00001 /* zla_porfsx_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_b11 = {-1.,0.}; 00020 static doublecomplex c_b12 = {1.,0.}; 00021 static doublereal c_b33 = 1.; 00022 00023 /* Subroutine */ int zla_porfsx_extended__(integer *prec_type__, char *uplo, 00024 integer *n, integer *nrhs, doublecomplex *a, integer *lda, 00025 doublecomplex *af, integer *ldaf, logical *colequ, doublereal *c__, 00026 doublecomplex *b, integer *ldb, doublecomplex *y, integer *ldy, 00027 doublereal *berr_out__, integer *n_norms__, doublereal * 00028 err_bnds_norm__, doublereal *err_bnds_comp__, doublecomplex *res, 00029 doublereal *ayb, doublecomplex *dy, doublecomplex *y_tail__, 00030 doublereal *rcond, integer *ithresh, doublereal *rthresh, doublereal * 00031 dz_ub__, logical *ignore_cwise__, integer *info, ftnlen uplo_len) 00032 { 00033 /* System generated locals */ 00034 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, 00035 y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00036 err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4; 00037 doublereal d__1, d__2; 00038 00039 /* Builtin functions */ 00040 double d_imag(doublecomplex *); 00041 00042 /* Local variables */ 00043 doublereal dxratmax, dzratmax; 00044 integer i__, j; 00045 logical incr_prec__; 00046 extern /* Subroutine */ int zla_heamv__(integer *, integer *, doublereal * 00047 , doublecomplex *, integer *, doublecomplex *, integer *, 00048 doublereal *, doublereal *, integer *); 00049 doublereal prev_dz_z__, yk, final_dx_x__, final_dz_z__; 00050 extern /* Subroutine */ int zla_wwaddw__(integer *, doublecomplex *, 00051 doublecomplex *, doublecomplex *); 00052 doublereal prevnormdx; 00053 integer cnt; 00054 doublereal dyk, eps, incr_thresh__, dx_x__, dz_z__, ymin; 00055 extern /* Subroutine */ int zla_lin_berr__(integer *, integer *, integer * 00056 , doublecomplex *, doublereal *, doublereal *); 00057 integer y_prec_state__; 00058 extern /* Subroutine */ int blas_zhemv_x__(integer *, integer *, 00059 doublecomplex *, doublecomplex *, integer *, doublecomplex *, 00060 integer *, doublecomplex *, doublecomplex *, integer *, integer *) 00061 ; 00062 integer uplo2; 00063 extern logical lsame_(char *, char *); 00064 extern /* Subroutine */ int blas_zhemv2_x__(integer *, integer *, 00065 doublecomplex *, doublecomplex *, integer *, doublecomplex *, 00066 doublecomplex *, integer *, doublecomplex *, doublecomplex *, 00067 integer *, integer *); 00068 doublereal dxrat, dzrat; 00069 extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *, 00070 doublecomplex *, integer *, doublecomplex *, integer *, 00071 doublecomplex *, doublecomplex *, integer *); 00072 doublereal normx, normy; 00073 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 00074 doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, 00075 doublecomplex *, integer *, doublecomplex *, integer *); 00076 extern doublereal dlamch_(char *); 00077 doublereal normdx; 00078 extern /* Subroutine */ int zpotrs_(char *, integer *, integer *, 00079 doublecomplex *, integer *, doublecomplex *, integer *, integer *); 00080 doublereal hugeval; 00081 extern integer ilauplo_(char *); 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_PORFSX_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 ZPORFSX 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 /* UPLO (input) CHARACTER*1 */ 00124 /* = 'U': Upper triangle of A is stored; */ 00125 /* = 'L': Lower triangle of A is stored. */ 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*16 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*16 array, dimension (LDAF,N) */ 00142 /* The triangular factor U or L from the Cholesky factorization */ 00143 /* A = U**T*U or A = L*L**T, as computed by ZPOTRF. */ 00144 00145 /* LDAF (input) INTEGER */ 00146 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00147 00148 /* COLEQU (input) LOGICAL */ 00149 /* If .TRUE. then column equilibration was done to A before calling */ 00150 /* this routine. This is needed to compute the solution and error */ 00151 /* bounds correctly. */ 00152 00153 /* C (input) DOUBLE