00001 /* dla_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 doublereal c_b9 = -1.; 00020 static doublereal c_b11 = 1.; 00021 00022 /* Subroutine */ int dla_porfsx_extended__(integer *prec_type__, char *uplo, 00023 integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal * 00024 af, integer *ldaf, logical *colequ, doublereal *c__, doublereal *b, 00025 integer *ldb, doublereal *y, integer *ldy, doublereal *berr_out__, 00026 integer *n_norms__, doublereal *err_bnds_norm__, doublereal * 00027 err_bnds_comp__, doublereal *res, doublereal *ayb, doublereal *dy, 00028 doublereal *y_tail__, doublereal *rcond, integer *ithresh, doublereal 00029 *rthresh, doublereal *dz_ub__, logical *ignore_cwise__, integer *info, 00030 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; 00036 doublereal d__1, d__2; 00037 00038 /* Local variables */ 00039 doublereal dxratmax, dzratmax; 00040 integer i__, j; 00041 logical incr_prec__; 00042 extern /* Subroutine */ int dla_syamv__(integer *, integer *, doublereal * 00043 , doublereal *, integer *, doublereal *, integer *, doublereal *, 00044 doublereal *, integer *); 00045 doublereal prev_dz_z__, yk, final_dx_x__; 00046 extern /* Subroutine */ int dla_wwaddw__(integer *, doublereal *, 00047 doublereal *, doublereal *); 00048 doublereal final_dz_z__, prevnormdx; 00049 integer cnt; 00050 doublereal dyk, eps, incr_thresh__, dx_x__, dz_z__; 00051 extern /* Subroutine */ int dla_lin_berr__(integer *, integer *, integer * 00052 , doublereal *, doublereal *, doublereal *); 00053 doublereal ymin; 00054 integer y_prec_state__; 00055 extern /* Subroutine */ int blas_dsymv_x__(integer *, integer *, 00056 doublereal *, doublereal *, integer *, doublereal *, integer *, 00057 doublereal *, doublereal *, integer *, integer *); 00058 integer uplo2; 00059 extern logical lsame_(char *, char *); 00060 extern /* Subroutine */ int blas_dsymv2_x__(integer *, integer *, 00061 doublereal *, doublereal *, integer *, doublereal *, doublereal *, 00062 integer *, doublereal *, doublereal *, integer *, integer *), 00063 dcopy_(integer *, doublereal *, integer *, doublereal *, integer * 00064 ); 00065 doublereal dxrat, dzrat; 00066 extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 00067 integer *, doublereal *, integer *), dsymv_(char *, integer *, 00068 doublereal *, doublereal *, integer *, doublereal *, integer *, 00069 doublereal *, doublereal *, integer *); 00070 doublereal normx, normy; 00071 extern doublereal dlamch_(char *); 00072 doublereal normdx; 00073 extern /* Subroutine */ int dpotrs_(char *, integer *, integer *, 00074 doublereal *, integer *, doublereal *, integer *, integer *); 00075 doublereal hugeval; 00076 extern integer ilauplo_(char *); 00077 integer x_state__, z_state__; 00078 00079 00080 /* -- LAPACK routine (version 3.2.1) -- */ 00081 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00082 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00083 /* -- April 2009 -- */ 00084 00085 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00086 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00087 00088 /* .. */ 00089 /* .. Scalar Arguments .. */ 00090 /* .. */ 00091 /* .. Array Arguments .. */ 00092 /* .. */ 00093 00094 /* Purpose */ 00095 /* ======= */ 00096 00097 /* DLA_PORFSX_EXTENDED improves the computed solution to a system of */ 00098 /* linear equations by performing extra-precise iterative refinement */ 00099 /* and provides error bounds and backward error estimates for the solution. */ 00100 /* This subroutine is called by DPORFSX to perform iterative refinement. */ 00101 /* In addition to normwise error bound, the code provides maximum */ 00102 /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ 00103 /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ 00104 /* subroutine is only resonsible for setting the second fields of */ 00105 /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ 00106 00107 /* Arguments */ 00108 /* ========= */ 00109 00110 /* PREC_TYPE (input) INTEGER */ 00111 /* Specifies the intermediate precision to be used in refinement. */ 00112 /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ 00113 /* P = 'S': Single */ 00114 /* = 'D': Double */ 00115 /* = 'I': Indigenous */ 00116 /* = 'X', 'E': Extra */ 00117 00118 /* UPLO (input) CHARACTER*1 */ 00119 /* = 'U': Upper triangle of A is stored; */ 00120 /* = 'L': Lower triangle of A is stored. */ 00121 00122 /* N (input) INTEGER */ 00123 /* The number of linear equations, i.e., the order of the */ 00124 /* matrix A. N >= 0. */ 00125 00126 /* NRHS (input) INTEGER */ 00127 /* The number of right-hand-sides, i.e., the number of columns of the */ 00128 /* matrix B. */ 00129 00130 /* A (input) DOUBLE PRECISION array, dimension (LDA,N) */ 00131 /* On entry, the N-by-N matrix A. */ 00132 00133 /* LDA (input) INTEGER */ 00134 /* The leading dimension of the array A. LDA >= max(1,N). */ 00135 00136 /* AF (input) DOUBLE PRECISION array, dimension (LDAF,N) */ 00137 /* The triangular factor U or L from the Cholesky factorization */ 00138 /* A = U**T*U or A = L*L**T, as computed by DPOTRF. */ 00139 00140 /* LDAF (input) INTEGER */ 00141 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00142 00143 /* COLEQU (input) LOGICAL */ 00144 /* If .TRUE. then column equilibration was done to A before calling */ 00145 /* this routine. This is needed to compute the solution and error */ 00146 /* bounds correctly. */ 00147 00148 /* C (input) DOUBLE PRECISION array, dimension (N) */ 00149 /* The column scale factors for A. If COLEQU = .FALSE., C */ 00150 /* is not accessed. If C is input, each element of C should be a power */ 00151 /* of the radix to ensure a reliable solution and error estimates. */ 00152 /* Scaling by powers of the radix does not cause rounding errors unless */ 00153 /* the result underflows or overflows. Rounding errors during scaling */ 00154 /* lead to refining with a matrix that is not equivalent to the */ 00155 /* input matrix, producing error estimates that may not be */ 00156 /* reliable. */ 00157 00158 /* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */ 00159 /* The right-hand-side matrix B. */ 00160 00161 /* LDB (input) INTEGER */ 00162 /* The leading dimension of the array B. LDB >= max(1,N). */ 00163 00164 /* Y (input/output) DOUBLE PRECISION array, dimension */ 00165 /* (LDY,NRHS) */ 00166 /* On entry, the solution matrix X, as computed by DPOTRS. */ 00167 /* On exit, the improved solution matrix Y. */ 00168 00169 /* LDY (input) INTEGER */ 00170 /* The leading dimension of the array Y. LDY >= max(1,N). */ 00171 00172 /* BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS) */ 00173 /* On exit, BERR_OUT(j) contains the componentwise relative backward */ 00174 /* error for right-hand-side j from the formula */ 00175 /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00176 /* where abs(Z) is the componentwise absolute value of the matrix */ 00177 /* or vector Z. This is computed by DLA_LIN_BERR. */ 00178 00179 /* N_NORMS (input) INTEGER */ 00180 /* Determines which error bounds to return (see ERR_BNDS_NORM */ 00181 /* and ERR_BNDS_COMP). */ 00182 /* If N_NORMS >= 1 return normwise error bounds. */ 00183 /* If N_NORMS >= 2 return componentwise error bounds. */ 00184 00185 /* ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension */ 00186 /* (NRHS, N_ERR_BNDS) */ 00187 /* For each right-hand side, this array contains information about */ 00188 /* various error bounds and condition numbers corresponding to the */ 00189 /* normwise relative error, which is defined as follows: */ 00190 00191 /* Normwise relative error in the ith solution vector: */ 00192 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00193 /* ------------------------------ */ 00194 /* max_j abs(X(j,i)) */ 00195 00196 /* The array is indexed by the type of error information as described */ 00197 /* below. There currently are up to three pieces of information */ 00198 /* returned. */ 00199 00200 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00201 /* right-hand side. */ 00202 00203 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00204 /* three fields: */ 00205 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00206 /* reciprocal condition number is less than the threshold */ 00207 /* sqrt(n) * slamch('Epsilon'). */ 00208 00209 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00210 /* almost certainly within a factor of 10 of the true error */ 00211 /* so long as the next entry is greater than the threshold */ 00212 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00213 /* be trusted if the previous boolean is true. */ 00214 00215 /* err = 3 Reciprocal condition number: Estimated normwise */ 00216 /* reciprocal condition number. Compared with the threshold */ 00217 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00218 /* estimate is "guaranteed". These reciprocal condition */ 00219 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00220 /* appropriately scaled matrix Z. */ 00221 /* Let Z = S*A, where S scales each row by a power of the */ 00222 /* radix so all absolute row sums of Z are approximately 1. */ 00223 00224 /* This subroutine is only responsible for setting the second field */ 00225 /* above. */ 00226 /* See Lapack Working Note 165 for further details and extra */ 00227 /* cautions. */ 00228 00229 /* ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension */ 00230 /* (NRHS, N_ERR_BNDS) */ 00231 /* For each right-hand side, this array contains information about */ 00232 /* various error bounds and condition numbers corresponding to the */ 00233 /* componentwise relative error, which is defined as follows: */ 00234 00235 /* Componentwise relative error in the ith solution vector: */ 00236 /* abs(XTRUE(j,i) - X(j,i)) */ 00237 /* max_j ---------------------- */ 00238 /* abs(X(j,i)) */ 00239 00240 /* The array is indexed by the right-hand side i (on which the */ 00241 /* componentwise relative error depends), and the type of error */ 00242 /* information as described below. There currently are up to three */ 00243 /* pieces of information returned for each right-hand side. If */ 00244 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00245 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00246 /* the first (:,N_ERR_BNDS) entries are returned. */ 00247 00248 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00249 /* right-hand side. */ 00250 00251 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00252 /* three fields: */ 00253 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00254 /* reciprocal condition number is less than the threshold */ 00255 /* sqrt(n) * slamch('Epsilon'). */ 00256 00257 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00258 /* almost certainly within a factor of 10 of the true error */ 00259 /* so long as the next entry is greater than the threshold */ 00260 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00261 /* be trusted if the previous boolean is