00001 /* cporfsx.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 logical c_true = TRUE_; 00019 static logical c_false = FALSE_; 00020 00021 /* Subroutine */ int cporfsx_(char *uplo, char *equed, integer *n, integer * 00022 nrhs, complex *a, integer *lda, complex *af, integer *ldaf, real *s, 00023 complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real 00024 *berr, integer *n_err_bnds__, real *err_bnds_norm__, real * 00025 err_bnds_comp__, integer *nparams, real *params, complex *work, real * 00026 rwork, integer *info) 00027 { 00028 /* System generated locals */ 00029 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 00030 x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00031 err_bnds_comp_dim1, err_bnds_comp_offset, i__1; 00032 real r__1, r__2; 00033 00034 /* Builtin functions */ 00035 double sqrt(doublereal); 00036 00037 /* Local variables */ 00038 real illrcond_thresh__, unstable_thresh__, err_lbnd__; 00039 integer ref_type__; 00040 integer j; 00041 real rcond_tmp__; 00042 integer prec_type__; 00043 real cwise_wrong__; 00044 extern /* Subroutine */ int cla_porfsx_extended__(integer *, char *, 00045 integer *, integer *, complex *, integer *, complex *, integer *, 00046 logical *, real *, complex *, integer *, complex *, integer *, 00047 real *, integer *, real *, real *, complex *, real *, complex *, 00048 complex *, real *, integer *, real *, real *, logical *, integer * 00049 , ftnlen); 00050 char norm[1]; 00051 logical ignore_cwise__; 00052 extern logical lsame_(char *, char *); 00053 real anorm; 00054 logical rcequ; 00055 extern doublereal cla_porcond_c__(char *, integer *, complex *, integer *, 00056 complex *, integer *, real *, logical *, integer *, complex *, 00057 real *, ftnlen), cla_porcond_x__(char *, integer *, complex *, 00058 integer *, complex *, integer *, complex *, integer *, complex *, 00059 real *, ftnlen), clanhe_(char *, char *, integer *, complex *, 00060 integer *, real *), slamch_(char *); 00061 extern /* Subroutine */ int xerbla_(char *, integer *), cpocon_( 00062 char *, integer *, complex *, integer *, real *, real *, complex * 00063 , real *, integer *); 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 /* CPORFSX improves the computed solution to a system of linear */ 00087 /* equations when the coefficient matrix is symmetric positive */ 00088 /* definite, and provides error bounds and backward error estimates */ 00089 /* for the solution. In addition to normwise error bound, the code */ 00090 /* provides maximum componentwise error bound if possible. See */ 00091 /* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */ 00092 /* error bounds. */ 00093 00094 /* The original system of linear equations may have been equilibrated */ 00095 /* before calling this routine, as described by arguments EQUED and S */ 00096 /* below. In this case, the solution and error bounds returned are */ 00097 /* for the original unequilibrated system. */ 00098 00099 /* Arguments */ 00100 /* ========= */ 00101 00102 /* Some optional parameters are bundled in the PARAMS array. These */ 00103 /* settings determine how refinement is performed, but often the */ 00104 /* defaults are acceptable. If the defaults are acceptable, users */ 00105 /* can pass NPARAMS = 0 which prevents the source code from accessing */ 00106 /* the PARAMS argument. */ 00107 00108 /* UPLO (input) CHARACTER*1 */ 00109 /* = 'U': Upper triangle of A is stored; */ 00110 /* = 'L': Lower triangle of A is stored. */ 00111 00112 /* EQUED (input) CHARACTER*1 */ 00113 /* Specifies the form of equilibration that was done to A */ 00114 /* before calling this routine. This is needed to compute */ 00115 /* the solution and error bounds correctly. */ 00116 /* = 'N': No equilibration */ 00117 /* = 'Y': Both row and column equilibration, i.e., A has been */ 00118 /* replaced by diag(S) * A * diag(S). */ 00119 /* The right hand side B has been changed accordingly. */ 00120 00121 /* N (input) INTEGER */ 00122 /* The order of the matrix A. N >= 0. */ 00123 00124 /* NRHS (input) INTEGER */ 00125 /* The number of right hand sides, i.e., the number of columns */ 00126 /* of the matrices B and X. NRHS >= 0. */ 00127 00128 /* A (input) COMPLEX array, dimension (LDA,N) */ 00129 /* The symmetric matrix A. If UPLO = 'U', the leading N-by-N */ 00130 /* upper triangular part of A contains the upper triangular part */ 00131 /* of the matrix A, and the strictly lower triangular part of A */ 00132 /* is not referenced. If UPLO = 'L', the leading N-by-N lower */ 00133 /* triangular part of A contains the lower triangular part of */ 00134 /* the matrix A, and the strictly upper triangular part of A is */ 00135 /* not referenced. */ 00136 00137 /* LDA (input) INTEGER */ 00138 /* The leading dimension of the array A. LDA >= max(1,N). */ 00139 00140 /* AF (input) COMPLEX array, dimension (LDAF,N) */ 00141 /* The triangular factor U or L from the Cholesky factorization */ 00142 /* A = U**T*U or A = L*L**T, as computed by SPOTRF. */ 00143 00144 /* LDAF (input) INTEGER */ 00145 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00146 00147 /* S (input or output) REAL array, dimension (N) */ 00148 /* The row scale factors for A. If EQUED = 'Y', A is multiplied on */ 00149 /* the left and right by diag(S). S is an input argument if FACT = */ 00150 /* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */ 00151 /* = 'Y', each element of S must be positive. If S is output, each */ 00152 /* element of S is a power of the radix. If S is input, each element */ 00153 /* of S should be a power of the radix to ensure a reliable solution */ 00154 /* and error estimates. Scaling by powers of the radix does not cause */ 00155 /* rounding errors unless the result underflows or overflows. */ 00156 /* Rounding errors during scaling lead to refining with a matrix that */ 00157 /* is not equivalent to the input matrix, producing error estimates */ 00158 /* that may not be reliable. */ 00159 00160 /* B (input) COMPLEX array, dimension (LDB,NRHS) */ 00161 /* The right hand side matrix B. */ 00162 00163 /* LDB (input) INTEGER */ 00164 /* The leading dimension of the array B. LDB >= max(1,N). */ 00165 00166 /* X (input/output) COMPLEX array, dimension (LDX,NRHS) */ 00167 /* On entry, the solution matrix X, as computed by SGETRS. */ 00168 /* On exit, the improved solution matrix X. */ 00169 00170 /* LDX (input) INTEGER */ 00171 /* The leading dimension of the array X. LDX >= max(1,N). */ 00172 00173 /* RCOND (output) REAL */ 00174 /* Reciprocal scaled condition number. This is an estimate of the */ 00175 /* reciprocal Skeel condition number of the matrix A after */ 00176 /* equilibration (if done). If this is less than the machine */ 00177 /* precision (in particular, if it is zero), the matrix is singular */ 00178 /* to working precision. Note that the error may still be small even */ 00179 /* if this number is very small and the matrix appears ill- */ 00180 /* conditioned. */ 00181 00182 /* BERR (output) REAL array, dimension (NRHS) */ 00183 /* Componentwise relative backward error. This is the */ 00184 /* componentwise relative backward error of each solution vector X(j) */ 00185 /* (i.e., the smallest relative change in any element of A or B that */ 00186 /* makes X(j) an exact solution). */ 00187 00188 /* N_ERR_BNDS (input) INTEGER */ 00189 /* Number of error bounds to return for each right hand side */ 00190 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00191 /* ERR_BNDS_COMP below. */ 00192 00193 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00194 /* For each right-hand side, this array contains information about */ 00195 /* various error bounds and condition numbers corresponding to the */ 00196 /* normwise relative error, which is defined as follows: */ 00197 00198 /* Normwise relative error in the ith solution vector: */ 00199 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00200 /* ------------------------------ */ 00201 /* max_j abs(X(j,i)) */ 00202 00203 /* The array is indexed by the type of error information as described */ 00204 /* below. There currently are up to three pieces of information */ 00205 /* returned. */ 00206 00207 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00208 /* right-hand side. */ 00209 00210 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00211 /* three fields: */ 00212 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00213 /* reciprocal condition number is less than the threshold */ 00214 /* sqrt(n) * slamch('Epsilon'). */ 00215 00216 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00217 /* almost certainly within a factor of 10 of the true error */ 00218 /* so long as the next entry is greater than the threshold */ 00219 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00220 /* be trusted if the previous boolean is true. */ 00221 00222 /* err = 3 Reciprocal condition number: Estimated normwise */ 00223 /* reciprocal condition number. Compared with the threshold */ 00224 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00225 /* estimate is "guaranteed". These reciprocal condition */ 00226 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00227 /* appropriately scaled matrix Z. */ 00228 /* Let Z = S*A, where S scales each row by a power of the */ 00229 /* radix so all absolute row sums of Z are approximately 1. */ 00230 00231 /* See Lapack Working Note 165 for further details and extra */ 00232 /* cautions. */ 00233 00234 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00235 /* For each right-hand side, this array contains information about */ 00236 /* various error bounds and condition numbers corresponding to the */ 00237 /* componentwise relative error, which is defined as follows: */ 00238 00239 /* Componentwise relative error in the ith solution vector: */ 00240 /* abs(XTRUE(j,i) - X(j,i)) */ 00241 /* max_j ---------------------- */ 00242 /* abs(X(j,i)) */ 00243 00244 /* The array is indexed by the right-hand side i (on which the */ 00245 /* componentwise relative error depends), and the type of error */ 00246 /* information as described below. There currently are up to three */ 00247 /* pieces of information returned for each right-hand side. If */ 00248 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00249 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00250 /* the first (:,N_ERR_BNDS) entries are returned. */ 00251 00252 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00253 /* right-hand side. */ 00254 00255 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00256 /* three fields: */ 00257 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00258 /* reciprocal condition number is less than the threshold */ 00259 /* sqrt(n) * slamch('Epsilon'). */ 00260 00261 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00262 /* almost certainly within a factor of 10 of the true error */ 00263 /* so long as the next entry is greater than the threshold */ 00264 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00265 /* be trusted if the previous boolean is true. */ 00266 00267 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00268 /* reciprocal condition number. Compared with the threshold */ 00269 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00270 /* estimate is "guaranteed". These reciprocal condition */ 00271 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00272 /* appropriately scaled matrix Z. */ 00273 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00274 /* current right-hand side and S scales each row of */ 00275 /* A*diag(x) by a power of the radix so all absolute row */ 00276 /* sums of Z are approximately 1. */ 00277 00278 /* See Lapack Working Note 165 for further details and extra */ 00279 /* cautions. */ 00280 00281 /* NPARAMS (input) INTEGER */ 00282 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00283 /* PARAMS array is never referenced and default values are used. */ 00284 00285 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00286 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00287 /* that entry will be filled with default value used for that */ 00288 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00289 /* are used for higher-numbered parameters. */ 00290 00291 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00292 /* refinement or not. */ 00293 /* Default: 1.0 */ 00294 /* = 0.0 : No refinement is performed, and no error bounds are */ 00295 /* computed. */ 00296 /* = 1.0 : Use the double-precision refinement algorithm, */ 00297 /* possibly with doubled-single computations if the */ 00298 /* compilation environment does not support DOUBLE */ 00299 /* PRECISION. */ 00300 /* (other values are reserved for future use) */ 00301 00302 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00303 /* computations allowed for refinement. */ 00304 /* Default: 10 */ 00305 /* Aggressive: Set to 100 to permit convergence using approximate */ 00306 /* factorizations or factorizations other than LU. If */ 00307 /* the factorization uses a technique other than */ 00308 /* Gaussian elimination, the guarantees in */ 00309 /* err_bnds_norm and err_bnds_comp may no longer be */ 00310 /* trustworthy. */ 00311 00312 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00313 /* will attempt to find a solution with small componentwise */ 00314 /* relative error in the double-precision algorithm. Positive */ 00315 /* is true, 0.0 is false. */ 00316 /* Default: 1.0 (attempt componentwise convergence) */ 00317 00318 /* WORK (workspace) COMPLEX array, dimension (2*N) */ 00319 00320 /* RWORK (workspace) REAL array, dimension (2*N) */ 00321 00322 /* INFO (output) INTEGER */ 00323 /* = 0: Successful exit. The solution to every right-hand side is */ 00324 /* guaranteed. */ 00325 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00326 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00327 /* has been completed, but the factor U is exactly singular, so */ 00328 /* the solution and error bounds could not be computed. RCOND = 0 */ 00329 /* is