00001 SUBROUTINE CLA_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 00021 LOGICAL COLEQU, IGNORE_CWISE 00022 INTEGER ITHRESH 00023 REAL RTHRESH, DZ_UB 00024 * .. 00025 * .. Array Arguments 00026 INTEGER IPIV( * ) 00027 COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00028 $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * ) 00029 REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), 00030 $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) 00031 * .. 00032 * 00033 * Purpose 00034 * ======= 00035 * 00036 * CLA_GERFSX_EXTENDED improves the computed solution to a system of 00037 * linear equations by performing extra-precise iterative refinement 00038 * and provides error bounds and backward error estimates for the solution. 00039 * This subroutine is called by CGERFSX to perform iterative refinement. 00040 * In addition to normwise error bound, the code provides maximum 00041 * componentwise error bound if possible. See comments for ERR_BNDS_NORM 00042 * and ERR_BNDS_COMP for details of the error bounds. Note that this 00043 * subroutine is only resonsible for setting the second fields of 00044 * ERR_BNDS_NORM and ERR_BNDS_COMP. 00045 * 00046 * Arguments 00047 * ========= 00048 * 00049 * PREC_TYPE (input) INTEGER 00050 * Specifies the intermediate precision to be used in refinement. 00051 * The value is defined by ILAPREC(P) where P is a CHARACTER and 00052 * P = 'S': Single 00053 * = 'D': Double 00054 * = 'I': Indigenous 00055 * = 'X', 'E': Extra 00056 * 00057 * TRANS_TYPE (input) INTEGER 00058 * Specifies the transposition operation on A. 00059 * The value is defined by ILATRANS(T) where T is a CHARACTER and 00060 * T = 'N': No transpose 00061 * = 'T': Transpose 00062 * = 'C': Conjugate transpose 00063 * 00064 * N (input) INTEGER 00065 * The number of linear equations, i.e., the order of the 00066 * matrix A. N >= 0. 00067 * 00068 * NRHS (input) INTEGER 00069 * The number of right-hand-sides, i.e., the number of columns of the 00070 * matrix B. 00071 * 00072 * A (input) COMPLEX array, dimension (LDA,N) 00073 * On entry, the N-by-N matrix A. 00074 * 00075 * LDA (input) INTEGER 00076 * The leading dimension of the array A. LDA >= max(1,N). 00077 * 00078 * AF (input) COMPLEX array, dimension (LDAF,N) 00079 * The factors L and U from the factorization 00080 * A = P*L*U as computed by CGETRF. 00081 * 00082 * LDAF (input) INTEGER 00083 * The leading dimension of the array AF. LDAF >= max(1,N). 00084 * 00085 * IPIV (input) INTEGER array, dimension (N) 00086 * The pivot indices from the factorization A = P*L*U 00087 * as computed by CGETRF; row i of the matrix was interchanged 00088 * with row IPIV(i). 00089 * 00090 * COLEQU (input) LOGICAL 00091 * If .TRUE. then column equilibration was done to A before calling 00092 * this routine. This is needed to compute the solution and error 00093 * bounds correctly. 00094 * 00095 * C (input) REAL array, dimension (N) 00096 * The column scale factors for A. If COLEQU = .FALSE., C 00097 * is not accessed. If C is input, each element of C should be a power 00098 * of the radix to ensure a reliable solution and error estimates. 00099 * Scaling by powers of the radix does not cause rounding errors unless 00100 * the result underflows or overflows. Rounding errors during scaling 00101 * lead to refining with a matrix that is not equivalent to the 00102 * input matrix, producing error estimates that may not be 00103 * reliable. 00104 * 00105 * B (input) COMPLEX array, dimension (LDB,NRHS) 00106 * The right-hand-side matrix B. 00107 * 00108 * LDB (input) INTEGER 00109 * The leading dimension of the array B. LDB >= max(1,N). 00110 * 00111 * Y (input/output) COMPLEX array, dimension (LDY,NRHS) 00112 * On entry, the solution matrix X, as computed by CGETRS. 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) REAL 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 CLA_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) REAL array, dimension (NRHS, N_ERR_BNDS) 00132 * For each right-hand side, this array contains information about 00133 * various error bounds and condition numbers corresponding to the 00134 * normwise relative error, which is defined as follows: 00135 * 00136 * Normwise relative error in the ith solution vector: 00137 * max_j (abs(XTRUE(j,i) - X(j,i))) 00138 * ------------------------------ 00139 * max_j abs(X(j,i)) 00140 * 00141 * The array is indexed by the type of error information as described 00142 * below. There currently are up to three pieces of information 00143 * returned. 