PRECISION array, dimension (N) */ 00154 /* The column scale factors for A. If COLEQU = .FALSE., C */ 00155 /* is not accessed. If C is input, each element of C should be a power */ 00156 /* of the radix to ensure a reliable solution and error estimates. */ 00157 /* Scaling by powers of the radix does not cause rounding errors unless */ 00158 /* the result underflows or overflows. Rounding errors during scaling */ 00159 /* lead to refining with a matrix that is not equivalent to the */ 00160 /* input matrix, producing error estimates that may not be */ 00161 /* reliable. */ 00162 00163 /* B (input) COMPLEX*16 array, dimension (LDB,NRHS) */ 00164 /* The right-hand-side matrix B. */ 00165 00166 /* LDB (input) INTEGER */ 00167 /* The leading dimension of the array B. LDB >= max(1,N). */ 00168 00169 /* Y (input/output) COMPLEX*16 array, dimension */ 00170 /* (LDY,NRHS) */ 00171 /* On entry, the solution matrix X, as computed by ZPOTRS. */ 00172 /* On exit, the improved solution matrix Y. */ 00173 00174 /* LDY (input) INTEGER */ 00175 /* The leading dimension of the array Y. LDY >= max(1,N). */ 00176 00177 /* BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS) */ 00178 /* On exit, BERR_OUT(j) contains the componentwise relative backward */ 00179 /* error for right-hand-side j from the formula */ 00180 /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00181 /* where abs(Z) is the componentwise absolute value of the matrix */ 00182 /* or vector Z. This is computed by ZLA_LIN_BERR. */ 00183 00184 /* N_NORMS (input) INTEGER */ 00185 /* Determines which error bounds to return (see ERR_BNDS_NORM */ 00186 /* and ERR_BNDS_COMP). */ 00187 /* If N_NORMS >= 1 return normwise error bounds. */ 00188 /* If N_NORMS >= 2 return componentwise error bounds. */ 00189 00190 /* ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension */ 00191 /* (NRHS, N_ERR_BNDS) */ 00192 /* For each right-hand side, this array contains information about */ 00193 /* various error bounds and condition numbers corresponding to the */ 00194 /* normwise relative error, which is defined as follows: */ 00195 00196 /* Normwise relative error in the ith solution vector: */ 00197 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00198 /* ------------------------------ */ 00199 /* max_j abs(X(j,i)) */ 00200 00201 /* The array is indexed by the type of error information as described */ 00202 /* below. There currently are up to three pieces of information */ 00203 /* returned. */ 00204 00205 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00206 /* right-hand side. */ 00207 00208 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00209 /* three fields: */ 00210 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00211 /* reciprocal condition number is less than the threshold */ 00212 /* sqrt(n) * slamch('Epsilon'). */ 00213 00214 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00215 /* almost certainly within a factor of 10 of the true error */ 00216 /* so long as the next entry is greater than the threshold */ 00217 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00218 /* be trusted if the previous boolean is true. */ 00219 00220 /* err = 3 Reciprocal condition number: Estimated normwise */ 00221 /* reciprocal condition number. Compared with the threshold */ 00222 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00223 /* estimate is "guaranteed". These reciprocal condition */ 00224 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00225 /* appropriately scaled matrix Z. */ 00226 /* Let Z = S*A, where S scales each row by a power of the */ 00227 /* radix so all absolute row sums of Z are approximately 1. */ 00228 00229 /* This subroutine is only responsible for setting the second field */ 00230 /* above. */ 00231 /* See Lapack Working Note 165 for further details and extra */ 00232 /* cautions. */ 00233 00234 /* ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension */ 00235 /* (NRHS, N_ERR_BNDS) */ 00236 /* For each right-hand side, this array contains information about */ 00237 /* various error bounds and condition