00001 /* sgbrfsx.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 sgbrfsx_(char *trans, char *equed, integer *n, integer * 00023 kl, integer *ku, integer *nrhs, real *ab, integer *ldab, real *afb, 00024 integer *ldafb, integer *ipiv, real *r__, real *c__, real *b, integer 00025 *ldb, real *x, integer *ldx, real *rcond, real *berr, integer * 00026 n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, integer * 00027 nparams, real *params, real *work, integer *iwork, integer *info) 00028 { 00029 /* System generated locals */ 00030 integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 00031 x_dim1, 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__; 00041 extern integer ilatrans_(char *); 00042 integer j; 00043 real rcond_tmp__; 00044 integer prec_type__, trans_type__; 00045 extern doublereal sla_gbrcond__(char *, integer *, integer *, integer *, 00046 real *, integer *, real *, integer *, integer *, integer *, real * 00047 , integer *, real *, integer *, ftnlen); 00048 real cwise_wrong__; 00049 extern /* Subroutine */ int sla_gbrfsx_extended__(integer *, integer *, 00050 integer *, integer *, integer *, integer *, real *, integer *, 00051 real *, integer *, integer *, logical *, real *, real *, integer * 00052 , real *, integer *, real *, integer *, real *, real *, real *, 00053 real *, real *, real *, real *, integer *, real *, real *, 00054 logical *, integer *); 00055 char norm[1]; 00056 logical ignore_cwise__; 00057 extern logical lsame_(char *, char *); 00058 real anorm; 00059 extern doublereal slangb_(char *, integer *, integer *, integer *, real *, 00060 integer *, real *), slamch_(char *); 00061 extern /* Subroutine */ int sgbcon_(char *, integer *, integer *, integer 00062 *, real *, integer *, integer *, real *, real *, real *, integer * 00063 , integer *), xerbla_(char *, integer *); 00064 logical colequ, notran, rowequ; 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 /* SGBRFSX improves the computed solution to a system of linear */ 00088 /* equations and provides error bounds and backward error estimates */ 00089 /* for the solution. In addition to normwise error bound, the code */ 00090 /* provides maximum componentwise error bound if possible. See */ 00091 /* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */ 00092 /* error bounds. */ 00093 00094 /* The original system of linear equations may have been equilibrated */ 00095 /* before calling this routine, as described by arguments EQUED, R */ 00096 /* and C below. In this case, the solution and error bounds returned */ 00097 /* are 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 /* TRANS (input) CHARACTER*1 */ 00109 /* Specifies the form of the system of equations: */ 00110 /* = 'N': A * X = B (No transpose) */ 00111 /* = 'T': A**T * X = B (Transpose) */ 00112 /* = 'C': A**H * X = B (Conjugate transpose = Transpose) */ 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 /* = 'R': Row equilibration, i.e., A has been premultiplied by */ 00120 /* diag(R). */ 00121 /* = 'C': Column equilibration, i.e., A has been postmultiplied */ 00122 /* by diag(C). */ 00123 /* = 'B': Both row and column equilibration, i.e., A has been */ 00124 /* replaced by diag(R) * A * diag(C). */ 00125 /* The right hand side B has been changed accordingly. */ 00126 00127 /* N (input) INTEGER */ 00128 /* The order of the matrix A. N >= 0. */ 00129 00130 /* KL (input) INTEGER */ 00131 /* The number of subdiagonals within the band of A. KL >= 0. */ 00132 00133 /* KU (input) INTEGER */ 00134 /* The number of superdiagonals within the band of A. KU >= 0. */ 00135 00136 /* NRHS (input) INTEGER */ 00137 /* The number of right hand sides, i.e., the number of columns */ 00138 /* of the matrices B and X. NRHS >= 0. */ 00139 00140 /* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) */ 00141 /* The original band matrix A, stored in rows 1 to KL+KU+1. */ 00142 /* The j-th column of A is stored in the j-th column of the */ 00143 /* array AB as follows: */ 00144 /* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). */ 00145 00146 /* LDAB (input) INTEGER */ 00147 /* The leading dimension of the array AB. LDAB >= KL+KU+1. */ 00148 00149 /* AFB (input) DOUBLE PRECISION array, dimension (LDAFB,N) */ 00150 /* Details of the LU factorization of the band matrix A, as */ 00151 /* computed by DGBTRF. U is stored as an upper triangular band */ 00152 /* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */ 00153 /* the multipliers used during the factorization are stored in */ 00154 /* rows KL+KU+2 to 2*KL+KU+1. */ 00155 00156 /* LDAFB (input) INTEGER */ 00157 /* The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. */ 00158 00159 /* IPIV (input) INTEGER array, dimension (N) */ 00160 /* The pivot indices from SGETRF; for 1<=i<=N, row i of the */ 00161 /* matrix was interchanged with row IPIV(i). */ 00162 00163 /* R (input or output) REAL array, dimension (N) */ 00164 /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ 00165 /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ 00166 /* is not accessed. R is an input argument if FACT = 'F'; */ 00167 /* otherwise, R is an output argument. If FACT = 'F' and */ 00168 /* EQUED = 'R' or 'B', each element of R must be positive. */ 00169 /* If R is output, each element of R is a power of the radix. */ 00170 /* If R is input, each element of R should be a power of the radix */ 00171 /* to ensure a reliable solution and error estimates. Scaling by */ 00172 /* powers of the radix does not cause rounding errors unless the */ 00173 /* result underflows or overflows. Rounding errors during scaling */ 00174 /* lead to refining with a matrix that is not equivalent to the */ 00175 /* input matrix, producing error estimates that may not be */ 00176 /* reliable. */ 00177 00178 /* C (input or output) REAL array, dimension (N) */ 00179 /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ 00180 /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ 00181 /* is not accessed. C is an input argument if FACT = 'F'; */ 00182 /* otherwise, C is an output argument. If FACT = 'F' and */ 00183 /* EQUED = 'C' or 'B', each element of C must be positive. */ 00184 /* If C is output, each element of C is a power of the radix. */ 00185 /* If C is input, each element of C should be a power of the radix */ 00186 /* to ensure a reliable solution and error estimates. Scaling by */ 00187 /* powers of the radix does not cause rounding errors unless the */ 00188 /* result underflows or overflows. Rounding errors during scaling */ 00189 /* lead to refining with a matrix that is not equivalent to the */ 00190 /* input matrix, producing error estimates that may not be */ 00191 /* reliable. */ 00192 00193 /* B (input) REAL array, dimension (LDB,NRHS) */ 00194 /* The right hand side matrix B. */ 00195 00196 /* LDB (input) INTEGER */ 00197 /* The leading dimension of the array B. LDB >= max(1,N). */ 00198 00199 /* X (input/output) REAL array, dimension (LDX,NRHS) */ 00200 /* On entry, the solution matrix X, as computed by SGETRS. */ 00201 /* On exit, the improved solution matrix X. */ 00202 00203 /* LDX (input) INTEGER */ 00204 /* The leading dimension of the array X. LDX >= max(1,N). */ 00205 00206 /* RCOND (output) REAL */ 00207 /* Reciprocal scaled condition number. This is an estimate of the */ 00208 /* reciprocal Skeel condition number of the matrix A after */ 00209 /* equilibration (if done). If this is less than the machine */ 00210 /* precision (in particular, if it is zero), the matrix is singular */ 00211 /* to working precision. Note that the error may still be small even */ 00212 /* if this number is very small and the matrix appears ill- */ 00213 /* conditioned. */ 00214 00215 /* BERR (output) REAL array, dimension (NRHS) */ 00216 /* Componentwise relative backward error. This is the */ 00217 /* componentwise relative backward error of each solution vector X(j) */ 00218 /* (i.e., the smallest relative change in any element of A or B that */ 00219 /* makes X(j) an exact solution). */ 00220 00221 /* N_ERR_BNDS (input) INTEGER */ 00222 /* Number of error bounds to return for each right hand side */ 00223 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00224 /* ERR_BNDS_COMP below. */ 00225 00226 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00227 /* For each right-hand side, this array contains information about */ 00228 /* various error bounds and condition numbers corresponding to the */ 00229 /* normwise relative