00001 /* zla_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 doublecomplex c_b6 = {-1.,0.}; 00020 static doublecomplex c_b8 = {1.,0.}; 00021 static doublereal c_b31 = 1.; 00022 00023 /* Subroutine */ int zla_gerfsx_extended__(integer *prec_type__, integer * 00024 trans_type__, integer *n, integer *nrhs, doublecomplex *a, integer * 00025 lda, doublecomplex *af, integer *ldaf, integer *ipiv, logical *colequ, 00026 doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *y, 00027 integer *ldy, doublereal *berr_out__, integer *n_norms__, doublereal * 00028 errs_n__, doublereal *errs_c__, doublecomplex *res, doublereal *ayb, 00029 doublecomplex *dy, doublecomplex *y_tail__, doublereal *rcond, 00030 integer *ithresh, doublereal *rthresh, doublereal *dz_ub__, logical * 00031 ignore_cwise__, integer *info) 00032 { 00033 /* System generated locals */ 00034 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, 00035 y_offset, errs_n_dim1, errs_n_offset, errs_c_dim1, errs_c_offset, 00036 i__1, i__2, i__3, i__4; 00037 doublereal d__1, d__2; 00038 char ch__1[1]; 00039 00040 /* Builtin functions */ 00041 double d_imag(doublecomplex *); 00042 00043 /* Local variables */ 00044 doublereal dxratmax, dzratmax; 00045 integer i__, j; 00046 logical incr_prec__; 00047 extern /* Subroutine */ int zla_geamv__(integer *, integer *, integer *, 00048 doublereal *, doublecomplex *, integer *, doublecomplex *, 00049 integer *, doublereal *, doublereal *, integer *); 00050 doublereal prev_dz_z__, yk, final_dx_x__, final_dz_z__; 00051 extern /* Subroutine */ int zla_wwaddw__(integer *, doublecomplex *, 00052 doublecomplex *, doublecomplex *); 00053 doublereal prevnormdx; 00054 integer cnt; 00055 doublereal dyk, eps, incr_thresh__, dx_x__, dz_z__, ymin; 00056 extern /* Subroutine */ int zla_lin_berr__(integer *, integer *, integer * 00057 , doublecomplex *, doublereal *, doublereal *), blas_zgemv_x__( 00058 integer *, integer *, integer *, doublecomplex *, doublecomplex *, 00059 integer *, doublecomplex *, integer *, doublecomplex *, 00060 doublecomplex *, integer *, integer *); 00061 integer y_prec_state__; 00062 extern /* Subroutine */ int blas_zgemv2_x__(integer *, integer *, integer 00063 *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, 00064 doublecomplex *, integer *, doublecomplex *, doublecomplex *, 00065 integer *, integer *); 00066 doublereal dxrat, dzrat; 00067 char trans[1]; 00068 extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 00069 doublecomplex *, doublecomplex *, integer *, doublecomplex *, 00070 integer *, doublecomplex *, doublecomplex *, integer *); 00071 doublereal normx, normy; 00072 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 00073 doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, 00074 doublecomplex *, integer *, doublecomplex *, integer *); 00075 extern doublereal dlamch_(char *); 00076 doublereal normdx; 00077 extern /* Subroutine */ int zgetrs_(char *, integer *, integer *, 00078 doublecomplex *, integer *, integer *, doublecomplex *, integer *, 00079 integer *); 00080 extern /* Character */ VOID chla_transtype__(char *, ftnlen, integer *); 00081 doublereal hugeval; 00082 integer x_state__, z_state__; 00083 00084 00085 /* -- LAPACK routine (version 3.2.1) -- */ 00086 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00087 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00088 /* -- April 2009 -- */ 00089 00090 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00091 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00092 00093 /* .. */ 00094 /* .. Scalar Arguments .. */ 00095 /* .. */ 00096 /* .. Array Arguments */ 00097 /* .. */ 00098 00099 /* Purpose */ 00100 /* ======= */ 00101 00102 /* ZLA_GERFSX_EXTENDED improves the computed solution to a system of */ 00103 /* linear equations by performing extra-precise iterative refinement */ 00104 /* and provides