numbers corresponding to the */ 00238 /* componentwise relative error, which is defined as follows: */ 00239 00240 /* Componentwise relative error in the ith solution vector: */ 00241 /* abs(XTRUE(j,i) - X(j,i)) */ 00242 /* max_j ---------------------- */ 00243 /* abs(X(j,i)) */ 00244 00245 /* The array is indexed by the right-hand side i (on which the */ 00246 /* componentwise relative error depends), and the type of error */ 00247 /* information as described below. There currently are up to three */ 00248 /* pieces of information returned for each right-hand side. If */ 00249 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00250 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00251 /* the first (:,N_ERR_BNDS) entries are returned. */ 00252 00253 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00254 /* right-hand side. */ 00255 00256 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00257 /* three fields: */ 00258 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00259 /* reciprocal condition number is less than the threshold */ 00260 /* sqrt(n) * slamch('Epsilon'). */ 00261 00262 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00263 /* almost certainly within a factor of 10 of the true error */ 00264 /* so long as the next entry is greater than the threshold */ 00265 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00266 /* be trusted if the previous boolean is true. */ 00267 00268 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00269 /* reciprocal condition number. Compared with the threshold */ 00270 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00271 /* estimate is "guaranteed". These reciprocal condition */ 00272 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00273 /* appropriately scaled matrix Z. */ 00274 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00275 /* current right-hand side and S scales each row of */ 00276 /* A*diag(x) by a power of the radix so all absolute row */ 00277 /* sums of Z are approximately 1. */ 00278 00279 /* This subroutine is only responsible for setting the second field */ 00280 /* above. */ 00281 /* See Lapack Working Note 165 for further details and extra */ 00282 /* cautions. */ 00283 00284 /* RES (input) COMPLEX*16 array, dimension (N) */ 00285 /* Workspace to hold the intermediate residual. */ 00286 00287 /* AYB (input) DOUBLE PRECISION array, dimension (N) */ 00288 /* Workspace. */ 00289 00290 /* DY (input) COMPLEX*16 PRECISION array, dimension (N) */ 00291 /* Workspace to hold the intermediate solution. */ 00292 00293 /* Y_TAIL (input) COMPLEX*16 array, dimension (N) */ 00294 /* Workspace to hold the trailing bits of the intermediate solution. */ 00295 00296 /* RCOND (input) DOUBLE PRECISION */ 00297 /* Reciprocal scaled condition number. This is an estimate of the */ 00298 /* reciprocal Skeel condition number of the matrix A after */ 00299 /* equilibration (if done). If this is less than the machine */ 00300 /* precision (in particular, if it is zero), the matrix is singular */ 00301 /* to working precision. Note that the error may still be small even */ 00302 /* if this number is very small and the matrix appears ill- */ 00303 /* conditioned. */ 00304 00305 /* ITHRESH (input) INTEGER */ 00306 /* The maximum number of residual computations allowed for */ 00307 /* refinement. The default is 10. For 'aggressive' set to 100 to */ 00308 /* permit convergence using approximate factorizations or */ 00309 /* factorizations other than LU. If the factorization uses a */ 00310 /* technique other than Gaussian elimination, the guarantees in */ 00311 /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ 00312 00313 /* RTHRESH (input) DOUBLE PRECISION */ 00314 /* Determines when to stop refinement if the error estimate stops */ 00315 /* decreasing. Refinement will stop when the next solution no longer */ 00316 /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ 00317 /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ 00318 /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ 00319 /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ 00320 /* for more details. */ 00321 00322 /* DZ_UB (input) DOUBLE PRECISION */ 00323 /* Determines when to start considering componentwise convergence. */ 00324 /* Componentwise convergence is only considered after each component */ 00325 /* of the solution Y is stable, which we definte as the relative */ 00326 /* change in each component being less than DZ_UB. The default value */ 00327 /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ 00328 /* more details. */ 00329 00330 /* IGNORE_CWISE (input) LOGICAL */ 00331 /* If .TRUE. then ignore componentwise convergence. Default value */ 00332 /* is .FALSE.. */ 00333 00334 /* INFO (output) INTEGER */ 00335 /* = 0: Successful exit. */ 00336 /* < 0: if INFO = -i, the ith argument to ZPOTRS had an illegal */ 00337 /* value */ 00338 00339 /* ===================================================================== */ 00340 00341 /* .. Local Scalars .. */ 00342 /* .. */ 00343 /* .. Parameters .. */ 00344 /* .. */ 00345 /* .. External Functions .. */ 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 err_bnds_comp_dim1 = *nrhs; 00359 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00360 err_bnds_comp__ -= err_bnds_comp_offset; 00361 err_bnds_norm_dim1 = *nrhs; 00362 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00363 err_bnds_norm__ -= err_bnds_norm_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 --c__; 00371 b_dim1 = *ldb; 00372 b_offset = 1 + b_dim1; 00373 b -= b_offset; 00374 y_dim1 = *ldy; 00375 y_offset = 1 + y_dim1; 00376 y -= y_offset; 00377 --berr_out__; 00378 --res; 00379 --ayb; 00380 --dy; 00381 --y_tail__; 00382 00383 /* Function Body */ 00384 if (*info != 0) { 00385 return 0; 00386 } 00387 eps = dlamch_("Epsilon"); 00388 hugeval = dlamch_("Overflow"); 00389 /* Force HUGEVAL to Inf */ 00390 hugeval *= hugeval; 00391 /* Using HUGEVAL may lead to spurious underflows. */ 00392 incr_thresh__ = (doublereal) (*n) * eps; 00393 if (lsame_(uplo, "L")) { 00394 uplo2 = ilauplo_("L"); 00395 } else { 00396 uplo2 = ilauplo_("U"); 00397 } 00398 i__1 = *nrhs; 00399 for (j = 1; j <= i__1; ++j) { 00400 y_prec_state__ = 1; 00401 if (y_prec_state__ == 2) { 00402 i__2 = *n; 00403 for (i__ = 1; i__ <= i__2; ++i__) { 00404 i__3 = i__; 00405 y_tail__[i__3].r = 0., y_tail__[i__3].i = 0.; 00406 } 00407 } 00408 dxrat = 0.; 00409 dxratmax = 0.; 00410 dzrat = 0.; 00411 dzratmax = 0.; 00412 final_dx_x__ = hugeval; 00413 final_dz_z__ = hugeval; 00414 prevnormdx = hugeval; 00415 prev_dz_z__ = hugeval; 00416 dz_z__ = hugeval; 00417 dx_x__ = hugeval; 00418 x_state__ = 1; 00419 z_state__ = 0; 00420 incr_prec__ = FALSE_; 00421 i__2 = *ithresh; 00422 for (cnt = 1; cnt <= i__2; ++cnt) { 00423 00424 /* Compute residual RES = B_s - op(A_s) * Y, */ 00425 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00426 00427 zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00428 if (y_prec_state__ == 0) { 00429 zhemv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], 00430 &c__1, &c_b12, &res[1], &c__1); 00431 } else if (y_prec_state__ == 1) { 00432 blas_zhemv_x__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * 00433 y_dim1 + 1], &c__1, &c_b12, &res[1], &c__1, 00434 prec_type__); 00435 } else { 00436 blas_zhemv2_x__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * 00437 y_dim1 + 1], &y_tail__[1], &c__1, &c_b12, &res[1], & 00438 c__1, prec_type__); 00439 } 00440 /* XXX: RES is no longer needed. */ 00441 zcopy_(n, &res[1], &c__1, &dy[1], &c__1); 00442 zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &dy[1], n, info); 00443 00444 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00445 00446 normx = 0.; 00447 normy = 0.; 00448 normdx = 0.; 00449 dz_z__ = 0.; 00450 ymin = hugeval; 00451 i__3 = *n; 00452 for (i__ = 1; i__ <= i__3; ++i__) { 00453 i__4 = i__ + j * y_dim1; 00454 yk = (d__1 = y[i__4].r, abs(d__1)) + (d__2 = d_imag(&y[i__ + 00455 j * y_dim1]), abs(d__2)); 00456 i__4 = i__; 00457 dyk = (d__1 = dy[i__4].r, abs(d__1)) + (d__2 = d_imag(&dy[i__] 00458 ), abs(d__2)); 00459 if (yk != 0.) { 00460 /* Computing MAX */ 00461 d__1 = dz_z__, d__2 = dyk / yk; 00462 dz_z__ = max(d__1,d__2); 00463 } else if (dyk != 0.) { 00464 dz_z__ = hugeval; 00465 } 00466 ymin = min(ymin,yk); 00467 normy = max(normy,yk); 00468 if (*colequ) { 00469 /* Computing MAX */ 00470 d__1 = normx, d__2 = yk * c__[i__]; 00471 normx = max(d__1,d__2); 00472 /* Computing MAX */ 00473 d__1 = normdx, d__2 = dyk * c__[i__]; 00474 normdx = max(d__1,d__2); 00475 } else { 00476 normx = normy; 00477 normdx = max(normdx,dyk); 00478 } 00479 } 00480 if (normx != 0.) { 00481 dx_x__ = normdx / normx; 00482 } else if (normdx == 0.) { 00483 dx_x__ = 0.; 00484 } else { 00485 dx_x__ = hugeval; 00486 } 00487 dxrat = normdx / prevnormdx; 00488 dzrat = dz_z__ / prev_dz_z__; 00489 00490 /* Check termination criteria. */ 00491 00492 if (ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2) { 00493 incr_prec__ = TRUE_; 00494 } 00495 if (x_state__ == 3 && dxrat <= *rthresh) { 00496 x_state__ = 1; 00497 } 00498 if (x_state__ == 1) { 00499 if (dx_x__ <= eps) { 00500 x_state__ = 2; 00501 } else if (dxrat > *rthresh) { 00502 if (y_prec_state__ != 2) { 00503 incr_prec__ = TRUE_; 00504 } else { 00505 x_state__ = 3; 00506 } 00507 } else { 00508 if (dxrat > dxratmax) { 00509 dxratmax = dxrat; 00510 } 00511 } 00512 if (x_state__ > 1) { 00513 final_dx_x__ = dx_x__; 00514 } 00515 } 00516 if (z_state__ == 0 && dz_z__ <= *dz_ub__) { 00517 z_state__ = 1; 00518 } 00519 if (z_state__ == 3 && dzrat <= *rthresh) { 00520 z_state__ = 1; 00521 } 00522 if (z_state__ == 1) { 00523 if (dz_z__ <= eps) { 00524 z_state__ = 2; 00525 } else if (dz_z__ > *dz_ub__) { 00526 z_state__ = 0; 00527 dzratmax = 0.; 00528 final_dz_z__ = hugeval; 00529 } else if (dzrat > *rthresh) { 00530 if (y_prec_state__ != 2) { 00531 incr_prec__ = TRUE_; 00532 } else { 00533 z_state__ = 3; 00534 } 00535 } else { 00536 if (dzrat > dzratmax) { 00537 dzratmax = dzrat; 00538 } 00539 } 00540 if (z_state__ > 1) { 00541 final_dz_z__ = dz_z__; 00542 } 00543 } 00544 if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1)) { 00545 goto L666; 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 i__4 = i__; 00553 y_tail__[i__4].r = 0., y_tail__[i__4].i = 0.; 00554 } 00555 } 00556 prevnormdx = normdx; 00557 prev_dz_z__ = dz_z__; 00558 00559 /* Update soluton. */ 00560 00561 if (y_prec_state__ < 2) { 00562 zaxpy_(n, &c_b12, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00563 } else { 00564 zla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00565 } 00566 } 00567 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00568 L666: 00569 00570 /* Set final_* when cnt hits ithresh. */ 00571 00572 if (x_state__ == 1) { 00573 final_dx_x__ = dx_x__; 00574 } 00575 if (z_state__ == 1) { 00576 final_dz_z__ = dz_z__; 00577 } 00578 00579 /* Compute error bounds. */ 00580 00581 if (*n_norms__ >= 1) { 00582 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 00583 1 - dxratmax); 00584 } 00585 if (*n_norms__ >= 2) { 00586 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 00587 1 - dzratmax); 00588 } 00589 00590 /* Compute componentwise relative backward error from formula */ 00591 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00592 /* where abs(Z) is the componentwise absolute value of the matrix */ 00593 /* or vector Z. */ 00594 00595 /* Compute residual RES = B_s - op(A_s) * Y, */ 00596 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00597 00598 zcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00599 zhemv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, 00600 &c_b12, &res[1], &c__1); 00601 i__2 = *n; 00602 for (i__ = 1; i__ <= i__2; ++i__) { 00603 i__3 = i__ + j * b_dim1; 00604 ayb[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[i__ 00605 + j * b_dim1]), abs(d__2)); 00606 } 00607 00608 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00609 00610 zla_heamv__(&uplo2, n, &c_b33, &a[a_offset], lda, &y[j * y_dim1 + 1], 00611 &c__1, &c_b33, &ayb[1], &c__1); 00612 zla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00613 00614 /* End of loop for each RHS. */ 00615 00616 } 00617 00618 return 0; 00619 } /* zla_porfsx_extended__ */