00001 /* sla_gerfsx_extended.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__1 = 1; 00019 static real c_b6 = -1.f; 00020 static real c_b8 = 1.f; 00021 00022 /* Subroutine */ int sla_gerfsx_extended__(integer *prec_type__, integer * 00023 trans_type__, integer *n, integer *nrhs, real *a, integer *lda, real * 00024 af, integer *ldaf, integer *ipiv, logical *colequ, real *c__, real *b, 00025 integer *ldb, real *y, integer *ldy, real *berr_out__, integer * 00026 n_norms__, real *err_bnds_norm__, real *err_bnds_comp__, real *res, 00027 real *ayb, real *dy, real *y_tail__, real *rcond, integer *ithresh, 00028 real *rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info) 00029 { 00030 /* System generated locals */ 00031 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, 00032 y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00033 err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3; 00034 real r__1, r__2; 00035 char ch__1[1]; 00036 00037 /* Local variables */ 00038 real dxratmax, dzratmax; 00039 integer i__, j; 00040 extern /* Subroutine */ int sla_geamv__(integer *, integer *, integer *, 00041 real *, real *, integer *, real *, integer *, real *, real *, 00042 integer *); 00043 logical incr_prec__; 00044 real prev_dz_z__, yk, final_dx_x__, final_dz_z__; 00045 extern /* Subroutine */ int sla_wwaddw__(integer *, real *, real *, real * 00046 ); 00047 real prevnormdx; 00048 integer cnt; 00049 real dyk, eps, incr_thresh__, dx_x__, dz_z__, ymin; 00050 extern /* Subroutine */ int sla_lin_berr__(integer *, integer *, integer * 00051 , real *, real *, real *), blas_sgemv_x__(integer *, integer *, 00052 integer *, real *, real *, integer *, real *, integer *, real *, 00053 real *, integer *, integer *); 00054 integer y_prec_state__; 00055 extern /* Subroutine */ int blas_sgemv2_x__(integer *, integer *, integer 00056 *, real *, real *, integer *, real *, real *, integer *, real *, 00057 real *, integer *, integer *), sgemv_(char *, integer *, integer * 00058 , real *, real *, integer *, real *, integer *, real *, real *, 00059 integer *); 00060 real dxrat, dzrat; 00061 char trans[1]; 00062 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 00063 integer *); 00064 real normx, normy; 00065 extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 00066 real *, integer *); 00067 extern doublereal slamch_(char *); 00068 real normdx; 00069 extern /* Subroutine */ int sgetrs_(char *, integer *, integer *, real *, 00070 integer *, integer *, real *, integer *, integer *); 00071 extern /* Character */ VOID chla_transtype__(char *, ftnlen, integer *); 00072 real hugeval; 00073 integer x_state__, z_state__; 00074 00075 00076 /* -- LAPACK routine (version 3.2.1) -- */ 00077 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00078 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00079 /* -- April 2009 -- */ 00080 00081 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00082 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00083 00084 /* .. */ 00085 /* .. Scalar Arguments .. */ 00086 /* .. */ 00087 /* .. Array Arguments .. */ 00088 /* .. */ 00089 00090 /* Purpose */ 00091 /* ======= */ 00092 00093 /* SLA_GERFSX_EXTENDED improves the computed solution to a system of */ 00094 /* linear equations by performing extra-precise iterative refinement */ 00095 /* and provides error bounds and backward error estimates for the solution. */ 00096 /* This subroutine is called by SGERFSX to perform iterative refinement. */ 00097 /* In addition to normwise error bound, the code provides maximum */ 00098 /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ 00099 /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ 00100 /* subroutine is only resonsible for setting the second fields of */ 00101 /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ 00102 00103 /* Arguments */ 00104 /* ========= */ 00105 00106 /* PREC_TYPE (input) INTEGER */ 00107 /* Specifies the intermediate precision to be used in refinement. */ 00108 /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ 00109 /* P = 'S': Single */ 00110 /* = 'D': Double */ 00111 /* = 'I': Indigenous */ 00112 /* = 'X', 'E': Extra */ 00113 00114 /* TRANS_TYPE (input) INTEGER */ 00115 /* Specifies the transposition operation on A. */ 00116 /* The value is defined by ILATRANS(T) where T is a CHARACTER and */ 00117 /* T = 'N': No transpose */ 00118 /* = 'T': Transpose */ 00119 /* = 'C': Conjugate