error bounds and backward error estimates for the solution. */ 00105 /* This subroutine is called by ZGERFSX to perform iterative refinement. */ 00106 /* In addition to normwise error bound, the code provides maximum */ 00107 /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ 00108 /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ 00109 /* subroutine is only resonsible for setting the second fields of */ 00110 /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ 00111 00112 /* Arguments */ 00113 /* ========= */ 00114 00115 /* PREC_TYPE (input) INTEGER */ 00116 /* Specifies the intermediate precision to be used in refinement. */ 00117 /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ 00118 /* P = 'S': Single */ 00119 /* = 'D': Double */ 00120 /* = 'I': Indigenous */ 00121 /* = 'X', 'E': Extra */ 00122 00123 /* TRANS_TYPE (input) INTEGER */ 00124 /* Specifies the transposition operation on A. */ 00125 /* The value is defined by ILATRANS(T) where T is a CHARACTER and */ 00126 /* T = 'N': No transpose */ 00127 /* = 'T': Transpose */ 00128 /* = 'C': Conjugate transpose */ 00129 00130 /* N (input) INTEGER */ 00131 /* The number of linear equations, i.e., the order of the */ 00132 /* matrix A. N >= 0. */ 00133 00134 /* NRHS (input) INTEGER */ 00135 /* The number of right-hand-sides, i.e., the number of columns of the */ 00136 /* matrix B. */ 00137 00138 /* A (input) COMPLEX*16 array, dimension (LDA,N) */ 00139 /* On entry, the N-by-N matrix A. */ 00140 00141 /* LDA (input) INTEGER */ 00142 /* The leading dimension of the array A. LDA >= max(1,N). */ 00143 00144 /* AF (input) COMPLEX*16 array, dimension (LDAF,N) */ 00145 /* The factors L and U from the factorization */ 00146 /* A = P*L*U as computed by ZGETRF. */ 00147 00148 /* LDAF (input) INTEGER */ 00149 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00150 00151 /* IPIV (input) INTEGER array, dimension (N) */ 00152 /* The pivot indices from the factorization A = P*L*U */ 00153 /* as computed by ZGETRF; row i of the matrix was interchanged */ 00154 /* with row IPIV(i). */ 00155 00156 /* COLEQU (input) LOGICAL */ 00157 /* If .TRUE. then column equilibration was done to A before calling */ 00158 /* this routine. This is needed to compute the solution and error */ 00159 /* bounds correctly. */ 00160 00161 /* C (input) DOUBLE PRECISION array, dimension (N) */ 00162 /* The column scale factors for A. If COLEQU = .FALSE., C */ 00163 /* is not accessed. If C is input, each element of C should be a power */ 00164 /* of the radix to ensure a reliable solution and error estimates. */ 00165 /* Scaling by powers of the radix does not cause rounding errors unless */ 00166 /* the result underflows or overflows. Rounding errors during scaling */ 00167 /* lead to refining with a matrix that is not equivalent to the */ 00168 /* input matrix, producing error estimates that may not be */ 00169 /* reliable. */ 00170 00171 /* B (input) COMPLEX*16 array, dimension (LDB,NRHS) */ 00172 /* The right-hand-side matrix B. */ 00173 00174 /* LDB (input) INTEGER */ 00175 /* The leading dimension of the array B. LDB >= max(1,N). */ 00176 00177 /* Y (input/output) COMPLEX*16 array, dimension (LDY,NRHS) */ 00178 /* On entry, the solution matrix X, as computed by ZGETRS. */ 00179 /* On exit, the improved solution matrix Y. */ 00180 00181 /* LDY (input) INTEGER */ 00182 /* The leading dimension of the array Y. LDY >= max(1,N). */ 00183 00184 /* BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS) */ 00185 /* On exit, BERR_OUT(j) contains the componentwise relative backward */ 00186 /* error for right-hand-side j from the formula */ 00187 /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00188 /* where abs(Z) is the componentwise absolute value of the matrix */ 00189 /* or vector Z. This is computed by ZLA_LIN_BERR. */ 00190 00191 /* N_NORMS (input) INTEGER */ 