00001 /* sgerfsx.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 /* Table of constant values */ 00017 00018 static integer c_n1 = -1; 00019 static integer c__0 = 0; 00020 static integer c__1 = 1; 00021 00022 /* Subroutine */ int sgerfsx_(char *trans, char *equed, integer *n, integer * 00023 nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, 00024 real *r__, real *c__, real *b, integer *ldb, real *x, integer *ldx, 00025 real *rcond, real *berr, integer *n_err_bnds__, real *err_bnds_norm__, 00026 real *err_bnds_comp__, integer *nparams, real *params, real *work, 00027 integer *iwork, integer *info) 00028 { 00029 /* System generated locals */ 00030 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 00031 x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00032 err_bnds_comp_dim1, err_bnds_comp_offset, i__1; 00033 real r__1, r__2; 00034 00035 /* Builtin functions */ 00036 double sqrt(doublereal); 00037 00038 /* Local variables */ 00039 real illrcond_thresh__, unstable_thresh__, err_lbnd__; 00040 integer ref_type__; 00041 extern integer ilatrans_(char *); 00042 integer j; 00043 real rcond_tmp__; 00044 integer prec_type__, trans_type__; 00045 extern doublereal sla_gercond__(char *, integer *, real *, integer *, 00046 real *, integer *, integer *, integer *, real *, integer *, real * 00047 , integer *, ftnlen); 00048 real cwise_wrong__; 00049 extern /* Subroutine */ int sla_gerfsx_extended__(integer *, integer *, 00050 integer *, integer *, real *, integer *, real *, integer *, 00051 integer *, logical *, real *, real *, integer *, real *, integer * 00052 , real *, integer *, real *, real *, real *, real *, real *, real 00053 *, real *, integer *, real *, real *, logical *, integer *); 00054 char norm[1]; 00055 logical ignore_cwise__; 00056 extern logical lsame_(char *, char *); 00057 real anorm; 00058 extern doublereal slamch_(char *), slange_(char *, integer *, 00059 integer *, real *, integer *, real *); 00060 extern /* Subroutine */ int xerbla_(char *, integer *), sgecon_( 00061 char *, integer *, real *, integer *, real *, real *, real *, 00062 integer *, integer *); 00063 logical colequ, notran, rowequ; 00064 extern integer ilaprec_(char *); 00065 integer ithresh, n_norms__; 00066 real rthresh; 00067 00068 00069 /* -- LAPACK routine (version 3.2.1) -- */ 00070 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00071 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00072 /* -- April 2009 -- */ 00073 00074 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00075 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00076 00077 /* .. */ 00078 /* .. Scalar Arguments .. */ 00079 /* .. */ 00080 /* .. Array Arguments .. */ 00081 /* .. */ 00082 00083 /* Purpose */ 00084 /* ======= */ 00085 00086 /* SGERFSX improves the computed solution to a system of linear */ 00087 /* equations and provides error bounds and backward error estimates */ 00088 /* for the solution. In addition to normwise error bound, the code */ 00089 /* provides maximum componentwise error bound if possible. See */ 00090 /* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */ 00091 /* error bounds. */ 00092 00093 /* The original system of linear equations may have been equilibrated */ 00094 /* before calling this routine, as described by arguments EQUED, R */ 00095 /* and C below. In this case, the solution and error bounds returned */ 00096 /* are for the original unequilibrated system. */ 00097 00098 /* Arguments */ 00099 /* ========= */ 00100 00101 /* Some optional parameters are bundled in the PARAMS array. These */ 00102 /* settings determine how refinement is performed, but often the */ 00103 /* defaults are acceptable. If the defaults are acceptable, users */ 00104 /* can pass NPARAMS = 0 which prevents the source code from accessing */ 00105 /* the PARAMS argument. */ 00106 00107 /* TRANS (input) CHARACTER*1 */ 00108 /* Specifies the form of the system of equations: */ 00109 /* = 'N': A * X = B (No transpose) */ 00110 /* = 'T': A**T * X = B (Transpose) */ 00111 /* = 'C': A**H * X = B (Conjugate transpose = Transpose) */ 00112 00113 /* EQUED (input) CHARACTER*1 */ 00114 /* Specifies the form of equilibration that was done to A */ 00115 /* before calling this routine. This is needed to compute */ 00116 /* the solution and error bounds