00001 /* sporfsx.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 sporfsx_(char *uplo, char *equed, integer *n, integer * 00023 nrhs, real *a, integer *lda, real *af, integer *ldaf, real *s, real * 00024 b, integer *ldb, real *x, integer *ldx, real *rcond, real *berr, 00025 integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, 00026 integer *nparams, real *params, real *work, integer *iwork, integer * 00027 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__, j; 00041 real rcond_tmp__; 00042 integer prec_type__; 00043 extern doublereal sla_porcond__(char *, integer *, real *, integer *, 00044 real *, integer *, integer *, real *, integer *, real *, integer * 00045 , ftnlen); 00046 real cwise_wrong__; 00047 extern /* Subroutine */ int sla_porfsx_extended__(integer *, char *, 00048 integer *, integer *, real *, integer *, real *, integer *, 00049 logical *, real *, real *, integer *, real *, integer *, real *, 00050 integer *, real *, real *, real *, real *, real *, real *, real *, 00051 integer *, real *, real *, logical *, integer *, ftnlen); 00052 char norm[1]; 00053 logical ignore_cwise__; 00054 extern logical lsame_(char *, char *); 00055 real anorm; 00056 logical rcequ; 00057 extern doublereal slamch_(char *); 00058 extern /* Subroutine */ int xerbla_(char *, integer *), spocon_( 00059 char *, integer *, real *, integer *, real *, real *, real *, 00060 integer *, integer *); 00061 extern doublereal slansy_(char *, char *, integer *, real *, integer *, 00062 real *); 00063 extern integer ilaprec_(char *); 00064 integer ithresh, n_norms__; 00065 real rthresh; 00066 00067 00068 /* -- LAPACK routine (version 3.2.1) -- */ 00069 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00070 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00071 /* -- April 2009 -- */ 00072 00073 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00074 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ 00075 00076 /* .. */ 00077 /* .. Scalar Arguments .. */ 00078 /* .. */ 00079 /* .. Array Arguments .. */ 00080 /* .. */ 00081 00082 /* Purpose */ 00083 /* ======= */ 00084 00085 /* SPORFSX improves the computed solution to a system of linear */ 00086 /* equations when the coefficient matrix is symmetric positive */ 00087 /* definite, 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 and S */ 00095 /* below. In this case, the solution and error bounds returned are */ 00096 /* 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 /* UPLO (input) CHARACTER*1 */ 00108 /* = 'U': Upper triangle of A is stored; */ 00109 /* = 'L': Lower triangle of A is stored. */ 00110 00111 /* EQUED (input) CHARACTER*1 */ 00112 /* Specifies the form of equilibration that was done to A */ 00113 /* before calling this routine. This is needed to compute */ 00114 /* the solution and error bounds correctly. */ 00115 /* = 'N': No equilibration */ 00116 /* = 'Y': Both row and column equilibration, i.e., A has been */ 00117 /* replaced by diag(S) * A * diag(S). */ 00118 /* The right hand side B has been changed accordingly. */ 00119 00120 /* N (input) INTEGER */ 00121 /* The order of the matrix A. N >= 0. */ 00122 00123 /* NRHS (input) INTEGER */ 00124 /* The number of right hand sides, i.e., the number of columns */ 00125 /* of the matrices B and X. NRHS >= 0. */ 00126 00127 /* A (input) REAL array, dimension (LDA,N) */ 00128 /* The symmetric matrix A. If UPLO = 'U', the leading N-by-N */ 00129 /* upper triangular part of A contains the upper triangular part */ 00130 /* of the matrix A, and the strictly lower triangular part of A */ 00131 /* is not referenced. If UPLO = 'L', the leading N-by-N lower */ 00132 /* triangular part of A contains the lower triangular part of */ 00133 /* the matrix A, and the strictly upper triangular part of A is */ 00134 /* not referenced. */ 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 triangular factor U or L from the Cholesky factorization */ 00141 /* A = U**T*U or A = L*L**T, as computed by SPOTRF. */ 00142 00143 /* LDAF (input) INTEGER */ 00144 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00145 00146 /* S (input or output) REAL array, dimension (N) */ 00147 /* The row scale factors for A. If EQUED = 'Y', A is multiplied on */ 00148 /* the left and right by diag(S). S is an input argument if FACT = */ 00149 /* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */ 00150 /* = 'Y', each element of S must be positive. If S is output, each */ 00151 /* element of S