00001 /* csyrfsx.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 csyrfsx_(char *uplo, char *equed, integer *n, integer * 00022 nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * 00023 ipiv, real *s, complex *b, integer *ldb, complex *x, integer *ldx, 00024 real *rcond, real *berr, integer *n_err_bnds__, real *err_bnds_norm__, 00025 real *err_bnds_comp__, integer *nparams, real *params, complex *work, 00026 real *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_syrfsx_extended__(integer *, char *, 00045 integer *, integer *, complex *, integer *, complex *, integer *, 00046 integer *, logical *, real *, complex *, integer *, complex *, 00047 integer *, real *, integer *, real *, real *, complex *, real *, 00048 complex *, complex *, real *, integer *, real *, real *, logical * 00049 , integer *, 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_syrcond_c__(char *, integer *, complex *, integer *, 00056 complex *, integer *, integer *, real *, logical *, integer *, 00057 complex *, real *, ftnlen), cla_syrcond_x__(char *, integer *, 00058 complex *, integer *, complex *, integer *, integer *, complex *, 00059 integer *, complex *, real *, ftnlen), slamch_(char *); 00060 extern /* Subroutine */ int xerbla_(char *, integer *); 00061 extern doublereal clansy_(char *, char *, integer *, complex *, integer *, 00062 real *); 00063 extern /* Subroutine */ int csycon_(char *, integer *, complex *, integer 00064 *, integer *, real *, real *, complex *, integer *); 00065 extern integer ilaprec_(char *); 00066 integer ithresh, n_norms__; 00067 real rthresh; 00068 00069 00070 /* -- LAPACK routine (version 3.2.1) -- */ 00071 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00072 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00073 /* -- April 2009 -- */ 00074 00075 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00076 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00077 00078 /* .. */ 00079 /* .. Scalar Arguments .. */ 00080 /* .. */ 00081 /* .. Array Arguments .. */ 00082 /* .. */ 00083 00084 /* Purpose */ 00085 /* ======= */ 00086 00087 /* CSYRFSX improves the computed solution to a system of linear */ 00088 /* equations when the coefficient matrix is symmetric indefinite, and */ 00089 /* provides error bounds and backward error estimates for the */ 00090 /* solution. In addition to normwise error bound, the code provides */ 00091 /* maximum componentwise error bound if possible. See comments for */ 00092 /* ERR_BNDS_NORM and ERR_BNDS_COMP for details of the 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 */ 00131 /* part of the matrix A, and the strictly lower triangular */ 00132 /* part of A is not referenced. If UPLO = 'L', the leading */ 00133 /* N-by-N lower triangular part of A contains the lower */ 00134 /* triangular part of the matrix A, and the strictly upper */ 00135 /* triangular part of A is 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 factored form of the matrix A. AF contains the block */ 00142 /* diagonal matrix D and the multipliers used to obtain the */ 00143 /* factor U or L from the factorization A = U*D*U**T or A = */ 00144 /* L*D*L**T as computed by SSYTRF. */ 00145 00146 /* LDAF (input) INTEGER */ 00147 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00148 00149 /* IPIV (input) INTEGER array, dimension (N) */ 00150 /* Details of the interchanges and the block structure of D */ 00151 /* as determined by SSYTRF. */ 00152 00153 /* S (input or output) REAL array, dimension (N) */ 00154 /* The scale factors for A. If EQUED = 'Y', A is multiplied on */ 00155 /* the left and right by diag(S). S is an input argument if FACT = */ 00156 /* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */ 00157 /* = 'Y', each element of S must be positive. If S is output, each */ 00158 /* element of S is a power of the radix. If S is input, each element */ 00159 /* of S should be a power of the radix to ensure a reliable solution */ 00160 /* and error estimates. Scaling by powers of the radix does not cause */ 00161 /* rounding errors unless the result underflows or overflows. */ 00162 /* Rounding errors during scaling lead to refining with a matrix that */ 00163 /* is not equivalent to the input matrix, producing error estimates */ 00164 /* that may not be reliable. */ 00165 00166 /* B (input) COMPLEX array, dimension (LDB,NRHS) */ 00167 /* The right hand side matrix B. */ 00168 00169 /* LDB (input) INTEGER */ 00170 /* The leading dimension of the array B. LDB >= max(1,N). */ 00171 00172 /* X (input/output) COMPLEX array, dimension (LDX,NRHS) */ 00173 /* On entry, the solution matrix X, as computed by SGETRS. */ 00174 /* On exit, the improved solution matrix X. */ 00175 00176 /* LDX (input) INTEGER */ 00177 /* The leading dimension of the array X. LDX >= max(1,N). */ 00178 00179 /* RCOND (output) REAL */ 00180 /* Reciprocal scaled condition number. This is an estimate of the */ 00181 /* reciprocal Skeel condition number of the matrix A after */ 00182 /* equilibration (if done). If this is less than the machine */ 00183 /* precision (in particular, if it is zero), the matrix is singular */ 00184 /* to working precision. Note that the error may still be small even */ 00185 /* if this number is very small and the matrix appears ill- */ 00186 /* conditioned. */ 00187 00188 /* BERR (output) REAL array, dimension (NRHS) */ 00189 /* Componentwise relative backward error. This is the */ 00190 /* componentwise relative backward error of each solution vector X(j) */ 00191 /* (i.e., the smallest relative change in any element of A or B that */ 00192 /* makes X(j) an exact solution). */ 00193 00194 /* N_ERR_BNDS (input) INTEGER */ 00195 /* Number of error bounds to return for each right hand side */ 00196 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00197 /* ERR_BNDS_COMP below. */ 00198 00199 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00200 /* For each right-hand side, this array contains information about */ 00201 /* various error bounds and condition numbers corresponding to the */ 00202 /* normwise relative error, which is defined as follows: */ 00203 00204 /* Normwise relative error in the ith solution vector: */ 00205 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00206 /* ------------------------------ */ 00207 /* max_j abs(X(j,i)) */ 00208 00209 /* The array is indexed by the type of error information as described */ 00210 /* below. There currently are up to three pieces of information */ 00211 /* returned. */ 00212 00213 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00214 /* right-hand side. */ 00215 00216 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00217 /* three fields: */ 00218 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00219 /* reciprocal condition number is less than the threshold */ 00220 /* sqrt(n) * slamch('Epsilon'). */ 00221 00222 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00223 /* almost certainly within a factor of 10 of the true error */ 00224 /* so long as the next entry is greater than the threshold */ 00225 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00226 /* be trusted if the previous boolean is true. */ 00227 00228 /* err = 3 Reciprocal condition number: Estimated normwise */ 00229 /* reciprocal condition number. Compared with the threshold */ 00230 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00231 /* estimate is "guaranteed". These reciprocal condition */ 00232 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00233 /* appropriately scaled matrix Z. */ 00234 /* Let Z = S*A, where S scales each row by a power of the */ 00235 /* radix so all absolute row sums of Z are approximately 1. */ 00236 00237 /* See Lapack Working Note 165 for further details and extra */ 00238 /* cautions. */ 00239 00240 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00241 /* For each right-hand side, this array contains information about */ 00242 /* various error bounds and condition numbers corresponding to the */ 00243 /* componentwise relative error, which is defined as follows: */ 00244 00245 /* Componentwise relative error in the ith solution vector: */ 00246 /* abs(XTRUE(j,i) - X(j,i)) */ 00247 /* max_j ---------------------- */ 00248 /* abs(X(j,i)) */ 00249 00250 /* The array is indexed by the right-hand side i (on which the */ 00251 /* componentwise relative error depends), and the type of error */ 00252 /* information as described below. There currently are up to three */ 00253 /* pieces of information returned for each right-hand side. If */ 00254 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00255 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00256 /* the first (:,N_ERR_BNDS) entries are