transpose */ 00120 00121 /* N (input) INTEGER */ 00122 /* The number of linear equations, i.e., the order of the */ 00123 /* matrix A. N >= 0. */ 00124 00125 /* NRHS (input) INTEGER */ 00126 /* The number of right-hand-sides, i.e., the number of columns of the */ 00127 /* matrix B. */ 00128 00129 /* A (input) REAL array, dimension (LDA,N) */ 00130 /* On entry, the N-by-N matrix A. */ 00131 00132 /* LDA (input) INTEGER */ 00133 /* The leading dimension of the array A. LDA >= max(1,N). */ 00134 00135 /* AF (input) REAL array, dimension (LDAF,N) */ 00136 /* The factors L and U from the factorization */ 00137 /* A = P*L*U as computed by SGETRF. */ 00138 00139 /* LDAF (input) INTEGER */ 00140 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00141 00142 /* IPIV (input) INTEGER array, dimension (N) */ 00143 /* The pivot indices from the factorization A = P*L*U */ 00144 /* as computed by SGETRF; row i of the matrix was interchanged */ 00145 /* with row IPIV(i). */ 00146 00147 /* COLEQU (input) LOGICAL */ 00148 /* If .TRUE. then column equilibration was done to A before calling */ 00149 /* this routine. This is needed to compute the solution and error */ 00150 /* bounds correctly. */ 00151 00152 /* C (input) REAL array, dimension (N) */ 00153 /* The column scale factors for A. If COLEQU = .FALSE., C */ 00154 /* is not accessed. If C is input, each element of C should be a power */ 00155 /* of the radix to ensure a reliable solution and error estimates. */ 00156 /* Scaling by powers of the radix does not cause rounding errors unless */ 00157 /* the result underflows or overflows. Rounding errors during scaling */ 00158 /* lead to refining with a matrix that is not equivalent to the */ 00159 /* input matrix, producing error estimates that may not be */ 00160 /* reliable. */ 00161 00162 /* B (input) REAL 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 /* Y (input/output) REAL array, dimension (LDY,NRHS) */ 00169 /* On entry, the solution matrix X, as computed by SGETRS. */ 00170 /* On exit, the improved solution matrix Y. */ 00171 00172 /* LDY (input) INTEGER */ 00173 /* The leading dimension of the array Y. LDY >= max(1,N). */ 00174 00175 /* BERR_OUT (output) REAL array, dimension (NRHS) */ 00176 /* On exit, BERR_OUT(j) contains the componentwise relative backward */ 00177 /* error for right-hand-side j from the formula */ 00178 /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00179 /* where abs(Z) is the componentwise absolute value of the matrix */ 00180 /* or vector Z. This is computed by SLA_LIN_BERR. */ 00181 00182 /* N_NORMS (input) INTEGER */ 00183 /* Determines which error bounds to return (see ERR_BNDS_NORM */ 00184 /* and ERR_BNDS_COMP). */ 00185 /* If N_NORMS >= 1 return normwise error bounds. */ 00186 /* If N_NORMS >= 2 return componentwise error bounds. */ 00187 00188 /* ERR_BNDS_NORM (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00189 /* For each right-hand side, this array contains information about */ 00190 /* various error bounds and condition numbers corresponding to the */ 00191 /* normwise relative error, which is defined as follows: */ 00192 00193 /* Normwise relative error in the ith solution vector: */ 00194 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00195 /* ------------------------------ */ 00196 /* max_j abs(X(j,i)) */ 00197 00198 /* The array is indexed by the type of error information as described */ 00199 /* below. There currently are up to three pieces of information */ 00200 /* returned. */ 00201 00202 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00203 /* right-hand side. */ 00204 00205 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00206 /* three fields: */ 00207 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00208 /* reciprocal condition number is less than the threshold */ 00209 /* sqrt(n) * slamch('Epsilon'). */ 00210 00211 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00212 /* almost certainly within a factor of 10 of the true error */ 00213 /* so long as the next entry is greater than the threshold */ 00214 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00215 /* be trusted if the previous boolean is true. */ 00216 00217 /* err = 3 Reciprocal condition number: Estimated normwise */ 00218 /* reciprocal condition number. Compared with the threshold */ 00219 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00220 /* estimate is "guaranteed". These reciprocal