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