returned. */ 00257 00258 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00259 /* right-hand side. */ 00260 00261 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00262 /* three fields: */ 00263 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00264 /* reciprocal condition number is less than the threshold */ 00265 /* sqrt(n) * slamch('Epsilon'). */ 00266 00267 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00268 /* almost certainly within a factor of 10 of the true error */ 00269 /* so long as the next entry is greater than the threshold */ 00270 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00271 /* be trusted if the previous boolean is true. */ 00272 00273 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00274 /* reciprocal condition number. Compared with the threshold */ 00275 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00276 /* estimate is "guaranteed". These reciprocal condition */ 00277 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00278 /* appropriately scaled matrix Z. */ 00279 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00280 /* current right-hand side and S scales each row of */ 00281 /* A*diag(x) by a power of the radix so all absolute row */ 00282 /* sums of Z are approximately 1. */ 00283 00284 /* See Lapack Working Note 165 for further details and extra */ 00285 /* cautions. */ 00286 00287 /* NPARAMS (input) INTEGER */ 00288 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00289 /* PARAMS array is never referenced and default values are used. */ 00290 00291 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00292 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00293 /* that entry will be filled with default value used for that */ 00294 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00295 /* are used for higher-numbered parameters. */ 00296 00297 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00298 /* refinement or not. */ 00299 /* Default: 1.0 */ 00300 /* = 0.0 : No refinement is performed, and no error bounds are */ 00301 /* computed. */ 00302 /* = 1.0 : Use the double-precision refinement algorithm, */ 00303 /* possibly with doubled-single computations if the */ 00304 /* compilation environment does not support DOUBLE */ 00305 /* PRECISION. */ 00306 /* (other values are reserved for future use) */ 00307 00308 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00309 /* computations allowed for refinement. */ 00310 /* Default: 10 */ 00311 /* Aggressive: Set to 100 to permit convergence using approximate */ 00312 /* factorizations or factorizations other than LU. If */ 00313 /* the factorization uses a technique other than */ 00314 /* Gaussian elimination, the guarantees in */ 00315 /* err_bnds_norm and err_bnds_comp may no longer be */ 00316 /* trustworthy. */ 00317 00318 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00319 /* will attempt to find a solution with small componentwise */ 00320 /* relative error in the double-precision algorithm. Positive */ 00321 /* is true, 0.0 is false. */ 00322 /* Default: 1.0 (attempt componentwise convergence) */ 00323 00324 /* WORK (workspace) COMPLEX array, dimension (2*N) */ 00325 00326 /* RWORK (workspace) REAL array, dimension (2*N) */ 00327 00328 /* INFO (output) INTEGER */ 00329 /* = 0: Successful exit. The solution to every right-hand side is */ 00330 /* guaranteed. */ 00331 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00332 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00333 /* has been completed, but the factor U is exactly singular, so */ 00334 /* the solution and error bounds could not be computed. RCOND = 0 */ 00335 /* is returned. */ 00336 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00337 /* not guaranteed. The solutions corresponding to other right- */ 00338 /* hand sides K with K > J may not be guaranteed as well, but */ 00339 /* only the first such right-hand side is reported. If a small */ 00340 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00341 /* the Jth right-hand side is the first with a normwise error */ 00342 /* bound that is not guaranteed (the smallest J such */ 00343 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00344 /* the Jth right-hand side is the first with either a normwise or */ 00345 /* componentwise error bound that is not guaranteed (the smallest */ 00346 