00001 /* cla_gbrfsx_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_gbrfsx_extended__(integer *prec_type__, integer * 00024 trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs, 00025 complex *ab, integer *ldab, complex *afb, integer *ldafb, integer * 00026 ipiv, logical *colequ, real *c__, complex *b, integer *ldb, complex * 00027 y, integer *ldy, real *berr_out__, integer *n_norms__, real * 00028 err_bnds_norm__, real *err_bnds_comp__, complex *res, real *ayb, 00029 complex *dy, complex *y_tail__, real *rcond, integer *ithresh, real * 00030 rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info) 00031 { 00032 /* System generated locals */ 00033 integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 00034 y_dim1, 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 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, m; 00045 extern /* Subroutine */ int cla_gbamv__(integer *, integer *, integer *, 00046 integer *, integer *, real *, complex *, integer *, complex *, 00047 integer *, real *, real *, 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_cgbmv_x__(integer *, integer *, integer * 00059 , integer *, integer *, complex *, complex *, integer *, complex * 00060 , integer *, complex *, complex *, integer *, integer *); 00061 integer y_prec_state__; 00062 extern /* Subroutine */ int blas_cgbmv2_x__(integer *, integer *, integer 00063 *, integer *, integer *, complex *, complex *, integer *, complex 00064 *, complex *, integer *, complex *, complex *, integer *, integer 00065 *), cgbmv_(char *, integer *, integer *, integer *, integer *, 00066 complex *, complex *, integer *, complex *, integer *, complex *, 00067 complex *, integer *), ccopy_(integer *, complex *, 00068 integer *, complex *, integer *); 00069 real dxrat, dzrat; 00070 extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, 00071 integer *, complex *, integer *); 00072 char trans[1]; 00073 real normx, normy; 00074 extern doublereal slamch_(char *); 00075 extern /* Subroutine */ int cgbtrs_(char *, integer *, integer *, integer 00076 *, integer *, complex *, integer *, integer *, complex *, integer 00077 *, integer *); 00078 real normdx; 00079 extern /* Character */ VOID chla_transtype__(char *, ftnlen, integer *); 00080 real hugeval; 00081 integer x_state__, z_state__; 00082 00083 00084 /* -- LAPACK routine (version 3.2.1) -- */ 00085 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00086 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00087 /* -- April 2009 -- */ 00088 00089 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00090 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00091 00092 /* .. */ 00093 /* .. Scalar Arguments .. */ 00094 /* .. */ 00095 /* .. Array Arguments .. */ 00096 /* .. */ 00097 00098 /* Purpose */ 00099 /* ======= */ 00100 00101 /* CLA_GBRFSX_EXTENDED improves the computed solution to a system of */ 00102 /* linear equations by performing extra-precise iterative refinement */ 00103 /* and provides error bounds and backward error estimates for the solution. */ 00104 /* This subroutine is called by CGBRFSX to perform iterative refinement. */ 00105 /* In addition to normwise error bound, the code provides maximum */ 00106 /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ 00107 /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ 00108 /* subroutine is only resonsible for setting the second fields of */ 00109 /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ 00110 00111 /* Arguments */ 00112 /* ========= */ 00113 00114 /* PREC_TYPE (input) INTEGER */ 00115 /* Specifies the intermediate precision to be used in refinement. */ 00116 /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ 00117 /* P = 'S': Single */ 00118 /* = 'D': Double */ 00119 /* = 'I': Indigenous */ 00120 /* = 'X', 'E': Extra */ 00121 00122 /* TRANS_TYPE (input) INTEGER */ 00123 /* Specifies the transposition operation on A. */ 00124 /* The value is defined by ILATRANS(T) where T is a CHARACTER and */ 00125 /* T = 'N': No transpose */ 00126 /* = 'T': Transpose */ 00127 /* = 'C': Conjugate transpose */ 00128 00129 /* N (input) INTEGER */ 00130 /* The number of linear equations, i.e., the order of the */ 00131 /* matrix A. N >= 0. */ 00132 00133 /* KL (input) INTEGER */ 00134 /* The number of subdiagonals within the band of A. KL >= 0. */ 00135 00136 /* KU (input) INTEGER */ 00137 /* The number of superdiagonals within the band of A. KU >= 0 */ 00138 00139 /* NRHS (input) INTEGER */ 00140 /* The number of right-hand-sides, i.e., the number of columns of the */ 00141 /* matrix B. */ 00142 00143 /* AB (input) COMPLEX array, dimension (LDA,N) */ 00144 /* On entry, the N-by-N matrix A. */ 00145 00146 /* LDAB (input) INTEGER */ 00147 /* The leading dimension of the array A. LDA >= max(1,N). */ 00148 00149 /* AFB (input) COMPLEX array, dimension (LDAF,N) */ 00150 /* The factors L and U from the factorization */ 00151 /* A = P*L*U as computed by CGBTRF. */ 00152 00153 /* LDAFB (input) INTEGER */ 00154 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00155 00156 /* IPIV (input) INTEGER array, dimension (N) */ 00157 /* The pivot indices from the factorization A = P*L*U */ 00158 /* as computed by CGBTRF; row i of the matrix was interchanged */ 00159 /* with row IPIV(i). */ 00160 00161 /* COLEQU (input) LOGICAL */ 00162 /* If .TRUE. then column equilibration was done to A before calling */ 00163 /* this routine. This is needed to compute the solution and error */ 00164 /* bounds correctly. */ 00165 00166 /* C (input) REAL array, dimension (N) */ 00167 /* The column scale factors for A. If COLEQU = .FALSE., C */ 00168 /* is not accessed. If C is input, each element of C should be a power */ 00169 /* of the radix to ensure a reliable solution and error estimates. */ 00170 /* Scaling by powers of the radix does not cause rounding errors unless */ 00171 /* the result underflows or overflows. Rounding errors during scaling */ 00172 /* lead to refining with a matrix that is not equivalent to the */ 00173 /* input matrix, producing error estimates that may not be */ 00174 /* reliable. */ 00175 00176 /* B (input) COMPLEX array, dimension (LDB,NRHS) */ 00177 /* The right-hand-side matrix B. */ 00178 00179 /* LDB (input) INTEGER */ 00180 /* The leading dimension of the array B. LDB >= max(1,N). */ 00181 00182 /* Y (input/output) COMPLEX array, dimension (LDY,NRHS) */ 00183 /* On entry, the solution matrix X, as computed by CGBTRS. */ 00184 /* On exit, the improved solution matrix Y. */ 00185 00186 /* LDY (input) INTEGER */ 00187 /* The leading dimension of the array Y. LDY >= max(1,N). */ 00188 00189 /* BERR_OUT (output) REAL array, dimension (NRHS) */ 00190 /* On exit, BERR_OUT(j) contains the componentwise relative backward */ 00191 /* error for right-hand-side j from the formula */ 00192 /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00193 /* where abs(Z) is the componentwise absolute value of the matrix */ 00194 /* or vector Z. This is computed by CLA_LIN_BERR. */ 00195 00196 /* N_NORMS (input) INTEGER */ 00197 /* Determines which error bounds to return (see ERR_BNDS_NORM */ 00198 /* and ERR_BNDS_COMP). */ 00199 /* If N_NORMS >= 1 return normwise error bounds. */ 00200 /* If N_NORMS >= 2 return componentwise error bounds. */ 00201 00202 /* ERR_BNDS_NORM (input/output) REAL array, dimension */ 00203 /* (NRHS, N_ERR_BNDS) */ 00204 /* For each right-hand side, this array contains information about */ 00205 /* various error bounds and condition numbers corresponding to the */ 00206 /* normwise relative error, which is defined as