00001 SUBROUTINE SLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU, 00002 $ NRHS, AB, LDAB, AFB, LDAFB, IPIV, 00003 $ COLEQU, C, B, LDB, Y, LDY, 00004 $ BERR_OUT, N_NORMS, ERR_BNDS_NORM, 00005 $ ERR_BNDS_COMP, RES, AYB, DY, 00006 $ Y_TAIL, RCOND, ITHRESH, RTHRESH, 00007 $ DZ_UB, IGNORE_CWISE, INFO ) 00008 * 00009 * -- LAPACK routine (version 3.2.1) -- 00010 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 00011 * -- Jason Riedy of Univ. of California Berkeley. -- 00012 * -- April 2009 -- 00013 * 00014 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00015 * -- Univ. of California Berkeley and NAG Ltd. -- 00016 * 00017 IMPLICIT NONE 00018 * .. 00019 * .. Scalar Arguments .. 00020 INTEGER INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS, 00021 $ PREC_TYPE, TRANS_TYPE, N_NORMS, ITHRESH 00022 LOGICAL COLEQU, IGNORE_CWISE 00023 REAL RTHRESH, DZ_UB 00024 * .. 00025 * .. Array Arguments .. 00026 INTEGER IPIV( * ) 00027 REAL AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), 00028 $ Y( LDY, * ), RES(*), DY(*), Y_TAIL(*) 00029 REAL C( * ), AYB(*), RCOND, BERR_OUT(*), 00030 $ ERR_BNDS_NORM( NRHS, * ), 00031 $ ERR_BNDS_COMP( NRHS, * ) 00032 * .. 00033 * 00034 * Purpose 00035 * ======= 00036 * 00037 * SLA_GBRFSX_EXTENDED improves the computed solution to a system of 00038 * linear equations by performing extra-precise iterative refinement 00039 * and provides error bounds and backward error estimates for the solution. 00040 * This subroutine is called by SGBRFSX to perform iterative refinement. 00041 * In addition to normwise error bound, the code provides maximum 00042 * componentwise error bound if possible. See comments for ERR_BNDS_NORM 00043 * and ERR_BNDS_COMP for details of the error bounds. Note that this 00044 * subroutine is only resonsible for setting the second fields of 00045 * ERR_BNDS_NORM and ERR_BNDS_COMP. 00046 * 00047 * Arguments 00048 * ========= 00049 * 00050 * PREC_TYPE (input) INTEGER 00051 * Specifies the intermediate precision to be used in refinement. 00052 * The value is defined by ILAPREC(P) where P is a CHARACTER and 00053 * P = 'S': Single 00054 * = 'D': Double 00055 * = 'I': Indigenous 00056 * = 'X', 'E': Extra 00057 * 00058 * TRANS_TYPE (input) INTEGER 00059 * Specifies the transposition operation on A. 00060 * The value is defined by ILATRANS(T) where T is a CHARACTER and 00061 * T = 'N': No transpose 00062 * = 'T': Transpose 00063 * = 'C': Conjugate transpose 00064 * 00065 * N (input) INTEGER 00066 * The number of linear equations, i.e., the order of the 00067 * matrix A. N >= 0. 00068 * 00069 * KL (input) INTEGER 00070 * The number of subdiagonals within the band of A. KL >= 0. 00071 * 00072 * KU (input) INTEGER 00073 * The number of superdiagonals within the band of A. KU >= 0 00074 * 00075 * NRHS (input) INTEGER 00076 * The number of right-hand-sides, i.e., the number of columns of the 00077 * matrix B. 00078 * 00079 * A (input) REAL array, dimension (LDA,N) 00080 * On entry, the N-by-N matrix A. 00081 * 00082 * LDA (input) INTEGER 00083 * The leading dimension of the array A. LDA >= max(1,N). 00084 * 00085 * AF (input) REAL array, dimension (LDAF,N) 00086 * The factors L and U from the factorization 00087 * A = P*L*U as computed by SGBTRF. 00088 * 00089 * LDAF (input) INTEGER 00090 * The leading dimension of the array AF. LDAF >= max(1,N). 00091 * 00092 * IPIV (input) INTEGER array, dimension (N) 00093 * The pivot indices from the factorization A = P*L*U 00094 * as computed by SGBTRF; row i of the matrix was interchanged 00095 * with row IPIV(i). 