00001 /* dsyrfsx.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 dsyrfsx_(char *uplo, char *equed, integer *n, integer * 00023 nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, 00024 integer *ipiv, doublereal *s, doublereal *b, integer *ldb, doublereal 00025 *x, integer *ldx, doublereal *rcond, doublereal *berr, integer * 00026 n_err_bnds__, doublereal *err_bnds_norm__, doublereal * 00027 err_bnds_comp__, integer *nparams, doublereal *params, doublereal * 00028 work, integer *iwork, integer *info) 00029 { 00030 /* System generated locals */ 00031 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 00032 x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00033 err_bnds_comp_dim1, err_bnds_comp_offset, i__1; 00034 doublereal d__1, d__2; 00035 00036 /* Builtin functions */ 00037 double sqrt(doublereal); 00038 00039 /* Local variables */ 00040 doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__; 00041 integer ref_type__, j; 00042 doublereal rcond_tmp__; 00043 integer prec_type__; 00044 extern doublereal dla_syrcond__(char *, integer *, doublereal *, integer * 00045 , doublereal *, integer *, integer *, integer *, doublereal *, 00046 integer *, doublereal *, integer *, ftnlen); 00047 doublereal cwise_wrong__; 00048 extern /* Subroutine */ int dla_syrfsx_extended__(integer *, char *, 00049 integer *, integer *, doublereal *, integer *, doublereal *, 00050 integer *, integer *, logical *, doublereal *, doublereal *, 00051 integer *, doublereal *, integer *, doublereal *, integer *, 00052 doublereal *, doublereal *, doublereal *, doublereal *, 00053 doublereal *, doublereal *, doublereal *, integer *, doublereal *, 00054 doublereal *, logical *, integer *, ftnlen); 00055 char norm[1]; 00056 logical ignore_cwise__; 00057 extern logical lsame_(char *, char *); 00058 doublereal anorm; 00059 logical rcequ; 00060 extern doublereal dlamch_(char *); 00061 extern /* Subroutine */ int xerbla_(char *, integer *); 00062 extern doublereal dlansy_(char *, char *, integer *, doublereal *, 00063 integer *, doublereal *); 00064 extern /* Subroutine */ int dsycon_(char *, integer *, doublereal *, 00065 integer *, integer *, doublereal *, doublereal *, doublereal *, 00066 integer *, integer *); 00067 extern integer ilaprec_(char *); 00068 integer ithresh, n_norms__; 00069 doublereal rthresh; 00070 00071 00072 /* -- LAPACK routine (version 3.2.1) -- */ 00073 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00074 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00075 /* -- April 2009 -- */ 00076 00077 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00078 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00079 00080 /* .. */ 00081 /* .. Scalar Arguments .. */ 00082 /* .. */ 00083 /* .. Array Arguments .. */ 00084 /* .. */ 00085 00086 /* Purpose */ 00087 /* ======= */ 00088 00089 /* DSYRFSX improves the computed solution to a system of linear */ 00090 /* equations when the coefficient matrix is symmetric indefinite, and */ 00091 /* provides error bounds and backward error estimates for the */ 00092 /* solution. In addition to normwise error bound, the code provides */ 00093 /* maximum componentwise error bound if possible. See comments for */ 00094 /* ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds. */ 00095 00096 /* The original system of linear equations may have been equilibrated */ 00097 /* before calling this routine, as described by arguments EQUED and S */ 00098 /* below. In this case, the solution and error bounds returned are */ 00099 /* for the original unequilibrated system. */ 00100 00101 /* Arguments */ 00102 /* ========= */ 00103 00104 /* Some optional parameters are bundled in the PARAMS array. These */ 00105 /* settings determine how refinement is performed, but often the */ 00106 /* defaults are acceptable. If the defaults are acceptable, users */ 00107 /* can pass NPARAMS = 0 which prevents the source code from accessing */ 00108 /* the PARAMS argument. */ 00109 00110 /* UPLO (input) CHARACTER*1 */ 00111 /* = 'U': Upper triangle of A is stored; */ 00112 /* = 