condition */ 00221 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00222 /* appropriately scaled matrix Z. */ 00223 /* Let Z = S*A, where S scales each row by a power of the */ 00224 /* radix so all absolute row sums of Z are approximately 1. */ 00225 00226 /* This subroutine is only responsible for setting the second field */ 00227 /* above. */ 00228 /* See Lapack Working Note 165 for further details and extra */ 00229 /* cautions. */ 00230 00231 /* ERR_BNDS_COMP (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00232 /* For each right-hand side, this array contains information about */ 00233 /* various error bounds and condition numbers corresponding to the */ 00234 /* componentwise relative error, which is defined as follows: */ 00235 00236 /* Componentwise relative error in the ith solution vector: */ 00237 /* abs(XTRUE(j,i) - X(j,i)) */ 00238 /* max_j ---------------------- */ 00239 /* abs(X(j,i)) */ 00240 00241 /* The array is indexed by the right-hand side i (on which the */ 00242 /* componentwise relative error depends), and the type of error */ 00243 /* information as described below. There currently are up to three */ 00244 /* pieces of information returned for each right-hand side. If */ 00245 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00246 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00247 /* the first (:,N_ERR_BNDS) entries are returned. */ 00248 00249 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00250 /* right-hand side. */ 00251 00252 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00253 /* three fields: */ 00254 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00255 /* reciprocal condition number is less than the threshold */ 00256 /* sqrt(n) * slamch('Epsilon'). */ 00257 00258 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00259 /* almost certainly within a factor of 10 of the true error */ 00260 /* so long as the next entry is greater than the threshold */ 00261 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00262 /* be trusted if the previous boolean is true. */ 00263 00264 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00265 /* reciprocal condition number. Compared with the threshold */ 00266 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00267 /* estimate is "guaranteed". These reciprocal condition */ 00268 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00269 /* appropriately scaled matrix Z. */ 00270 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00271 /* current right-hand side and S scales each row of */ 00272 /* A*diag(x) by a power of the radix so all absolute row */ 00273 /* sums of Z are approximately 1. */ 00274 00275 /* This subroutine is only responsible for setting the second field */ 00276 /* above. */ 00277 /* See Lapack Working Note 165 for further details and extra */ 00278 /* cautions. */ 00279 00280 /* RES (input) REAL array, dimension (N) */ 00281 /* Workspace to hold the intermediate residual. */ 00282 00283 /* AYB (input) REAL array, dimension (N) */ 00284 /* Workspace. This can be the same workspace passed for Y_TAIL. */ 00285 00286 /* DY (input) REAL array, dimension (N) */ 00287 /* Workspace to hold the intermediate solution. */ 00288 00289 /* Y_TAIL (input) REAL array, dimension (N) */ 00290 /* Workspace to hold the trailing bits of the intermediate solution. */ 00291 00292 /* RCOND (input) REAL */ 00293 /* Reciprocal scaled condition number. This is an estimate of the */ 00294 /* reciprocal Skeel condition number of the matrix A after */ 00295 /* equilibration (if done). If this is less than the machine */ 00296 /* precision (in particular, if it is zero), the matrix is singular */ 00297 /* to working precision. Note that the error may still be small even */ 00298 /* if this number is very small and the matrix appears ill- */ 00299 /* conditioned. */ 00300 00301 /* ITHRESH (input) INTEGER */ 00302 /* The maximum number of residual computations allowed for */ 00303 /* refinement. The default is 10. For 'aggressive' set to 100 to */ 00304 /* permit convergence using approximate factorizations or */ 00305 /* factorizations other than LU. If the factorization uses a */ 00306 /* technique other than Gaussian elimination, the guarantees in */ 00307 /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ 00308 00309 /* RTHRESH (input) REAL */ 00310 /* Determines when to stop refinement if the error estimate stops */ 00311 /* decreasing. Refinement will stop when the next solution no longer */ 00312 /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ 00313 /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ 00314 /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ 00315 /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ 00316 /* for more details. */ 00317 00318 /* DZ_UB (input) REAL */ 00319 /* Determines when to start considering componentwise convergence. */ 00320 /* Componentwise convergence is only considered after each component */ 00321 /* of the solution Y is stable, which we definte as the relative */ 00322 /* change in each component being less than DZ_UB. The default value */ 00323 /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ 00324 /* more details. */ 00325 00326 /* IGNORE_CWISE (input) LOGICAL */ 00327 /* If .TRUE. then ignore componentwise convergence. Default value */ 00328 /* is .FALSE.. */ 00329 00330 /* INFO (output) INTEGER */ 00331 /* = 0: Successful exit. */ 00332 /* < 0: if INFO = -i, the ith argument to SGETRS had an illegal */ 00333 /* value */ 00334 00335 /* ===================================================================== */ 00336 00337 /* .. Local Scalars .. */ 00338 /* .. */ 00339 /* .. Parameters .. */ 00340 /* .. */ 00341 /* .. External Subroutines .. */ 00342 /* .. */ 00343 /* .. Intrinsic Functions .. */ 00344 /* .. */ 00345 /* .. Executable Statements .. */ 00346 00347 /* Parameter adjustments */ 00348 err_bnds_comp_dim1 = *nrhs; 00349 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00350 err_bnds_comp__ -= err_bnds_comp_offset; 00351 err_bnds_norm_dim1 = *nrhs; 00352 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00353 err_bnds_norm__ -= err_bnds_norm_offset; 00354 a_dim1 = *lda; 00355 a_offset = 1 + a_dim1; 00356 a -= a_offset; 00357 af_dim1 = *ldaf; 00358 af_offset = 1 + af_dim1; 00359 af -= af_offset; 00360 --ipiv; 00361 --c__; 00362 b_dim1 = *ldb; 00363 b_offset = 1 + b_dim1; 00364 b -= b_offset; 00365 y_dim1 = *ldy; 00366 y_offset = 1 + y_dim1; 00367 y -= y_offset; 00368 --berr_out__; 00369 --res; 00370 --ayb; 00371 --dy; 00372 --y_tail__; 00373 00374 /* Function Body */ 00375 if (*info != 0) { 00376 return 0; 00377 } 00378 chla_transtype__(ch__1, (ftnlen)1, trans_type__); 00379 *(unsigned char *)trans = *(unsigned char *)&ch__1[0]; 00380 eps = slamch_("Epsilon"); 00381 hugeval = slamch_("Overflow"); 00382 /* Force HUGEVAL to Inf */ 00383 hugeval *= hugeval; 00384 /* Using HUGEVAL may lead to spurious underflows. */ 00385 incr_thresh__ = (real) (*n) * eps; 00386 00387 i__1 = *nrhs; 00388 for (j = 1; j <= i__1; ++j) { 00389 y_prec_state__ = 1; 00390 if (y_prec_state__ == 2) { 00391 i__2 = *n; 00392 for (i__ = 1; i__ <= i__2; ++i__) { 00393 y_tail__[i__] = 0.f; 00394 } 00395 } 00396 dxrat = 0.f; 00397 dxratmax = 0.f; 00398 dzrat = 0.f; 00399 dzratmax = 0.f; 00400 final_dx_x__ = hugeval; 00401 final_dz_z__ = hugeval; 00402 prevnormdx = hugeval; 00403 prev_dz_z__ = hugeval; 00404 dz_z__ = hugeval; 00405 dx_x__ = hugeval; 00406 x_state__ = 1; 00407 z_state__ = 0; 00408 incr_prec__ = FALSE_; 00409 i__2 = *ithresh; 00410 for (cnt = 1; cnt <= i__2; ++cnt) { 00411 00412 /* Compute residual RES = B_s - op(A_s) * Y, */ 00413 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00414 00415 scopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00416 if (y_prec_state__ == 0) { 00417 sgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 00418 1], &c__1, &c_b8, &res[1], &c__1); 00419 } else if (y_prec_state__ == 1) { 00420 blas_sgemv_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, & 00421 y[j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1, 00422 prec_type__); 00423 } else { 00424 blas_sgemv2_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, 00425 &y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b8, &res[ 00426 1], &c__1, prec_type__); 00427 } 00428 /* XXX: RES is no longer needed. */ 00429 scopy_(n, &res[1], &c__1, &dy[1], &c__1); 00430 sgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &dy[1], 00431 n, info); 00432 00433 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00434 00435 normx = 0.f; 00436 normy = 0.f; 00437 normdx = 0.f; 00438 dz_z__ = 0.f; 00439 ymin = hugeval; 00440 00441 i__3 = *n; 00442 for (i__ = 1; i__ <= i__3; ++i__) { 00443 yk = (r__1 = y[i__ + j * y_dim1], dabs(r__1)); 00444 dyk = (r__1 = dy[i__], dabs(r__1)); 00445 if (yk != 0.f) { 00446 /* Computing MAX */ 00447 r__1 = dz_z__, r__2 = dyk / yk; 00448 dz_z__ = dmax(r__1,r__2); 00449 } else if (dyk != 0.f) { 00450 dz_z__ = hugeval; 00451 } 00452 ymin = dmin(ymin,yk); 00453 normy = dmax(normy,yk); 00454 if (*colequ) { 00455 /* Computing MAX */ 00456 r__1 = normx, r__2 = yk * c__[i__]; 00457 normx = dmax(r__1,r__2); 00458 /* Computing MAX */ 00459 r__1 = normdx, r__2 = dyk * c__[i__]; 00460 normdx = dmax(r__1,r__2); 00461 } else { 00462 normx = normy; 00463 normdx = dmax(normdx,dyk); 00464 } 00465 } 00466 if (normx != 0.f) { 00467 dx_x__ = normdx / normx; 00468 } else if (normdx == 0.f) { 00469 dx_x__ = 0.f; 00470 } else { 00471 dx_x__ = hugeval; 00472 } 00473 dxrat = normdx / prevnormdx; 00474 dzrat = dz_z__ / prev_dz_z__; 00475 00476 /* Check termination criteria */ 00477 00478 if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy 00479 && y_prec_state__ < 2) { 00480 incr_prec__ = TRUE_; 00481 } 00482 if (x_state__ == 3 && dxrat <= *rthresh) { 00483 x_state__ = 1; 00484 } 00485 if (x_state__ == 1) { 00486 if (dx_x__ <= eps) { 00487 x_state__ = 2; 00488 } else if (dxrat > *rthresh) { 00489 if (y_prec_state__ != 2) { 00490 incr_prec__ = TRUE_; 00491 } else { 00492 x_state__ = 3; 00493 } 00494 } else { 00495 if (dxrat > dxratmax) { 00496 dxratmax = dxrat; 00497 } 00498 } 00499 if (x_state__ > 1) { 00500 final_dx_x__ = dx_x__; 00501 } 00502 } 00503 if (z_state__ == 0 && dz_z__ <= *dz_ub__) { 00504 z_state__ = 1; 00505 } 00506 if (z_state__ == 3 && dzrat <= *rthresh) { 00507 z_state__ = 1; 00508 } 00509 if (z_state__ == 1) { 00510 if (dz_z__ <= eps) { 00511 z_state__ = 2; 00512 } else if (dz_z__ > *dz_ub__) { 00513 z_state__ = 0; 00514 dzratmax = 0.f; 00515 final_dz_z__ = hugeval; 00516 } else if (dzrat > *rthresh) { 00517 if (y_prec_state__ != 2) { 00518 incr_prec__ = TRUE_; 00519 } else { 00520 z_state__ = 3; 00521 } 00522 } else { 00523 if (dzrat > dzratmax) { 00524 dzratmax = dzrat; 00525 } 00526 } 00527 if (z_state__ > 1) { 00528 final_dz_z__ = dz_z__; 00529 } 00530 } 00531 00532 /* Exit if both normwise and componentwise stopped working, */ 00533 /* but if componentwise is unstable, let it go at least two */ 00534 /* iterations. */ 00535 00536 if (x_state__ != 1) { 00537 if (*ignore_cwise__) { 00538 goto L666; 00539 } 00540 if (z_state__ == 3 || z_state__ == 2) { 00541 goto L666; 00542 } 00543 if (z_state__ == 0 && cnt > 1) { 00544 goto L666; 00545 } 00546 } 00547 if (incr_prec__) { 00548 incr_prec__ = FALSE_; 00549 ++y_prec_state__; 00550 i__3 = *n; 00551 for (i__ = 1; i__ <= i__3; ++i__) { 00552 y_tail__[i__] = 0.f; 00553 } 00554 } 00555 prevnormdx = normdx; 00556 prev_dz_z__ = dz_z__; 00557 00558 /* Update soluton. */ 00559 00560 if (y_prec_state__ < 2) { 00561 saxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00562 } else { 00563 sla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00564 } 00565 } 00566 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00567 L666: 00568 00569 /* Set final_* when cnt hits ithresh. */ 00570 00571 if (x_state__ == 1) { 00572 final_dx_x__ = dx_x__; 00573 } 00574 if (z_state__ == 1) { 00575 final_dz_z__ = dz_z__; 00576 } 00577 00578 /* Compute error bounds */ 00579 00580 if (*n_norms__ >= 1) { 00581 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 00582 1 - dxratmax); 00583 } 00584 if (*n_norms__ >= 2) { 00585 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 00586 1 - dzratmax); 00587 } 00588 00589 /* Compute componentwise relative backward error from formula */ 00590 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00591 /* where abs(Z) is the componentwise absolute value of the matrix */ 00592 /* or vector Z. */ 00593 00594 /* Compute residual RES = B_s - op(A_s) * Y, */ 00595 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00596 00597 scopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00598 sgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 1], & 00599 c__1, &c_b8, &res[1], &c__1); 00600 i__2 = *n; 00601 for (i__ = 1; i__ <= i__2; ++i__) { 00602 ayb[i__] = (r__1 = b[i__ + j * b_dim1], dabs(r__1)); 00603 } 00604 00605 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00606 00607 sla_geamv__(trans_type__, n, n, &c_b8, &a[a_offset], lda, &y[j * 00608 y_dim1 + 1], &c__1, &c_b8, &ayb[1], &c__1); 00609 sla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00610 00611 /* End of loop for each RHS. */ 00612 00613 } 00614 00615 return 0; 00616 } /* sla_gerfsx_extended__ */