (RCOND_TMP .LT. ILLRCOND_THRESH) THEN 00632 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00633 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0 00634 IF ( INFO .LE. N ) INFO = N + J 00635 ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND ) 00636 $ THEN 00637 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND 00638 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00639 END IF 00640 * 00641 * Save the condition number. 00642 * 00643 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN 00644 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00645 END IF 00646 END DO 00647 END IF 00648 00649 IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN 00650 * 00651 * Compute componentwise condition number cond(A*diag(Y(:,J))) for 00652 * each right-hand side using the current solution as an estimate of 00653 * the true solution. If the componentwise error estimate is too 00654 * large, then the solution is a lousy estimate of truth and the 00655 * estimated RCOND may be too optimistic. To avoid misleading users, 00656 * the inverse condition number is set to 0.0 when the estimated 00657 * cwise error is at least CWISE_WRONG. 00658 * 00659 CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) ) 00660 DO J = 1, NRHS 00661 IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG ) 00662 $ THEN 00663 RCOND_TMP = ZLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF, 00664 $ IPIV, X( 1, J ), INFO, WORK, RWORK ) 00665 ELSE 00666 RCOND_TMP = 0.0D+0 00667 END IF 00668 * 00669 * Cap the error at 1.0. 00670 * 00671 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I 00672 $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 ) 00673 $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00674 * 00675 * Threshold the error (see LAWN). 00676 * 00677 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN 00678 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00679 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0 00680 IF ( .NOT. IGNORE_CWISE 00681 $ .AND. INFO.LT.N + J ) INFO = N + J 00682 ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) 00683 $ .LT. ERR_LBND ) THEN 00684 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND 00685 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00686 END IF 00687 * 00688 * Save the condition number. 00689 * 00690 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN 00691 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00692 END IF 00693 00694 END DO 00695 END IF 00696 * 00697 RETURN 00698 * 00699 * End of ZHERFSX 00700 * 00701 END