00001 SUBROUTINE DLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A, 00002 $ LDA, AF, LDAF, IPIV, COLEQU, C, B, 00003 $ LDB, Y, LDY, BERR_OUT, N_NORMS, 00004 $ ERRS_N, ERRS_C, RES, AYB, DY, 00005 $ Y_TAIL, RCOND, ITHRESH, RTHRESH, 00006 $ DZ_UB, IGNORE_CWISE, INFO ) 00007 * 00008 * -- LAPACK routine (version 3.2.1) -- 00009 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 00010 * -- Jason Riedy of Univ. of California Berkeley. -- 00011 * -- April 2009 -- 00012 * 00013 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00014 * -- Univ. of California Berkeley and NAG Ltd. -- 00015 * 00016 IMPLICIT NONE 00017 * .. 00018 * .. Scalar Arguments .. 00019 INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE, 00020 $ TRANS_TYPE, N_NORMS, ITHRESH 00021 LOGICAL COLEQU, IGNORE_CWISE 00022 DOUBLE PRECISION RTHRESH, DZ_UB 00023 * .. 00024 * .. Array Arguments .. 00025 INTEGER IPIV( * ) 00026 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00027 $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * ) 00028 DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), 00029 $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) 00030 * .. 00031 * 00032 * Purpose 00033 * ======= 00034 * 00035 * DLA_GERFSX_EXTENDED improves the computed solution to a system of 00036 * linear equations by performing extra-precise iterative refinement 00037 * and provides error bounds and backward error estimates for the solution. 00038 * This subroutine is called by DGERFSX to perform iterative refinement. 00039 * In addition to normwise error bound, the code provides maximum 00040 * componentwise error bound if possible. See comments for ERR_BNDS_NORM 00041 * and ERR_BNDS_COMP for details of the error bounds. Note that this 00042 * subroutine is only resonsible for setting the second fields of 00043 * ERR_BNDS_NORM and ERR_BNDS_COMP. 00044 * 00045 * Arguments 00046 * ========= 00047 * 00048 * PREC_TYPE (input) INTEGER 00049 * Specifies the intermediate precision to be used in refinement. 00050 * The value is defined by ILAPREC(P) where P is a CHARACTER and 00051 * P = 'S': Single 00052 * = 'D': Double 00053 * = 'I': Indigenous 00054 * = 'X', 'E': Extra 00055 * 00056 * TRANS_TYPE (input) INTEGER 00057 * Specifies the transposition operation on A. 00058 * The value is defined by ILATRANS(T) where T is a CHARACTER and 00059 * T = 'N': No transpose 00060 * = 'T': Transpose 00061 * = 'C': Conjugate transpose 00062 * 00063 * N (input) INTEGER 00064 * The number of linear equations, i.e., the order of the 00065 * matrix A. N >= 0. 00066 * 00067 * NRHS (input) INTEGER 00068 * The number of right-hand-sides, i.e., the number of columns of the 00069 * matrix B. 00070 * 00071 * A (input) DOUBLE PRECISION array, dimension (LDA,N) 00072 * On entry, the N-by-N matrix A. 00073 * 00074 * LDA (input) INTEGER 00075 * The leading dimension of the array A. LDA >= max(1,N). 00076 * 00077 * AF (input) DOUBLE PRECISION array, dimension (LDAF,N) 00078 * The factors L and U from the factorization 00079 * A = P*L*U as computed by DGETRF. 00080 * 00081 * LDAF (input) INTEGER 00082 * The leading dimension of the array AF. LDAF >= max(1,N). 00083 * 00084 * IPIV (input) INTEGER array, dimension (N) 00085 * The pivot indices from the factorization A = P*L*U 00086 * as computed by DGETRF; row i of the matrix was interchanged 00087 * with row IPIV(i). 00088 * 00089 * COLEQU (input) LOGICAL 00090 * If .TRUE. then column equilibration was done to A before calling 00091 * this routine. This is needed to compute the solution and error 00092 * bounds correctly. 00093 * 00094 * C (input) DOUBLE PRECISION array, dimension (N) 00095 * The column scale factors for A. If COLEQU = .FALSE., C 00096 * is not accessed. If C is input, each element of C should be a power 00097 * of the radix to ensure a reliable solution and error estimates. 00098 * Scaling by powers of the radix does not cause rounding errors unless 00099 * the result underflows or overflows. Rounding errors during scaling 00100 * lead to refining with a matrix that is not equivalent to the 00101 * input matrix, producing error estimates that may not be 00102 * reliable. 