'L': Lower triangle of A is stored. */ 00113 00114 /* EQUED (input) CHARACTER*1 */ 00115 /* Specifies the form of equilibration that was done to A */ 00116 /* before calling this routine. This is needed to compute */ 00117 /* the solution and error bounds correctly. */ 00118 /* = 'N': No equilibration */ 00119 /* = 'Y': Both row and column equilibration, i.e., A has been */ 00120 /* replaced by diag(S) * A * diag(S). */ 00121 /* The right hand side B has been changed accordingly. */ 00122 00123 /* N (input) INTEGER */ 00124 /* The order of the matrix A. N >= 0. */ 00125 00126 /* NRHS (input) INTEGER */ 00127 /* The number of right hand sides, i.e., the number of columns */ 00128 /* of the matrices B and X. NRHS >= 0. */ 00129 00130 /* A (input) DOUBLE PRECISION array, dimension (LDA,N) */ 00131 /* The symmetric matrix A. If UPLO = 'U', the leading N-by-N */ 00132 /* upper triangular part of A contains the upper triangular */ 00133 /* part of the matrix A, and the strictly lower triangular */ 00134 /* part of A is not referenced. If UPLO = 'L', the leading */ 00135 /* N-by-N lower triangular part of A contains the lower */ 00136 /* triangular part of the matrix A, and the strictly upper */ 00137 /* triangular part of A is not referenced. */ 00138 00139 /* LDA (input) INTEGER */ 00140 /* The leading dimension of the array A. LDA >= max(1,N). */ 00141 00142 /* AF (input) DOUBLE PRECISION array, dimension (LDAF,N) */ 00143 /* The factored form of the matrix A. AF contains the block */ 00144 /* diagonal matrix D and the multipliers used to obtain the */ 00145 /* factor U or L from the factorization A = U*D*U**T or A = */ 00146 /* L*D*L**T as computed by DSYTRF. */ 00147 00148 /* LDAF (input) INTEGER */ 00149 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00150 00151 /* IPIV (input) INTEGER array, dimension (N) */ 00152 /* Details of the interchanges and the block structure of D */ 00153 /* as determined by DSYTRF. */ 00154 00155 /* S (input or output) DOUBLE PRECISION array, dimension (N) */ 00156 /* The scale factors for A. If EQUED = 'Y', A is multiplied on */ 00157 /* the left and right by diag(S). S is an input argument if FACT = */ 00158 /* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */ 00159 /* = 'Y', each element of S must be positive. If S is output, each */ 00160 /* element of S is a power of the radix. If S is input, each element */ 00161 /* of S should be a power of the radix to ensure a reliable solution */ 00162 /* and error estimates. Scaling by powers of the radix does not cause */ 00163 /* rounding errors unless the result underflows or overflows. */ 00164 /* Rounding errors during scaling lead to refining with a matrix that */ 00165 /* is not equivalent to the input matrix, producing error estimates */ 00166 /* that may not be reliable. */ 00167 00168 /* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */ 00169 /* The right hand side matrix B. */ 00170 00171 /* LDB (input) INTEGER */ 00172 /* The leading dimension of the array B. LDB >= max(1,N). */ 00173 00174 /* X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS) */ 00175 /* On entry, the solution matrix X, as computed by DGETRS. */ 00176 /* On exit, the improved solution matrix X. */ 00177 00178 /* LDX (input) INTEGER */ 00179 /* The leading dimension of the array X. LDX >= max(1,N). */ 00180 00181 /* RCOND (output) DOUBLE PRECISION */ 00182 /* Reciprocal scaled condition number. This is an estimate of the */ 00183 /* reciprocal Skeel condition number of the matrix A after */ 00184 /* equilibration (if done). If this is less than the machine */ 00185 /* precision (in particular, if it is zero), the matrix is singular */ 00186 /* to working precision. Note that the error may still be small even */ 00187 /* if this number is very small and the matrix appears ill- */ 00188 /* conditioned. */ 00189 00190 /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ 00191 /* Componentwise relative backward error. This is the */ 00192 /* componentwise relative backward error of each solution vector X(j) */ 00193 /* (i.e., the