00001 /* cla_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 complex c_b6 = {-1.f,0.f}; 00020 static complex c_b8 = {1.f,0.f}; 00021 static real c_b31 = 1.f; 00022 00023 /* Subroutine */ int cla_gerfsx_extended__(integer *prec_type__, integer * 00024 trans_type__, integer *n, integer *nrhs, complex *a, integer *lda, 00025 complex *af, integer *ldaf, integer *ipiv, logical *colequ, real *c__, 00026 complex *b, integer *ldb, complex *y, integer *ldy, real *berr_out__, 00027 integer *n_norms__, real *errs_n__, real *errs_c__, complex *res, 00028 real *ayb, complex *dy, complex *y_tail__, real *rcond, integer * 00029 ithresh, real *rthresh, real *dz_ub__, logical *ignore_cwise__, 00030 integer *info) 00031 { 00032 /* System generated locals */ 00033 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, 00034 y_offset, errs_n_dim1, errs_n_offset, errs_c_dim1, errs_c_offset, 00035 i__1, i__2, i__3, i__4; 00036 real r__1, r__2; 00037 char ch__1[1]; 00038 00039 /* Builtin functions */ 00040 double r_imag(complex *); 00041 00042 /* Local variables */ 00043 real dxratmax, dzratmax; 00044 integer i__, j; 00045 extern /* Subroutine */ int cla_geamv__(integer *, integer *, integer *, 00046 real *, complex *, integer *, complex *, integer *, real *, real * 00047 , integer *); 00048 logical incr_prec__; 00049 real prev_dz_z__, yk, final_dx_x__; 00050 extern /* Subroutine */ int cla_wwaddw__(integer *, complex *, complex *, 00051 complex *); 00052 real final_dz_z__, prevnormdx; 00053 integer cnt; 00054 real dyk, eps, incr_thresh__, dx_x__, dz_z__; 00055 extern /* Subroutine */ int cla_lin_berr__(integer *, integer *, integer * 00056 , complex *, real *, real *); 00057 real ymin; 00058 extern /* Subroutine */ int blas_cgemv_x__(integer *, integer *, integer * 00059 , complex *, complex *, integer *, complex *, integer *, complex * 00060 , complex *, integer *, integer *); 00061 integer y_prec_state__; 00062 extern /* Subroutine */ int blas_cgemv2_x__(integer *, integer *, integer 00063 *, complex *, complex *, integer *, complex *, complex *, integer 00064 *, complex *, complex *, integer *, integer *), cgemv_(char *, 00065 integer *, integer *, complex *, complex *, integer *, complex *, 00066 integer *, complex *, complex *, integer *), ccopy_( 00067 integer *, complex *, integer *, complex *, integer *); 00068 real dxrat, dzrat; 00069 extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, 00070 integer *, complex *, integer *); 00071 char trans[1]; 00072 real normx, normy; 00073 extern doublereal slamch_(char *); 00074 extern /* Subroutine */ int cgetrs_(char *, integer *, integer *, complex 00075 *, integer *, integer *, complex *, integer *, integer *); 00076 real normdx; 00077 extern /* Character */ VOID chla_transtype__(char *, ftnlen, integer *); 00078 real hugeval; 00079 integer x_state__, z_state__; 00080 00081 00082 /* -- LAPACK routine (version 3.2.1) -- */ 00083 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00084 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00085 /* -- April 2009 -- */ 00086 00087 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00088 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00089 00090 /* .. */ 00091 /* .. Scalar Arguments .. */ 00092 /* .. */ 00093 /* .. Array Arguments */ 00094 /* .. */ 00095 00096 /* Purpose */ 00097 /* ======= */ 00098 00099 /* CLA_GERFSX_EXTENDED improves the computed solution to a system of */ 00100 /* linear equations by performing extra-precise iterative refinement */ 00101 /* and provides error bounds and backward error estimates for the solution. */ 00102 /* This subroutine is called by CGERFSX to perform iterative refinement. */ 00103 /* In addition to normwise error bound, the code provides maximum */ 00104 /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ 00105 /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ 00106 /* subroutine is only resonsible for setting the second fields of */ 00107 /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ 00108 00109 /* Arguments */ 00110 /* ========= */ 00111 00112 /* PREC_TYPE (input) INTEGER */ 00113 /* Specifies the intermediate precision to be used in refinement. */ 00114 /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ 00115 /* P = 'S': Single */ 00116 /* = 'D': Double */ 00117 /* = 'I': Indigenous */ 00118 /* = 'X', 'E': Extra */ 00119 00120 /* TRANS_TYPE (input) INTEGER */ 00121 /* Specifies the transposition operation on A. */ 00122 /* The value is defined by ILATRANS(T) where T is a CHARACTER and */ 00123 /* T = 'N': No transpose */ 00124 /* = 'T': Transpose */ 00125 /* = 'C': Conjugate transpose */ 00126 00127 /* N (input) INTEGER */ 00128 /* The number of linear equations, i.e., the order of the */ 00129 /* matrix A. N >= 0. */ 00130 00131 /* NRHS (input) INTEGER */ 00132 /* The number of right-hand-sides, i.e., the number of columns of the */ 00133 /* matrix B. */ 00134 00135 /* A (input) COMPLEX array, dimension (LDA,N) */ 00136 /* On entry, the N-by-N matrix A. */ 00137 00138 /* LDA (input) INTEGER */ 00139 /* The leading dimension of the array A. LDA >= max(1,N). */ 00140 00141 /* AF (input) COMPLEX array, dimension (LDAF,N) */ 00142 /* The factors L and U from the factorization */ 00143 /* A = P*L*U as computed by CGETRF. */ 00144 00145 /* LDAF (input) INTEGER */ 00146 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00147 00148 /* IPIV (input) INTEGER array, dimension (N) */ 00149 /* The pivot indices from the factorization A = P*L*U */ 00150 /* as computed by CGETRF; row i of the matrix was interchanged */ 00151 /* with row IPIV(i). */ 00152 00153 /* COLEQU (input) LOGICAL */ 00154 /* If .TRUE. then column equilibration was done to A before calling */ 00155 /* this routine. This is needed to compute the solution and error */ 00156 /* bounds correctly. */ 00157 00158 /* C (input) REAL array, dimension (N) */ 00159 /* The column scale factors for A. If COLEQU = .FALSE., C */ 00160 /* is not accessed. If C is input, each element of C should be a power */ 00161 /* of the radix to ensure a reliable solution and error estimates. */ 00162 /* Scaling by powers of the radix does not cause rounding errors unless */ 00163 /* the result underflows or overflows. Rounding errors during scaling */ 00164 /* lead to refining with a matrix that is not equivalent to the */ 00165 /* input matrix, producing error estimates that may not be */ 00166 /* reliable. */ 00167 00168 /* B (input) COMPLEX 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 /* Y (input/output) COMPLEX array, dimension (LDY,NRHS) */ 00175 /* On entry, the solution matrix X, as computed by CGETRS. */ 00176 /* On exit, the improved solution matrix Y. */ 00177 00178 /* LDY (input) INTEGER */ 00179 /* The leading dimension of the array Y. LDY >= max(1,N). */ 00180 00181 /* BERR_OUT (output) REAL array, dimension (NRHS) */ 00182 /* On exit, BERR_OUT(j) contains the componentwise relative backward */ 00183 /* error for right-hand-side j from the formula */ 00184 /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00185 /* where abs(Z) is the componentwise absolute value of the matrix */ 00186 /* or vector Z. This is computed by CLA_LIN_BERR. */ 00187 00188 /* N_NORMS (input) INTEGER */ 00189 /* Determines which error bounds to return (see ERR_BNDS_NORM */ 00190 /* and ERR_BNDS_COMP). */ 00191 /* If N_NORMS >= 1 return normwise error bounds. */ 00192 /* If N_NORMS >= 2 return componentwise error bounds. */ 00193 00194 /* ERR_BNDS_NORM (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00195 /* For each right-hand side, this array contains information about */ 00196 /* various error bounds and condition numbers corresponding to the */ 00197 /* normwise relative error, which is defined as follows: */ 00198 00199 /* Normwise relative error in the ith solution vector: */ 00200 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00201 /* ------------------------------ */ 00202 /* max_j abs(X(j,i)) */ 00203 00204 /* The array is indexed by the type of error information as described */ 00205 /* below. There currently are up to three pieces of information */ 00206 /* returned. */ 00207 00208 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00209 /* right-hand side. */ 00210 00211 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00212 /* three fields: */ 00213 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00214 /* reciprocal condition number is less than the threshold */ 00215 /* sqrt(n) * slamch('Epsilon'). */ 00216 00217 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00218 /* almost certainly within a factor of 10 of the true error */ 00219 /* so long as the next entry is greater than the threshold */ 00220 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00221 /* be trusted if the previous boolean is true. */ 00222 00223 /* err = 3 Reciprocal condition number: Estimated normwise */ 00224 /* reciprocal condition number. Compared with the threshold */ 00225 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00226 /* estimate is "guaranteed". These reciprocal condition */ 00227 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00228 /* appropriately scaled matrix Z. */ 00229 /* Let Z = S*A, where S scales each row by a power of the */ 00230 /* radix so all absolute row sums of Z are approximately 1. */ 00231 00232 /* This subroutine is only responsible for setting the second field */ 00233 /* above. */ 00234 /* See Lapack Working Note 165 for further details and extra */ 00235 /* cautions. */ 00236 00237 /* ERR_BNDS_COMP (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00238 /* For each right-hand side, this array contains information about */ 00239 /* various error bounds and condition numbers corresponding to the */ 00240 /* componentwise relative error, which is defined as follows: */ 00241 00242 /* Componentwise relative error in the ith solution vector: */ 00243 /* abs(XTRUE(j,i) - X(j,i)) */ 00244 /* max_j ---------------------- */ 00245 /* abs(X(j,i)) */ 00246 00247 /* The array is indexed by the right-hand side i (on which the */ 00248 /* componentwise relative error depends), and the type of error */ 00249 /* information as described below. There currently are up to three */ 00250 /* pieces of information returned for each right-hand side. If */ 00251 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00252 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00253 /* the first (:,N_ERR_BNDS) entries are returned. */ 00254 00255 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00256 /* right-hand side. */ 00257 00258 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00259 /* three fields: */ 00260 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00261 /* reciprocal condition number is less than the threshold */ 00262 /* sqrt(n) * slamch('Epsilon'). */ 00263 00264 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00265 /* almost certainly within a factor of 10 of the true error */ 00266 /* so long as the next entry is greater than the threshold */ 00267 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00268 /* be trusted if the previous boolean is true. */ 00269 00270 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00271 /* reciprocal condition number. Compared with the threshold */ 00272 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00273 /* estimate is "guaranteed". These reciprocal condition */ 00274 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00275 /* appropriately scaled matrix Z. */ 00276 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00277 /* current right-hand side and S scales each row of */ 00278 /* A*diag(x) by a power of the radix so all absolute row */ 00279 /* sums of Z are approximately 1. */ 00280 00281 /* This subroutine is only responsible for setting the second field */ 00282 /* above. */ 00283 /* See Lapack Working Note 165 for further details and extra */ 00284 /* cautions. */ 00285 00286 /* RES (input) COMPLEX array, dimension (N) */ 00287 /* Workspace to hold the intermediate residual. */ 00288 00289 /* AYB (input) REAL array, dimension (N) */ 00290 /* Workspace. */ 00291 00292 /* DY (input) COMPLEX array, dimension (N) */ 00293 /* Workspace to hold the intermediate solution. */ 00294 00295 /* Y_TAIL (input) COMPLEX array, dimension (N) */ 00296 /* Workspace to hold the trailing bits of the intermediate solution. */ 00297 00298 /* RCOND (input) REAL */ 00299 /* Reciprocal scaled condition number. This is an estimate of the */ 00300 /* reciprocal Skeel condition number of the matrix A after */ 00301 /* equilibration (if done). If this is less than the machine */ 00302 /* precision (in particular, if it is zero), the matrix is singular */ 00303 /* to working precision. Note that the error may still be small even */ 00304 /* if this number is very small and the matrix appears ill- */ 00305 /* conditioned. */ 00306 00307 /* ITHRESH (input) INTEGER */ 00308 /* The maximum number of residual computations allowed for */ 00309 /* refinement. The default is 10. For 'aggressive' set to 100 to */ 00310 /* permit convergence using approximate factorizations or */ 00311 /* factorizations other than LU. If the factorization uses a */ 00312 /* technique other than Gaussian elimination, the guarantees in */ 00313 /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ 00314 00315 /* RTHRESH (input) REAL */ 00316 /* Determines when to stop refinement if the error estimate stops */ 00317 /* decreasing. Refinement will stop when the next solution no longer */ 00318 /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ 00319 /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ 00320 /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ 00321 /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ 00322 /* for more details. */ 00323 00324 /* DZ_UB (input) REAL */ 00325 /* Determines when to start considering componentwise convergence. */ 00326 /* Componentwise convergence is only considered after each component */ 00327 /* of the solution Y is stable, which we definte as the relative */ 00328 /* change in each component being less than DZ_UB. The default value */ 00329 /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ 00330 /* more details. */ 00331 00332 /* IGNORE_CWISE (input) LOGICAL */ 00333 /* If .TRUE. then ignore componentwise convergence. Default value */ 00334 /* is .FALSE.. */ 00335 00336 /* INFO (output) INTEGER */ 00337 /* = 0: Successful exit. */ 00338 /* < 0: if INFO = -i, the ith argument to CGETRS had an illegal */ 00339 /* value */ 00340 00341 /* ===================================================================== */ 00342 00343 /* .. Local Scalars .. */ 00344 /* .. */ 00345 /* .. Parameters .. */ 00346 /* .. */ 00347 /* .. External Subroutines .. */ 00348 /* .. */ 00349 /* .. Intrinsic Functions .. */ 00350 /* .. */ 00351 /* .. Statement Functions .. */ 00352 /* .. */ 00353 /* .. Statement Function Definitions .. */ 00354 /* .. */ 00355 /* .. Executable Statements .. */ 00356 00357 /* Parameter adjustments */ 00358 errs_c_dim1 = *nrhs; 00359 errs_c_offset = 1 + errs_c_dim1; 