error, which is defined as follows: */ 00230 00231 /* Normwise relative error in the ith solution vector: */ 00232 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00233 /* ------------------------------ */ 00234 /* max_j abs(X(j,i)) */ 00235 00236 /* The array is indexed by the type of error information as described */ 00237 /* below. There currently are up to three pieces of information */ 00238 /* returned. */ 00239 00240 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00241 /* right-hand side. */ 00242 00243 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00244 /* three fields: */ 00245 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00246 /* reciprocal condition number is less than the threshold */ 00247 /* sqrt(n) * slamch('Epsilon'). */ 00248 00249 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00250 /* almost certainly within a factor of 10 of the true error */ 00251 /* so long as the next entry is greater than the threshold */ 00252 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00253 /* be trusted if the previous boolean is true. */ 00254 00255 /* err = 3 Reciprocal condition number: Estimated normwise */ 00256 /* reciprocal condition number. Compared with the threshold */ 00257 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00258 /* estimate is "guaranteed". These reciprocal condition */ 00259 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00260 /* appropriately scaled matrix Z. */ 00261 /* Let Z = S*A, where S scales each row by a power of the */ 00262 /* radix so all absolute row sums of Z are approximately 1. */ 00263 00264 /* See Lapack Working Note 165 for further details and extra */ 00265 /* cautions. */ 00266 00267 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00268 /* For each right-hand side, this array contains information about */ 00269 /* various error bounds and condition numbers corresponding to the */ 00270 /* componentwise relative error, which is defined as follows: */ 00271 00272 /* Componentwise relative error in the ith solution vector: */ 00273 /* abs(XTRUE(j,i) - X(j,i)) */ 00274 /* max_j ---------------------- */ 00275 /* abs(X(j,i)) */ 00276 00277 /* The array is indexed by the right-hand side i (on which the */ 00278 /* componentwise relative error depends), and the type of error */ 00279 /* information as described below. There currently are up to three */ 00280 /* pieces of information returned for each right-hand side. If */ 00281 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00282 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00283 /* the first (:,N_ERR_BNDS) entries are returned. */ 00284 00285 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00286 /* right-hand side. */ 00287 00288 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00289 /* three fields: */ 00290 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00291 /* reciprocal condition number is less than the threshold */ 00292 /* sqrt(n) * slamch('Epsilon'). */ 00293 00294 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00295 /* almost certainly within a factor of 10 of the true error */ 00296 /* so long as the next entry is greater than the threshold */ 00297 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00298 /* be trusted if the previous boolean is true. */ 00299 00300 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00301 /* reciprocal condition number. Compared with the threshold */ 00302 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00303 /* estimate is "guaranteed". These reciprocal condition */ 00304 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00305 /* appropriately scaled matrix Z. */ 00306 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00307 /* current right-hand side and S scales each row of */ 00308 /* A*diag(x) by a power of the radix so all absolute row */ 00309 /* sums of Z are approximately 1. */ 00310 00311 /* See Lapack Working Note 165 for further details and extra */ 00312 /* cautions. */ 00313 00314 /* NPARAMS (input) INTEGER */ 00315 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00316 /* PARAMS array is never referenced and default values are used. */ 00317 00318 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00319 