follows: */ 00207 00208 /* Normwise relative error in the ith solution vector: */ 00209 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00210 /* ------------------------------ */ 00211 /* max_j abs(X(j,i)) */ 00212 00213 /* The array is indexed by the type of error information as described */ 00214 /* below. There currently are up to three pieces of information */ 00215 /* returned. */ 00216 00217 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00218 /* right-hand side. */ 00219 00220 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00221 /* three fields: */ 00222 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00223 /* reciprocal condition number is less than the threshold */ 00224 /* sqrt(n) * slamch('Epsilon'). */ 00225 00226 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00227 /* almost certainly within a factor of 10 of the true error */ 00228 /* so long as the next entry is greater than the threshold */ 00229 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00230 /* be trusted if the previous boolean is true. */ 00231 00232 /* err = 3 Reciprocal condition number: Estimated normwise */ 00233 /* reciprocal condition number. Compared with the threshold */ 00234 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00235 /* estimate is "guaranteed". These reciprocal condition */ 00236 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00237 /* appropriately scaled matrix Z. */ 00238 /* Let Z = S*A, where S scales each row by a power of the */ 00239 /* radix so all absolute row sums of Z are approximately 1. */ 00240 00241 /* This subroutine is only responsible for setting the second field */ 00242 /* above. */ 00243 /* See Lapack Working Note 165 for further details and extra */ 00244 /* cautions. */ 00245 00246 /* ERR_BNDS_COMP (input/output) REAL array, dimension */ 00247 /* (NRHS, N_ERR_BNDS) */ 00248 /* For each right-hand side, this array contains information about */ 00249 /* various error bounds and condition numbers corresponding to the */ 00250 /* componentwise relative error, which is defined as follows: */ 00251 00252 /* Componentwise relative error in the ith solution vector: */ 00253 /* abs(XTRUE(j,i) - X(j,i)) */ 00254 /* max_j ---------------------- */ 00255 /* abs(X(j,i)) */ 00256 00257 /* The array is indexed by the right-hand side i (on which the */ 00258 /* componentwise relative error depends), and the type of error */ 00259 /* information as described below. There currently are up to three */ 00260 /* pieces of information returned for each right-hand side. If */ 00261 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00262 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00263 /* the first (:,N_ERR_BNDS) entries are returned. */ 00264 00265 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00266 /* right-hand side. */ 00267 00268 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00269 /* three fields: */ 00270 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00271 /* reciprocal condition number is less than the threshold */ 00272 /* sqrt(n) * slamch('Epsilon'). */ 00273 00274 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00275 /* almost certainly within a factor of 10 of the true error */ 00276 /* so long as the next entry is greater than the threshold */ 00277 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00278 /* be trusted if the previous boolean is true. */ 00279 00280 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00281 /* reciprocal condition number. Compared with the threshold */ 00282 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00283 /* estimate is "guaranteed". These reciprocal condition */ 00284 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00285 /* appropriately scaled matrix Z. */ 00286 