00001 /* ssyrfsx.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 ssyrfsx_(char *uplo, char *equed, integer *n, integer * 00023 nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, 00024 real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond, 00025 real *berr, integer *n_err_bnds__, real *err_bnds_norm__, real * 00026 err_bnds_comp__, integer *nparams, real *params, real *work, integer * 00027 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__, j; 00041 real rcond_tmp__; 00042 integer prec_type__; 00043 extern doublereal sla_syrcond__(char *, integer *, real *, integer *, 00044 real *, integer *, integer *, integer *, real *, integer *, real * 00045 , integer *, ftnlen); 00046 real cwise_wrong__; 00047 extern /* Subroutine */ int sla_syrfsx_extended__(integer *, char *, 00048 integer *, integer *, real *, integer *, real *, integer *, 00049 integer *, logical *, real *, real *, integer *, real *, integer * 00050 , real *, integer *, real *, real *, real *, real *, real *, real 00051 *, real *, integer *, real *, real *, logical *, integer *, 00052 ftnlen); 00053 char norm[1]; 00054 logical ignore_cwise__; 00055 extern logical lsame_(char *, char *); 00056 real anorm; 00057 logical rcequ; 00058 extern doublereal slamch_(char *); 00059 extern /* Subroutine */ int xerbla_(char *, integer *); 00060 extern doublereal slansy_(char *, char *, integer *, real *, integer *, 00061 real *); 00062 extern /* Subroutine */ int ssycon_(char *, integer *, real *, integer *, 00063 integer *, real *, real *, real *, integer *, 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 /* SSYRFSX improves the computed solution to a system of linear */ 00087 /* equations when the coefficient matrix is symmetric indefinite, and */ 00088 /* provides error bounds and backward error estimates for the */ 00089 /* solution. In addition to normwise error bound, the code provides */ 00090 /* maximum componentwise error bound if possible. See comments for */ 00091 /* ERR_BNDS_NORM and ERR_BNDS_COMP for details of the 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 */ 00130 /* part of the matrix A, and the strictly lower triangular */ 00131 /* part of A is not referenced. If UPLO = 'L', the leading */ 00132 /* N-by-N lower triangular part of A contains the lower */ 00133 /* triangular part of the matrix A, and the strictly upper */ 00134 /* triangular part of A is 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 factored form of the matrix A. AF contains the block */ 00141 /* diagonal matrix D and the multipliers used to obtain the */ 00142 /* factor U or L from the factorization A = U*D*U**T or A = */ 00143 /* L*D*L**T as computed by SSYTRF. */ 00144 00145 /* LDAF (input) INTEGER */ 00146 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00147 00148 /* IPIV (input) INTEGER array, dimension (N) */ 00149 /* Details of the interchanges and the block structure of D */ 00150 /* as determined by SSYTRF. */ 00151 00152 /* S (input or output) REAL array, dimension (N) */ 00153 /* The scale factors for A. If EQUED = 'Y', A is multiplied on */ 00154 /* the left and right by diag(S). S is an input argument if FACT = */ 00155 /* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */ 00156 /* = 'Y', each element of S must be positive. If S is output, each */ 00157 /* element of S is a power of the radix. If S is input, each element */ 00158 /* of S should be a power of the radix to ensure a reliable solution */ 00159 /* and error estimates. Scaling by powers of the radix does not cause */ 00160 /* rounding errors unless the result underflows or overflows. */ 00161 /* Rounding errors during scaling lead to refining with a matrix that */ 00162 /* is not equivalent to the input matrix, producing error estimates */ 00163 /* that may not be reliable. */ 00164 00165 /* B (input) REAL array, dimension (LDB,NRHS) */ 00166 /* The right hand side matrix B. */ 00167 00168 /* LDB (input) INTEGER */ 00169 /* The leading dimension of the array B. LDB >= max(1,N). */ 00170 00171 /* X (input/output) REAL array, dimension (LDX,NRHS) */ 00172 /* On entry, the solution matrix X, as computed by SGETRS. */ 00173 /* On exit, the improved solution matrix X. */ 00174 00175 /* LDX (input) INTEGER */ 00176 /* The