correctly. */ 00117 /* = 'N': No equilibration */ 00118 /* = 'R': Row equilibration, i.e., A has been premultiplied by */ 00119 /* diag(R). */ 00120 /* = 'C': Column equilibration, i.e., A has been postmultiplied */ 00121 /* by diag(C). */ 00122 /* = 'B': Both row and column equilibration, i.e., A has been */ 00123 /* replaced by diag(R) * A * diag(C). */ 00124 /* The right hand side B has been changed accordingly. */ 00125 00126 /* N (input) INTEGER */ 00127 /* The order of the matrix A. N >= 0. */ 00128 00129 /* NRHS (input) INTEGER */ 00130 /* The number of right hand sides, i.e., the number of columns */ 00131 /* of the matrices B and X. NRHS >= 0. */ 00132 00133 /* A (input) REAL array, dimension (LDA,N) */ 00134 /* The original N-by-N matrix A. */ 00135 00136 /* LDA (input) INTEGER */ 00137 /* The leading dimension of the array A. LDA >= max(1,N). */ 00138 00139 /* AF (input) REAL array, dimension (LDAF,N) */ 00140 /* The factors L and U from the factorization A = P*L*U */ 00141 /* as computed by SGETRF. */ 00142 00143 /* LDAF (input) INTEGER */ 00144 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00145 00146 /* IPIV (input) INTEGER array, dimension (N) */ 00147 /* The pivot indices from SGETRF; for 1<=i<=N, row i of the */ 00148 /* matrix was interchanged with row IPIV(i). */ 00149 00150 /* R (input or output) REAL array, dimension (N) */ 00151 /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ 00152 /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ 00153 /* is not accessed. R is an input argument if FACT = 'F'; */ 00154 /* otherwise, R is an output argument. If FACT = 'F' and */ 00155 /* EQUED = 'R' or 'B', each element of R must be positive. */ 00156 /* If R is output, each element of R is a power of the radix. */ 00157 /* If R is input, each element of R should be a power of the radix */ 00158 /* to ensure a reliable solution and error estimates. Scaling by */ 00159 /* powers of the radix does not cause rounding errors unless the */ 00160 /* result underflows or overflows. Rounding errors during scaling */ 00161 /* lead to refining with a matrix that is not equivalent to the */ 00162 /* input matrix, producing error estimates that may not be */ 00163 /* reliable. */ 00164 00165 /* C (input or output) REAL array, dimension (N) */ 00166 /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ 00167 /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ 00168 /* is not accessed. C is an input argument if FACT = 'F'; */ 00169 /* otherwise, C is an output argument. If FACT = 'F' and */ 00170 /* EQUED = 'C' or 'B', each element of C must be positive. */ 00171 /* If C is output, each element of C is a power of the radix. */ 00172 /* If C is input, each element of C should be a power of the radix */ 00173 /* to ensure a reliable solution and error estimates. Scaling by */ 00174 /* powers of the radix does not cause rounding errors unless the */ 00175 /* result underflows or overflows. Rounding errors during scaling */ 00176 /* lead to refining with a matrix that is not equivalent to the */ 00177 /* input matrix, producing error estimates that may not be */ 00178 /* reliable. */ 00179 00180 /* B (input) REAL array, dimension (LDB,NRHS) */ 00181 /* The right hand side matrix B. */ 00182 00183 /* LDB (input) INTEGER */ 00184 /* The leading dimension of the array B. LDB >= max(1,N). */ 00185 00186 /* X (input/output) REAL array, dimension (LDX,NRHS) */ 00187 /* On entry, the solution matrix X, as computed by SGETRS. */ 00188 /* On exit, the improved solution matrix X. */ 00189 00190 /* LDX (input) INTEGER */ 00191 /* The leading dimension of the array X. LDX >= max(1,N). */ 00192 00193 /* RCOND (output) REAL */ 00194 /* Reciprocal scaled condition number. This is an estimate of the */ 00195 /* reciprocal Skeel condition number of the matrix A after */ 00196 /* equilibration (if done). If this is less than the machine */ 00197 /* precision (in particular, if it is zero), the matrix is singular */ 00198 /* to working precision. Note that the error may still be small even */ 00199 /* if this number is very small and the matrix appears ill- */ 00200 /* conditioned. */ 00201 00202 /* BERR (output) REAL array, dimension (NRHS) */ 00203 /* Componentwise relative backward error. This is the */ 00204 /* componentwise relative