true. */ 00262 00263 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00264 /* reciprocal condition number. Compared with the threshold */ 00265 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00266 /* estimate is "guaranteed". These reciprocal condition */ 00267 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00268 /* appropriately scaled matrix Z. */ 00269 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00270 /* current right-hand side and S scales each row of */ 00271 /* A*diag(x) by a power of the radix so all absolute row */ 00272 /* sums of Z are approximately 1. */ 00273 00274 /* This subroutine is only responsible for setting the second field */ 00275 /* above. */ 00276 /* See Lapack Working Note 165 for further details and extra */ 00277 /* cautions. */ 00278 00279 /* RES (input) DOUBLE PRECISION array, dimension (N) */ 00280 /* Workspace to hold the intermediate residual. */ 00281 00282 /* AYB (input) DOUBLE PRECISION array, dimension (N) */ 00283 /* Workspace. This can be the same workspace passed for Y_TAIL. */ 00284 00285 /* DY (input) DOUBLE PRECISION array, dimension (N) */ 00286 /* Workspace to hold the intermediate solution. */ 00287 00288 /* Y_TAIL (input) DOUBLE PRECISION array, dimension (N) */ 00289 /* Workspace to hold the trailing bits of the intermediate solution. */ 00290 00291 /* RCOND (input) DOUBLE PRECISION */ 00292 /* Reciprocal scaled condition number. This is an estimate of the */ 00293 /* reciprocal Skeel condition number of the matrix A after */ 00294 /* equilibration (if done). If this is less than the machine */ 00295 /* precision (in particular, if it is zero), the matrix is singular */ 00296 /* to working precision. Note that the error may still be small even */ 00297 /* if this number is very small and the matrix appears ill- */ 00298 /* conditioned. */ 00299 00300 /* ITHRESH (input) INTEGER */ 00301 /* The maximum number of residual computations allowed for */ 00302 /* refinement. The default is 10. For 'aggressive' set to 100 to */ 00303 /* permit convergence using approximate factorizations or */ 00304 /* factorizations other than LU. If the factorization uses a */ 00305 /* technique other than Gaussian elimination, the guarantees in */ 00306 /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ 00307 00308 /* RTHRESH (input) DOUBLE PRECISION */ 00309 /* Determines when to stop refinement if the error estimate stops */ 00310 /* decreasing. Refinement will stop when the next solution no longer */ 00311 /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ 00312 /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ 00313 /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ 00314 /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ 00315 /* for more details. */ 00316 00317 /* DZ_UB (input) DOUBLE PRECISION */ 00318 /* Determines when to start considering componentwise convergence. */ 00319 /* Componentwise convergence is only considered after each component */ 00320 /* of the solution Y is stable, which we definte as the relative */ 00321 /* change in each component being less than DZ_UB. The default value */ 00322 /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ 00323 /* more details. */ 00324 00325 /* IGNORE_CWISE (input) LOGICAL */ 00326 /* If .TRUE. then ignore componentwise convergence. Default value */ 00327 /* is .FALSE.. */ 00328 00329 /* INFO (output) INTEGER */ 00330 /* = 0: Successful exit. */ 00331 /* < 0: if INFO = -i, the ith argument to DPOTRS had an illegal */ 00332 /* value */ 00333 00334 /* ===================================================================== */ 00335 00336 /* .. Local Scalars .. */ 