smallest relative change in any element of A or B that */ 00194 /* makes X(j) an exact solution). */ 00195 00196 /* N_ERR_BNDS (input) INTEGER */ 00197 /* Number of error bounds to return for each right hand side */ 00198 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00199 /* ERR_BNDS_COMP below. */ 00200 00201 /* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ 00202 /* For each right-hand side, this array contains information about */ 00203 /* various error bounds and condition numbers corresponding to the */ 00204 /* normwise relative error, which is defined as follows: */ 00205 00206 /* Normwise relative error in the ith solution vector: */ 00207 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00208 /* ------------------------------ */ 00209 /* max_j abs(X(j,i)) */ 00210 00211 /* The array is indexed by the type of error information as described */ 00212 /* below. There currently are up to three pieces of information */ 00213 /* returned. */ 00214 00215 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00216 /* right-hand side. */ 00217 00218 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00219 /* three fields: */ 00220 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00221 /* reciprocal condition number is less than the threshold */ 00222 /* sqrt(n) * dlamch('Epsilon'). */ 00223 00224 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00225 /* almost certainly within a factor of 10 of the true error */ 00226 /* so long as the next entry is greater than the threshold */ 00227 /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ 00228 /* be trusted if the previous boolean is true. */ 00229 00230 /* err = 3 Reciprocal condition number: Estimated normwise */ 00231 /* reciprocal condition number. Compared with the threshold */ 00232 /* sqrt(n) * dlamch('Epsilon') to determine if the error */ 00233 /* estimate is "guaranteed". These reciprocal condition */ 00234 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00235 /* appropriately scaled matrix Z. */ 00236 /* Let Z = S*A, where S scales each row by a power of the */ 00237 /* radix so all absolute row sums of Z are approximately 1. */ 00238 00239 /* See Lapack Working Note 165 for further details and extra */ 00240 /* cautions. */ 00241 00242 /* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ 00243 /* For each right-hand side, this array contains information about */ 00244 /* various error bounds and condition numbers corresponding to the */ 00245 /* componentwise relative error, which is defined as follows: */ 00246 00247 /* Componentwise relative error in the ith solution vector: */ 00248 /* abs(XTRUE(j,i) - X(j,i)) */ 00249 /* max_j ---------------------- */ 00250 /* abs(X(j,i)) */ 00251 00252 /* The array is indexed by the right-hand side i (on which the */ 00253 /* componentwise relative error depends), and the type of error */ 00254 /* information as described below. There currently are up to three */ 00255 /* pieces of information returned for each right-hand side. If */ 00256 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00257 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00258 /* the first (:,N_ERR_BNDS) entries are returned. */ 00259 00260 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00261 /* right-hand side. */ 00262 00263 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00264 /* three fields: */ 00265 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00266 /* reciprocal condition number is less than the threshold */ 00267 /* sqrt(n) * dlamch('Epsilon'). */ 00268 00269 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00270 /* almost certainly within a factor of 10 of the true error */ 00271 /* so long as the next entry is greater than the threshold */ 00272 /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ 00273 /* be trusted if the previous boolean is true. */ 00274 00275 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00276 /* reciprocal condition number. Compared with the threshold */ 00277 /* sqrt(n) * dlamch('Epsilon') to determine if the