backward error of each solution vector X(j) */ 00205 /* (i.e., the smallest relative change in any element of A or B that */ 00206 /* makes X(j) an exact solution). */ 00207 00208 /* N_ERR_BNDS (input) INTEGER */ 00209 /* Number of error bounds to return for each right hand side */ 00210 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00211 /* ERR_BNDS_COMP below. */ 00212 00213 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00214 /* For each right-hand side, this array contains information about */ 00215 /* various error bounds and condition numbers corresponding to the */ 00216 /* normwise relative error, which is defined as follows: */ 00217 00218 /* Normwise relative error in the ith solution vector: */ 00219 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00220 /* ------------------------------ */ 00221 /* max_j abs(X(j,i)) */ 00222 00223 /* The array is indexed by the type of error information as described */ 00224 /* below. There currently are up to three pieces of information */ 00225 /* returned. */ 00226 00227 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00228 /* right-hand side. */ 00229 00230 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00231 /* three fields: */ 00232 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00233 /* reciprocal condition number is less than the threshold */ 00234 /* sqrt(n) * slamch('Epsilon'). */ 00235 00236 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00237 /* almost certainly within a factor of 10 of the true error */ 00238 /* so long as the next entry is greater than the threshold */ 00239 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00240 /* be trusted if the previous boolean is true. */ 00241 00242 /* err = 3 Reciprocal condition number: Estimated normwise */ 00243 /* reciprocal condition number. Compared with the threshold */ 00244 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00245 /* estimate is "guaranteed". These reciprocal condition */ 00246 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00247 /* appropriately scaled matrix Z. */ 00248 /* Let Z = S*A, where S scales each row by a power of the */ 00249 /* radix so all absolute row sums of Z are approximately 1. */ 00250 00251 /* See Lapack Working Note 165 for further details and extra */ 00252 /* cautions. */ 00253 00254 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00255 /* For each right-hand side, this array contains information about */ 00256 /* various error bounds and condition numbers corresponding to the */ 00257 /* componentwise relative error, which is defined as follows: */ 00258 00259 /* Componentwise relative error in the ith solution vector: */ 00260 /* abs(XTRUE(j,i) - X(j,i)) */ 00261 /* max_j ---------------------- */ 00262 /* abs(X(j,i)) */ 00263 00264 /* The array is indexed by the right-hand side i (on which the */ 00265 /* componentwise relative error depends), and the type of error */ 00266 /* information as described below. There currently are up to three */ 00267 /* pieces of information returned for each right-hand side. If */ 00268 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00269 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00270 /* the first (:,N_ERR_BNDS) entries are returned. */ 00271 00272 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00273 /* right-hand side. */ 00274 00275 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00276 /* three fields: */ 00277 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00278 /* reciprocal condition number is less than the threshold */ 00279 /* sqrt(n) * slamch('Epsilon'). */ 00280 00281 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00282 /* almost certainly within a factor of 10 of the true error */ 00283 /* so long as the next entry is greater than the threshold */ 00284 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00285 /* be trusted if the previous boolean is true. */ 00286 00287 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00288 /* reciprocal condition number. Compared with the threshold */ 00289 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00290 /* estimate is "guaranteed". These reciprocal condition */ 00291 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00292 /* appropriately scaled matrix Z. */ 00293 