00192 /* Determines which error bounds to return (see ERR_BNDS_NORM */ 00193 /* and ERR_BNDS_COMP). */ 00194 /* If N_NORMS >= 1 return normwise error bounds. */ 00195 /* If N_NORMS >= 2 return componentwise error bounds. */ 00196 00197 /* ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension */ 00198 /* (NRHS, N_ERR_BNDS) */ 00199 /* For each right-hand side, this array contains information about */ 00200 /* various error bounds and condition numbers corresponding to the */ 00201 /* normwise relative error, which is defined as follows: */ 00202 00203 /* Normwise relative error in the ith solution vector: */ 00204 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00205 /* ------------------------------ */ 00206 /* max_j abs(X(j,i)) */ 00207 00208 /* The array is indexed by the type of error information as described */ 00209 /* below. There currently are up to three pieces of information */ 00210 /* returned. */ 00211 00212 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00213 /* right-hand side. */ 00214 00215 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00216 /* three fields: */ 00217 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00218 /* reciprocal condition number is less than the threshold */ 00219 /* sqrt(n) * slamch('Epsilon'). */ 00220 00221 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00222 /* almost certainly within a factor of 10 of the true error */ 00223 /* so long as the next entry is greater than the threshold */ 00224 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00225 /* be trusted if the previous boolean is true. */ 00226 00227 /* err = 3 Reciprocal condition number: Estimated normwise */ 00228 /* reciprocal condition number. Compared with the threshold */ 00229 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00230 /* estimate is "guaranteed". These reciprocal condition */ 00231 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00232 /* appropriately scaled matrix Z. */ 00233 /* Let Z = S*A, where S scales each row by a power of the */ 00234 /* radix so all absolute row sums of Z are approximately 1. */ 00235 00236 /* This subroutine is only responsible for setting the second field */ 00237 /* above. */ 00238 /* See Lapack Working Note 165 for further details and extra */ 00239 /* cautions. */ 00240 00241 /* ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension */ 00242 /* (NRHS, N_ERR_BNDS) */ 00243 /* For each right-hand side, this array contains information about */ 00244 /* various error bounds and condition numbers corresponding to the */ 00245 /* componentwise relative error, which is defined as follows: */ 00246 00247 /* Componentwise relative error in the ith solution vector: */ 00248 /* abs(XTRUE(j,i) - X(j,i)) */ 00249 /* max_j ---------------------- */ 00250 /* abs(X(j,i)) */ 00251 00252 /* The array is indexed by the right-hand side i (on which the */ 00253 /* componentwise relative error depends), and the type of error */ 00254 /* information as described below. There currently are up to three */ 00255 /* pieces of information returned for each right-hand side. If */ 00256 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00257 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00258 /* the first (:,N_ERR_BNDS) entries are returned. */ 00259 00260 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00261 /* right-hand side. */ 00262 00263 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00264 /* three fields: */ 00265 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00266 /* reciprocal condition number is less than the threshold */ 00267 /* sqrt(n) * slamch('Epsilon'). */ 00268 00269 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00270 /* almost certainly within a factor of 10 of the true error */ 00271 /* so long as the next entry is greater than the threshold */ 00272 