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00287 /* current right-hand side and S scales each row of */ 00288 /* A*diag(x) by a power of the radix so all absolute row */ 00289 /* sums of Z are approximately 1. */ 00290 00291 /* This subroutine is only responsible for setting the second field */ 00292 /* above. */ 00293 /* See Lapack Working Note 165 for further details and extra */ 00294 /* cautions. */ 00295 00296 /* RES (input) COMPLEX array, dimension (N) */ 00297 /* Workspace to hold the intermediate residual. */ 00298 00299 /* AYB (input) REAL array, dimension (N) */ 00300 /* Workspace. */ 00301 00302 /* DY (input) COMPLEX array, dimension (N) */ 00303 /* Workspace to hold the intermediate solution. */ 00304 00305 /* Y_TAIL (input) COMPLEX array, dimension (N) */ 00306 /* Workspace to hold the trailing bits of the intermediate solution. */ 00307 00308 /* RCOND (input) REAL */ 00309 /* Reciprocal scaled condition number. This is an estimate of the */ 00310 /* reciprocal Skeel condition number of the matrix A after */ 00311 /* equilibration (if done). If this is less than the machine */ 00312 /* precision (in particular, if it is zero), the matrix is singular */ 00313 /* to working precision. Note that the error may still be small even */ 00314 /* if this number is very small and the matrix appears ill- */ 00315 /* conditioned. */ 00316 00317 /* ITHRESH (input) INTEGER */ 00318 /* The maximum number of residual computations allowed for */ 00319 /* refinement. The default is 10. For 'aggressive' set to 100 to */ 00320 /* permit convergence using approximate factorizations or */ 00321 /* factorizations other than LU. If the factorization uses a */ 00322 /* technique other than Gaussian elimination, the guarantees in */ 00323 /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ 00324 00325 /* RTHRESH (input) REAL */ 00326 /* Determines when to stop refinement if the error estimate stops */ 00327 /* decreasing. Refinement will stop when the next solution no longer */ 00328 /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ 00329 /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ 00330 /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ 00331 /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ 00332 /* for more details. */ 00333 00334 /* DZ_UB (input) REAL */ 00335 /* Determines when to start considering componentwise convergence. */ 00336 /* Componentwise convergence is only considered after each component */ 00337 /* of the solution Y is stable, which we definte as the relative */ 00338 /* change in each component being less than DZ_UB. The default value */ 00339 /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ 00340 /* more details. */ 00341 00342 /* IGNORE_CWISE (input) LOGICAL */ 00343 /* If .TRUE. then ignore componentwise convergence. Default value */ 00344 /* is .FALSE.. */ 00345 00346 /* INFO (output) INTEGER */ 00347 /* = 0: Successful exit. */ 00348 /* < 0: if INFO = -i, the ith argument to CGBTRS had an illegal */ 00349 /* value */ 00350 00351 /* ===================================================================== */ 00352 00353 /* .. Local Scalars .. */ 00354 /* .. */ 00355 /* .. Parameters .. */ 00356 /* .. */ 00357 /* .. External Subroutines .. */ 00358 /* .. */ 00359 /* .. Intrinsic Functions.. */ 00360 /* .. */ 00361 /* .. Statement Functions .. */ 00362 /* .. */ 00363 /* .. Statement Function Definitions .. */ 00364 /* .. */ 00365 /* .. Executable Statements .. */ 00366 00367 /* Parameter adjustments */ 00368 err_bnds_comp_dim1 = *nrhs; 00369 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00370 err_bnds_comp__ -= err_bnds_comp_offset; 00371 err_bnds_norm_dim1 = *nrhs; 00372 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00373 err_bnds_norm__ -= err_bnds_norm_offset; 