00144 * 00145 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00146 * right-hand side. 00147 * 00148 * The second index in ERR_BNDS_NORM(:,err) contains the following 00149 * three fields: 00150 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00151 * reciprocal condition number is less than the threshold 00152 * sqrt(n) * slamch('Epsilon'). 00153 * 00154 * err = 2 "Guaranteed" error bound: The estimated forward error, 00155 * almost certainly within a factor of 10 of the true error 00156 * so long as the next entry is greater than the threshold 00157 * sqrt(n) * slamch('Epsilon'). This error bound should only 00158 * be trusted if the previous boolean is true. 00159 * 00160 * err = 3 Reciprocal condition number: Estimated normwise 00161 * reciprocal condition number. Compared with the threshold 00162 * sqrt(n) * slamch('Epsilon') to determine if the error 00163 * estimate is "guaranteed". These reciprocal condition 00164 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00165 * appropriately scaled matrix Z. 00166 * Let Z = S*A, where S scales each row by a power of the 00167 * radix so all absolute row sums of Z are approximately 1. 00168 * 00169 * This subroutine is only responsible for setting the second field 00170 * above. 00171 * See Lapack Working Note 165 for further details and extra 00172 * cautions. 00173 * 00174 * ERR_BNDS_COMP (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) 00175 * For each right-hand side, this array contains information about 00176 * various error bounds and condition numbers corresponding to the 00177 * componentwise relative error, which is defined as follows: 00178 * 00179 * Componentwise relative error in the ith solution vector: 00180 * abs(XTRUE(j,i) - X(j,i)) 00181 * max_j ---------------------- 00182 * abs(X(j,i)) 00183 * 00184 * The array is indexed by the right-hand side i (on which the 00185 * componentwise relative error depends), and the type of error 00186 * information as described below. There currently are up to three 00187 * pieces of information returned for each right-hand side. If 00188 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00189 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00190 * the first (:,N_ERR_BNDS) entries are returned. 00191 * 00192 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00193 * right-hand side. 00194 * 00195 * The second index in ERR_BNDS_COMP(:,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 componentwise 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*diag(x)), where x is the solution for the 00214 * current right-hand side and S scales each row of 00215 * A*diag(x) by a power of the radix so all absolute row 00216 * sums of Z are approximately 1. 00217 * 00218 * This subroutine is only responsible for setting the second field 00219 * above. 00220 * See Lapack Working Note 165 for further details and extra 00221 * cautions. 00222 * 00223 * RES (input) COMPLEX array, dimension (N) 00224 * Workspace to hold the intermediate residual. 00225 * 00226 * AYB (input) REAL array, dimension (N) 00227 * Workspace. 00228 * 00229 * DY (input) COMPLEX array, dimension (N) 00230 * Workspace to hold the intermediate solution. 00231 * 00232 * Y_TAIL (input) COMPLEX array, dimension (N) 00233 * Workspace to hold the trailing bits of the intermediate solution. 00234 * 00235 * RCOND (input) REAL 00236 * Reciprocal scaled condition number. This is an estimate of the 00237 * reciprocal Skeel condition number of the matrix A after 00238 * equilibration (if done). If this is less than the machine 00239 * precision (in particular, if it is zero), the matrix is singular 00240 * to working precision. Note that the error may still be small even 00241 * if this number is very small and the matrix appears ill- 00242 * conditioned. 00243 * 00244 * ITHRESH (input) INTEGER 00245 * The maximum number of residual computations allowed for 00246 * refinement. The default is 10. For 'aggressive' set to 100 to 00247 * permit convergence using approximate factorizations or 00248 * factorizations other than LU. If the factorization uses a 00249 * technique other than Gaussian elimination, the guarantees in 00250 * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00251 * 00252 * RTHRESH (input) REAL 00253 * Determines when to stop refinement if the error estimate stops 00254 * decreasing. Refinement will stop when the next solution no longer 00255 * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00256 * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00257 * default value is 0.5. For 'aggressive' set to 0.9 to permit 00258 * convergence on extremely ill-conditioned matrices. See LAWN 165 00259 * for more details. 