leading dimension of the array X. LDX >= max(1,N). */ 00177 00178 /* RCOND (output) REAL */ 00179 /* Reciprocal scaled condition number. This is an estimate of the */ 00180 /* reciprocal Skeel condition number of the matrix A after */ 00181 /* equilibration (if done). If this is less than the machine */ 00182 /* precision (in particular, if it is zero), the matrix is singular */ 00183 /* to working precision. Note that the error may still be small even */ 00184 /* if this number is very small and the matrix appears ill- */ 00185 /* conditioned. */ 00186 00187 /* BERR (output) REAL array, dimension (NRHS) */ 00188 /* Componentwise relative backward error. This is the */ 00189 /* componentwise relative backward error of each solution vector X(j) */ 00190 /* (i.e., the smallest relative change in any element of A or B that */ 00191 /* makes X(j) an exact solution). */ 00192 00193 /* N_ERR_BNDS (input) INTEGER */ 00194 /* Number of error bounds to return for each right hand side */ 00195 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00196 /* ERR_BNDS_COMP below. */ 00197 00198 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00199 /* For each right-hand side, this array contains information about */ 00200 /* various error bounds and condition numbers corresponding to the */ 00201 /* normwise relative error, which is defined as follows: */ 00202 00203 /* Normwise relative error in the ith solution vector: */ 00204 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00205 /* ------------------------------ */ 00206 /* max_j abs(X(j,i)) */ 00207 00208 /* The array is indexed by the type of error information as described */ 00209 /* below. There currently are up to three pieces of information */ 00210 /* returned. */ 00211 00212 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00213 /* right-hand side. */ 00214 00215 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00216 /* three fields: */ 00217 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00218 /* reciprocal condition number is less than the threshold */ 00219 /* sqrt(n) * slamch('Epsilon'). */ 00220 00221 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00222 /* almost certainly within a factor of 10 of the true error */ 00223 /* so long as the next entry is greater than the threshold */ 00224 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00225 /* be trusted if the previous boolean is true. */ 00226 00227 /* err = 3 Reciprocal condition number: Estimated normwise */ 00228 /* reciprocal condition number. Compared with the threshold */ 00229 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00230 /* estimate is "guaranteed". These reciprocal condition */ 00231 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00232 /* appropriately scaled matrix Z. */ 00233 /* Let Z = S*A, where S scales each row by a power of the */ 00234 /* radix so all absolute row sums of Z are approximately 1. */ 00235 00236 /* See Lapack Working Note 165 for further details and extra */ 00237 /* cautions. */ 00238 00239 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00240 /* For each right-hand side, this array contains information about */ 00241 /* various error bounds and condition numbers corresponding to the */ 00242 /* componentwise relative error, which is defined as follows: */ 00243 00244 /* Componentwise relative error in the ith solution vector: */ 00245 /* abs(XTRUE(j,i) - X(j,i)) */ 00246 /* max_j ---------------------- */ 00247 /* abs(X(j,i)) */ 00248 00249 /* The array is indexed by the right-hand side i (on which the */ 00250 /* componentwise relative error depends), and the type of error */ 00251 /* information as described below. There currently are up to three */ 00252 /* pieces of information returned for each right-hand side. If */ 00253 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00254 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00255 /* the first (:,N_ERR_BNDS) entries are returned. */ 00256 00257 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00258 /* right-hand side. */ 00259 00260 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00261 /* three fields: */ 00262 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00263 /* reciprocal condition number is