is a power of the radix. If S is input, each element */ 00152 /* of S should be a power of the radix to ensure a reliable solution */ 00153 /* and error estimates. Scaling by powers of the radix does not cause */ 00154 /* rounding errors unless the result underflows or overflows. */ 00155 /* Rounding errors during scaling lead to refining with a matrix that */ 00156 /* is not equivalent to the input matrix, producing error estimates */ 00157 /* that may not be reliable. */ 00158 00159 /* B (input) REAL array, dimension (LDB,NRHS) */ 00160 /* The right hand side matrix B. */ 00161 00162 /* LDB (input) INTEGER */ 00163 /* The leading dimension of the array B. LDB >= max(1,N). */ 00164 00165 /* X (input/output) REAL array, dimension (LDX,NRHS) */ 00166 /* On entry, the solution matrix X, as computed by SGETRS. */ 00167 /* On exit, the improved solution matrix X. */ 00168 00169 /* LDX (input) INTEGER */ 00170 /* The leading dimension of the array X. LDX >= max(1,N). */ 00171 00172 /* RCOND (output) REAL */ 00173 /* Reciprocal scaled condition number. This is an estimate of the */ 00174 /* reciprocal Skeel condition number of the matrix A after */ 00175 /* equilibration (if done). If this is less than the machine */ 00176 /* precision (in particular, if it is zero), the matrix is singular */ 00177 /* to working precision. Note that the error may still be small even */ 00178 /* if this number is very small and the matrix appears ill- */ 00179 /* conditioned. */ 00180 00181 /* BERR (output) REAL array, dimension (NRHS) */ 00182 /* Componentwise relative backward error. This is the */ 00183 /* componentwise relative backward error of each solution vector X(j) */ 00184 /* (i.e., the smallest relative change in any element of A or B that */ 00185 /* makes X(j) an exact solution). */ 00186 00187 /* N_ERR_BNDS (input) INTEGER */ 00188 /* Number of error bounds to return for each right hand side */ 00189 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00190 /* ERR_BNDS_COMP below. */ 00191 00192 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00193 /* For each right-hand side, this array contains information about */ 00194 /* various error bounds and condition numbers corresponding to the */ 00195 /* normwise relative error, which is defined as follows: */ 00196 00197 /* Normwise relative error in the ith solution vector: */ 00198 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00199 /* ------------------------------ */ 00200 /* max_j abs(X(j,i)) */ 00201 00202 /* The array is indexed by the type of error information as described */ 00203 /* below. There currently are up to three pieces of information */ 00204 /* returned. */ 00205 00206 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00207 /* right-hand side. */ 00208 00209 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00210 /* three fields: */ 00211 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00212 /* reciprocal condition number is less than the threshold */ 00213 /* sqrt(n) * slamch('Epsilon'). */ 00214 00215 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00216 /* almost certainly within a factor of 10 of the true error */ 00217 /* so long as the next entry is greater than the threshold */ 00218 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00219 /* be trusted if the previous boolean is true. */ 00220 00221 /* err = 3 Reciprocal condition number: Estimated normwise */ 00222 /* reciprocal condition number. Compared with the threshold */ 00223 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00224 /* estimate is "guaranteed". These reciprocal condition */ 00225 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00226 /* appropriately scaled matrix Z. */ 00227 /* Let Z = S*A, where S scales each row by a power of the */ 00228 /* radix so all absolute row sums of Z are approximately 1. */ 00229 00230 /* See Lapack Working Note 165 for further details and extra */ 00231 /* cautions. */ 00232 00233 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00234 /* For each right-hand side, this array contains information about */ 00235 /* various error bounds and condition numbers corresponding to the */ 00236 /* componentwise relative error, which is defined as follows: */ 00237 00238 /* Componentwise relative error in the ith solution vector: */ 00239 /* abs(XTRUE(j,i) - X(j,i)) */ 00240 /* max_j ---------------------- */ 00241 /* abs(X(j,i)) */ 00242 00243 /* The array is indexed by the right-hand