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00320 /* that entry will be filled with default value used for that */ 00321 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00322 /* are used for higher-numbered parameters. */ 00323 00324 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00325 /* refinement or not. */ 00326 /* Default: 1.0 */ 00327 /* = 0.0 : No refinement is performed, and no error bounds are */ 00328 /* computed. */ 00329 /* = 1.0 : Use the double-precision refinement algorithm, */ 00330 /* possibly with doubled-single computations if the */ 00331 /* compilation environment does not support DOUBLE */ 00332 /* PRECISION. */ 00333 /* (other values are reserved for future use) */ 00334 00335 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00336 /* computations allowed for refinement. */ 00337 /* Default: 10 */ 00338 /* Aggressive: Set to 100 to permit convergence using approximate */ 00339 /* factorizations or factorizations other than LU. If */ 00340 /* the factorization uses a technique other than */ 00341 /* Gaussian elimination, the guarantees in */ 00342 /* err_bnds_norm and err_bnds_comp may no longer be */ 00343 /* trustworthy. */ 00344 00345 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00346 /* will attempt to find a solution with small componentwise */ 00347 /* relative error in the double-precision algorithm. Positive */ 00348 /* is true, 0.0 is false. */ 00349 /* Default: 1.0 (attempt componentwise convergence) */ 00350 00351 /* WORK (workspace) REAL array, dimension (4*N) */ 00352 00353 /* IWORK (workspace) INTEGER array, dimension (N) */ 00354 00355 /* INFO (output) INTEGER */ 00356 /* = 0: Successful exit. The solution to every right-hand side is */ 00357 /* guaranteed. */ 00358 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00359 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00360 /* has been completed, but the factor U is exactly singular, so */ 00361 /* the solution and error bounds could not be computed. RCOND = 0 */ 00362 /* is returned. */ 00363 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00364 /* not guaranteed. The solutions corresponding to other right- */ 00365 /* hand sides K with K > J may not be guaranteed as well, but */ 00366 /* only the first such right-hand side is reported. If a small */ 00367 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00368 /* the Jth right-hand side is the first with a normwise error */ 00369 /* bound that is not guaranteed (the smallest J such */ 00370 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00371 /* the Jth right-hand side is the first with either a normwise or */ 00372 /* componentwise error bound that is not guaranteed (the smallest */ 00373 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00374 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00375 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00376 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00377 /* ERR_BNDS_COMP. */ 00378 00379 /* ================================================================== */ 00380 00381 /* .. Parameters .. */ 00382 /* .. */ 00383 /* .. Local Scalars .. */ 00384 /* .. */ 00385 /* .. External Subroutines .. */ 00386 /* .. */ 00387 /* .. Intrinsic Functions .. */ 00388 /* .. */ 00389 /* .. External Functions .. */ 00390 /* .. */ 00391 /* .. Executable Statements .. */ 00392 00393 /* Check the input parameters. */ 00394 00395 /* Parameter adjustments */ 00396 err_bnds_comp_dim1 = *nrhs; 00397 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00398 err_bnds_comp__ -= err_bnds_comp_offset; 00399 err_bnds_norm_dim1 = *nrhs; 00400 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00401 err_bnds_norm__ -= err_bnds_norm_offset; 00402 ab_dim1 = *ldab; 00403 ab_offset = 1 + ab_dim1; 00404 ab -= ab_offset; 00405 afb_dim1 = *ldafb; 00406 afb_offset = 1 + afb_dim1; 00407 afb -= afb_offset; 00408 --ipiv; 00409 --r__; 00410 --c__; 00411 b_dim1 = *ldb; 00412 b_offset = 1 + b_dim1; 00413 b -= b_offset; 00414 x_dim1 = *ldx; 00415 x_offset = 1 + x_dim1; 00416 x -= x_offset; 00417 --berr; 00418 --params; 00419 --work; 00420 --iwork; 00421 00422 /* Function Body */ 00423 *info = 0; 00424 trans_type__ = ilatrans_(trans); 