less than the threshold */ 00264 /* sqrt(n) * slamch('Epsilon'). */ 00265 00266 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00267 /* almost certainly within a factor of 10 of the true error */ 00268 /* so long as the next entry is greater than the threshold */ 00269 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00270 /* be trusted if the previous boolean is true. */ 00271 00272 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00273 /* reciprocal condition number. Compared with the threshold */ 00274 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00275 /* estimate is "guaranteed". These reciprocal condition */ 00276 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00277 /* appropriately scaled matrix Z. */ 00278 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00279 /* current right-hand side and S scales each row of */ 00280 /* A*diag(x) by a power of the radix so all absolute row */ 00281 /* sums of Z are approximately 1. */ 00282 00283 /* See Lapack Working Note 165 for further details and extra */ 00284 /* cautions. */ 00285 00286 /* NPARAMS (input) INTEGER */ 00287 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00288 /* PARAMS array is never referenced and default values are used. */ 00289 00290 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00291 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00292 /* that entry will be filled with default value used for that */ 00293 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00294 /* are used for higher-numbered parameters. */ 00295 00296 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00297 /* refinement or not. */ 00298 /* Default: 1.0 */ 00299 /* = 0.0 : No refinement is performed, and no error bounds are */ 00300 /* computed. */ 00301 /* = 1.0 : Use the double-precision refinement algorithm, */ 00302 /* possibly with doubled-single computations if the */ 00303 /* compilation environment does not support DOUBLE */ 00304 /* PRECISION. */ 00305 /* (other values are reserved for future use) */ 00306 00307 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00308 /* computations allowed for refinement. */ 00309 /* Default: 10 */ 00310 /* Aggressive: Set to 100 to permit convergence using approximate */ 00311 /* factorizations or factorizations other than LU. If */ 00312 /* the factorization uses a technique other than */ 00313 /* Gaussian elimination, the guarantees in */ 00314 /* err_bnds_norm and err_bnds_comp may no longer be */ 00315 /* trustworthy. */ 00316 00317 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00318 /* will attempt to find a solution with small componentwise */ 00319 /* relative error in the double-precision algorithm. Positive */ 00320 /* is true, 0.0 is false. */ 00321 /* Default: 1.0 (attempt componentwise convergence) */ 00322 00323 /* WORK (workspace) REAL array, dimension (4*N) */ 00324 00325 /* IWORK (workspace) INTEGER array, dimension (N) */ 00326 00327 /* INFO (output) INTEGER */ 00328 /* = 0: Successful exit. The solution to every right-hand side is */ 00329 /* guaranteed. */ 00330 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00331 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00332 /* has been completed, but the factor U is exactly singular, so */ 00333 /* the solution and error bounds could not be computed. RCOND = 0 */ 00334 /* is returned. */ 00335 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00336 /* not guaranteed. The solutions corresponding to other right- */ 00337 /* hand sides K with K > J may not be guaranteed as well, but */ 00338 /* only the first such right-hand side is reported. If a small */ 00339 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00340 /* the Jth right-hand side is the first with a normwise error */ 00341 /* bound that is not guaranteed (the smallest J such */ 00342 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00343 /* the Jth right-hand side is the first with either a normwise or */ 00344 /* componentwise error bound that is not guaranteed (the smallest */ 00345 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00346 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00347 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00348 