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00273 /* be trusted if the previous boolean is true. */ 00274 00275 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00276 /* reciprocal condition number. Compared with the threshold */ 00277 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00278 /* estimate is "guaranteed". These reciprocal condition */ 00279 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00280 /* appropriately scaled matrix Z. */ 00281 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00282 /* current right-hand side and S scales each row of */ 00283 /* A*diag(x) by a power of the radix so all absolute row */ 00284 /* sums of Z are approximately 1. */ 00285 00286 /* This subroutine is only responsible for setting the second field */ 00287 /* above. */ 00288 /* See Lapack Working Note 165 for further details and extra */ 00289 /* cautions. */ 00290 00291 /* RES (input) COMPLEX*16 array, dimension (N) */ 00292 /* Workspace to hold the intermediate residual. */ 00293 00294 /* AYB (input) DOUBLE PRECISION array, dimension (N) */ 00295 /* Workspace. */ 00296 00297 /* DY (input) COMPLEX*16 array, dimension (N) */ 00298 /* Workspace to hold the intermediate solution. */ 00299 00300 /* Y_TAIL (input) COMPLEX*16 array, dimension (N) */ 00301 /* Workspace to hold the trailing bits of the intermediate solution. */ 00302 00303 /* RCOND (input) DOUBLE PRECISION */ 00304 /* Reciprocal scaled condition number. This is an estimate of the */ 00305 /* reciprocal Skeel condition number of the matrix A after */ 00306 /* equilibration (if done). If this is less than the machine */ 00307 /* precision (in particular, if it is zero), the matrix is singular */ 00308 /* to working precision. Note that the error may still be small even */ 00309 /* if this number is very small and the matrix appears ill- */ 00310 /* conditioned. */ 00311 00312 /* ITHRESH (input) INTEGER */ 00313 /* The maximum number of residual computations allowed for */ 00314 /* refinement. The default is 10. For 'aggressive' set to 100 to */ 00315 /* permit convergence using approximate factorizations or */ 00316 /* factorizations other than LU. If the factorization uses a */ 00317 /* technique other than Gaussian elimination, the guarantees in */ 00318 /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ 00319 00320 /* RTHRESH (input) DOUBLE PRECISION */ 00321 /* Determines when to stop refinement if the error estimate stops */ 00322 /* decreasing. Refinement will stop when the next solution no longer */ 00323 /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ 00324 /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ 00325 /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ 00326 /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ 00327 /* for more details. */ 00328 00329 /* DZ_UB (input) DOUBLE PRECISION */ 00330 /* Determines when to start considering componentwise convergence. */ 00331 /* Componentwise convergence is only considered after each component */ 00332 /* of the solution Y is stable, which we definte as the relative */ 00333 /* change in each component being less than DZ_UB. The default value */ 00334 /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ 00335 /* more details. */ 00336 00337 /* IGNORE_CWISE (input) LOGICAL */ 00338 /* If .TRUE. then ignore componentwise convergence. Default value */ 00339 /* is .FALSE.. */ 00340 00341 /* INFO (output) INTEGER */ 00342 /* = 0: Successful exit. */ 00343 /* < 0: if INFO = -i, the ith argument to ZGETRS had an illegal */ 00344 /* value */ 00345 00346 /* ===================================================================== */ 00347 00348 /* .. Local Scalars .. */ 00349 /* .. */ 00350 /* .. Parameters .. */ 00351 /* .. */ 00352 /* .. External Subroutines .. */ 00353 /* .. */ 00354 /* .. Intrinsic Functions .. */ 00355 /* .. */ 00356 /* .. Statement Functions .. */ 00357 /* .. */ 00358 /* .. Statement Function Definitions .. */ 00359 /* .. */ 00360 /* .. Executable Statements .. */ 00361 00362 /* Parameter adjustments */ 00363 errs_c_dim1 = *nrhs; 00364 errs_c_offset = 1 + errs_c_dim1; 00365 errs_c__ -= errs_c_offset; 00366 errs_n_dim1 = *nrhs; 00367 errs_n_offset = 1 + errs_n_dim1; 00368 errs_n__ -= errs_n_offset; 00369 a_dim1 = *lda; 00370 a_offset = 1 + a_dim1; 00371 a -= a_offset; 00372 af_dim1 = *ldaf; 00373 af_offset = 1 + af_dim1; 00374 af -= af_offset; 00375 --ipiv; 00376 --c__; 00377 b_dim1 = *ldb; 00378 b_offset = 1 + b_dim1; 00379 b -= b_offset; 00380 y_dim1 = *ldy; 00381 y_offset = 1 + y_dim1; 00382 y -= y_offset; 00383 --berr_out__; 00384 --res; 00385 --ayb; 00386 --dy; 00387 --y_tail__; 00388 00389 /* Function Body */ 00390 if (*info != 0) { 00391 return 0; 00392 } 00393 chla_transtype__(ch__1, (ftnlen)1, trans_type__); 00394 *(unsigned char *)trans = *(unsigned char *)&ch__1[0]; 00395 eps = dlamch_("Epsilon"); 00396 hugeval = dlamch_("Overflow"); 00397 /* Force HUGEVAL to Inf */ 00398 hugeval *= hugeval; 00399 /* Using HUGEVAL may lead to spurious underflows. */ 00400 incr_thresh__ = (doublereal) (*n) * eps; 00401 00402 i__1 = *nrhs; 00403 for (j = 1; j <= i__1; ++j) { 00404 y_prec_state__ = 1; 00405 if (y_prec_state__ == 2) { 00406 i__2 = *n; 00407 for (i__ = 1; i__ <= i__2; ++i__) { 00408 i__3 = i__; 00409 y_tail__[i__3].r = 0., y_tail__[i__3].i = 0.; 00410 } 00411 } 00412 dxrat = 0.; 00413 dxratmax = 0.; 00414 dzrat = 0.; 00415 dzratmax = 0.; 00416 final_dx_x__ = hugeval; 00417 final_dz_z__ = hugeval; 00418 prevnormdx = hugeval; 00419 prev_dz_z__ = hugeval; 00420 dz_z__ = hugeval; 00421 dx_x__ = hugeval; 00422 x_state__ = 1; 00423 z_state__ = 0; 00424 incr_prec__ = FALSE_; 00425 i__2 = *ithresh; 00426 for (cnt = 1; cnt <= i__2; ++cnt) { 00427 00428 /* Compute residual RES = B_s - op(A_s) * Y, */ 00429 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00430 00431 zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00432 if (y_prec_state__ == 0) { 00433 zgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 00434 1], &c__1, &c_b8, &res[1], &c__1); 00435 } else if (y_prec_state__ == 1) { 00436 blas_zgemv_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, & 00437 y[j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1, 00438 prec_type__); 00439 } else { 00440 blas_zgemv2_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, 00441 &y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b8, &res[ 00442 1], &c__1, prec_type__); 00443 } 00444 /* XXX: RES is no longer needed. */ 00445 zcopy_(n, &res[1], &c__1, &dy[1], &c__1); 00446 zgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &dy[1], 00447 n, info); 00448 00449 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00450 00451 normx = 0.; 00452 normy = 0.; 00453 normdx = 0.; 00454 dz_z__ = 0.; 00455 ymin = hugeval; 00456 00457 i__3 = *n; 00458 for (i__ = 1; i__ <= i__3; ++i__) { 00459 i__4 = i__ + j * y_dim1; 00460 yk = (d__1 = y[i__4].r, abs(d__1)) + (d__2 = d_imag(&y[i__ + 00461 j * y_dim1]), abs(d__2)); 00462 i__4 = i__; 00463 dyk = (d__1 = dy[i__4].r, abs(d__1)) + (d__2 = d_imag(&dy[i__] 00464 ), abs(d__2)); 00465 if (yk != 0.) { 00466 /* Computing MAX */ 00467 d__1 = dz_z__, d__2 = dyk / yk; 00468 dz_z__ = max(d__1,d__2); 00469 } else if (dyk != 0.) { 00470 dz_z__ = hugeval; 00471 } 00472 ymin = min(ymin,yk); 00473 normy = max(normy,yk); 00474 if (*colequ) { 00475 /* Computing MAX */ 00476 d__1 = normx, d__2 = yk * c__[i__]; 00477 normx = max(d__1,d__2); 00478 /* Computing MAX */ 00479 d__1 = normdx, d__2 = dyk * c__[i__]; 00480 normdx = max(d__1,d__2); 00481 } else { 00482 normx = normy; 00483 normdx = max(normdx,dyk); 00484 } 00485 } 00486 if (normx != 0.) { 00487 dx_x__ = normdx / normx; 00488 } else if (normdx == 0.) { 00489 dx_x__ = 0.; 00490 } else { 00491 dx_x__ = hugeval; 