00001 /* sla_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 real c_b9 = -1.f; 00020 static real c_b11 = 1.f; 00021 00022 /* Subroutine */ int sla_porfsx_extended__(integer *prec_type__, char *uplo, 00023 integer *n, integer *nrhs, real *a, integer *lda, real *af, integer * 00024 ldaf, logical *colequ, real *c__, real *b, integer *ldb, real *y, 00025 integer *ldy, real *berr_out__, integer *n_norms__, real * 00026 err_bnds_norm__, real *err_bnds_comp__, real *res, real *ayb, real * 00027 dy, real *y_tail__, real *rcond, integer *ithresh, real *rthresh, 00028 real *dz_ub__, logical *ignore_cwise__, integer *info, ftnlen 00029 uplo_len) 00030 { 00031 /* System generated locals */ 00032 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1, 00033 y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00034 err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3; 00035 real r__1, r__2; 00036 00037 /* Local variables */ 00038 real dxratmax, dzratmax; 00039 integer i__, j; 00040 logical incr_prec__; 00041 extern /* Subroutine */ int sla_syamv__(integer *, integer *, real *, 00042 real *, integer *, real *, integer *, real *, real *, integer *); 00043 real prev_dz_z__, yk, final_dx_x__, final_dz_z__; 00044 extern /* Subroutine */ int sla_wwaddw__(integer *, real *, real *, real * 00045 ); 00046 real prevnormdx; 00047 integer cnt; 00048 real dyk, eps, incr_thresh__, dx_x__, dz_z__, ymin; 00049 extern /* Subroutine */ int sla_lin_berr__(integer *, integer *, integer * 00050 , real *, real *, real *); 00051 integer y_prec_state__, uplo2; 00052 extern /* Subroutine */ int blas_ssymv_x__(integer *, integer *, real *, 00053 real *, integer *, real *, integer *, real *, real *, integer *, 00054 integer *); 00055 extern logical lsame_(char *, char *); 00056 real dxrat, dzrat; 00057 extern /* Subroutine */ int blas_ssymv2_x__(integer *, integer *, real *, 00058 real *, integer *, real *, real *, integer *, real *, real *, 00059 integer *, integer *), scopy_(integer *, real *, integer *, real * 00060 , integer *); 00061 real normx, normy; 00062 extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 00063 real *, integer *), ssymv_(char *, integer *, real *, real *, 00064 integer *, real *, integer *, real *, real *, integer *); 00065 extern doublereal slamch_(char *); 00066 real normdx; 00067 extern /* Subroutine */ int spotrs_(char *, integer *, integer *, real *, 00068 integer *, real *, integer *, integer *); 00069 real hugeval; 00070 extern integer ilauplo_(char *); 00071 integer x_state__, z_state__; 00072 00073 00074 /* -- LAPACK routine (version 3.2.1) -- */ 00075 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00076 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00077 /* -- April 2009 -- */ 00078 00079 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00080 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00081 00082 /* .. */ 00083 /* .. Scalar Arguments .. */ 00084 /* .. */ 00085 /* .. Array Arguments .. */ 00086 /* .. */ 00087 00088 /* Purpose */ 00089 /* ======= */ 00090 00091 /* SLA_PORFSX_EXTENDED improves the computed solution to a system of */ 00092 /* linear equations by performing extra-precise iterative refinement */ 00093 /* and provides error bounds and backward error estimates for the solution. */ 00094 /* This subroutine is called by SPORFSX to perform iterative refinement. */ 00095 /* In addition to normwise error bound, the code provides maximum */ 00096 /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ 00097 /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ 00098 /* subroutine is only resonsible for setting the second fields of */ 00099 /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ 00100 00101 /* Arguments */ 00102 /* ========= */ 00103 00104 /* PREC_TYPE (input) INTEGER */ 00105 /* Specifies the intermediate precision to be used in refinement. */ 00106 /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ 00107 /* P = 'S': Single */ 00108 /* = 'D': Double */ 00109 /* = 'I': Indigenous */ 00110 /* = 'X', 'E': Extra */ 00111 00112 /* UPLO (input) CHARACTER*1 */ 00113 /* = 'U': Upper triangle of A is stored; */ 00114 /* = 'L': Lower triangle of A is stored. */ 00115 00116 /* N (input) INTEGER */ 00117 /* The number of linear equations, i.e., the order of the */ 00118 /* matrix A. N >= 0. */ 00119 00120 /* NRHS (input) INTEGER */ 00121 /* The number of right-hand-sides, i.e., the number of columns of the */ 00122 /* matrix B. */ 00123 00124 /* A (input) REAL array, dimension (LDA,N) */ 00125 /* On entry, the N-by-N matrix A. */ 00126 00127 /* LDA (input) INTEGER */ 00128 /* The leading dimension of the array A. LDA >= max(1,N). */ 00129 00130 /* AF (input) REAL array, dimension (LDAF,N) */ 00131 /* The triangular factor U or L from the Cholesky factorization */ 00132 /* A = U**T*U or A = L*L**T, as computed by SPOTRF. */ 00133 00134 /* LDAF (input) INTEGER */ 00135 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00136 00137 /* COLEQU (input) LOGICAL */ 00138 /* If .TRUE. then column equilibration was done to A before calling */ 00139 /* this routine. This is needed to compute the solution and error */ 00140 /* bounds correctly. */ 00141 00142 /* C (input) REAL array, dimension (N) */ 00143 /* The column scale factors for A. If COLEQU = .FALSE., C */ 00144 /* is not accessed. If C is input, each element of C should be a power */ 00145 /* of the radix to ensure a reliable solution and error estimates. */ 00146 /* Scaling by powers of the radix does not cause rounding errors unless */ 00147 /* the result underflows or overflows. Rounding errors during scaling */ 00148 /* lead to refining with a matrix that is not equivalent to the */ 00149 /* input matrix, producing error estimates that may not be */ 00150 /* reliable. */ 00151 00152 /* B (input) REAL array, dimension (LDB,NRHS) */ 00153 /* The right-hand-side matrix B. */ 00154 00155 /* LDB (input) INTEGER */ 00156 /* The leading dimension of the array B. LDB >= max(1,N). */ 00157 00158 /* Y (input/output) REAL array, dimension (LDY,NRHS) */ 00159 /* On entry, the solution matrix X, as computed by SPOTRS. */ 00160 /* On exit, the improved solution matrix Y. */ 00161 00162 /* LDY (input) INTEGER */ 00163 /* The leading dimension of the array Y. LDY >= max(1,N). */ 00164 00165 /* BERR_OUT (output) REAL array, dimension (NRHS) */ 00166 /* On exit, BERR_OUT(j) contains the componentwise relative backward */ 00167 /* error for right-hand-side j from the formula */ 00168 /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00169 /* where abs(Z) is the componentwise absolute value of the matrix */ 00170 /* or vector Z. This is computed by SLA_LIN_BERR. */ 00171 00172 /* N_NORMS (input) INTEGER */ 00173 /* Determines which error bounds to return (see ERR_BNDS_NORM */ 00174 /* and ERR_BNDS_COMP). */ 00175 /* If N_NORMS >= 1 return normwise error bounds. */ 00176 /* If N_NORMS >= 2 return componentwise error bounds. */ 00177 00178 /* ERR_BNDS_NORM (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00179 /* For each right-hand side, this array contains information about */ 00180 /* various error bounds and condition numbers corresponding to the */ 00181 /* normwise relative error, which is defined as follows: */ 00182 00183 /* Normwise relative error in the ith solution vector: */ 00184 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00185 /* ------------------------------ */ 00186 /* max_j abs(X(j,i)) */ 00187 00188 /* The array is indexed by the type of error information as described */ 00189 /* below. There currently are up to three pieces of information */ 00190 /* returned. */ 00191 00192 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00193 /* right-hand side. */ 00194 00195 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00196 /* three fields: */ 00197 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00198 /* reciprocal condition number is less than the threshold */ 00199 /* sqrt(n) * slamch('Epsilon'). */ 00200 00201 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00202 /* almost certainly within a factor of 10 of the true error */ 00203 /* so long as the next entry is greater than the threshold */ 00204 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00205 /* be trusted if the previous boolean is true. */ 00206 00207 /* err = 3 Reciprocal condition number: Estimated normwise */ 00208 /* reciprocal condition number. Compared with the threshold */ 00209 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00210 /* estimate is "guaranteed". These reciprocal condition */ 00211 