00425 ref_type__ = 1; 00426 if (*nparams >= 1) { 00427 if (params[1] < 0.f) { 00428 params[1] = 1.f; 00429 } else { 00430 ref_type__ = params[1]; 00431 } 00432 } 00433 00434 /* Set default parameters. */ 00435 00436 illrcond_thresh__ = (real) (*n) * slamch_("Epsilon"); 00437 ithresh = 10; 00438 rthresh = .5f; 00439 unstable_thresh__ = .25f; 00440 ignore_cwise__ = FALSE_; 00441 00442 if (*nparams >= 2) { 00443 if (params[2] < 0.f) { 00444 params[2] = (real) ithresh; 00445 } else { 00446 ithresh = (integer) params[2]; 00447 } 00448 } 00449 if (*nparams >= 3) { 00450 if (params[3] < 0.f) { 00451 if (ignore_cwise__) { 00452 params[3] = 0.f; 00453 } else { 00454 params[3] = 1.f; 00455 } 00456 } else { 00457 ignore_cwise__ = params[3] == 0.f; 00458 } 00459 } 00460 if (ref_type__ == 0 || *n_err_bnds__ == 0) { 00461 n_norms__ = 0; 00462 } else if (ignore_cwise__) { 00463 n_norms__ = 1; 00464 } else { 00465 n_norms__ = 2; 00466 } 00467 00468 notran = lsame_(trans, "N"); 00469 rowequ = lsame_(equed, "R") || lsame_(equed, "B"); 00470 colequ = lsame_(equed, "C") || lsame_(equed, "B"); 00471 00472 /* Test input parameters. */ 00473 00474 if (trans_type__ == -1) { 00475 *info = -1; 00476 } else if (! rowequ && ! colequ && ! lsame_(equed, "N")) { 00477 *info = -2; 00478 } else if (*n < 0) { 00479 *info = -3; 00480 } else if (*kl < 0) { 00481 *info = -4; 00482 } else if (*ku < 0) { 00483 *info = -5; 00484 } else if (*nrhs < 0) { 00485 *info = -6; 00486 } else if (*ldab < *kl + *ku + 1) { 00487 *info = -8; 00488 } else if (*ldafb < (*kl << 1) + *ku + 1) { 00489 *info = -10; 00490 } else if (*ldb < max(1,*n)) { 00491 *info = -13; 00492 } else if (*ldx < max(1,*n)) { 00493 *info = -15; 00494 } 00495 if (*info != 0) { 00496 i__1 = -(*info); 00497 xerbla_("SGBRFSX", &i__1); 00498 return 0; 00499 } 00500 00501 /* Quick return if possible. */ 00502 00503 if (*n == 0 || *nrhs == 0) { 00504 *rcond = 1.f; 00505 i__1 = *nrhs; 00506 for (j = 1; j <= i__1; ++j) { 00507 berr[j] = 0.f; 00508 if (*n_err_bnds__ >= 1) { 00509 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00510 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00511 } else if (*n_err_bnds__ >= 2) { 00512 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f; 00513 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f; 00514 } else if (*n_err_bnds__ >= 3) { 00515 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f; 00516 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f; 00517 } 00518 } 00519 return 0; 00520 } 00521 00522 /* Default to failure. */ 00523 00524 *rcond = 0.f; 00525 i__1 = *nrhs; 00526 for (j = 1; j <= i__1; ++j) { 00527 berr[j] = 1.f; 00528 if (*n_err_bnds__ >= 1) { 00529 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00530 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00531 } else if (*n_err_bnds__ >= 2) { 00532 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00533 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00534 } else if (*n_err_bnds__ >= 3) { 00535 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f; 00536 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f; 00537 } 00538 } 00539 00540 /* Compute the norm of A and the reciprocal of the condition */ 00541 /* number of A. */ 00542 00543 if (notran) { 00544 *(unsigned char *)norm = 'I'; 00545 } else { 00546 *(unsigned char *)norm = '1'; 00547 } 00548 anorm = slangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &work[1]); 00549 sgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond, 00550 &work[1], &iwork[1], info); 00551 00552 /* Perform refinement on each right-hand side */ 00553 00554 if (ref_type__ != 0) { 00555 prec_type__ = ilaprec_("D"); 00556 if (notran) { 00557 sla_gbrfsx_extended__(&prec_type__, &trans_type__, n, kl, ku, 00558 nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, & 00559 ipiv[1], &colequ, &c__[1], &b[b_offset], ldb, &x[x_offset] 00560 , ldx, &berr[1], &n_norms__, &err_bnds_norm__[ 00561 err_bnds_norm_offset], &err_bnds_comp__[ 00562 err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n 00563 << 1) + 1], &work[1], rcond, &ithresh, &rthresh, & 00564 unstable_thresh__, &ignore_cwise__, info); 00565 } else { 00566 sla_gbrfsx_extended__(&prec_type__, &trans_type__, n, kl, ku, 