00103 * 00104 * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) 00105 * The right-hand-side matrix B. 00106 * 00107 * LDB (input) INTEGER 00108 * The leading dimension of the array B. LDB >= max(1,N). 00109 * 00110 * Y (input/output) DOUBLE PRECISION array, dimension 00111 * (LDY,NRHS) 00112 * On entry, the solution matrix X, as computed by DGETRS. 00113 * On exit, the improved solution matrix Y. 00114 * 00115 * LDY (input) INTEGER 00116 * The leading dimension of the array Y. LDY >= max(1,N). 00117 * 00118 * BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS) 00119 * On exit, BERR_OUT(j) contains the componentwise relative backward 00120 * error for right-hand-side j from the formula 00121 * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00122 * where abs(Z) is the componentwise absolute value of the matrix 00123 * or vector Z. This is computed by DLA_LIN_BERR. 00124 * 00125 * N_NORMS (input) INTEGER 00126 * Determines which error bounds to return (see ERR_BNDS_NORM 00127 * and ERR_BNDS_COMP). 00128 * If N_NORMS >= 1 return normwise error bounds. 00129 * If N_NORMS >= 2 return componentwise error bounds. 00130 * 00131 * ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension 00132 * (NRHS, N_ERR_BNDS) 00133 * For each right-hand side, this array contains information about 00134 * various error bounds and condition numbers corresponding to the 00135 * normwise relative error, which is defined as follows: 00136 * 00137 * Normwise relative error in the ith solution vector: 00138 * max_j (abs(XTRUE(j,i) - X(j,i))) 00139 * ------------------------------ 00140 * max_j abs(X(j,i)) 00141 * 00142 * The array is indexed by the type of error information as described 00143 * below. There currently are up to three pieces of information 00144 * returned. 00145 * 00146 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00147 * right-hand side. 00148 * 00149 * The second index in ERR_BNDS_NORM(:,err) contains the following 00150 * three fields: 00151 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00152 * reciprocal condition number is less than the threshold 00153 * sqrt(n) * slamch('Epsilon'). 00154 * 00155 * err = 2 "Guaranteed" error bound: The estimated forward error, 00156 * almost certainly within a factor of 10 of the true error 00157 * so long as the next entry is greater than the threshold 00158 * sqrt(n) * slamch('Epsilon'). This error bound should only 00159 * be trusted if the previous boolean is true. 00160 * 00161 * err = 3 Reciprocal condition number: Estimated normwise 00162 * reciprocal condition number. Compared with the threshold 00163 * sqrt(n) * slamch('Epsilon') to determine if the error 00164 * estimate is "guaranteed". These reciprocal condition 00165 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00166 * appropriately scaled matrix Z. 00167 * Let Z = S*A, where S scales each row by a power of the 00168 * radix so all absolute row sums of Z are approximately 1. 00169 * 00170 * This subroutine is only responsible for setting the second field 00171 * above. 00172 * See Lapack Working Note 165 for further details and extra 00173 * cautions. 00174 * 00175 * ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension 00176 * (NRHS, N_ERR_BNDS) 00177 * For each right-hand side, this array contains information about 00178 * various error bounds and condition numbers corresponding to the 00179 * componentwise relative error, which is defined as follows: 00180 * 00181 * Componentwise relative error in the ith solution vector: 00182 * abs(XTRUE(j,i) - X(j,i)) 00183 * max_j ---------------------- 00184 * abs(X(j,i)) 00185 * 00186 * The array is indexed by the right-hand side i (on which the 00187 * componentwise relative error depends), and the type of error 00188 * information as described below. There currently are up to three 00189 * pieces of information returned for each right-hand side. If 00190 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00191 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00192 * the first (:,N_ERR_BNDS) entries are returned. 