00260 * 00261 * DZ_UB (input) REAL 00262 * Determines when to start considering componentwise convergence. 00263 * Componentwise convergence is only considered after each component 00264 * of the solution Y is stable, which we definte as the relative 00265 * change in each component being less than DZ_UB. The default value 00266 * is 0.25, requiring the first bit to be stable. See LAWN 165 for 00267 * more details. 00268 * 00269 * IGNORE_CWISE (input) LOGICAL 00270 * If .TRUE. then ignore componentwise convergence. Default value 00271 * is .FALSE.. 00272 * 00273 * INFO (output) INTEGER 00274 * = 0: Successful exit. 00275 * < 0: if INFO = -i, the ith argument to CGETRS had an illegal 00276 * value 00277 * 00278 * ===================================================================== 00279 * 00280 * .. Local Scalars .. 00281 CHARACTER TRANS 00282 INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE 00283 REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00284 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00285 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00286 $ EPS, HUGEVAL, INCR_THRESH 00287 LOGICAL INCR_PREC 00288 COMPLEX ZDUM 00289 * .. 00290 * .. Parameters .. 00291 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00292 $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL, 00293 $ EXTRA_Y 00294 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00295 $ CONV_STATE = 2, 00296 $ 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 CAXPY, CCOPY, CGETRS, CGEMV, BLAS_CGEMV_X, 00319 $ BLAS_CGEMV2_X, CLA_GEAMV, CLA_WWADDW, SLAMCH, 00320 $ CHLA_TRANSTYPE, CLA_LIN_BERR 00321 REAL SLAMCH 00322 CHARACTER CHLA_TRANSTYPE 00323 * .. 00324 * .. Intrinsic Functions .. 00325 INTRINSIC ABS, MAX, MIN 00326 * .. 00327 * .. Statement Functions .. 00328 REAL CABS1 00329 * .. 00330 * .. Statement Function Definitions .. 00331 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) 00332 * .. 00333 * .. Executable Statements .. 00334 * 00335 IF ( INFO.NE.0 ) RETURN 00336 TRANS = CHLA_TRANSTYPE(TRANS_TYPE) 00337 EPS = SLAMCH( 'Epsilon' ) 00338 HUGEVAL = SLAMCH( 'Overflow' ) 00339 * Force HUGEVAL to Inf 00340 HUGEVAL = HUGEVAL * HUGEVAL 00341 * Using HUGEVAL may lead to spurious underflows. 00342 INCR_THRESH = REAL( N ) * EPS 00343 * 00344 DO J = 1, NRHS 00345 Y_PREC_STATE = EXTRA_RESIDUAL 00346 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00347 DO I = 1, N 00348 Y_TAIL( I ) = 0.0 00349 END DO 00350 END IF 00351 00352 DXRAT = 0.0 00353 DXRATMAX = 0.0 00354 DZRAT = 0.0 00355 DZRATMAX = 0.0 00356 FINAL_DX_X = HUGEVAL 00357 FINAL_DZ_Z = HUGEVAL 00358 PREVNORMDX = HUGEVAL 00359 PREV_DZ_Z = HUGEVAL 00360 DZ_Z = HUGEVAL 00361 DX_X = HUGEVAL 00362 00363 X_STATE = WORKING_STATE 00364 Z_STATE = UNSTABLE_STATE 00365 INCR_PREC = .FALSE. 00366 00367 DO CNT = 1, ITHRESH 00368 * 00369 * Compute residual RES = B_s - op(A_s) * Y, 00370 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00371 * 00372 CALL CCOPY( N, B( 1, J ), 1, RES, 1 ) 00373 IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN 00374 CALL CGEMV( TRANS, N, N, (-1.0E+0,0.0E+0), A, LDA, 00375 $ Y( 1, J ), 1, (1.0E+0,0.0E+0), RES, 1) 00376 ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN 00377 CALL BLAS_CGEMV_X( TRANS_TYPE, N, N, (-1.0E+0,0.0E+0), A, 00378 $ LDA, Y( 1, J ), 1, (1.0E+0,0.0E+0), 00379 $ RES, 1, PREC_TYPE ) 00380 ELSE 00381 CALL BLAS_CGEMV2_X( TRANS_TYPE, N, N, (-1.0E+0,0.0E+0), 00382 $ A, LDA, Y(1, J), Y_TAIL, 1, (1.0E+0,0.0E+0), RES, 1, 00383 $ PREC_TYPE) 00384 END IF 00385 00386 ! XXX: RES is no longer needed. 