error */ 00278 /* estimate is "guaranteed". These reciprocal condition */ 00279 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00280 /* appropriately scaled matrix Z. */ 00281 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00282 /* current right-hand side and S scales each row of */ 00283 /* A*diag(x) by a power of the radix so all absolute row */ 00284 /* sums of Z are approximately 1. */ 00285 00286 /* See Lapack Working Note 165 for further details and extra */ 00287 /* cautions. */ 00288 00289 /* NPARAMS (input) INTEGER */ 00290 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00291 /* PARAMS array is never referenced and default values are used. */ 00292 00293 /* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS */ 00294 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00295 /* that entry will be filled with default value used for that */ 00296 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00297 /* are used for higher-numbered parameters. */ 00298 00299 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00300 /* refinement or not. */ 00301 /* Default: 1.0D+0 */ 00302 /* = 0.0 : No refinement is performed, and no error bounds are */ 00303 /* computed. */ 00304 /* = 1.0 : Use the double-precision refinement algorithm, */ 00305 /* possibly with doubled-single computations if the */ 00306 /* compilation environment does not support DOUBLE */ 00307 /* PRECISION. */ 00308 /* (other values are reserved for future use) */ 00309 00310 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00311 /* computations allowed for refinement. */ 00312 /* Default: 10 */ 00313 /* Aggressive: Set to 100 to permit convergence using approximate */ 00314 /* factorizations or factorizations other than LU. If */ 00315 /* the factorization uses a technique other than */ 00316 /* Gaussian elimination, the guarantees in */ 00317 /* err_bnds_norm and err_bnds_comp may no longer be */ 00318 /* trustworthy. */ 00319 00320 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00321 /* will attempt to find a solution with small componentwise */ 00322 /* relative error in the double-precision algorithm. Positive */ 00323 /* is true, 0.0 is false. */ 00324 /* Default: 1.0 (attempt componentwise convergence) */ 00325 00326 /* WORK (workspace) DOUBLE PRECISION array, dimension (4*N) */ 00327 00328 /* IWORK (workspace) INTEGER array, dimension (N) */ 00329 00330 /* INFO (output) INTEGER */ 00331 /* = 0: Successful exit. The solution to every right-hand side is */ 00332 /* guaranteed. */ 00333 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00334 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00335 /* has been completed, but the factor U is exactly singular, so */ 00336 /* the solution and error bounds could not be computed. RCOND = 0 */ 00337 /* is returned. */ 00338 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00339 /* not guaranteed. The solutions corresponding to other right- */ 00340 /* hand sides K with K > J may not be guaranteed as well, but */ 00341 /* only the first such right-hand side is reported. If a small */ 00342 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00343 /* the Jth right-hand side is the first with a normwise error */ 00344 /* bound that is not guaranteed (the smallest J such */ 00345 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00346 /* the Jth right-hand side is the first with either a normwise or */ 00347 /* componentwise error bound that is not guaranteed (the smallest */ 00348 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00349 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00350 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00351 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00352 /* ERR_BNDS_COMP. */ 00353 00354 /* ================================================================== */ 00355 00356 /* .. Parameters .. */ 00357 /* .. */ 00358 /* .. Local Scalars .. */ 00359 /* .. */ 00360 /* .. External Subroutines .. */ 00361 /* .. */ 00362 /* .. Intrinsic Functions .. */ 00363 /* .. */ 00364 /* .. External