00492 } 00493 dxrat = normdx / prevnormdx; 00494 dzrat = dz_z__ / prev_dz_z__; 00495 00496 /* Check termination criteria */ 00497 00498 if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy 00499 && y_prec_state__ < 2) { 00500 incr_prec__ = TRUE_; 00501 } 00502 if (x_state__ == 3 && dxrat <= *rthresh) { 00503 x_state__ = 1; 00504 } 00505 if (x_state__ == 1) { 00506 if (dx_x__ <= eps) { 00507 x_state__ = 2; 00508 } else if (dxrat > *rthresh) { 00509 if (y_prec_state__ != 2) { 00510 incr_prec__ = TRUE_; 00511 } else { 00512 x_state__ = 3; 00513 } 00514 } else { 00515 if (dxrat > dxratmax) { 00516 dxratmax = dxrat; 00517 } 00518 } 00519 if (x_state__ > 1) { 00520 final_dx_x__ = dx_x__; 00521 } 00522 } 00523 if (z_state__ == 0 && dz_z__ <= *dz_ub__) { 00524 z_state__ = 1; 00525 } 00526 if (z_state__ == 3 && dzrat <= *rthresh) { 00527 z_state__ = 1; 00528 } 00529 if (z_state__ == 1) { 00530 if (dz_z__ <= eps) { 00531 z_state__ = 2; 00532 } else if (dz_z__ > *dz_ub__) { 00533 z_state__ = 0; 00534 dzratmax = 0.; 00535 final_dz_z__ = hugeval; 00536 } else if (dzrat > *rthresh) { 00537 if (y_prec_state__ != 2) { 00538 incr_prec__ = TRUE_; 00539 } else { 00540 z_state__ = 3; 00541 } 00542 } else { 00543 if (dzrat > dzratmax) { 00544 dzratmax = dzrat; 00545 } 00546 } 00547 if (z_state__ > 1) { 00548 final_dz_z__ = dz_z__; 00549 } 00550 } 00551 00552 /* Exit if both normwise and componentwise stopped working, */ 00553 /* but if componentwise is unstable, let it go at least two */ 00554 /* iterations. */ 00555 00556 if (x_state__ != 1) { 00557 if (*ignore_cwise__) { 00558 goto L666; 00559 } 00560 if (z_state__ == 3 || z_state__ == 2) { 00561 goto L666; 00562 } 00563 if (z_state__ == 0 && cnt > 1) { 00564 goto L666; 00565 } 00566 } 00567 if (incr_prec__) { 00568 incr_prec__ = FALSE_; 00569 ++y_prec_state__; 00570 i__3 = *n; 00571 for (i__ = 1; i__ <= i__3; ++i__) { 00572 i__4 = i__; 00573 y_tail__[i__4].r = 0., y_tail__[i__4].i = 0.; 00574 } 00575 } 00576 prevnormdx = normdx; 00577 prev_dz_z__ = dz_z__; 00578 00579 /* Update soluton. */ 00580 00581 if (y_prec_state__ < 2) { 00582 zaxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00583 } else { 00584 zla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00585 } 00586 } 00587 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00588 L666: 00589 00590 /* Set final_* when cnt hits ithresh */ 00591 00592 if (x_state__ == 1) { 00593 final_dx_x__ = dx_x__; 00594 } 00595 if (z_state__ == 1) { 00596 final_dz_z__ = dz_z__; 00597 } 00598 00599 /* Compute error bounds */ 00600 00601 if (*n_norms__ >= 1) { 00602 errs_n__[j + (errs_n_dim1 << 1)] = final_dx_x__ / (1 - dxratmax); 00603 } 00604 if (*n_norms__ >= 2) { 00605 errs_c__[j + (errs_c_dim1 << 1)] = final_dz_z__ / (1 - dzratmax); 00606 } 00607 00608 /* Compute componentwise relative backward error from formula */ 00609 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00610 /* where abs(Z) is the componentwise absolute value of the matrix */ 00611 /* or vector Z. */ 00612 00613 /* Compute residual RES = B_s - op(A_s) * Y, */ 00614 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00615 00616 zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00617 zgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 1], & 00618 c__1, &c_b8, &res[1], &c__1); 00619 i__2 = *n; 00620 for (i__ = 1; i__ <= i__2; ++i__) { 00621 i__3 = i__ + j * b_dim1; 00622 ayb[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[i__ 00623 + j * b_dim1]), abs(d__2)); 00624 } 00625 00626 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00627 00628 zla_geamv__(trans_type__, n, n, &c_b31, &a[a_offset], lda, &y[j * 00629 y_dim1 + 1], &c__1, &c_b31, &ayb[1], &c__1); 00630 zla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00631 00632 /* End of loop for each RHS. */ 00633 00634 } 00635 00636 return 0; 00637 } /* zla_gerfsx_extended__ */