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00294 /* current right-hand side and S scales each row of */ 00295 /* A*diag(x) by a power of the radix so all absolute row */ 00296 /* sums of Z are approximately 1. */ 00297 00298 /* See Lapack Working Note 165 for further details and extra */ 00299 /* cautions. */ 00300 00301 /* NPARAMS (input) INTEGER */ 00302 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00303 /* PARAMS array is never referenced and default values are used. */ 00304 00305 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00306 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00307 /* that entry will be filled with default value used for that */ 00308 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00309 /* are used for higher-numbered parameters. */ 00310 00311 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00312 /* refinement or not. */ 00313 /* Default: 1.0 */ 00314 /* = 0.0 : No refinement is performed, and no error bounds are */ 00315 /* computed. */ 00316 /* = 1.0 : Use the double-precision refinement algorithm, */ 00317 /* possibly with doubled-single computations if the */ 00318 /* compilation environment does not support DOUBLE */ 00319 /* PRECISION. */ 00320 /* (other values are reserved for future use) */ 00321 00322 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00323 /* computations allowed for refinement. */ 00324 /* Default: 10 */ 00325 /* Aggressive: Set to 100 to permit convergence using approximate */ 00326 /* factorizations or factorizations other than LU. If */ 00327 /* the factorization uses a technique other than */ 00328 /* Gaussian elimination, the guarantees in */ 00329 /* err_bnds_norm and err_bnds_comp may no longer be */ 00330 /* trustworthy. */ 00331 00332 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00333 /* will attempt to find a solution with small componentwise */ 00334 /* relative error in the double-precision algorithm. Positive */ 00335 /* is true, 0.0 is false. */ 00336 /* Default: 1.0 (attempt componentwise convergence) */ 00337 00338 /* WORK (workspace) REAL array, dimension (4*N) */ 00339 00340 /* IWORK (workspace) INTEGER array, dimension (N) */ 00341 00342 /* INFO (output) INTEGER */ 00343 /* = 0: Successful exit. The solution to every right-hand side is */ 00344 /* guaranteed. */ 00345 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00346 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00347 /* has been completed, but the factor U is exactly singular, so */ 00348 /* the solution and error bounds could not be computed. RCOND = 0 */ 00349 /* is returned. */ 00350 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00351 /* not guaranteed. The solutions corresponding to other right- */ 00352 /* hand sides K with K > J may not be guaranteed as well, but */ 00353 /* only the first such right-hand side is reported. If a small */ 00354 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00355 /* the Jth right-hand side is the first with a normwise error */ 00356 /* bound that is not guaranteed (the smallest J such */ 00357 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00358 /* the Jth right-hand side is the first with either a normwise or */ 00359 /* componentwise error bound that is not guaranteed (the smallest */ 00360 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00361 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00362 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00363 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00364 /* ERR_BNDS_COMP. */ 00365 00366 /* ================================================================== */ 00367 00368 /* .. Parameters .. */ 00369 /* .. */ 00370 /* .. Local Scalars .. */ 00371 /* .. */ 00372 /* .. External Subroutines .. */ 00373 /* .. */ 00374 /* .. Intrinsic Functions .. */ 00375 /* .. */ 00376 /* .. External Functions .. */ 00377 /* .. */ 00378 /* .. Executable Statements .. */ 00379 00380 /* Check the input parameters. */ 00381 00382 /* Parameter adjustments */ 00383 err_bnds_comp_dim1 = *nrhs; 00384 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00385 err_bnds_comp__ -= err_bnds_comp_offset; 00386 err_bnds_norm_dim1 = *nrhs; 00387 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00388 err_bnds_norm__ -= err_bnds_norm_offset; 00389 a_dim1 = *lda; 