00193 * 00194 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00195 * right-hand side. 00196 * 00197 * The second index in ERR_BNDS_COMP(:,err) contains the following 00198 * three fields: 00199 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00200 * reciprocal condition number is less than the threshold 00201 * sqrt(n) * slamch('Epsilon'). 00202 * 00203 * err = 2 "Guaranteed" error bound: The estimated forward error, 00204 * almost certainly within a factor of 10 of the true error 00205 * so long as the next entry is greater than the threshold 00206 * sqrt(n) * slamch('Epsilon'). This error bound should only 00207 * be trusted if the previous boolean is true. 00208 * 00209 * err = 3 Reciprocal condition number: Estimated componentwise 00210 * reciprocal condition number. Compared with the threshold 00211 * sqrt(n) * slamch('Epsilon') to determine if the error 00212 * estimate is "guaranteed". These reciprocal condition 00213 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00214 * appropriately scaled matrix Z. 00215 * Let Z = S*(A*diag(x)), where x is the solution for the 00216 * current right-hand side and S scales each row of 00217 * A*diag(x) by a power of the radix so all absolute row 00218 * sums of Z are approximately 1. 00219 * 00220 * This subroutine is only responsible for setting the second field 00221 * above. 00222 * See Lapack Working Note 165 for further details and extra 00223 * cautions. 00224 * 00225 * RES (input) DOUBLE PRECISION array, dimension (N) 00226 * Workspace to hold the intermediate residual. 00227 * 00228 * AYB (input) DOUBLE PRECISION array, dimension (N) 00229 * Workspace. This can be the same workspace passed for Y_TAIL. 00230 * 00231 * DY (input) DOUBLE PRECISION array, dimension (N) 00232 * Workspace to hold the intermediate solution. 00233 * 00234 * Y_TAIL (input) DOUBLE PRECISION array, dimension (N) 00235 * Workspace to hold the trailing bits of the intermediate solution. 00236 * 00237 * RCOND (input) DOUBLE PRECISION 00238 * Reciprocal scaled condition number. This is an estimate of the 00239 * reciprocal Skeel condition number of the matrix A after 00240 * equilibration (if done). If this is less than the machine 00241 * precision (in particular, if it is zero), the matrix is singular 00242 * to working precision. Note that the error may still be small even 00243 * if this number is very small and the matrix appears ill- 00244 * conditioned. 00245 * 00246 * ITHRESH (input) INTEGER 00247 * The maximum number of residual computations allowed for 00248 * refinement. The default is 10. For 'aggressive' set to 100 to 00249 * permit convergence using approximate factorizations or 00250 * factorizations other than LU. If the factorization uses a 00251 * technique other than Gaussian elimination, the guarantees in 00252 * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00253 * 00254 * RTHRESH (input) DOUBLE PRECISION 00255 * Determines when to stop refinement if the error estimate stops 00256 * decreasing. Refinement will stop when the next solution no longer 00257 * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00258 * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00259 * default value is 0.5. For 'aggressive' set to 0.9 to permit 00260 * convergence on extremely ill-conditioned matrices. See LAWN 165 00261 * for more details. 00262 * 00263 * DZ_UB (input) DOUBLE PRECISION 00264 * Determines when to start considering componentwise convergence. 00265 * Componentwise convergence is only considered after each component 00266 * of the solution Y is stable, which we definte as the relative 00267 * change in each component being less than DZ_UB. The default value 00268 * is 0.25, requiring the first bit to be stable. See LAWN 165 for 00269 * more details. 00270 * 00271 * IGNORE_CWISE (input) LOGICAL 00272 * If .TRUE. then ignore componentwise convergence. Default value 00273 * is .FALSE.. 00274 * 00275 * INFO (output) INTEGER 00276 * = 0: Successful exit. 00277 * < 0: if INFO = -i, the ith argument to DGETRS had an illegal 00278 * value 00279 * 00280 * ===================================================================== 00281 * 00282 * .. Local Scalars .. 