Functions .. */ 00365 /* .. */ 00366 /* .. Executable Statements .. */ 00367 00368 /* Check the input parameters. */ 00369 00370 /* Parameter adjustments */ 00371 err_bnds_comp_dim1 = *nrhs; 00372 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00373 err_bnds_comp__ -= err_bnds_comp_offset; 00374 err_bnds_norm_dim1 = *nrhs; 00375 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00376 err_bnds_norm__ -= err_bnds_norm_offset; 00377 a_dim1 = *lda; 00378 a_offset = 1 + a_dim1; 00379 a -= a_offset; 00380 af_dim1 = *ldaf; 00381 af_offset = 1 + af_dim1; 00382 af -= af_offset; 00383 --ipiv; 00384 --s; 00385 b_dim1 = *ldb; 00386 b_offset = 1 + b_dim1; 00387 b -= b_offset; 00388 x_dim1 = *ldx; 00389 x_offset = 1 + x_dim1; 00390 x -= x_offset; 00391 --berr; 00392 --params; 00393 --work; 00394 --iwork; 00395 00396 /* Function Body */ 00397 *info = 0; 00398 ref_type__ = 1; 00399 if (*nparams >= 1) { 00400 if (params[1] < 0.) { 00401 params[1] = 1.; 00402 } else { 00403 ref_type__ = (integer) params[1]; 00404 } 00405 } 00406 00407 /* Set default parameters. */ 00408 00409 illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon"); 00410 ithresh = 10; 00411 rthresh = .5; 00412 unstable_thresh__ = .25; 00413 ignore_cwise__ = FALSE_; 00414 00415 if (*nparams >= 2) { 00416 if (params[2] < 0.) { 00417 params[2] = (doublereal) ithresh; 00418 } else { 00419 ithresh = (integer) params[2]; 00420 } 00421 } 00422 if (*nparams >= 3) { 00423 if (params[3] < 0.) { 00424 if (ignore_cwise__) { 00425 params[3] = 0.; 00426 } else { 00427 params[3] = 1.; 00428 } 00429 } else { 00430 ignore_cwise__ = params[3] == 0.; 00431 } 00432 } 00433 if (ref_type__ == 0 || *n_err_bnds__ == 0) { 00434 n_norms__ = 0; 00435 } else if (ignore_cwise__) { 00436 n_norms__ = 1; 00437 } else { 00438 n_norms__ = 2; 00439 } 00440 00441 rcequ = lsame_(equed, "Y"); 00442 00443 /* Test input parameters. */ 00444 00445 if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { 00446 *info = -1; 00447 } else if (! rcequ && ! lsame_(equed, "N")) { 00448 *info = -2; 00449 } else if (*n < 0) { 00450 *info = -3; 00451 } else if (*nrhs < 0) { 00452 *info = -4; 00453 } else if (*lda < max(1,*n)) { 00454 *info = -6; 00455 } else if (*ldaf < max(1,*n)) { 00456 *info = -8; 00457 } else if (*ldb < max(1,*n)) { 00458 *info = -11; 00459 } else if (*ldx < max(1,*n)) { 00460 *info = -13; 00461 } 00462 if (*info != 0) { 00463 i__1 = -(*info); 00464 xerbla_("DSYRFSX", &i__1); 00465 return 0; 00466 } 00467 00468 /* Quick return if possible. */ 00469 00470 if (*n == 0 || *nrhs == 0) { 00471 *rcond = 1.; 00472 i__1 = *nrhs; 00473 for (j = 1; j <= i__1; ++j) { 00474 berr[j] = 0.; 00475 if (*n_err_bnds__ >= 1) { 00476 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; 00477 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; 00478 } else if (*n_err_bnds__ >= 2) { 00479 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.; 00480 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.; 00481 } else if (*n_err_bnds__ >= 3) { 00482 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.; 00483 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.; 00484 } 00485 } 00486 return 0; 00487 } 00488 00489 /* Default to failure. */ 00490 00491 *rcond = 0.; 00492 i__1 = *nrhs; 00493 for (j = 1; j <= i__1; ++j) { 00494 berr[j] = 1.; 00495 if (*n_err_bnds__ >= 1) { 00496 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; 00497 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; 00498 } else if (*n_err_bnds__ >= 2) { 00499 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; 00500 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; 00501 } else if (*n_err_bnds__ >= 3) { 00502 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.; 00503 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.; 00504 } 00505 } 00506 00507 /* Compute the norm of A and the reciprocal of the condition */ 00508 /* number of A. */ 00509 00510 *(unsigned char *)norm = 'I'; 00511 anorm = dlansy_(norm, uplo, n, &a[a_offset], lda, &work[1]); 00512 dsycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], 