00374 ab_dim1 = *ldab; 00375 ab_offset = 1 + ab_dim1; 00376 ab -= ab_offset; 00377 afb_dim1 = *ldafb; 00378 afb_offset = 1 + afb_dim1; 00379 afb -= afb_offset; 00380 --ipiv; 00381 --c__; 00382 b_dim1 = *ldb; 00383 b_offset = 1 + b_dim1; 00384 b -= b_offset; 00385 y_dim1 = *ldy; 00386 y_offset = 1 + y_dim1; 00387 y -= y_offset; 00388 --berr_out__; 00389 --res; 00390 --ayb; 00391 --dy; 00392 --y_tail__; 00393 00394 /* Function Body */ 00395 if (*info != 0) { 00396 return 0; 00397 } 00398 chla_transtype__(ch__1, (ftnlen)1, trans_type__); 00399 *(unsigned char *)trans = *(unsigned char *)&ch__1[0]; 00400 eps = slamch_("Epsilon"); 00401 hugeval = slamch_("Overflow"); 00402 /* Force HUGEVAL to Inf */ 00403 hugeval *= hugeval; 00404 /* Using HUGEVAL may lead to spurious underflows. */ 00405 incr_thresh__ = (real) (*n) * eps; 00406 m = *kl + *ku + 1; 00407 i__1 = *nrhs; 00408 for (j = 1; j <= i__1; ++j) { 00409 y_prec_state__ = 1; 00410 if (y_prec_state__ == 2) { 00411 i__2 = *n; 00412 for (i__ = 1; i__ <= i__2; ++i__) { 00413 i__3 = i__; 00414 y_tail__[i__3].r = 0.f, y_tail__[i__3].i = 0.f; 00415 } 00416 } 00417 dxrat = 0.f; 00418 dxratmax = 0.f; 00419 dzrat = 0.f; 00420 dzratmax = 0.f; 00421 final_dx_x__ = hugeval; 00422 final_dz_z__ = hugeval; 00423 prevnormdx = hugeval; 00424 prev_dz_z__ = hugeval; 00425 dz_z__ = hugeval; 00426 dx_x__ = hugeval; 00427 x_state__ = 1; 00428 z_state__ = 0; 00429 incr_prec__ = FALSE_; 00430 i__2 = *ithresh; 00431 for (cnt = 1; cnt <= i__2; ++cnt) { 00432 00433 /* Compute residual RES = B_s - op(A_s) * Y, */ 00434 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00435 00436 ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00437 if (y_prec_state__ == 0) { 00438 cgbmv_(trans, &m, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[ 00439 j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1); 00440 } else if (y_prec_state__ == 1) { 00441 blas_cgbmv_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[ 00442 ab_offset], ldab, &y[j * y_dim1 + 1], &c__1, &c_b8, & 00443 res[1], &c__1, prec_type__); 00444 } else { 00445 blas_cgbmv2_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[ 00446 ab_offset], ldab, &y[j * y_dim1 + 1], &y_tail__[1], & 00447 c__1, &c_b8, &res[1], &c__1, prec_type__); 00448 } 00449 /* XXX: RES is no longer needed. */ 00450 ccopy_(n, &res[1], &c__1, &dy[1], &c__1); 00451 cgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1] 00452 , &dy[1], n, info); 00453 00454 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00455 00456 normx = 0.f; 00457 normy = 0.f; 00458 normdx = 0.f; 00459 dz_z__ = 0.f; 00460 ymin = hugeval; 00461 i__3 = *n; 00462 for (i__ = 1; i__ <= i__3; ++i__) { 00463 i__4 = i__ + j * y_dim1; 00464 yk = (r__1 = y[i__4].r, dabs(r__1)) + (r__2 = r_imag(&y[i__ + 00465 j * y_dim1]), dabs(r__2)); 00466 i__4 = i__; 00467 dyk = (r__1 = dy[i__4].r, dabs(r__1)) + (r__2 = r_imag(&dy[ 00468 i__]), dabs(r__2)); 00469 if (yk != 0.f) { 00470 /* Computing MAX */ 00471 r__1 = dz_z__, r__2 = dyk / yk; 00472 dz_z__ = dmax(r__1,r__2); 00473 } else if (dyk != 0.f) { 00474 dz_z__ = hugeval; 00475 } 00476 ymin = dmin(ymin,yk); 00477 normy = dmax(normy,yk); 00478 if (*colequ) { 00479 /* Computing MAX */ 00480 r__1 = normx, r__2 = yk * c__[i__]; 00481 normx = dmax(r__1,r__2); 00482 /* Computing MAX */ 00483 r__1 = normdx, r__2 = dyk * c__[i__]; 00484 normdx = dmax(r__1,r__2); 00485 } else { 00486 normx = normy; 00487 normdx = dmax(normdx,dyk); 00488 } 00489 } 00490 if (normx != 0.f) { 00491 dx_x__ = normdx / normx; 00492 } else if (normdx == 0.f) { 00493 dx_x__ = 0.f; 00494 } else { 00495 dx_x__ = hugeval; 00496 } 00497 dxrat = normdx / prevnormdx; 00498 dzrat = dz_z__ / prev_dz_z__; 00499 00500 /* Check termination criteria. */ 00501 00502 