00337 /* .. */ 00338 /* .. Parameters .. */ 00339 /* .. */ 00340 /* .. External Functions .. */ 00341 /* .. */ 00342 /* .. External Subroutines .. */ 00343 /* .. */ 00344 /* .. Intrinsic Functions .. */ 00345 /* .. */ 00346 /* .. Executable Statements .. */ 00347 00348 /* Parameter adjustments */ 00349 err_bnds_comp_dim1 = *nrhs; 00350 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00351 err_bnds_comp__ -= err_bnds_comp_offset; 00352 err_bnds_norm_dim1 = *nrhs; 00353 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00354 err_bnds_norm__ -= err_bnds_norm_offset; 00355 a_dim1 = *lda; 00356 a_offset = 1 + a_dim1; 00357 a -= a_offset; 00358 af_dim1 = *ldaf; 00359 af_offset = 1 + af_dim1; 00360 af -= af_offset; 00361 --c__; 00362 b_dim1 = *ldb; 00363 b_offset = 1 + b_dim1; 00364 b -= b_offset; 00365 y_dim1 = *ldy; 00366 y_offset = 1 + y_dim1; 00367 y -= y_offset; 00368 --berr_out__; 00369 --res; 00370 --ayb; 00371 --dy; 00372 --y_tail__; 00373 00374 /* Function Body */ 00375 if (*info != 0) { 00376 return 0; 00377 } 00378 eps = dlamch_("Epsilon"); 00379 hugeval = dlamch_("Overflow"); 00380 /* Force HUGEVAL to Inf */ 00381 hugeval *= hugeval; 00382 /* Using HUGEVAL may lead to spurious underflows. */ 00383 incr_thresh__ = (doublereal) (*n) * eps; 00384 if (lsame_(uplo, "L")) { 00385 uplo2 = ilauplo_("L"); 00386 } else { 00387 uplo2 = ilauplo_("U"); 00388 } 00389 i__1 = *nrhs; 00390 for (j = 1; j <= i__1; ++j) { 00391 y_prec_state__ = 1; 00392 if (y_prec_state__ == 2) { 00393 i__2 = *n; 00394 for (i__ = 1; i__ <= i__2; ++i__) { 00395 y_tail__[i__] = 0.; 00396 } 00397 } 00398 dxrat = 0.; 00399 dxratmax = 0.; 00400 dzrat = 0.; 00401 dzratmax = 0.; 00402 final_dx_x__ = hugeval; 00403 final_dz_z__ = hugeval; 00404 prevnormdx = hugeval; 00405 prev_dz_z__ = hugeval; 00406 dz_z__ = hugeval; 00407 dx_x__ = hugeval; 00408 x_state__ = 1; 00409 z_state__ = 0; 00410 incr_prec__ = FALSE_; 00411 i__2 = *ithresh; 00412 for (cnt = 1; cnt <= i__2; ++cnt) { 00413 00414 /* Compute residual RES = B_s - op(A_s) * Y, */ 00415 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00416 00417 dcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00418 if (y_prec_state__ == 0) { 00419 dsymv_(uplo, n, &c_b9, &a[a_offset], lda, &y[j * y_dim1 + 1], 00420 &c__1, &c_b11, &res[1], &c__1); 00421 } else if (y_prec_state__ == 1) { 00422 blas_dsymv_x__(&uplo2, n, &c_b9, &a[a_offset], lda, &y[j * 00423 y_dim1 + 1], &c__1, &c_b11, &res[1], &c__1, 00424 prec_type__); 00425 } else { 00426 blas_dsymv2_x__(&uplo2, n, &c_b9, &a[a_offset], lda, &y[j * 00427 y_dim1 + 1], &y_tail__[1], &c__1, &c_b11, &res[1], & 00428 c__1, prec_type__); 00429 } 00430 /* XXX: RES is no longer needed. */ 00431 dcopy_(n, &res[1], &c__1, &dy[1], &c__1); 00432 dpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &dy[1], n, info); 00433 00434 /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ 00435 00436 normx = 0.; 00437 normy = 0.; 00438 normdx = 0.; 00439 dz_z__ = 0.; 00440 ymin = hugeval; 00441 i__3 = *n; 00442 for (i__ = 1; i__ <= i__3; ++i__) { 00443 yk = (d__1 = y[i__ + j * y_dim1], abs(d__1)); 00444 dyk = (d__1 = dy[i__], abs(d__1)); 00445 if (yk != 0.) { 00446 /* Computing MAX */ 00447 d__1 = dz_z__, d__2 = dyk / yk; 00448 dz_z__ = max(d__1,d__2); 00449 } else if (dyk != 0.) { 00450 dz_z__ = hugeval; 00451 } 00452 ymin = min(ymin,yk); 00453 normy = max(normy,yk); 00454 if (*colequ) { 00455 /* Computing MAX */ 00456 d__1 = normx, d__2 = yk * c__[i__]; 00457 normx = max(d__1,d__2); 00458 /* Computing MAX */ 00459 d__1 = normdx, d__2 = dyk * c__[i__]; 00460 normdx = max(d__1,d__2); 00461 } else { 00462 normx = normy; 00463 normdx = max(normdx,dyk); 00464 } 00465 } 00466 if (normx != 0.) { 00467 dx_x__ = normdx / normx; 00468 } else if (normdx == 0.) { 00469 dx_x__ = 0.; 00470 } else { 00471 dx_x__ = hugeval; 00472 } 00473 dxrat = normdx / prevnormdx; 00474 dzrat = dz_z__ / prev_dz_z__; 00475 00476 /* Check termination criteria. */ 00477 00478 if (ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2) { 00479 incr_prec__ = TRUE_; 00480 } 00481 if (x_state__ == 3 && dxrat <= *rthresh) { 00482 x_state__ = 1; 00483 } 00484 if (x_state__ == 1) { 00485 if (dx_x__ <= eps) { 00486 x_state__ = 2; 00487 } else if (dxrat > *rthresh) { 00488 if (y_prec_state__ != 2) { 00489 incr_prec__ = TRUE_; 00490 } else { 00491 x_state__ = 3; 00492 } 00493 } else { 00494 if (dxrat > dxratmax) { 00495 dxratmax = dxrat; 00496 } 00497 } 00498 if (x_state__ > 1) { 00499 final_dx_x__ = dx_x__; 00500 } 00501 } 00502 if (z_state__ == 0 && dz_z__ <= *dz_ub__) { 00503 z_state__ = 1; 00504 } 00505 if (z_state__ == 3 && dzrat <= *rthresh) { 00506 z_state__ = 1; 00507 } 00508 if (z_state__ == 1) { 00509 if (dz_z__ <= eps) { 00510 z_state__ = 2; 00511 } else if (dz_z__ > *dz_ub__) { 00512 z_state__ = 0; 00513 dzratmax = 0.; 00514 final_dz_z__ = hugeval; 00515 } else if (dzrat > *rthresh) { 00516 if (y_prec_state__ != 2) { 00517 incr_prec__ = TRUE_; 00518 } else { 00519 z_state__ = 3; 00520 } 00521 } else { 00522 if (dzrat > dzratmax) { 00523 dzratmax = dzrat; 00524 } 00525 } 00526 if (z_state__ > 1) { 00527 final_dz_z__ = dz_z__; 00528 } 00529 } 00530 if (x_state__ != 1 && (*ignore_cwise__ || z_state__ != 1)) { 00531 goto L666; 00532 } 00533 if (incr_prec__) { 00534 incr_prec__ = FALSE_; 00535 ++y_prec_state__; 00536 i__3 = *n; 00537 for (i__ = 1; i__ <= i__3; ++i__) { 00538 y_tail__[i__] = 0.; 00539 } 00540 } 00541 prevnormdx = normdx; 00542 prev_dz_z__ = dz_z__; 00543 00544 /* Update soluton. */ 00545 00546 if (y_prec_state__ < 2) { 00547 daxpy_(n, &c_b11, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); 00548 } else { 00549 dla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); 00550 } 00551 } 00552 /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ 00553 L666: 00554 00555 /* Set final_* when cnt hits ithresh. */ 00556 00557 if (x_state__ == 1) { 00558 final_dx_x__ = dx_x__; 00559 } 00560 if (z_state__ == 1) { 00561 final_dz_z__ = dz_z__; 00562 } 00563 00564 /* Compute error bounds. */ 00565 00566 if (*n_norms__ >= 1) { 00567 err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 00568 1 - dxratmax); 00569 } 00570 if (*n_norms__ >= 2) { 00571 err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 00572 1 - dzratmax); 00573 } 00574 00575 /* Compute componentwise relative backward error from formula */ 00576 /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ 00577 /* where abs(Z) is the componentwise absolute value of the matrix */ 00578 /* or vector Z. */ 00579 00580 /* Compute residual RES = B_s - op(A_s) * Y, */ 00581 /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ 00582 00583 dcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); 00584 dsymv_(uplo, n, &c_b9, &a[a_offset], lda, &y[j * y_dim1 + 1], &c__1, & 00585 c_b11, &res[1], &c__1); 00586 i__2 = *n; 00587 for (i__ = 1; i__ <= i__2; ++i__) { 00588 ayb[i__] = (d__1 = b[i__ + j * b_dim1], abs(d__1)); 00589 } 00590 00591 /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ 00592 00593 dla_syamv__(&uplo2, n, &c_b11, &a[a_offset], lda, &y[j * y_dim1 + 1], 00594 &c__1, &c_b11, &ayb[1], &c__1); 00595 dla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); 00596 00597 /* End of loop for each RHS. */ 00598 00599 } 00600 00601 return 0; 00602 } /* dla_porfsx_extended__ */