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00212 /* appropriately scaled matrix Z. */ 00213 /* Let Z = S*A, where S scales each row by a power of the */ 00214 /* radix so all absolute row sums of Z are approximately 1. */ 00215 00216 /* This subroutine is only responsible for setting the second field */ 00217 /* above. */ 00218 /* See Lapack Working Note 165 for further details and extra */ 00219 /* cautions. */ 00220 00221 /* ERR_BNDS_COMP (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00222 /* For each right-hand side, this array contains information about */ 00223 /* various error bounds and condition numbers corresponding to the */ 00224 /* componentwise relative error, which is defined as follows: */ 00225 00226 /* Componentwise relative error in the ith solution vector: */ 00227 /* abs(XTRUE(j,i) - X(j,i)) */ 00228 /* max_j ---------------------- */ 00229 /* abs(X(j,i)) */ 00230 00231 /* The array is indexed by the right-hand side i (on which the */ 00232 /* componentwise relative error depends), and the type of error */ 00233 /* information as described below. There currently are up to three */ 00234 /* pieces of information returned for each right-hand side. If */ 00235 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00236 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00237 /* the first (:,N_ERR_BNDS) entries are returned. */ 00238 00239 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00240 /* right-hand side. */ 00241 00242 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00243 /* three fields: */ 00244 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00245 /* reciprocal condition number is less than the threshold */ 00246 /* sqrt(n) * slamch('Epsilon'). */ 00247 00248 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00249 /* almost certainly within a factor of 10 of the true error */ 00250 /* so long as the next entry is greater than the threshold */ 00251 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00252 /* be trusted if the previous boolean is true. */ 00253 00254 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00255 /* reciprocal condition number. Compared with the threshold */ 00256 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00257 /* estimate is "guaranteed". These reciprocal condition */ 00258 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00259 /* appropriately scaled matrix Z. */ 00260 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00261 /* current right-hand side and S scales each row of */ 00262 /* A*diag(x) by a power of the radix so all absolute row */ 00263 /* sums of Z are approximately 1. */ 00264 00265 /* This subroutine is only responsible for setting the second field */ 00266 /* above. */ 00267 /* See Lapack Working Note 165 for further details and extra */ 00268 /* cautions. */ 00269 00270 /* RES (input) REAL array, dimension (N) */ 00271 /* Workspace to hold the intermediate residual. */ 00272 00273 /* AYB (input) REAL array, dimension (N) */ 00274 /* Workspace. This can be the same workspace passed for Y_TAIL. */ 00275 00276 /* DY (input) REAL array, dimension (N) */ 00277 /* Workspace to hold the intermediate solution. */ 00278 00279 /* Y_TAIL (input) REAL array, dimension (N) */ 00280 /* Workspace to hold the trailing bits of the intermediate solution. */ 00281 00282 /* RCOND (input) REAL */ 00283 /* Reciprocal scaled condition number. This is an estimate of the */ 00284 /* reciprocal Skeel condition number of the matrix A after */ 00285 /* equilibration (if done). If this is less than the machine */ 00286 /* precision (in particular, if it is zero), the matrix is singular */ 00287 /* to working precision. Note that the error may still be small even */ 00288 /* if this number is very small and the matrix appears ill- */ 00289 /* conditioned. */ 00290 00291 /* ITHRESH (input) INTEGER */ 00292 /* The maximum number of residual computations allowed for */ 00293 /* refinement. The default is 10. For 'aggressive' set to 100 to */ 00294 /* permit convergence using approximate factorizations or */ 00295 /* factorizations other than LU. If the factorization uses a */ 00296 /* technique other than Gaussian elimination, the guarantees in */ 00297 /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ 00298 00299 /* RTHRESH (input) REAL */ 