side i (on which the */ 00244 /* componentwise relative error depends), and the type of error */ 00245 /* information as described below. There currently are up to three */ 00246 /* pieces of information returned for each right-hand side. If */ 00247 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00248 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00249 /* the first (:,N_ERR_BNDS) entries are returned. */ 00250 00251 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00252 /* right-hand side. */ 00253 00254 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00255 /* three fields: */ 00256 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00257 /* reciprocal condition number is less than the threshold */ 00258 /* sqrt(n) * slamch('Epsilon'). */ 00259 00260 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00261 /* almost certainly within a factor of 10 of the true error */ 00262 /* so long as the next entry is greater than the threshold */ 00263 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00264 /* be trusted if the previous boolean is true. */ 00265 00266 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00267 /* reciprocal condition number. Compared with the threshold */ 00268 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00269 /* estimate is "guaranteed". These reciprocal condition */ 00270 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00271 /* appropriately scaled matrix Z. */ 00272 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00273 /* current right-hand side and S scales each row of */ 00274 /* A*diag(x) by a power of the radix so all absolute row */ 00275 /* sums of Z are approximately 1. */ 00276 00277 /* See Lapack Working Note 165 for further details and extra */ 00278 /* cautions. */ 00279 00280 /* NPARAMS (input) INTEGER */ 00281 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00282 /* PARAMS array is never referenced and default values are used. */ 00283 00284 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00285 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00286 /* that entry will be filled with default value used for that */ 00287 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00288 /* are used for higher-numbered parameters. */ 00289 00290 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00291 /* refinement or not. */ 00292 /* Default: 1.0 */ 00293 /* = 0.0 : No refinement is performed, and no error bounds are */ 00294 /* computed. */ 00295 /* = 1.0 : Use the double-precision refinement algorithm, */ 00296 /* possibly with doubled-single computations if the */ 00297 /* compilation environment does not support DOUBLE */ 00298 /* PRECISION. */ 00299 /* (other values are reserved for future use) */ 00300 00301 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00302 /* computations allowed for refinement. */ 00303 /* Default: 10 */ 00304 /* Aggressive: Set to 100 to permit convergence using approximate */ 00305 /* factorizations or factorizations other than LU. If */ 00306 /* the factorization uses a technique other than */ 00307 /* Gaussian elimination, the guarantees in */ 00308 /* err_bnds_norm and err_bnds_comp may no longer be */ 00309 /* trustworthy. */ 00310 00311 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00312 /* will attempt to find a solution with small componentwise */ 00313 /* relative error in the double-precision algorithm. Positive */ 00314 /* is true, 0.0 is false. */ 00315 /* Default: 1.0 (attempt componentwise convergence) */ 00316 00317 /* WORK (workspace) REAL array, dimension (4*N) */ 00318 00319 /* IWORK (workspace) INTEGER array, dimension (N) */ 00320 00321 /* INFO (output) INTEGER */ 00322 /* = 0: Successful exit. The solution to every right-hand side is */ 00323 /* guaranteed. */ 00324 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00325 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00326 /* has been completed, but the factor U is exactly singular, so */ 00327 /* the solution and error bounds could not be computed. RCOND = 0 */ 00328 /* is returned. */ 00329 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00330 /* not guaranteed. The solutions corresponding to other right- */ 00331 /* hand sides K with K > J may not be guaranteed as well, but */ 00332 /* only the first such right-hand side is reported. If a small */ 00333 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00334 /* the Jth right-hand side is the first with a normwise