00390 a_offset = 1 + a_dim1; 00391 a -= a_offset; 00392 af_dim1 = *ldaf; 00393 af_offset = 1 + af_dim1; 00394 af -= af_offset; 00395 --ipiv; 00396 --r__; 00397 --c__; 00398 b_dim1 = *ldb; 00399 b_offset = 1 + b_dim1; 00400 b -= b_offset; 00401 x_dim1 = *ldx; 00402 x_offset = 1 + x_dim1; 00403 x -= x_offset; 00404 --berr; 00405 --params; 00406 --work; 00407 --iwork; 00408 00409 /* Function Body */ 00410 *info = 0; 00411 trans_type__ = ilatrans_(trans); 00412 ref_type__ = 1; 00413 if (*nparams >= 1) { 00414 if (params[1] < 0.f) { 00415 params[1] = 1.f; 00416 } else { 00417 ref_type__ = params[1]; 00418 } 00419 } 00420 00421 /* Set default parameters. */ 00422 00423 illrcond_thresh__ = (real) (*n) * slamch_("Epsilon"); 00424 ithresh = 10; 00425 rthresh = .5f; 00426 unstable_thresh__ = .25f; 00427 ignore_cwise__ = FALSE_; 00428 00429 if (*nparams >= 2) { 00430 if (params[2] < 0.f) { 00431 params[2] = (real) ithresh; 00432 } else { 00433 ithresh = (integer) params[2]; 00434 } 00435 } 00436 if (*nparams >= 3) { 00437 if (params[3] < 0.f) { 00438 if (ignore_cwise__) { 00439 params[3] = 0.f; 00440 } else { 00441 params[3] = 1.f; 00442 } 00443 } else { 00444 ignore_cwise__ = params[3] == 0.f; 00445 } 00446 } 00447 if (ref_type__ == 0 || *n_err_bnds__ == 0) { 00448 n_norms__ = 0; 00449 } else if (ignore_cwise__) { 00450 n_norms__ = 1; 00451 } else { 00452 n_norms__ = 2; 00453 } 00454 00455 notran = lsame_(trans, "N"); 00456 rowequ = lsame_(equed, "R") || lsame_(equed, "B"); 00457 colequ = lsame_(equed, "C") || lsame_(equed, "B"); 00458 00459 /* Test input parameters. */ 00460 00461 if (trans_type__ == -1) { 00462 *info = -1; 00463 } else if (! rowequ && ! colequ && ! lsame_(equed, "N")) { 00464 *info = -2; 00465 } else if (*n < 0) { 00466 *info = -3; 00467 } else if (*nrhs < 0) { 00468 *info = -4; 00469 } else if (*lda < max(1,*n)) { 00470 *info = -6; 00471 } else if (*ldaf < max(1,*n)) { 00472 *info = -8; 00473 } else if (*ldb < max(1,*n)) { 00474 *info = -13; 00475 } else if (*ldx < max(1,*n)) { 00476 *info = -15; 00477 } 00478 if (*info != 0) { 00479 i__1 = -(*info); 00480 xerbla_("SGERFSX", &i__1); 00481 return 0; 00482 } 00483 00484 /* Quick return if possible. */ 00485 00486 if (*n == 0 || *nrhs == 0) { 00487 *rcond = 1.f; 00488 i__1 = *nrhs; 00489 for (j = 1; j <= i__1; ++j) { 00490 berr[j] = 0.f; 00491 if (*n_err_bnds__ >= 1) { 00492 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00493 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00494 } else if (*n_err_bnds__ >= 2) { 00495 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f; 00496 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f; 00497 } else if (*n_err_bnds__ >= 3) { 00498 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f; 00499 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f; 00500 } 00501 } 00502 return 0; 00503 } 00504 00505 /* Default to failure. */ 00506 00507 *rcond = 0.f; 00508 i__1 = *nrhs; 00509 for (j = 1; j <= i__1; ++j) { 00510 berr[j] = 1.f; 00511 if (*n_err_bnds__ >= 1) { 00512 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00513 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00514 } else if (*n_err_bnds__ >= 2) { 00515 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00516 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00517 } else if (*n_err_bnds__ >= 3) { 00518 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f; 00519 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f; 00520 } 00521 } 00522 00523 /* Compute the norm of A and the reciprocal of the condition */ 00524 /* number of A. */ 00525 00526 if (notran) { 00527 *(unsigned char *)norm = 'I'; 00528 } else { 00529 *(unsigned char *)norm = '1'; 00530 } 00531 anorm = slange_(norm, n, n, &a[a_offset], lda, &work[1]); 00532 sgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1], 00533 info); 00534 00535 /* Perform refinement on each right-hand side */ 00536 00537 if (ref_type__ != 0) { 00538 prec_type__ = ilaprec_("D"); 00539 if (notran) { 00540 sla_gerfsx_extended__(&prec_type__, &trans_type__, n, nrhs, &a[ 00541 a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &colequ, & 00542 c__[1], &b[b_offset], ldb, &x[x_offset], ldx, &berr[1], & 00543 n_norms__, &err_bnds_norm__[err_bnds_norm_offset], & 00544 err_bnds_comp__[err_bnds_comp_offset], &work[*n + 1], & 00545 work[1], &work[(*n << 1) + 1], &work[1], rcond, &ithresh, 00546 &rthresh, &unstable_thresh__, &ignore_cwise__, info); 00547 } else { 00548 sla_gerfsx_extended__(&prec_type__, &trans_type__, n, nrhs, &a[ 00549 a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &rowequ, & 00550 r__[1], &b[b_offset], ldb, &x[x_offset], ldx, &berr[1], & 00551 n_norms__, &err_bnds_norm__[err_bnds_norm_offset], & 00552 err_bnds_comp__[err_bnds_comp_offset], &work[*n + 1], & 00553 work[1], &work[(*n << 1) + 1], &work[1], rcond, &ithresh, 00554 &rthresh, &unstable_thresh__, &ignore_cwise__, info); 00555 } 00556 } 00557 /* Computing MAX */ 00558 r__1 = 10.f, r__2 = sqrt((real) (*n)); 00559 err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon"); 00560 if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { 00561 00562 /* Compute scaled normwise condition number cond(A*C). */ 00563 00564 if (colequ && notran) { 00565 rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[ 00566 af_offset], ldaf, &ipiv[1], &c_n1, &c__[1], info, &work[1] 00567 , &iwork[1], (ftnlen)1); 00568 } else if (rowequ && ! notran) { 00569 rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[ 00570 af_offset], ldaf, &ipiv[1], &c_n1, &r__[1], info, &work[1] 00571 , &iwork[1], (ftnlen)1); 00572 } else { 00573 rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[ 00574 af_offset], ldaf, &ipiv[1], &c__0, &r__[1], info, &work[1] 00575 , &iwork[1], (ftnlen)1); 00576 } 00577 i__1 = *nrhs; 00578 for (j = 1; j <= i__1; ++j) { 00579 00580 /* Cap the error at 1.0. */ 00581 00582 if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 00583 << 1)] > 1.f) { 00584 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00585 } 00586 00587 /* Threshold the error (see LAWN). */ 00588 00589 if (rcond_tmp__ < illrcond_thresh__) { 00590 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00591 err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f; 00592 if (*info <= *n) { 00593 *info = *n + j; 00594 } 00595 } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 00596 err_lbnd__) { 00597 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; 00598 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00599 } 00600 00601 /* Save the condition number. */ 00602 00603 if (*n_err_bnds__ >= 3) { 00604 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; 00605 } 00606 } 00607 } 00608 if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { 00609 00610 /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ 00611 /* each right-hand side using the current solution as an estimate of */ 00612 /* the true solution. If the componentwise error estimate is too */ 00613 /* large, then the solution is a lousy estimate of truth and the */ 00614 /* estimated RCOND may be too optimistic. To avoid misleading users, */ 00615 /* the inverse condition number is set to 0.0 when the estimated */ 00616 /* cwise error is at least CWISE_WRONG. */ 00617 00618 cwise_wrong__ = sqrt(slamch_("Epsilon")); 00619 i__1 = *nrhs; 00620 for (j = 1; j <= i__1; ++j) { 00621 if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00622 cwise_wrong__) { 00623 rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[ 00624 af_offset], ldaf, &ipiv[1], &c__1, &x[j * x_dim1 + 1], 00625 info, &work[1], &iwork[1], (ftnlen)1); 00626 } else { 00627 rcond_tmp__ = 0.f; 00628 } 00629 00630 /* Cap the error at 1.0. */ 00631 00632 if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 00633 << 1)] > 1.f) { 00634 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00635 } 00636 00637 /* Threshold the error (see LAWN). */ 00638 00639 if (rcond_tmp__ < illrcond_thresh__) { 00640 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00641 err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f; 00642 if (params[3] == 1.f && *info < *n + j) { 00643 *info = *n + j; 00644 } 00645 } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00646 err_lbnd__) { 00647 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; 00648 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00649 } 00650 00651 /* Save the condition number. */ 00652 00653 if (*n_err_bnds__ >= 3) { 00654 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; 00655 } 00656 } 00657 } 00658 00659 return 0; 00660 00661 /* End of SGERFSX */ 00662 00663 } /* sgerfsx_ */