00001 /* cla_herfsx_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_b11 = {-1.f,0.f}; 00020 static complex c_b12 = {1.f,0.f}; 00021 static real c_b33 = 1.f; 00022 00023 /* Subroutine */ int cla_herfsx_extended__(integer *prec_type__, char *uplo, 00024 integer *n, integer *nrhs, complex *a, integer *lda, complex *af, 00025 integer *ldaf, integer *ipiv, logical *colequ, real *c__, complex *b, 00026 integer *ldb, complex *y, integer *ldy, real *berr_out__, integer * 00027 n_norms__, real *err_bnds_norm__, real *err_bnds_comp__, 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, ftnlen uplo_len) 00031 { 00032 /* System generated locals */ 00033 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, 00034 y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00035 err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4; 00036 real r__1, r__2; 00037 00038 /* Builtin functions */ 00039 double r_imag(complex *); 00040 00041 /* Local variables */ 00042 real dxratmax, dzratmax; 00043 integer i__, j; 00044 extern /* Subroutine */ int cla_heamv__(integer *, integer *, real *, 00045 complex *, integer *, complex *, integer *, real *, real *, 00046 integer *); 00047 logical incr_prec__; 00048 real prev_dz_z__, yk, final_dx_x__; 00049 extern /* Subroutine */ int cla_wwaddw__(integer *, complex *, complex *, 00050 complex *); 00051 real final_dz_z__, prevnormdx; 00052 integer cnt; 00053 real dyk, eps, incr_thresh__, dx_x__, dz_z__; 00054 extern /* Subroutine */ int cla_lin_berr__(integer *, integer *, integer * 00055 , complex *, real *, real *); 00056 real ymin; 00057 extern /* Subroutine */ int blas_chemv_x__(integer *, integer *, complex * 00058 , complex *, integer *, complex *, integer *, complex *, complex * 00059 , integer *, integer *); 00060 integer y_prec_state__, uplo2; 00061 extern /* Subroutine */ int blas_chemv2_x__(integer *, integer *, complex 00062 *, complex *, integer *, complex *, complex *, integer *, complex 00063 *, complex *, integer *, integer *); 00064 extern logical lsame_(char *, char *); 00065 extern /* Subroutine */ int chemv_(char *, integer *, complex *, complex * 00066 , integer *, complex *, integer *, complex *, complex *, integer * 00067 ), ccopy_(integer *, complex *, integer *, complex *, 00068 integer *); 00069 real dxrat, dzrat; 00070 extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, 00071 integer *, complex *, integer *); 00072 real normx, normy; 00073 extern doublereal slamch_(char *); 00074 extern /* Subroutine */ int chetrs_(char *, integer *, integer *, complex 00075 *, integer *, integer *, complex *, integer *, integer *); 00076 real normdx, hugeval; 00077 extern integer ilauplo_(char *); 00078 integer x_state__, z_state__; 00079 00080 00081 /* -- LAPACK routine (version 3.2.1) -- */ 00082 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00083 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00084 /* -- April 2009 -- */ 00085 00086 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00087 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00088 00089 /* .. */ 00090 /* .. Scalar Arguments .. */ 00091 /* .. */ 00092 /* .. Array Arguments .. */ 00093 /* .. */ 00094 00095 /* Purpose */ 00096 /* ======= */ 00097 00098 /* CLA_HERFSX_EXTENDED improves the computed solution to a system of */ 00099 /* linear equations by performing extra-precise iterative refinement */ 00100 /* and provides error bounds and backward error estimates for the solution. */ 00101 /* This subroutine is called by CHERFSX to perform iterative refinement. */ 00102 /* In addition to normwise error bound, the code provides maximum */ 00103 /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ 00104 /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ 00105 /* subroutine is only resonsible for setting the second fields of */ 00106 /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ 00107 00108 /* Arguments */ 00109 /* ========= */ 00110 00111 /* PREC_TYPE (input) INTEGER */ 00112 /* Specifies the intermediate precision to be used in