00300 /* Determines when to stop refinement if the error estimate stops */ 00301 /* decreasing. Refinement will stop when the next solution no longer */ 00302 /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ 00303 /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ 00304 /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ 00305 /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ 00306 /* for more details. */ 00307 00308 /* DZ_UB (input) REAL */ 00309 /* Determines when to start considering componentwise convergence. */ 00310 /* Componentwise convergence is only considered after each component */ 00311 /* of the solution Y is stable, which we definte as the relative */ 00312 /* change in each component being less than DZ_UB. The default value */ 00313 /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ 00314 /* more details. */ 00315 00316 /* IGNORE_CWISE (input) LOGICAL */ 00317 /* If .TRUE. then ignore componentwise convergence. Default value */ 00318 /* is .FALSE.. */ 00319 00320 /* INFO (output) INTEGER */ 00321 /* = 0: Successful exit. */ 00322 /* < 0: if INFO = -i, the ith argument to SPOTRS had an illegal */ 00323 /* value */ 00324 00325 /* ===================================================================== */ 00326 00327 /* .. Local Scalars .. */ 00328 /* .. */ 00329 /* .. Parameters .. */ 00330 /* .. */ 00331 /* .. External Functions .. */ 00332 /* .. */ 00333 /* .. External Subroutines .. */ 00334 /* .. */ 00335 /* .. Intrinsic Functions .. */ 00336 /* .. */ 00337 /* .. Executable Statements .. */ 00338 00339 /* Parameter adjustments */ 00340 err_bnds_comp_dim1 = *nrhs; 00341 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00342 err_bnds_comp__ -= err_bnds_comp_offset; 00343 err_bnds_norm_dim1 = *nrhs; 00344 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00345 err_bnds_norm__ -= err_bnds_norm_offset; 00346 a_dim1 = *lda; 00347 a_offset = 1 + a_dim1; 00348 a -= a_offset; 00349 af_dim1 = *ldaf; 00350 af_offset = 1 + af_dim1; 00351 af -= af_offset; 00352 --c__; 00353 b_dim1 = *ldb; 00354 b_offset = 1 + b_dim1; 00355 b -= b_offset; 00356 y_dim1 = *ldy; 00357 y_offset = 1 + y_dim1; 00358 y -= y_offset; 00359 --berr_out__; 00360 --res; 00361 --ayb; 00362 --dy; 00363 --y_tail__; 00364 00365 /* Function Body */ 00366 if (*info != 0) { 00367 return 0; 00368 } 00369 eps = slamch_("Epsilon"); 00370 hugeval = slamch_("Overflow"); 00371 /* Force HUGEVAL to Inf */ 00372 hugeval *= hugeval; 00373 /* Using HUGEVAL may lead to spurious underflows. */ 00374 incr_thresh__ = (real) (*n) * eps; 00375 if (lsame_(uplo, "L")) { 00376 uplo2 = ilauplo_("L"); 00377 } else { 00378 uplo2 = ilauplo_("U"); 00379 } 00380 i__1 = *nrhs; 00381 for (j = 1; j <= i__1; ++j) { 00382 y_prec_state__ = 1; 00383 if (y_prec_state__ == 2) { 00384 i__2 = *n; 00385 for (i__ = 1; i__ <= i__2; ++i__) { 00386 y_tail__[i__] = 0.f; 00387 } 00388 } 00389 dxrat = 0.f; 00390 dxratmax = 0.f; 00391 dzrat = 0.f; 00392 dzratmax = 0.f; 00393 final_dx_x__ = hugeval; 00394 final_dz_z__ = hugeval; 00395 prevnormdx = hugeval; 00396 prev_dz_z__ = hugeval; 00397 dz_z__ = hugeval; 00398 dx_x__ = hugeval; 00399 x_state__ = 1; 00400 z_state__ = 0; 00401 incr_prec__ = FALSE_; 00402 i__2 = *ithresh; 00403 for (cnt = 1; cnt <= i__2; ++cnt) { 00404 00405 /* Compute residual RES = B_s - op(A_s) * Y, */ 00406 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00407 00408 scopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00409 if (y_prec_state__ == 0) { 00410 ssymv_(uplo, n, &c_b9, &a[a_offset], lda, &y[j * y_dim1 + 1], 00411 &c__1, &c_b11, &res[1], &c__1); 00412 } else if (y_prec_state__ == 1) { 00413 blas_ssymv_x__(&uplo2, n, &c_b9, &a[a_offset], lda, &y[j * 00414 y_dim1 + 1], &c__1, &c_b11, &res[1], &c__1, 00415 prec_type__); 00416 } else { 00417 blas_ssymv2_x__(&uplo2, n, &c_b9, &a[a_offset], lda, &y[j * 00418 y_dim1 + 1], &y_tail__[1], &c__1, &c_b11, &res[1], & 00419 c__1, prec_type__); 00420 } 00421 /* XXX: RES is no longer needed. */ 00422 scopy_(n, &res[1], &c__1, &dy[1], &c__1); 00423 spotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &dy[1], n, info); 00424 00425 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00426 00427 normx = 0.f; 00428 normy = 0.f; 00429 normdx = 0.f; 00430 dz_z__ = 0.f; 00431 ymin = hugeval; 00432 i__3 = *n; 00433 for (i__ = 1; i__ <= i__3; ++i__) { 00434 yk = (r__1 = y[i__ + j * y_dim1], dabs(r__1)); 00435 dyk = (r__1 = dy[i__], dabs(r__1)); 00436 if (yk != 0.f) { 00437 /* Computing MAX */ 00438 r__1 = dz_z__, r__2 = dyk / yk; 00439 dz_z__ = dmax(r__1,r__2); 00440 } else if (dyk != 0.f) { 00441 dz_z__ = hugeval; 00442 } 00443 ymin = dmin(ymin,yk); 00444 normy = dmax(normy,yk); 00445 if (*colequ) { 00446 /* Computing MAX */ 00447 r__1 = normx, r__2 = yk * c__[i__]; 00448 normx = dmax(r__1,r__2); 00449 /* Computing MAX */ 00450 r__1 = normdx, r__2 = dyk * c__[i__]; 00451 normdx = dmax(r__1,r__2); 00452 } else { 00453 normx = normy; 00454 normdx = dmax(normdx,dyk); 00455 } 00456 } 00457 if (normx != 0.f) { 00458 dx_x__ = normdx / normx; 00459 } else if (normdx == 0.f) { 00460 dx_x__ = 0.f; 00461 } else { 00462 dx_x__ = hugeval; 00463 } 00464 dxrat = normdx / prevnormdx; 00465 dzrat = dz_z__ / prev_dz_z__; 00466 00467 /* Check termination criteria. */ 00468 00469 if (ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2) { 00470 incr_prec__ = TRUE_; 00471 } 00472 if (x_state__ == 3 && dxrat <= *rthresh) { 00473 x_state__ = 1; 00474 } 00475 if (x_state__ == 1) { 00476 if (dx_x__ <= eps) { 00477 x_state__ = 2; 00478 } else if (dxrat > *rthresh) { 00479 if (y_prec_state__ != 2) { 00480 incr_prec__ = TRUE_; 00481 } else { 00482 x_state__ = 3; 00483 } 00484 } else { 00485 if (dxrat > dxratmax) { 00486 dxratmax = dxrat; 00487 } 00488 } 00489 if (x_state__ > 1) { 00490 final_dx_x__ = dx_x__; 00491 } 00492 } 00493 if (z_state__ == 0 && dz_z__ <= *dz_ub__) { 00494 z_state__ = 1; 00495 } 00496 if (z_state__ == 3 && dzrat <= *rthresh) { 00497 z_state__ = 1; 00498 } 00499 if (z_state__ == 1) { 00500 if (dz_z__ <= eps) { 00501 z_state__ = 2; 00502 } else if (dz_z__ > *dz_ub__) { 00503 z_state__ = 0; 00504 dzratmax = 0.f; 00505 final_dz_z__ = hugeval; 00506 } else if (dzrat > *rthresh) { 00507 if (y_prec_state__ != 2) { 00508 incr_prec__ = TRUE_; 00509 } else { 00510 z_state__ = 3; 00511 } 00512 } else { 00513 if (dzrat > dzratmax) { 00514 dzratmax = dzrat; 00515 } 00516 } 00517 if (z_state__ > 1) { 00518 final_dz_z__ = dz_z__; 00519 } 00520 } 00521 if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1)) { 00522 goto L666; 00523 } 00524 if (incr_prec__) { 00525 incr_prec__ = FALSE_; 00526 ++y_prec_state__; 00527 i__3 = *n; 00528 for (i__ = 1; i__ <= i__3; ++i__) { 00529 y_tail__[i__] = 0.f; 00530 } 00531 } 00532 prevnormdx = normdx; 00533 prev_dz_z__ = dz_z__; 00534 00535 /* Update soluton. */ 00536 00537 if (y_prec_state__ < 2) { 00538 saxpy_(n, &c_b11, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00539 } else { 00540 sla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00541 } 00542 } 00543 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00544 L666: 00545 00546 /* Set final_* when cnt hits ithresh. */ 00547 00548 if (x_state__ == 1) { 00549 final_dx_x__ = dx_x__; 00550 } 00551 if (z_state__ == 1) { 00552 final_dz_z__ = dz_z__; 00553 } 00554 00555 /* Compute error bounds. */ 00556 00557 if (*n_norms__ >= 1) { 00558 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 00559 1 - dxratmax); 00560 } 00561 if (*n_norms__ >= 2) { 00562 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 00563 1 - dzratmax); 00564 } 00565 00566 /* Compute componentwise relative backward error from formula */ 00567 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00568 /* where abs(Z) is the componentwise absolute value of the matrix */ 00569 /* or vector Z. */ 00570 00571 /* Compute residual RES = B_s - op(A_s) * Y, */ 00572 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00573 00574 scopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00575 ssymv_(uplo, n, &c_b9, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, & 00576 c_b11, &res[1], &c__1); 00577 i__2 = *n; 00578 for (i__ = 1; i__ <= i__2; ++i__) { 00579 ayb[i__] = (r__1 = b[i__ + j * b_dim1], dabs(r__1)); 00580 } 00581 00582 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00583 00584 sla_syamv__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], 00585 &c__1, &c_b11, &ayb[1], &c__1); 00586 sla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00587 00588 /* End of loop for each RHS. */ 00589 00590 } 00591 00592 return 0; 00593 } /* sla_porfsx_extended__ */