if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy 00503 && y_prec_state__ < 2) { 00504 incr_prec__ = TRUE_; 00505 } 00506 if (x_state__ == 3 && dxrat <= *rthresh) { 00507 x_state__ = 1; 00508 } 00509 if (x_state__ == 1) { 00510 if (dx_x__ <= eps) { 00511 x_state__ = 2; 00512 } else if (dxrat > *rthresh) { 00513 if (y_prec_state__ != 2) { 00514 incr_prec__ = TRUE_; 00515 } else { 00516 x_state__ = 3; 00517 } 00518 } else { 00519 if (dxrat > dxratmax) { 00520 dxratmax = dxrat; 00521 } 00522 } 00523 if (x_state__ > 1) { 00524 final_dx_x__ = dx_x__; 00525 } 00526 } 00527 if (z_state__ == 0 && dz_z__ <= *dz_ub__) { 00528 z_state__ = 1; 00529 } 00530 if (z_state__ == 3 && dzrat <= *rthresh) { 00531 z_state__ = 1; 00532 } 00533 if (z_state__ == 1) { 00534 if (dz_z__ <= eps) { 00535 z_state__ = 2; 00536 } else if (dz_z__ > *dz_ub__) { 00537 z_state__ = 0; 00538 dzratmax = 0.f; 00539 final_dz_z__ = hugeval; 00540 } else if (dzrat > *rthresh) { 00541 if (y_prec_state__ != 2) { 00542 incr_prec__ = TRUE_; 00543 } else { 00544 z_state__ = 3; 00545 } 00546 } else { 00547 if (dzrat > dzratmax) { 00548 dzratmax = dzrat; 00549 } 00550 } 00551 if (z_state__ > 1) { 00552 final_dz_z__ = dz_z__; 00553 } 00554 } 00555 00556 /* Exit if both normwise and componentwise stopped working, */ 00557 /* but if componentwise is unstable, let it go at least two */ 00558 /* iterations. */ 00559 00560 if (x_state__ != 1) { 00561 if (*ignore_cwise__) { 00562 goto L666; 00563 } 00564 if (z_state__ == 3 || z_state__ == 2) { 00565 goto L666; 00566 } 00567 if (z_state__ == 0 && cnt > 1) { 00568 goto L666; 00569 } 00570 } 00571 if (incr_prec__) { 00572 incr_prec__ = FALSE_; 00573 ++y_prec_state__; 00574 i__3 = *n; 00575 for (i__ = 1; i__ <= i__3; ++i__) { 00576 i__4 = i__; 00577 y_tail__[i__4].r = 0.f, y_tail__[i__4].i = 0.f; 00578 } 00579 } 00580 prevnormdx = normdx; 00581 prev_dz_z__ = dz_z__; 00582 00583 /* Update soluton. */ 00584 00585 if (y_prec_state__ < 2) { 00586 caxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00587 } else { 00588 cla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00589 } 00590 } 00591 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00592 L666: 00593 00594 /* Set final_* when cnt hits ithresh. */ 00595 00596 if (x_state__ == 1) { 00597 final_dx_x__ = dx_x__; 00598 } 00599 if (z_state__ == 1) { 00600 final_dz_z__ = dz_z__; 00601 } 00602 00603 /* Compute error bounds. */ 00604 00605 if (*n_norms__ >= 1) { 00606 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 00607 1 - dxratmax); 00608 } 00609 if (*n_norms__ >= 2) { 00610 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 00611 1 - dzratmax); 00612 } 00613 00614 /* Compute componentwise relative backward error from formula */ 00615 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00616 /* where abs(Z) is the componentwise absolute value of the matrix */ 00617 /* or vector Z. */ 00618 00619 /* Compute residual RES = B_s - op(A_s) * Y, */ 00620 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00621 00622 ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00623 cgbmv_(trans, n, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[j * 00624 y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1); 00625 i__2 = *n; 00626 for (i__ = 1; i__ <= i__2; ++i__) { 00627 i__3 = i__ + j * b_dim1; 00628 ayb[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[i__ 00629 + j * b_dim1]), dabs(r__2)); 00630 } 00631 00632 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00633 00634 cla_gbamv__(trans_type__, n, n, kl, ku, &c_b31, &ab[ab_offset], ldab, 00635 &y[j * y_dim1 + 1], &c__1, &c_b31, &ayb[1], &c__1); 00636 cla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00637 00638 /* End of loop for each RHS. */ 00639 00640 } 00641 00642 return 0; 00643 } /* cla_gbrfsx_extended__ */