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00347 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00348 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00349 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00350 /* ERR_BNDS_COMP. */ 00351 00352 /* ================================================================== */ 00353 00354 /* .. Parameters .. */ 00355 /* .. */ 00356 /* .. Local Scalars .. */ 00357 /* .. */ 00358 /* .. External Subroutines .. */ 00359 /* .. */ 00360 /* .. Intrinsic Functions .. */ 00361 /* .. */ 00362 /* .. External Functions .. */ 00363 /* .. */ 00364 /* .. Executable Statements .. */ 00365 00366 /* Check the input parameters. */ 00367 00368 /* Parameter adjustments */ 00369 err_bnds_comp_dim1 = *nrhs; 00370 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00371 err_bnds_comp__ -= err_bnds_comp_offset; 00372 err_bnds_norm_dim1 = *nrhs; 00373 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00374 err_bnds_norm__ -= err_bnds_norm_offset; 00375 a_dim1 = *lda; 00376 a_offset = 1 + a_dim1; 00377 a -= a_offset; 00378 af_dim1 = *ldaf; 00379 af_offset = 1 + af_dim1; 00380 af -= af_offset; 00381 --ipiv; 00382 --s; 00383 b_dim1 = *ldb; 00384 b_offset = 1 + b_dim1; 00385 b -= b_offset; 00386 x_dim1 = *ldx; 00387 x_offset = 1 + x_dim1; 00388 x -= x_offset; 00389 --berr; 00390 --params; 00391 --work; 00392 --rwork; 00393 00394 /* Function Body */ 00395 *info = 0; 00396 ref_type__ = 1; 00397 if (*nparams >= 1) { 00398 if (params[1] < 0.f) { 00399 params[1] = 1.f; 00400 } else { 00401 ref_type__ = params[1]; 00402 } 00403 } 00404 00405 /* Set default parameters. */ 00406 00407 illrcond_thresh__ = (real) (*n) * slamch_("Epsilon"); 00408 ithresh = 10; 00409 rthresh = .5f; 00410 unstable_thresh__ = .25f; 00411 ignore_cwise__ = FALSE_; 00412 00413 if (*nparams >= 2) { 00414 if (params[2] < 0.f) { 00415 params[2] = (real) ithresh; 00416 } else { 00417 ithresh = (integer) params[2]; 00418 } 00419 } 00420 if (*nparams >= 3) { 00421 if (params[3] < 0.f) { 00422 if (ignore_cwise__) { 00423 params[3] = 0.f; 00424 } else { 00425 params[3] = 1.f; 00426 } 00427 } else { 00428 ignore_cwise__ = params[3] == 0.f; 00429 } 00430 } 00431 if (ref_type__ == 0 || *n_err_bnds__ == 0) { 00432 n_norms__ = 0; 00433 } else if (ignore_cwise__) { 00434 n_norms__ = 1; 00435 } else { 00436 n_norms__ = 2; 00437 } 00438 00439 rcequ = lsame_(equed, "Y"); 00440 00441 /* Test input parameters. */ 00442 00443 if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { 00444 *info = -1; 00445 } else if (! rcequ && ! lsame_(equed, "N")) { 00446 *info = -2; 00447 } else if (*n < 0) { 00448 *info = -3; 00449 } else if (*nrhs < 0) { 00450 *info = -4; 00451 } else if (*lda < max(1,*n)) { 00452 *info = -6; 00453 } else if (*ldaf < max(1,*n)) { 00454 *info = -8; 00455 } else if (*ldb < max(1,*n)) { 00456 *info = -11; 00457 } else if (*ldx < max(1,*n)) { 00458 *info = -13; 00459 } 00460 if (*info != 0) { 00461 i__1 = -(*info); 00462 xerbla_("CSYRFSX", &i__1); 00463 return 0; 00464 } 00465 00466 /* Quick return if possible. */ 00467 00468 if (*n == 0 || *nrhs == 0) { 00469 *rcond = 1.f; 00470 i__1 = *nrhs; 00471 for (j = 1; j <= i__1; ++j) { 00472 berr[j] = 0.f; 00473 if (*n_err_bnds__ >= 1) { 00474 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00475 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00476 } else if (*n_err_bnds__ >= 2) { 00477 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f; 00478 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f; 00479 } else if (*n_err_bnds__ >= 3) { 00480 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f; 00481 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f; 00482 } 00483 } 00484 return 0; 00485 } 00486 00487 /* Default to failure. */ 00488 00489 *rcond = 0.f; 00490 i__1 = *nrhs; 00491 for (j = 1; j <= i__1; ++j) { 00492 berr[j] = 1.f; 00493 if (*n_err_bnds__ >= 1) { 00494 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00495 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00496 } else if (*n_err_bnds__ >= 2) { 00497 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00498 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00499 } else if (*n_err_bnds__ >= 3) { 00500 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f; 00501 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f; 00502 } 00503 } 00504 