00360 errs_c__ -= errs_c_offset; 00361 errs_n_dim1 = *nrhs; 00362 errs_n_offset = 1 + errs_n_dim1; 00363 errs_n__ -= errs_n_offset; 00364 a_dim1 = *lda; 00365 a_offset = 1 + a_dim1; 00366 a -= a_offset; 00367 af_dim1 = *ldaf; 00368 af_offset = 1 + af_dim1; 00369 af -= af_offset; 00370 --ipiv; 00371 --c__; 00372 b_dim1 = *ldb; 00373 b_offset = 1 + b_dim1; 00374 b -= b_offset; 00375 y_dim1 = *ldy; 00376 y_offset = 1 + y_dim1; 00377 y -= y_offset; 00378 --berr_out__; 00379 --res; 00380 --ayb; 00381 --dy; 00382 --y_tail__; 00383 00384 /* Function Body */ 00385 if (*info != 0) { 00386 return 0; 00387 } 00388 chla_transtype__(ch__1, (ftnlen)1, trans_type__); 00389 *(unsigned char *)trans = *(unsigned char *)&ch__1[0]; 00390 eps = slamch_("Epsilon"); 00391 hugeval = slamch_("Overflow"); 00392 /* Force HUGEVAL to Inf */ 00393 hugeval *= hugeval; 00394 /* Using HUGEVAL may lead to spurious underflows. */ 00395 incr_thresh__ = (real) (*n) * eps; 00396 00397 i__1 = *nrhs; 00398 for (j = 1; j <= i__1; ++j) { 00399 y_prec_state__ = 1; 00400 if (y_prec_state__ == 2) { 00401 i__2 = *n; 00402 for (i__ = 1; i__ <= i__2; ++i__) { 00403 i__3 = i__; 00404 y_tail__[i__3].r = 0.f, y_tail__[i__3].i = 0.f; 00405 } 00406 } 00407 dxrat = 0.f; 00408 dxratmax = 0.f; 00409 dzrat = 0.f; 00410 dzratmax = 0.f; 00411 final_dx_x__ = hugeval; 00412 final_dz_z__ = hugeval; 00413 prevnormdx = hugeval; 00414 prev_dz_z__ = hugeval; 00415 dz_z__ = hugeval; 00416 dx_x__ = hugeval; 00417 x_state__ = 1; 00418 z_state__ = 0; 00419 incr_prec__ = FALSE_; 00420 i__2 = *ithresh; 00421 for (cnt = 1; cnt <= i__2; ++cnt) { 00422 00423 /* Compute residual RES = B_s - op(A_s) * Y, */ 00424 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00425 00426 ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00427 if (y_prec_state__ == 0) { 00428 cgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 00429 1], &c__1, &c_b8, &res[1], &c__1); 00430 } else if (y_prec_state__ == 1) { 00431 blas_cgemv_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, & 00432 y[j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1, 00433 prec_type__); 00434 } else { 00435 blas_cgemv2_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, 00436 &y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b8, &res[ 00437 1], &c__1, prec_type__); 00438 } 00439 /* XXX: RES is no longer needed. */ 00440 ccopy_(n, &res[1], &c__1, &dy[1], &c__1); 00441 cgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &dy[1], 00442 n, info); 00443 00444 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00445 00446 normx = 0.f; 00447 normy = 0.f; 00448 normdx = 0.f; 00449 dz_z__ = 0.f; 00450 ymin = hugeval; 00451 00452 i__3 = *n; 00453 for (i__ = 1; i__ <= i__3; ++i__) { 00454 i__4 = i__ + j * y_dim1; 00455 yk = (r__1 = y[i__4].r, dabs(r__1)) + (r__2 = r_imag(&y[i__ + 00456 j * y_dim1]), dabs(r__2)); 00457 i__4 = i__; 00458 dyk = (r__1 = dy[i__4].r, dabs(r__1)) + (r__2 = r_imag(&dy[ 00459 i__]), dabs(r__2)); 00460 if (yk != 0.f) { 00461 /* Computing MAX */ 00462 r__1 = dz_z__, r__2 = dyk / yk; 00463 dz_z__ = dmax(r__1,r__2); 00464 } else if (dyk != 0.f) { 00465 dz_z__ = hugeval; 00466 } 00467 ymin = dmin(ymin,yk); 00468 normy = dmax(normy,yk); 00469 if (*colequ) { 00470 /* Computing MAX */ 00471 r__1 = normx, r__2 = yk * c__[i__]; 00472 normx = dmax(r__1,r__2); 00473 /* Computing MAX */ 00474 r__1 = normdx, r__2 = dyk * c__[i__]; 00475 normdx = dmax(r__1,r__2); 00476 } else { 00477 normx = normy; 00478 normdx = dmax(normdx,dyk); 00479 } 00480 } 00481 if (normx != 0.f) { 00482 dx_x__ = normdx / normx; 00483 } else if (normdx == 0.f) { 00484 dx_x__ = 0.f; 00485 } else { 00486 dx_x__ = hugeval; 00487 } 00488 dxrat = normdx / prevnormdx; 00489 dzrat = dz_z__ / prev_dz_z__; 00490 00491 /* Check