00513 &iwork[1], info); 00514 00515 /* Perform refinement on each right-hand side */ 00516 00517 if (ref_type__ != 0) { 00518 prec_type__ = ilaprec_("E"); 00519 dla_syrfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, 00520 &af[af_offset], ldaf, &ipiv[1], &rcequ, &s[1], &b[b_offset], 00521 ldb, &x[x_offset], ldx, &berr[1], &n_norms__, & 00522 err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[ 00523 err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n << 00524 1) + 1], &work[1], rcond, &ithresh, &rthresh, & 00525 unstable_thresh__, &ignore_cwise__, info, (ftnlen)1); 00526 } 00527 /* Computing MAX */ 00528 d__1 = 10., d__2 = sqrt((doublereal) (*n)); 00529 err_lbnd__ = max(d__1,d__2) * dlamch_("Epsilon"); 00530 if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { 00531 00532 /* Compute scaled normwise condition number cond(A*C). */ 00533 00534 if (rcequ) { 00535 rcond_tmp__ = dla_syrcond__(uplo, n, &a[a_offset], lda, &af[ 00536 af_offset], ldaf, &ipiv[1], &c_n1, &s[1], info, &work[1], 00537 &iwork[1], (ftnlen)1); 00538 } else { 00539 rcond_tmp__ = dla_syrcond__(uplo, n, &a[a_offset], lda, &af[ 00540 af_offset], ldaf, &ipiv[1], &c__0, &s[1], info, &work[1], 00541 &iwork[1], (ftnlen)1); 00542 } 00543 i__1 = *nrhs; 00544 for (j = 1; j <= i__1; ++j) { 00545 00546 /* Cap the error at 1.0. */ 00547 00548 if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 00549 << 1)] > 1.) { 00550 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; 00551 } 00552 00553 /* Threshold the error (see LAWN). */ 00554 00555 if (rcond_tmp__ < illrcond_thresh__) { 00556 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; 00557 err_bnds_norm__[j + err_bnds_norm_dim1] = 0.; 00558 if (*info <= *n) { 00559 *info = *n + j; 00560 } 00561 } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 00562 err_lbnd__) { 00563 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; 00564 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; 00565 } 00566 00567 /* Save the condition number. */ 00568 00569 if (*n_err_bnds__ >= 3) { 00570 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; 00571 } 00572 } 00573 } 00574 if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { 00575 00576 /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ 00577 /* each right-hand side using the current solution as an estimate of */ 00578 /* the true solution. If the componentwise error estimate is too */ 00579 /* large, then the solution is a lousy estimate of truth and the */ 00580 /* estimated RCOND may be too optimistic. To avoid misleading users, */ 00581 /* the inverse condition number is set to 0.0 when the estimated */ 00582 /* cwise error is at least CWISE_WRONG. */ 00583 00584 cwise_wrong__ = sqrt(dlamch_("Epsilon")); 00585 i__1 = *nrhs; 00586 for (j = 1; j <= i__1; ++j) { 00587 if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00588 cwise_wrong__) { 00589 rcond_tmp__ = dla_syrcond__(uplo, n, &a[a_offset], lda, &af[ 00590 af_offset], ldaf, &ipiv[1], &c__1, &x[j * x_dim1 + 1], 00591 info, &work[1], &iwork[1], (ftnlen)1); 00592 } else { 00593 rcond_tmp__ = 0.; 00594 } 00595 00596 /* Cap the error at 1.0. */ 00597 00598 if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 00599 << 1)] > 1.) { 00600 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; 00601 } 00602 00603 /* Threshold the error (see LAWN). */ 00604 00605 if (rcond_tmp__ < illrcond_thresh__) { 00606 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; 00607 err_bnds_comp__[j + err_bnds_comp_dim1] = 0.; 00608 if (params[3] == 1. && *info < *n + j) { 00609 *info = *n + j; 00610 } 00611 } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00612 err_lbnd__) { 00613 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; 00614 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; 00615 } 00616 00617 /* Save the condition number. */ 00618 00619 if (*n_err_bnds__ >= 3) { 00620 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; 00621 } 00622 } 00623 } 00624 00625 return 0; 00626 00627 /* End of DSYRFSX */ 00628 00629 } /* dsyrfsx_ */