00283 CHARACTER TRANS 00284 INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE 00285 DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00286 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00287 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00288 $ EPS, HUGEVAL, INCR_THRESH 00289 LOGICAL INCR_PREC 00290 * .. 00291 * .. Parameters .. 00292 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00293 $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL, 00294 $ EXTRA_Y 00295 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00296 $ CONV_STATE = 2, NOPROG_STATE = 3 ) 00297 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00298 $ EXTRA_Y = 2 ) 00299 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00300 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00301 INTEGER CMP_ERR_I, PIV_GROWTH_I 00302 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00303 $ BERR_I = 3 ) 00304 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00305 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00306 $ PIV_GROWTH_I = 9 ) 00307 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00308 $ LA_LINRX_CWISE_I 00309 PARAMETER ( LA_LINRX_ITREF_I = 1, 00310 $ LA_LINRX_ITHRESH_I = 2 ) 00311 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00312 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00313 $ LA_LINRX_RCOND_I 00314 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00315 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00316 * .. 00317 * .. External Subroutines .. 00318 EXTERNAL DAXPY, DCOPY, DGETRS, DGEMV, BLAS_DGEMV_X, 00319 $ BLAS_DGEMV2_X, DLA_GEAMV, DLA_WWADDW, DLAMCH, 00320 $ CHLA_TRANSTYPE, DLA_LIN_BERR 00321 DOUBLE PRECISION DLAMCH 00322 CHARACTER CHLA_TRANSTYPE 00323 * .. 00324 * .. Intrinsic Functions .. 00325 INTRINSIC ABS, MAX, MIN 00326 * .. 00327 * .. Executable Statements .. 00328 * 00329 IF ( INFO.NE.0 ) RETURN 00330 TRANS = CHLA_TRANSTYPE(TRANS_TYPE) 00331 EPS = DLAMCH( 'Epsilon' ) 00332 HUGEVAL = DLAMCH( 'Overflow' ) 00333 * Force HUGEVAL to Inf 00334 HUGEVAL = HUGEVAL * HUGEVAL 00335 * Using HUGEVAL may lead to spurious underflows. 00336 INCR_THRESH = DBLE( N ) * EPS 00337 * 00338 DO J = 1, NRHS 00339 Y_PREC_STATE = EXTRA_RESIDUAL 00340 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00341 DO I = 1, N 00342 Y_TAIL( I ) = 0.0D+0 00343 END DO 00344 END IF 00345 00346 DXRAT = 0.0D+0 00347 DXRATMAX = 0.0D+0 00348 DZRAT = 0.0D+0 00349 DZRATMAX = 0.0D+0 00350 FINAL_DX_X = HUGEVAL 00351 FINAL_DZ_Z = HUGEVAL 00352 PREVNORMDX = HUGEVAL 00353 PREV_DZ_Z = HUGEVAL 00354 DZ_Z = HUGEVAL 00355 DX_X = HUGEVAL 00356 00357 X_STATE = WORKING_STATE 00358 Z_STATE = UNSTABLE_STATE 00359 INCR_PREC = .FALSE. 00360 00361 DO CNT = 1, ITHRESH 00362 * 00363 * Compute residual RES = B_s - op(A_s) * Y, 00364 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00365 * 00366 CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) 00367 IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN 00368 CALL DGEMV( TRANS, N, N, -1.0D+0, A, LDA, Y( 1, J ), 1, 00369 $ 1.0D+0, RES, 1 ) 00370 ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN 00371 CALL BLAS_DGEMV_X( TRANS_TYPE, N, N, -1.0D+0, A, LDA, 00372 $ Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE ) 00373 ELSE 00374 CALL BLAS_DGEMV2_X( TRANS_TYPE, N, N, -1.0D+0, A, LDA, 00375 $ Y( 1, J ), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE ) 00376 END IF 00377 00378 ! XXX: RES is no longer needed. 00379 CALL DCOPY( N, RES, 1, DY, 1 ) 00380 CALL DGETRS( TRANS, N, 1, AF, LDAF, IPIV, DY, N, INFO ) 00381 * 00382 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00383 * 00384 NORMX = 0.0D+0 00385 NORMY = 0.0D+0 00386 NORMDX = 0.0D+0 00387 DZ_Z = 0.0D+0 00388 YMIN = HUGEVAL 00389 * 00390 DO I = 1, N 00391 YK = ABS( Y( I, J ) ) 00392 DYK = ABS( DY( I ) ) 00393 00394 IF ( YK .NE. 0.0D+0 ) THEN 00395 DZ_Z = MAX( DZ_Z, DYK / YK ) 00396 ELSE IF ( DYK .NE. 0.0D+0 ) THEN 00397 DZ_Z = HUGEVAL 00398 END IF 00399 00400 YMIN = MIN( YMIN, YK ) 00401 00402 NORMY = MAX( NORMY, YK ) 00403 00404 IF ( COLEQU ) THEN 00405 NORMX = MAX( NORMX, YK * C( I ) ) 00406 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00407 ELSE 00408 NORMX = NORMY 00409 NORMDX = MAX( NORMDX, DYK ) 00410 END IF 00411 END DO 00412 00413 IF ( NORMX .NE. 0.0D+0 ) THEN 00414 DX_X = NORMDX / NORMX 00415 ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN 00416 DX_X = 0.0D+0 00417 ELSE 00418 DX_X = HUGEVAL 00419 END IF 00420 00421 DXRAT = NORMDX / PREVNORMDX 00422 DZRAT = DZ_Z / PREV_DZ_Z 00423 * 00424 * Check termination criteria 00425 * 00426 IF (.NOT.IGNORE_CWISE 00427 $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY 00428 $ .AND. Y_PREC_STATE .LT. EXTRA_Y) 00429 $ INCR_PREC = .TRUE. 00430 00431 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00432 $ X_STATE = WORKING_STATE 00433 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00434 IF ( DX_X .LE. EPS ) THEN 00435 X_STATE = CONV_STATE 00436 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00437 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00438 INCR_PREC = .TRUE. 00439 ELSE 00440 X_STATE = NOPROG_STATE 00441 END IF 00442 ELSE 00443 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00444 END IF 00445 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00446 END IF 00447 00448 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00449 $ Z_STATE = WORKING_STATE 00450 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00451 $ Z_STATE = WORKING_STATE 00452 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00453 IF ( DZ_Z .LE. EPS ) THEN 00454 Z_STATE = CONV_STATE 00455 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00456 Z_STATE = UNSTABLE_STATE 00457 DZRATMAX = 0.0D+0 00458 FINAL_DZ_Z = HUGEVAL 00459 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00460 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00461 INCR_PREC = .TRUE. 00462 ELSE 00463 Z_STATE = NOPROG_STATE 00464 END IF 00465 ELSE 00466 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00467 END IF 00468 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00469 END IF 00470 * 00471 * Exit if both normwise and componentwise stopped working, 00472 * but if componentwise is unstable, let it go at least two 00473 * iterations. 00474 * 00475 IF ( X_STATE.NE.WORKING_STATE ) THEN 00476 IF ( IGNORE_CWISE) GOTO 666 00477 IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE ) 00478 $ GOTO 666 00479 IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666 00480 END IF 00481 00482 IF ( INCR_PREC ) THEN 00483 INCR_PREC = .FALSE. 00484 Y_PREC_STATE = Y_PREC_STATE + 1 00485 DO I = 1, N 00486 Y_TAIL( I ) = 0.0D+0 00487 END DO 00488 END IF 00489 00490 PREVNORMDX = NORMDX 00491 PREV_DZ_Z = DZ_Z 00492 * 00493 * Update soluton. 00494 * 00495 IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN 00496 CALL DAXPY( N, 1.0D+0, DY, 1, Y( 1, J ), 1 ) 00497 ELSE 00498 CALL DLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY ) 00499 END IF 00500 00501 END DO 00502 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00503 666 CONTINUE 00504 * 00505 * Set final_* when cnt hits ithresh. 00506 * 00507 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00508 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00509 * 00510 * Compute error bounds 00511 * 00512 IF (N_NORMS .GE. 1) THEN 00513 ERRS_N( J, LA_LINRX_ERR_I ) = FINAL_DX_X / (1 - DXRATMAX) 00514 END IF 00515 IF ( N_NORMS .GE. 2 ) THEN 00516 ERRS_C( J, LA_LINRX_ERR_I ) = FINAL_DZ_Z / (1 - DZRATMAX) 00517 END IF 00518 * 00519 * Compute componentwise relative backward error from formula 00520 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00521 * where abs(Z) is the componentwise absolute value of the matrix 00522 * or vector Z. 00523 * 00524 * Compute residual RES = B_s - op(A_s) * Y, 00525 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00526 * 00527 CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) 00528 CALL DGEMV( TRANS, N, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, 00529 $ RES, 1 ) 00530 00531 DO I = 1, N 00532 AYB( I ) = ABS( B( I, J ) ) 00533 END DO 00534 * 00535 * Compute abs(op(A_s))*abs(Y) + abs(B_s). 00536 * 00537 CALL DLA_GEAMV ( TRANS_TYPE, N, N, 1.0D+0, 00538 $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 ) 00539 00540 CALL DLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) ) 00541 * 00542 * End of loop for each RHS. 00543 * 00544 END DO 00545 * 00546 RETURN 00547 END
1.7.2