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00349 /* ERR_BNDS_COMP. */ 00350 00351 /* ================================================================== */ 00352 00353 /* .. Parameters .. */ 00354 /* .. */ 00355 /* .. Local Scalars .. */ 00356 /* .. */ 00357 /* .. External Subroutines .. */ 00358 /* .. */ 00359 /* .. Intrinsic Functions .. */ 00360 /* .. */ 00361 /* .. External Functions .. */ 00362 /* .. */ 00363 /* .. Executable Statements .. */ 00364 00365 /* Check the input parameters. */ 00366 00367 /* Parameter adjustments */ 00368 err_bnds_comp_dim1 = *nrhs; 00369 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00370 err_bnds_comp__ -= err_bnds_comp_offset; 00371 err_bnds_norm_dim1 = *nrhs; 00372 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00373 err_bnds_norm__ -= err_bnds_norm_offset; 00374 a_dim1 = *lda; 00375 a_offset = 1 + a_dim1; 00376 a -= a_offset; 00377 af_dim1 = *ldaf; 00378 af_offset = 1 + af_dim1; 00379 af -= af_offset; 00380 --ipiv; 00381 --s; 00382 b_dim1 = *ldb; 00383 b_offset = 1 + b_dim1; 00384 b -= b_offset; 00385 x_dim1 = *ldx; 00386 x_offset = 1 + x_dim1; 00387 x -= x_offset; 00388 --berr; 00389 --params; 00390 --work; 00391 --iwork; 00392 00393 /* Function Body */ 00394 *info = 0; 00395 ref_type__ = 1; 00396 if (*nparams >= 1) { 00397 if (params[1] < 0.f) { 00398 params[1] = 1.f; 00399 } else { 00400 ref_type__ = params[1]; 00401 } 00402 } 00403 00404 /* Set default parameters. */ 00405 00406 illrcond_thresh__ = (real) (*n) * slamch_("Epsilon"); 00407 ithresh = 10; 00408 rthresh = .5f; 00409 unstable_thresh__ = .25f; 00410 ignore_cwise__ = FALSE_; 00411 00412 if (*nparams >= 2) { 00413 if (params[2] < 0.f) { 00414 params[2] = (real) ithresh; 00415 } else { 00416 ithresh = (integer) params[2]; 00417 } 00418 } 00419 if (*nparams >= 3) { 00420 if (params[3] < 0.f) { 00421 if (ignore_cwise__) { 00422 params[3] = 0.f; 00423 } else { 00424 params[3] = 1.f; 00425 } 00426 } else { 00427 ignore_cwise__ = params[3] == 0.f; 00428 } 00429 } 00430 if (ref_type__ == 0 || *n_err_bnds__ == 0) { 00431 n_norms__ = 0; 00432 } else if (ignore_cwise__) { 00433 n_norms__ = 1; 00434 } else { 00435 n_norms__ = 2; 00436 } 00437 00438 rcequ = lsame_(equed, "Y"); 00439 00440 /* Test input parameters. */ 00441 00442 if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { 00443 *info = -1; 00444 } else if (! rcequ && ! lsame_(equed, "N")) { 00445 *info = -2; 00446 } else if (*n < 0) { 00447 *info = -3; 00448 } else if (*nrhs < 0) { 00449 *info = -4; 00450 } else if (*lda < max(1,*n)) { 00451 *info = -6; 00452 } else if (*ldaf < max(1,*n)) { 00453 *info = -8; 00454 } else if (*ldb < max(1,*n)) { 00455 *info = -11; 00456 } else if (*ldx < max(1,*n)) { 00457 *info = -13; 00458 } 00459 if (*info != 0) { 00460 i__1 = -(*info); 00461 xerbla_("SSYRFSX", &i__1); 00462 return 0; 00463 } 00464 00465 /* Quick return if possible. */ 00466 00467 if (*n == 0 || *nrhs == 0) { 00468 *rcond = 1.f; 00469 i__1 = *nrhs; 00470 for (j = 1; j <= i__1; ++j) { 00471 berr[j] = 0.f; 00472 if (*n_err_bnds__ >= 1) { 00473 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00474 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00475 } else if (*n_err_bnds__ >= 2) { 00476 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f; 00477 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f; 00478 } else if (*n_err_bnds__ >= 3) { 00479 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f; 00480 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f; 00481 } 00482 } 00483 return 0; 00484 } 00485 00486 /* Default to failure. */ 00487 00488 *rcond = 0.f; 00489 i__1 = *nrhs; 00490 for (j = 1; j <= i__1; ++j) { 00491 berr[j] = 1.f; 00492 if (*n_err_bnds__ >= 1) { 00493 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00494 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00495 } else if (*n_err_bnds__ >= 2) { 00496 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00497 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00498 } else if (*n_err_bnds__ >= 3) { 00499 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f; 00500 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f; 00501 } 00502 } 00503 00504 /* Compute the norm of A and the reciprocal of the condition */ 00505 /* number of A. */ 