returned. */ 00330 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00331 /* not guaranteed. The solutions corresponding to other right- */ 00332 /* hand sides K with K > J may not be guaranteed as well, but */ 00333 /* only the first such right-hand side is reported. If a small */ 00334 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00335 /* the Jth right-hand side is the first with a normwise error */ 00336 /* bound that is not guaranteed (the smallest J such */ 00337 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00338 /* the Jth right-hand side is the first with either a normwise or */ 00339 /* componentwise error bound that is not guaranteed (the smallest */ 00340 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00341 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00342 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00343 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00344 /* ERR_BNDS_COMP. */ 00345 00346 /* ================================================================== */ 00347 00348 /* .. Parameters .. */ 00349 /* .. */ 00350 /* .. Local Scalars .. */ 00351 /* .. */ 00352 /* .. External Subroutines .. */ 00353 /* .. */ 00354 /* .. Intrinsic Functions .. */ 00355 /* .. */ 00356 /* .. External Functions .. */ 00357 /* .. */ 00358 /* .. Executable Statements .. */ 00359 00360 /* Check the input parameters. */ 00361 00362 /* Parameter adjustments */ 00363 err_bnds_comp_dim1 = *nrhs; 00364 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00365 err_bnds_comp__ -= err_bnds_comp_offset; 00366 err_bnds_norm_dim1 = *nrhs; 00367 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00368 err_bnds_norm__ -= err_bnds_norm_offset; 00369 a_dim1 = *lda; 00370 a_offset = 1 + a_dim1; 00371 a -= a_offset; 00372 af_dim1 = *ldaf; 00373 af_offset = 1 + af_dim1; 00374 af -= af_offset; 00375 --s; 00376 b_dim1 = *ldb; 00377 b_offset = 1 + b_dim1; 00378 b -= b_offset; 00379 x_dim1 = *ldx; 00380 x_offset = 1 + x_dim1; 00381 x -= x_offset; 00382 --berr; 00383 --params; 00384 --work; 00385 --rwork; 00386 00387 /* Function Body */ 00388 *info = 0; 00389 ref_type__ = 1; 00390 if (*nparams >= 1) { 00391 if (params[1] < 0.f) { 00392 params[1] = 1.f; 00393 } else { 00394 ref_type__ = params[1]; 00395 } 00396 } 00397 00398 /* Set default parameters. */ 00399 00400 illrcond_thresh__ = (real) (*n) * slamch_("Epsilon"); 00401 ithresh = 10; 00402 rthresh = .5f; 00403 unstable_thresh__ = .25f; 00404 ignore_cwise__ = FALSE_; 00405 00406 if (*nparams >= 2) { 00407 if (params[2] < 0.f) { 00408 params[2] = (real) ithresh; 00409 } else { 00410 ithresh = (integer) params[2]; 00411 } 00412 } 00413 if (*nparams >= 3) { 00414 if (params[3] < 0.f) { 00415 if (ignore_cwise__) { 00416 params[3] = 0.f; 00417 } else { 00418 params[3] = 1.f; 00419 } 00420 } else { 00421 ignore_cwise__ = params[3] == 0.f; 00422 } 00423 } 00424 if (ref_type__ == 0 || *n_err_bnds__ == 0) { 00425 n_norms__ = 0; 00426 } else if (ignore_cwise__) { 00427 n_norms__ = 1; 00428 } else { 00429 n_norms__ = 2; 00430 } 00431 00432 rcequ = lsame_(equed, "Y"); 00433 00434 /* Test input parameters. */ 00435 00436 if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { 00437 *info = -1; 00438 } else if (! rcequ && ! lsame_(equed, "N")) { 00439 *info = -2; 00440 } else if (*n < 0) { 00441 *info = -3; 00442 } else if (*nrhs < 0) { 00443 *info = -4; 00444 } else if (*lda < max(1,*n)) { 00445 *info = -6; 00446 } else if (*ldaf < max(1,*n)) { 00447 *info = -8; 00448 } else if (*ldb < max(1,*n)) { 00449 *info = -11; 00450 } else if (*ldx < max(1,*n)) { 00451 *info = -13; 00452 } 00453 if (*info != 0) { 00454 i__1 = -(*info); 00455 xerbla_("CPORFSX", &i__1); 00456 return 0; 00457 } 00458 00459 /* Quick return if possible. */ 00460 00461 if (*n == 0 || *nrhs == 0) { 00462 *rcond = 1.f; 00463 i__1 = *nrhs; 00464 for (j = 1; j <= i__1; ++j) { 00465 berr[j] = 0.f; 00466 if (*n_err_bnds__ >= 1) { 00467 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00468 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00469 } else if (*n_err_bnds__ >= 2) { 00470 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f; 00471 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f; 00472 } else if (*n_err_bnds__ >= 3) { 00473 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f; 00474 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f; 00475 } 00476 } 00477 return 0; 00478 } 00479 00480 /* Default to failure. */ 00481 00482 *rcond = 0.f; 00483 i__1 = *nrhs; 00484 for (j = 1; j <= i__1; ++j) { 00485 berr[j] = 1.f; 00486 if (*n_err_bnds__ >= 1) { 00487 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00488 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00489 } else if (*n_err_bnds__ >= 2) { 00490 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00491 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00492 } else if (*n_err_bnds__ >= 3) { 00493 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f; 00494 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f; 00495 } 00496 } 00497 00498 /* Compute the norm of A and the reciprocal of the condition */ 00499 /* number of A. */ 00500 00501 *(unsigned char *)norm = 'I'; 00502 anorm = clanhe_(norm, uplo, n, &a[a_offset], lda, &rwork[1]); 00503 cpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], 00504 info); 00505 00506 /* Perform refinement on each right-hand side */ 00507 00508 if (ref_type__ != 0) { 00509 prec_type__ = ilaprec_("D"); 00510 cla_porfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, 00511 &af[af_offset], ldaf, &rcequ, &s[1], &b[b_offset], ldb, &x[ 00512 x_offset], ldx, &berr[1], &n_norms__, &err_bnds_norm__[ 00513 err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset], 00514 &work[1], &rwork[1], &work[*n + 1], (complex *)(&rwork[1]), rcond, &ithresh, & 00515 rthresh, &unstable_thresh__, &ignore_cwise__, info, (ftnlen)1) 00516 ; 00517 } 00518 /* Computing MAX */ 00519 r__1 = 10.f, r__2 = sqrt((real) (*n)); 00520 err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon"); 00521 if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { 00522 00523 /* Compute scaled normwise condition number cond(A*C). */ 00524 00525 if (rcequ) { 00526 rcond_tmp__ = cla_porcond_c__(uplo, n, &a[a_offset], lda, &af[ 00527 af_offset], ldaf, &s[1], &c_true, info, &work[1], &rwork[ 00528 1], (ftnlen)1); 00529 } else { 00530 rcond_tmp__ = cla_porcond_c__(uplo, n, &a[a_offset], lda, &af[ 00531 af_offset], ldaf, &s[1], &c_false, info, &work[1], &rwork[ 00532 1], (ftnlen)1); 00533 } 00534 i__1 = *nrhs; 00535 for (j = 1; j <= i__1; ++j) { 00536 00537 /* Cap the error at 1.0. */ 00538 00539 if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 00540 << 1)] > 1.f) { 00541 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00542 } 00543 00544 /* Threshold the error (see LAWN). */ 00545 00546 if (rcond_tmp__ < illrcond_thresh__) { 00547 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00548 err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f; 00549 if (*info <= *n) { 00550 *info = *n + j; 00551 } 00552 } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 00553 err_lbnd__) { 00554 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; 00555 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00556 } 00557 00558 /* Save the condition number. */ 00559 00560 if (*n_err_bnds__ >= 3) { 00561 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; 00562 } 00563 } 00564 } 00565 if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { 00566 00567 /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ 00568 /* each right-hand side using the current solution as an estimate of */ 00569 /* the true solution. If the componentwise error estimate is too */ 00570 /* large, then the solution is a lousy estimate of truth and the */ 00571 /* estimated RCOND may be too optimistic. To avoid misleading users, */ 00572 /* the inverse condition number is set to 0.0 when the estimated */ 00573 /* cwise error is at least CWISE_WRONG. */ 00574 00575 cwise_wrong__ = sqrt(slamch_("Epsilon")); 00576 i__1 = *nrhs; 00577 for (j = 1; j <= i__1; ++j) { 00578 if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00579 cwise_wrong__) { 00580 rcond_tmp__ = cla_porcond_x__(uplo, n, &a[a_offset], lda, &af[ 00581 af_offset], ldaf, &x[j * x_dim1 + 1], info, &work[1], 00582 &rwork[1], (ftnlen)1); 00583 } else { 00584 rcond_tmp__ = 0.f; 00585 } 00586 00587 /* Cap the error at 1.0. */ 00588 00589 if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 00590 << 1)] > 1.f) { 00591 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00592 } 00593 00594 /* Threshold the error (see LAWN). */ 00595 00596 if (rcond_tmp__ < illrcond_thresh__) { 00597 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00598 err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f; 00599 if (params[3] == 1.f && *info < *n + j) { 00600 *info = *n + j; 00601 } 00602 } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00603 err_lbnd__) { 00604 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; 00605 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00606 } 00607 00608 /* Save the condition number. */ 00609 00610 if (*n_err_bnds__ >= 3) { 00611 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; 00612 } 00613 } 00614 } 00615 00616 return 0; 00617 00618 /* End of CPORFSX */ 00619 00620 } /* cporfsx_ */