refinement. */ 00113 /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ 00114 /* P = 'S': Single */ 00115 /* = 'D': Double */ 00116 /* = 'I': Indigenous */ 00117 /* = 'X', 'E': Extra */ 00118 00119 /* UPLO (input) CHARACTER*1 */ 00120 /* = 'U': Upper triangle of A is stored; */ 00121 /* = 'L': Lower triangle of A is stored. */ 00122 00123 /* N (input) INTEGER */ 00124 /* The number of linear equations, i.e., the order of the */ 00125 /* matrix A. N >= 0. */ 00126 00127 /* NRHS (input) INTEGER */ 00128 /* The number of right-hand-sides, i.e., the number of columns of the */ 00129 /* matrix B. */ 00130 00131 /* A (input) COMPLEX array, dimension (LDA,N) */ 00132 /* On entry, the N-by-N matrix A. */ 00133 00134 /* LDA (input) INTEGER */ 00135 /* The leading dimension of the array A. LDA >= max(1,N). */ 00136 00137 /* AF (input) COMPLEX array, dimension (LDAF,N) */ 00138 /* The block diagonal matrix D and the multipliers used to */ 00139 /* obtain the factor U or L as computed by CHETRF. */ 00140 00141 /* LDAF (input) INTEGER */ 00142 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00143 00144 /* IPIV (input) INTEGER array, dimension (N) */ 00145 /* Details of the interchanges and the block structure of D */ 00146 /* as determined by CHETRF. */ 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) REAL 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 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 array, dimension */ 00170 /* (LDY,NRHS) */ 00171 /* On entry, the solution matrix X, as computed by CHETRS. */ 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) REAL 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 CLA_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) REAL 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) REAL 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 array, dimension (N) */ 00285 /* Workspace to hold the intermediate residual. */ 00286 00287 /* AYB (input) REAL array, dimension (N) */ 00288 /* Workspace. */ 00289 00290 /* DY (input) COMPLEX array, dimension (N) */ 00291 /* Workspace to hold the intermediate solution. */ 00292 00293 /* Y_TAIL (input) COMPLEX array, dimension (N) */ 00294 /* Workspace to hold the trailing bits of the intermediate solution. */ 00295 00296 /* RCOND (input) REAL */ 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) REAL */ 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) REAL */ 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 CHETRS 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 --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 eps = slamch_("Epsilon"); 00389 hugeval = slamch_("Overflow"); 00390 /* Force HUGEVAL to Inf */ 00391 hugeval *= hugeval; 00392 /* Using HUGEVAL may lead to spurious underflows. */ 00393 incr_thresh__ = (real) (*n) * eps; 00394 if (lsame_(uplo, "L")) { 00395 uplo2 = ilauplo_("L"); 00396 } else { 00397 uplo2 = ilauplo_("U"); 00398 } 00399 i__1 = *nrhs; 00400 for (j = 1; j <= i__1; ++j) { 00401 y_prec_state__ = 1; 00402 if (y_prec_state__ == 2) { 00403 i__2 = *n; 00404 for (i__ = 1; i__ <= i__2; ++i__) { 00405 i__3 = i__; 00406 y_tail__[i__3].r = 0.f, y_tail__[i__3].i = 0.f; 00407 } 00408 } 00409 dxrat = 0.f; 00410 dxratmax = 0.f; 00411 dzrat = 0.f; 00412 dzratmax = 0.f; 00413 final_dx_x__ = hugeval; 00414 final_dz_z__ = hugeval; 00415 prevnormdx = hugeval; 00416 prev_dz_z__ = hugeval; 00417 dz_z__ = hugeval; 00418 dx_x__ = hugeval; 00419 x_state__ = 1; 00420 z_state__ = 0; 00421 incr_prec__ = FALSE_; 00422 i__2 = *ithresh; 00423 for (cnt = 1; cnt <= i__2; ++cnt) { 00424 00425 /* Compute residual RES = B_s - op(A_s) * Y, */ 00426 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00427 00428 ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00429 if (y_prec_state__ == 0) { 00430 chemv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], 00431 &c__1, &c_b12, &res[1], &c__1); 00432 } else if (y_prec_state__ == 1) { 00433 blas_chemv_x__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * 00434 y_dim1 + 1], &c__1, &c_b12, &res[1], &c__1, 