00505 /* Compute the norm of A and the reciprocal of the condition */ 00506 /* number of A. */ 00507 00508 *(unsigned char *)norm = 'I'; 00509 anorm = clansy_(norm, uplo, n, &a[a_offset], lda, &rwork[1]); 00510 csycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], 00511 info); 00512 00513 /* Perform refinement on each right-hand side */ 00514 00515 if (ref_type__ != 0) { 00516 prec_type__ = ilaprec_("D"); 00517 cla_syrfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, 00518 &af[af_offset], ldaf, &ipiv[1], &rcequ, &s[1], &b[b_offset], 00519 ldb, &x[x_offset], ldx, &berr[1], &n_norms__, & 00520 err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[ 00521 err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1], 00522 (complex *)(&rwork[1]), rcond, &ithresh, &rthresh, &unstable_thresh__, & 00523 ignore_cwise__, info, (ftnlen)1); 00524 } 00525 /* Computing MAX */ 00526 r__1 = 10.f, r__2 = sqrt((real) (*n)); 00527 err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon"); 00528 if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { 00529 00530 /* Compute scaled normwise condition number cond(A*C). */ 00531 00532 if (rcequ) { 00533 rcond_tmp__ = cla_syrcond_c__(uplo, n, &a[a_offset], lda, &af[ 00534 af_offset], ldaf, &ipiv[1], &s[1], &c_true, info, &work[1] 00535 , &rwork[1], (ftnlen)1); 00536 } else { 00537 rcond_tmp__ = cla_syrcond_c__(uplo, n, &a[a_offset], lda, &af[ 00538 af_offset], ldaf, &ipiv[1], &s[1], &c_false, info, &work[ 00539 1], &rwork[1], (ftnlen)1); 00540 } 00541 i__1 = *nrhs; 00542 for (j = 1; j <= i__1; ++j) { 00543 00544 /* Cap the error at 1.0. */ 00545 00546 if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 00547 << 1)] > 1.f) { 00548 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00549 } 00550 00551 /* Threshold the error (see LAWN). */ 00552 00553 if (rcond_tmp__ < illrcond_thresh__) { 00554 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00555 err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f; 00556 if (*info <= *n) { 00557 *info = *n + j; 00558 } 00559 } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 00560 err_lbnd__) { 00561 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; 00562 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00563 } 00564 00565 /* Save the condition number. */ 00566 00567 if (*n_err_bnds__ >= 3) { 00568 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; 00569 } 00570 } 00571 } 00572 if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { 00573 00574 /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ 00575 /* each right-hand side using the current solution as an estimate of */ 00576 /* the true solution. If the componentwise error estimate is too */ 00577 /* large, then the solution is a lousy estimate of truth and the */ 00578 /* estimated RCOND may be too optimistic. To avoid misleading users, */ 00579 /* the inverse condition number is set to 0.0 when the estimated */ 00580 /* cwise error is at least CWISE_WRONG. */ 00581 00582 cwise_wrong__ = sqrt(slamch_("Epsilon")); 00583 i__1 = *nrhs; 00584 for (j = 1; j <= i__1; ++j) { 00585 if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00586 cwise_wrong__) { 00587 rcond_tmp__ = cla_syrcond_x__(uplo, n, &a[a_offset], lda, &af[ 00588 af_offset], ldaf, &ipiv[1], &x[j * x_dim1 + 1], info, 00589 &work[1], &rwork[1], (ftnlen)1); 00590 } else { 00591 rcond_tmp__ = 0.f; 00592 } 00593 00594 /* Cap the error at 1.0. */ 00595 00596 if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 00597 << 1)] > 1.f) { 00598 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00599 } 00600 00601 /* Threshold the error (see LAWN). */ 00602 00603 if (rcond_tmp__ < illrcond_thresh__) { 00604 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00605 err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f; 00606 if (params[3] == 1.f && *info < *n + j) { 00607 *info = *n + j; 00608 } 00609 } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00610 err_lbnd__) { 00611 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; 00612 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00613 } 00614 00615 /* Save the condition number. */ 00616 00617 if (*n_err_bnds__ >= 3) { 00618 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; 00619 } 00620 } 00621 } 00622 00623 return 0; 00624 00625 /* End of CSYRFSX */ 00626 00627 } /* csyrfsx_ */