00506 00507 *(unsigned char *)norm = 'I'; 00508 anorm = slansy_(norm, uplo, n, &a[a_offset], lda, &work[1]); 00509 ssycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], 00510 &iwork[1], info); 00511 00512 /* Perform refinement on each right-hand side */ 00513 00514 if (ref_type__ != 0) { 00515 prec_type__ = ilaprec_("D"); 00516 sla_syrfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, 00517 &af[af_offset], ldaf, &ipiv[1], &rcequ, &s[1], &b[b_offset], 00518 ldb, &x[x_offset], ldx, &berr[1], &n_norms__, & 00519 err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[ 00520 err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n << 00521 1) + 1], &work[1], rcond, &ithresh, &rthresh, & 00522 unstable_thresh__, &ignore_cwise__, info, (ftnlen)1); 00523 } 00524 /* Computing MAX */ 00525 r__1 = 10.f, r__2 = sqrt((real) (*n)); 00526 err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon"); 00527 if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { 00528 00529 /* Compute scaled normwise condition number cond(A*C). */ 00530 00531 if (rcequ) { 00532 rcond_tmp__ = sla_syrcond__(uplo, n, &a[a_offset], lda, &af[ 00533 af_offset], ldaf, &ipiv[1], &c_n1, &s[1], info, &work[1], 00534 &iwork[1], (ftnlen)1); 00535 } else { 00536 rcond_tmp__ = sla_syrcond__(uplo, n, &a[a_offset], lda, &af[ 00537 af_offset], ldaf, &ipiv[1], &c__0, &s[1], info, &work[1], 00538 &iwork[1], (ftnlen)1); 00539 } 00540 i__1 = *nrhs; 00541 for (j = 1; j <= i__1; ++j) { 00542 00543 /* Cap the error at 1.0. */ 00544 00545 if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 00546 << 1)] > 1.f) { 00547 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00548 } 00549 00550 /* Threshold the error (see LAWN). */ 00551 00552 if (rcond_tmp__ < illrcond_thresh__) { 00553 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00554 err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f; 00555 if (*info <= *n) { 00556 *info = *n + j; 00557 } 00558 } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 00559 err_lbnd__) { 00560 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; 00561 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00562 } 00563 00564 /* Save the condition number. */ 00565 00566 if (*n_err_bnds__ >= 3) { 00567 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; 00568 } 00569 } 00570 } 00571 if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { 00572 00573 /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ 00574 /* each right-hand side using the current solution as an estimate of */ 00575 /* the true solution. If the componentwise error estimate is too */ 00576 /* large, then the solution is a lousy estimate of truth and the */ 00577 /* estimated RCOND may be too optimistic. To avoid misleading users, */ 00578 /* the inverse condition number is set to 0.0 when the estimated */ 00579 /* cwise error is at least CWISE_WRONG. */ 00580 00581 cwise_wrong__ = sqrt(slamch_("Epsilon")); 00582 i__1 = *nrhs; 00583 for (j = 1; j <= i__1; ++j) { 00584 if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00585 cwise_wrong__) { 00586 rcond_tmp__ = sla_syrcond__(uplo, n, &a[a_offset], lda, &af[ 00587 af_offset], ldaf, &ipiv[1], &c__1, &x[j * x_dim1 + 1], 00588 info, &work[1], &iwork[1], (ftnlen)1); 00589 } else { 00590 rcond_tmp__ = 0.f; 00591 } 00592 00593 /* Cap the error at 1.0. */ 00594 00595 if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 00596 << 1)] > 1.f) { 00597 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00598 } 00599 00600 /* Threshold the error (see LAWN). */ 00601 00602 if (rcond_tmp__ < illrcond_thresh__) { 00603 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00604 err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f; 00605 if (params[3] == 1.f && *info < *n + j) { 00606 *info = *n + j; 00607 } 00608 } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00609 err_lbnd__) { 00610 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; 00611 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00612 } 00613 00614 /* Save the condition number. */ 00615 00616 if (*n_err_bnds__ >= 3) { 00617 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; 00618 } 00619 } 00620 } 00621 00622 return 0; 00623 00624 /* End of SSYRFSX */ 00625 00626 } /* ssyrfsx_ */