00567 nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, & 00568 ipiv[1], &rowequ, &r__[1], &b[b_offset], ldb, &x[x_offset] 00569 , ldx, &berr[1], &n_norms__, &err_bnds_norm__[ 00570 err_bnds_norm_offset], &err_bnds_comp__[ 00571 err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n 00572 << 1) + 1], &work[1], rcond, &ithresh, &rthresh, & 00573 unstable_thresh__, &ignore_cwise__, info); 00574 } 00575 } 00576 /* Computing MAX */ 00577 r__1 = 10.f, r__2 = sqrt((real) (*n)); 00578 err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon"); 00579 if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { 00580 00581 /* Compute scaled normwise condition number cond(A*C). */ 00582 00583 if (colequ && notran) { 00584 rcond_tmp__ = sla_gbrcond__(trans, n, kl, ku, &ab[ab_offset], 00585 ldab, &afb[afb_offset], ldafb, &ipiv[1], &c_n1, &c__[1], 00586 info, &work[1], &iwork[1], (ftnlen)1); 00587 } else if (rowequ && ! notran) { 00588 rcond_tmp__ = sla_gbrcond__(trans, n, kl, ku, &ab[ab_offset], 00589 ldab, &afb[afb_offset], ldafb, &ipiv[1], &c_n1, &r__[1], 00590 info, &work[1], &iwork[1], (ftnlen)1); 00591 } else { 00592 rcond_tmp__ = sla_gbrcond__(trans, n, kl, ku, &ab[ab_offset], 00593 ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__0, &r__[1], 00594 info, &work[1], &iwork[1], (ftnlen)1); 00595 } 00596 i__1 = *nrhs; 00597 for (j = 1; j <= i__1; ++j) { 00598 00599 /* Cap the error at 1.0. */ 00600 00601 if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 00602 << 1)] > 1.f) { 00603 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00604 } 00605 00606 /* Threshold the error (see LAWN). */ 00607 00608 if (rcond_tmp__ < illrcond_thresh__) { 00609 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f; 00610 err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f; 00611 if (*info <= *n) { 00612 *info = *n + j; 00613 } 00614 } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 00615 err_lbnd__) { 00616 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; 00617 err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f; 00618 } 00619 00620 /* Save the condition number. */ 00621 00622 if (*n_err_bnds__ >= 3) { 00623 err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; 00624 } 00625 } 00626 } 00627 if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { 00628 00629 /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ 00630 /* each right-hand side using the current solution as an estimate of */ 00631 /* the true solution. If the componentwise error estimate is too */ 00632 /* large, then the solution is a lousy estimate of truth and the */ 00633 /* estimated RCOND may be too optimistic. To avoid misleading users, */ 00634 /* the inverse condition number is set to 0.0 when the estimated */ 00635 /* cwise error is at least CWISE_WRONG. */ 00636 00637 cwise_wrong__ = sqrt(slamch_("Epsilon")); 00638 i__1 = *nrhs; 00639 for (j = 1; j <= i__1; ++j) { 00640 if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00641 cwise_wrong__) { 00642 rcond_tmp__ = sla_gbrcond__(trans, n, kl, ku, &ab[ab_offset], 00643 ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__1, &x[j * 00644 x_dim1 + 1], info, &work[1], &iwork[1], (ftnlen)1); 00645 } else { 00646 rcond_tmp__ = 0.f; 00647 } 00648 00649 /* Cap the error at 1.0. */ 00650 00651 if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 00652 << 1)] > 1.f) { 00653 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00654 } 00655 00656 /* Threshold the error (see LAWN). */ 00657 00658 if (rcond_tmp__ < illrcond_thresh__) { 00659 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f; 00660 err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f; 00661 if (params[3] == 1.f && *info < *n + j) { 00662 *info = *n + j; 00663 } 00664 } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 00665 err_lbnd__) { 00666 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; 00667 err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f; 00668 } 00669 00670 /* Save the condition number. */ 00671 00672 if (*n_err_bnds__ >= 3) { 00673 err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; 00674 } 00675 } 00676 } 00677 00678 return 0; 00679 00680 /* End of SGBRFSX */ 00681 00682 } /* sgbrfsx_ */