00387 CALL CCOPY( N, RES, 1, DY, 1 ) 00388 CALL CGETRS( TRANS, N, 1, AF, LDAF, IPIV, DY, N, INFO ) 00389 * 00390 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00391 * 00392 NORMX = 0.0E+0 00393 NORMY = 0.0E+0 00394 NORMDX = 0.0E+0 00395 DZ_Z = 0.0E+0 00396 YMIN = HUGEVAL 00397 * 00398 DO I = 1, N 00399 YK = CABS1( Y( I, J ) ) 00400 DYK = CABS1( DY( I ) ) 00401 00402 IF ( YK .NE. 0.0E+0 ) THEN 00403 DZ_Z = MAX( DZ_Z, DYK / YK ) 00404 ELSE IF ( DYK .NE. 0.0 ) THEN 00405 DZ_Z = HUGEVAL 00406 END IF 00407 00408 YMIN = MIN( YMIN, YK ) 00409 00410 NORMY = MAX( NORMY, YK ) 00411 00412 IF ( COLEQU ) THEN 00413 NORMX = MAX( NORMX, YK * C( I ) ) 00414 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00415 ELSE 00416 NORMX = NORMY 00417 NORMDX = MAX(NORMDX, DYK) 00418 END IF 00419 END DO 00420 00421 IF ( NORMX .NE. 0.0 ) THEN 00422 DX_X = NORMDX / NORMX 00423 ELSE IF ( NORMDX .EQ. 0.0 ) THEN 00424 DX_X = 0.0 00425 ELSE 00426 DX_X = HUGEVAL 00427 END IF 00428 00429 DXRAT = NORMDX / PREVNORMDX 00430 DZRAT = DZ_Z / PREV_DZ_Z 00431 * 00432 * Check termination criteria 00433 * 00434 IF (.NOT.IGNORE_CWISE 00435 $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY 00436 $ .AND. Y_PREC_STATE .LT. EXTRA_Y ) 00437 $ INCR_PREC = .TRUE. 00438 00439 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00440 $ X_STATE = WORKING_STATE 00441 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00442 IF (DX_X .LE. EPS) THEN 00443 X_STATE = CONV_STATE 00444 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00445 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00446 INCR_PREC = .TRUE. 00447 ELSE 00448 X_STATE = NOPROG_STATE 00449 END IF 00450 ELSE 00451 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00452 END IF 00453 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00454 END IF 00455 00456 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00457 $ Z_STATE = WORKING_STATE 00458 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00459 $ Z_STATE = WORKING_STATE 00460 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00461 IF ( DZ_Z .LE. EPS ) THEN 00462 Z_STATE = CONV_STATE 00463 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00464 Z_STATE = UNSTABLE_STATE 00465 DZRATMAX = 0.0 00466 FINAL_DZ_Z = HUGEVAL 00467 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00468 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00469 INCR_PREC = .TRUE. 00470 ELSE 00471 Z_STATE = NOPROG_STATE 00472 END IF 00473 ELSE 00474 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00475 END IF 00476 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00477 END IF 00478 * 00479 * Exit if both normwise and componentwise stopped working, 00480 * but if componentwise is unstable, let it go at least two 00481 * iterations. 00482 * 00483 IF ( X_STATE.NE.WORKING_STATE ) THEN 00484 IF ( IGNORE_CWISE ) GOTO 666 00485 IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE ) 00486 $ GOTO 666 00487 IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666 00488 END IF 00489 00490 IF ( INCR_PREC ) THEN 00491 INCR_PREC = .FALSE. 00492 Y_PREC_STATE = Y_PREC_STATE + 1 00493 DO I = 1, N 00494 Y_TAIL( I ) = 0.0 00495 END DO 00496 END IF 00497 00498 PREVNORMDX = NORMDX 00499 PREV_DZ_Z = DZ_Z 00500 * 00501 * Update soluton. 00502 * 00503 IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN 00504 CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 ) 00505 ELSE 00506 CALL CLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY ) 00507 END IF 00508 00509 END DO 00510 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00511 666 CONTINUE 00512 * 00513 * Set final_* when cnt hits ithresh 00514 * 00515 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00516 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00517 * 00518 * Compute error bounds 00519 * 00520 IF (N_NORMS .GE. 1) THEN 00521 ERRS_N( J, LA_LINRX_ERR_I ) = FINAL_DX_X / (1 - DXRATMAX) 00522 00523 END IF 00524 IF ( N_NORMS .GE. 2 ) THEN 00525 ERRS_C( J, LA_LINRX_ERR_I ) = FINAL_DZ_Z / (1 - DZRATMAX) 00526 END IF 00527 * 00528 * Compute componentwise relative backward error from formula 00529 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00530 * where abs(Z) is the componentwise absolute value of the matrix 00531 * or vector Z. 00532 * 00533 * Compute residual RES = B_s - op(A_s) * Y, 00534 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00535 * 00536 CALL CCOPY( N, B( 1, J ), 1, RES, 1 ) 00537 CALL CGEMV( TRANS, N, N, (-1.0E+0,0.0E+0), A, LDA, Y(1,J), 1, 00538 $ (1.0E+0,0.0E+0), RES, 1 ) 00539 00540 DO I = 1, N 00541 AYB( I ) = CABS1( B( I, J ) ) 00542 END DO 00543 * 00544 * Compute abs(op(A_s))*abs(Y) + abs(B_s). 00545 * 00546 CALL CLA_GEAMV ( TRANS_TYPE, N, N, 1.0E+0, 00547 $ A, LDA, Y(1, J), 1, 1.0E+0, AYB, 1 ) 00548 00549 CALL CLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) ) 00550 * 00551 * End of loop for each RHS. 00552 * 00553 END DO 00554 * 00555 RETURN 00556 END
1.7.2