error */ 00335 /* bound that is not guaranteed (the smallest J such */ 00336 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00337 /* the Jth right-hand side is the first with either a normwise or */ 00338 /* componentwise error bound that is not guaranteed (the smallest */ 00339 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00340 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00341 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00342 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00343 /* ERR_BNDS_COMP. */ 00344 00345 /* ================================================================== */ 00346 00347 /* .. Parameters .. */ 00348 /* .. */ 00349 /* .. Local Scalars .. */ 00350 /* .. */ 00351 /* .. External Subroutines .. */ 00352 /* .. */ 00353 /* .. Intrinsic Functions .. */ 00354 /* .. */ 00355 /* .. External Functions .. */ 00356 /* .. */ 00357 /* .. Executable Statements .. */ 00358 00359 /* Check the input parameters. */ 00360 00361 /* Parameter adjustments */ 00362 err_bnds_comp_dim1 = *nrhs; 00363 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00364 err_bnds_comp__ -= err_bnds_comp_offset; 00365 err_bnds_norm_dim1 = *nrhs; 00366 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00367 err_bnds_norm__ -= err_bnds_norm_offset; 00368 a_dim1 = *lda; 00369 a_offset = 1 + a_dim1; 00370 a -= a_offset; 00371 af_dim1 = *ldaf; 00372 af_offset = 1 + af_dim1; 00373 af -= af_offset; 00374 --s; 00375 b_dim1 = *ldb; 00376 b_offset = 1 + b_dim1; 00377 b -= b_offset; 00378 x_dim1 = *ldx; 00379 x_offset = 1 + x_dim1; 00380 x -= x_offset; 00381 --berr; 00382 --params; 00383 --work; 00384 --iwork; 00385 00386 /* Function Body */ 00387 *info = 0; 00388 ref_type__ = 1; 00389 if (*nparams >= 1) { 00390 if (params[1] < 0.f) { 00391 params[1] = 1.f; 00392 } else { 00393 ref_type__ = params[1]; 00394 } 00395 } 00396 00397 /* Set default parameters. */ 00398 00399 illrcond_thresh__ = (real) (*n) * slamch_("Epsilon"); 00400 ithresh = 10; 00401 rthresh = .5f; 00402 unstable_thresh__ = .25f; 00403 ignore_cwise__ = FALSE_; 00404 00405 if (*nparams >= 2) { 00406 if (params[2] < 0.f) { 00407 params[2] = (real) ithresh; 00408 } else { 00409 ithresh = (integer) params[2]; 00410 } 00411 } 00412 if (*nparams >= 3) { 00413 if (params[3] < 0.f) { 00414 if (ignore_cwise__) { 00415 params[3] = 0.f; 00416 } else { 00417 params[3] = 1.f; 00418 } 00419 } else { 00420 ignore_cwise__ = params[3] == 0.f; 00421 } 00422 } 00423 if (ref_type__ == 0 || *n_err_bnds__ == 0) { 00424 n_norms__ = 0; 00425 } else if (ignore_cwise__) { 00426 n_norms__ = 1; 00427 } else { 00428 n_norms__ = 2; 00429 } 00430 00431 rcequ = lsame_(equed, "Y"); 00432 00433 /* Test input parameters. */ 00434 00435 if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { 00436 *info = -1; 00437 } else if (! rcequ && ! lsame_(equed, "N")) { 00438 *info = -2; 00439 } else if (*n < 0) { 00440 *info = -3; 00441 } else if (*nrhs < 0) { 00442 *info = -4; 00443 } else if (*lda < max(1,*n)) { 00444 *info = -6; 00445 } else if (*ldaf < max(1,*n)) { 00446 *info = -8; 00447 } else if (*ldb < max(1,*n)) { 00448 *info = -11; 00449 } else if (*ldx < max(1,*n)) { 00450 *info = -13; 00451 } 00452 if (*info != 0) { 00453 i__1 = -(*info); 00454 xerbla_("SPORFSX", &i__1); 00455 return 0; 00456 } 00457 00458 /* Quick return if possible. */ 00459 00460 if (*n == 0 || *nrhs == 0) { 00461 *rcond = 1.f; 00462 i__1 = *nrhs; 00463 for (j = 1; j <= i__1; ++j) { 00464 berr[j] = 0.f; 00465 if (*n_err_bnds__ >= 1) { 00466 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00467 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00468 } else if (*n_err_bnds__ >= 2) { 00469 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f; 00470 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f; 00471 } else if (*n_err_bnds__ >= 3) { 00472 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f; 00473 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f; 00474 } 00475 } 00476 return 0; 00477 } 00478 00479 /* Default to failure. */ 00480 00481 *rcond = 0.f; 00482 i__1 = *nrhs; 00483 for (j = 1; j <= i__1; ++j) { 00484 berr[j] = 1.f; 00485 if (*n_err_bnds__ >= 1) { 00486 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00487 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00488 } else if (*n_err_bnds__ >= 2) { 00489 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00490 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00491 } else if (*n_err_bnds__ >= 3) { 00492 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f; 00493 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f; 00494 } 00495 } 00496 00497 /* Compute the norm of A and the reciprocal of the condition */ 00498 /* number of A. */ 00499 00500 *(unsigned char *)norm = 'I'; 00501 anorm = slansy_(norm, uplo, n, &a[a_offset], lda, &work[1]); 00502 spocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1], 00503 info); 00504 00505 /* Perform refinement on each right-hand side */ 00506 00507 if (ref_type__ != 0) { 00508 prec_type__ = ilaprec_("D"); 00509 sla_porfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, 00510 &af[af_offset], ldaf, &rcequ, &s[1], &b[b_offset], ldb, &x[ 00511 x_offset], ldx, &berr[1], &n_norms__, &err_bnds_norm__[ 00512 err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset], 00513 &work[*n + 1], &work[1], &work[(*n << 1) + 1], &work[1], 00514 rcond, &ithresh, &rthresh, &unstable_thresh__, & 00515 ignore_cwise__, info, (ftnlen)1); 00516 } 00517 /* Computing MAX */ 00518 r__1 = 10.f, r__2 = sqrt((real) (*n)); 00519 err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon"); 00520 if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { 00521 00522 /* Compute scaled normwise condition number cond(A*C). */ 00523 00524 if (rcequ) { 00525 rcond_tmp__ = sla_porcond__(uplo, n, &a[a_offset], lda, &af[ 00526 af_offset], ldaf, &c_n1, &s[1], info, &work[1], &iwork[1], 00527 (ftnlen)1); 00528 } else { 00529 rcond_tmp__ = sla_porcond__(uplo, n, &a[a_offset], lda, &af[ 00530 af_offset], ldaf, &c__0, &s[1], info, &work[1], &iwork[1], 00531 (ftnlen)1); 00532 } 00533 i__1 = *nrhs; 00534 for (j = 1; j <= i__1; ++j) { 00535 00536 /* Cap the error at 1.0. */ 00537 00538 if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 00539 << 1)] > 1.f) { 00540 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00541 } 00542 00543 /* Threshold the error (see LAWN). */ 00544 00545 if (rcond_tmp__ < illrcond_thresh__) { 00546 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00547 err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f; 00548 if (*info <= *n) { 00549 *info = *n + j; 00550 } 00551 } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 00552 err_lbnd__) { 00553 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; 00554 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00555 } 00556 00557 /* Save the condition number. */ 00558 00559 if (*n_err_bnds__ >= 3) { 00560 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; 00561 } 00562 } 00563 } 00564 if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { 00565 00566 /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ 00567 /* each right-hand side using the current solution as an estimate of */ 00568 /* the true solution. If the componentwise error estimate is too */ 00569 /* large, then the solution is a lousy estimate of truth and the */ 00570 /* estimated RCOND may be too optimistic. To avoid misleading users, */ 00571 /* the inverse condition number is set to 0.0 when the estimated */ 00572 /* cwise error is at least CWISE_WRONG. */ 00573 00574 cwise_wrong__ = sqrt(slamch_("Epsilon")); 00575 i__1 = *nrhs; 00576 for (j = 1; j <= i__1; ++j) { 00577 if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00578 cwise_wrong__) { 00579 rcond_tmp__ = sla_porcond__(uplo, n, &a[a_offset], lda, &af[ 00580 af_offset], ldaf, &c__1, &x[j * x_dim1 + 1], info, & 00581 work[1], &iwork[1], (ftnlen)1); 00582 } else { 00583 rcond_tmp__ = 0.f; 00584 } 00585 00586 /* Cap the error at 1.0. */ 00587 00588 if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 00589 << 1)] > 1.f) { 00590 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00591 } 00592 00593 /* Threshold the error (see LAWN). */ 00594 00595 if (rcond_tmp__ < illrcond_thresh__) { 00596 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00597 err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f; 00598 if (params[3] == 1.f && *info < *n + j) { 00599 *info = *n + j; 00600 } 00601 } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00602 err_lbnd__) { 00603 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; 00604 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00605 } 00606 00607 /* Save the condition number. */ 00608 00609 if (*n_err_bnds__ >= 3) { 00610 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; 00611 } 00612 } 00613 } 00614 00615 return 0; 00616 00617 /* End of SPORFSX */ 00618 00619 } /* sporfsx_ */