00435 prec_type__); 00436 } else { 00437 blas_chemv2_x__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * 00438 y_dim1 + 1], &y_tail__[1], &c__1, &c_b12, &res[1], & 00439 c__1, prec_type__); 00440 } 00441 /* XXX: RES is no longer needed. */ 00442 ccopy_(n, &res[1], &c__1, &dy[1], &c__1); 00443 chetrs_(uplo, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &dy[1], n, 00444 info); 00445 00446 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00447 00448 normx = 0.f; 00449 normy = 0.f; 00450 normdx = 0.f; 00451 dz_z__ = 0.f; 00452 ymin = hugeval; 00453 i__3 = *n; 00454 for (i__ = 1; i__ <= i__3; ++i__) { 00455 i__4 = i__ + j * y_dim1; 00456 yk = (r__1 = y[i__4].r, dabs(r__1)) + (r__2 = r_imag(&y[i__ + 00457 j * y_dim1]), dabs(r__2)); 00458 i__4 = i__; 00459 dyk = (r__1 = dy[i__4].r, dabs(r__1)) + (r__2 = r_imag(&dy[ 00460 i__]), dabs(r__2)); 00461 if (yk != 0.f) { 00462 /* Computing MAX */ 00463 r__1 = dz_z__, r__2 = dyk / yk; 00464 dz_z__ = dmax(r__1,r__2); 00465 } else if (dyk != 0.f) { 00466 dz_z__ = hugeval; 00467 } 00468 ymin = dmin(ymin,yk); 00469 normy = dmax(normy,yk); 00470 if (*colequ) { 00471 /* Computing MAX */ 00472 r__1 = normx, r__2 = yk * c__[i__]; 00473 normx = dmax(r__1,r__2); 00474 /* Computing MAX */ 00475 r__1 = normdx, r__2 = dyk * c__[i__]; 00476 normdx = dmax(r__1,r__2); 00477 } else { 00478 normx = normy; 00479 normdx = dmax(normdx,dyk); 00480 } 00481 } 00482 if (normx != 0.f) { 00483 dx_x__ = normdx / normx; 00484 } else if (normdx == 0.f) { 00485 dx_x__ = 0.f; 00486 } else { 00487 dx_x__ = hugeval; 00488 } 00489 dxrat = normdx / prevnormdx; 00490 dzrat = dz_z__ / prev_dz_z__; 00491 00492 /* Check termination criteria. */ 00493 00494 if (ymin * *rcond < incr_thresh__ * normy && 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 if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1)) { 00547 goto L666; 00548 } 00549 if (incr_prec__) { 00550 incr_prec__ = FALSE_; 00551 ++y_prec_state__; 00552 i__3 = *n; 00553 for (i__ = 1; i__ <= i__3; ++i__) { 00554 i__4 = i__; 00555 y_tail__[i__4].r = 0.f, y_tail__[i__4].i = 0.f; 00556 } 00557 } 00558 prevnormdx = normdx; 00559 prev_dz_z__ = dz_z__; 00560 00561 /* Update soluton. */ 00562 00563 if (y_prec_state__ < 2) { 00564 caxpy_(n, &c_b12, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00565 } else { 00566 cla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00567 } 00568 } 00569 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00570 L666: 00571 00572 /* Set final_* when cnt hits ithresh. */ 00573 00574 if (x_state__ == 1) { 00575 final_dx_x__ = dx_x__; 00576 } 00577 if (z_state__ == 1) { 00578 final_dz_z__ = dz_z__; 00579 } 00580 00581 /* Compute error bounds. */ 00582 00583 if (*n_norms__ >= 1) { 00584 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 00585 1 - dxratmax); 00586 } 00587 if (*n_norms__ >= 2) { 00588 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 00589 1 - dzratmax); 00590 } 00591 00592 /* Compute componentwise relative backward error from formula */ 00593 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00594 /* where abs(Z) is the componentwise absolute value of the matrix */ 00595 /* or vector Z. */ 00596 00597 /* Compute residual RES = B_s - op(A_s) * Y, */ 00598 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00599 00600 ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00601 chemv_(uplo, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, 00602 &c_b12, &res[1], &c__1); 00603 i__2 = *n; 00604 for (i__ = 1; i__ <= i__2; ++i__) { 00605 i__3 = i__ + j * b_dim1; 00606 ayb[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[i__ 00607 + j * b_dim1]), dabs(r__2)); 00608 } 00609 00610 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00611 00612 cla_heamv__(&uplo2, n, &c_b33, &a[a_offset], lda, &y[j * y_dim1 + 1], 00613 &c__1, &c_b33, &ayb[1], &c__1); 00614 cla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00615 00616 /* End of loop for each RHS. */ 00617 00618 } 00619 00620 return 0; 00621 } /* cla_herfsx_extended__ */