termination criteria */ 00492 00493 if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy 00494 && y_prec_state__ < 2) { 00495 incr_prec__ = TRUE_; 00496 } 00497 if (x_state__ == 3 && dxrat <= *rthresh) { 00498 x_state__ = 1; 00499 } 00500 if (x_state__ == 1) { 00501 if (dx_x__ <= eps) { 00502 x_state__ = 2; 00503 } else if (dxrat > *rthresh) { 00504 if (y_prec_state__ != 2) { 00505 incr_prec__ = TRUE_; 00506 } else { 00507 x_state__ = 3; 00508 } 00509 } else { 00510 if (dxrat > dxratmax) { 00511 dxratmax = dxrat; 00512 } 00513 } 00514 if (x_state__ > 1) { 00515 final_dx_x__ = dx_x__; 00516 } 00517 } 00518 if (z_state__ == 0 && dz_z__ <= *dz_ub__) { 00519 z_state__ = 1; 00520 } 00521 if (z_state__ == 3 && dzrat <= *rthresh) { 00522 z_state__ = 1; 00523 } 00524 if (z_state__ == 1) { 00525 if (dz_z__ <= eps) { 00526 z_state__ = 2; 00527 } else if (dz_z__ > *dz_ub__) { 00528 z_state__ = 0; 00529 dzratmax = 0.f; 00530 final_dz_z__ = hugeval; 00531 } else if (dzrat > *rthresh) { 00532 if (y_prec_state__ != 2) { 00533 incr_prec__ = TRUE_; 00534 } else { 00535 z_state__ = 3; 00536 } 00537 } else { 00538 if (dzrat > dzratmax) { 00539 dzratmax = dzrat; 00540 } 00541 } 00542 if (z_state__ > 1) { 00543 final_dz_z__ = dz_z__; 00544 } 00545 } 00546 00547 /* Exit if both normwise and componentwise stopped working, */ 00548 /* but if componentwise is unstable, let it go at least two */ 00549 /* iterations. */ 00550 00551 if (x_state__ != 1) { 00552 if (*ignore_cwise__) { 00553 goto L666; 00554 } 00555 if (z_state__ == 3 || z_state__ == 2) { 00556 goto L666; 00557 } 00558 if (z_state__ == 0 && cnt > 1) { 00559 goto L666; 00560 } 00561 } 00562 if (incr_prec__) { 00563 incr_prec__ = FALSE_; 00564 ++y_prec_state__; 00565 i__3 = *n; 00566 for (i__ = 1; i__ <= i__3; ++i__) { 00567 i__4 = i__; 00568 y_tail__[i__4].r = 0.f, y_tail__[i__4].i = 0.f; 00569 } 00570 } 00571 prevnormdx = normdx; 00572 prev_dz_z__ = dz_z__; 00573 00574 /* Update soluton. */ 00575 00576 if (y_prec_state__ < 2) { 00577 caxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00578 } else { 00579 cla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00580 } 00581 } 00582 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00583 L666: 00584 00585 /* Set final_* when cnt hits ithresh */ 00586 00587 if (x_state__ == 1) { 00588 final_dx_x__ = dx_x__; 00589 } 00590 if (z_state__ == 1) { 00591 final_dz_z__ = dz_z__; 00592 } 00593 00594 /* Compute error bounds */ 00595 00596 if (*n_norms__ >= 1) { 00597 errs_n__[j + (errs_n_dim1 << 1)] = final_dx_x__ / (1 - dxratmax); 00598 } 00599 if (*n_norms__ >= 2) { 00600 errs_c__[j + (errs_c_dim1 << 1)] = final_dz_z__ / (1 - dzratmax); 00601 } 00602 00603 /* Compute componentwise relative backward error from formula */ 00604 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00605 /* where abs(Z) is the componentwise absolute value of the matrix */ 00606 /* or vector Z. */ 00607 00608 /* Compute residual RES = B_s - op(A_s) * Y, */ 00609 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00610 00611 ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00612 cgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 1], & 00613 c__1, &c_b8, &res[1], &c__1); 00614 i__2 = *n; 00615 for (i__ = 1; i__ <= i__2; ++i__) { 00616 i__3 = i__ + j * b_dim1; 00617 ayb[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[i__ 00618 + j * b_dim1]), dabs(r__2)); 00619 } 00620 00621 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00622 00623 cla_geamv__(trans_type__, n, n, &c_b31, &a[a_offset], lda, &y[j * 00624 y_dim1 + 1], &c__1, &c_b31, &ayb[1], &c__1); 00625 cla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00626 00627 /* End of loop for each RHS. */ 00628 00629 } 00630 00631 return 0; 00632 } /* cla_gerfsx_extended__ */