00096 * 00097 * COLEQU (input) LOGICAL 00098 * If .TRUE. then column equilibration was done to A before calling 00099 * this routine. This is needed to compute the solution and error 00100 * bounds correctly. 00101 * 00102 * C (input) REAL array, dimension (N) 00103 * The column scale factors for A. If COLEQU = .FALSE., C 00104 * is not accessed. If C is input, each element of C should be a power 00105 * of the radix to ensure a reliable solution and error estimates. 00106 * Scaling by powers of the radix does not cause rounding errors unless 00107 * the result underflows or overflows. Rounding errors during scaling 00108 * lead to refining with a matrix that is not equivalent to the 00109 * input matrix, producing error estimates that may not be 00110 * reliable. 00111 * 00112 * B (input) REAL array, dimension (LDB,NRHS) 00113 * The right-hand-side matrix B. 00114 * 00115 * LDB (input) INTEGER 00116 * The leading dimension of the array B. LDB >= max(1,N). 00117 * 00118 * Y (input/output) REAL array, dimension (LDY,NRHS) 00119 * On entry, the solution matrix X, as computed by SGBTRS. 00120 * On exit, the improved solution matrix Y. 00121 * 00122 * LDY (input) INTEGER 00123 * The leading dimension of the array Y. LDY >= max(1,N). 00124 * 00125 * BERR_OUT (output) REAL array, dimension (NRHS) 00126 * On exit, BERR_OUT(j) contains the componentwise relative backward 00127 * error for right-hand-side j from the formula 00128 * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00129 * where abs(Z) is the componentwise absolute value of the matrix 00130 * or vector Z. This is computed by SLA_LIN_BERR. 00131 * 00132 * N_NORMS (input) INTEGER 00133 * Determines which error bounds to return (see ERR_BNDS_NORM 00134 * and ERR_BNDS_COMP). 00135 * If N_NORMS >= 1 return normwise error bounds. 00136 * If N_NORMS >= 2 return componentwise error bounds. 00137 * 00138 * ERR_BNDS_NORM (input/output) REAL array, dimension 00139 * (NRHS, N_ERR_BNDS) 00140 * For each right-hand side, this array contains information about 00141 * various error bounds and condition numbers corresponding to the 00142 * normwise relative error, which is defined as follows: 00143 * 00144 * Normwise relative error in the ith solution vector: 00145 * max_j (abs(XTRUE(j,i) - X(j,i))) 00146 * ------------------------------ 00147 * max_j abs(X(j,i)) 00148 * 00149 * The array is indexed by the type of error information as described 00150 * below. There currently are up to three pieces of information 00151 * returned. 00152 * 00153 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00154 * right-hand side. 00155 * 00156 * The second index in ERR_BNDS_NORM(:,err) contains the following 00157 * three fields: 00158 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00159 * reciprocal condition number is less than the threshold 00160 * sqrt(n) * slamch('Epsilon'). 00161 * 00162 * err = 2 "Guaranteed" error bound: The estimated forward error, 00163 * almost certainly within a factor of 10 of the true error 00164 * so long as the next entry is greater than the threshold 00165 * sqrt(n) * slamch('Epsilon'). This error bound should only 00166 * be trusted if the previous boolean is true. 00167 * 00168 * err = 3 Reciprocal condition number: Estimated normwise 00169 * reciprocal condition number. Compared with the threshold 00170 * sqrt(n) * slamch('Epsilon') to determine if the error 00171 * estimate is "guaranteed". These reciprocal condition 00172 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00173 * appropriately scaled matrix Z. 00174 * Let Z = S*A, where S scales each row by a power of the 00175 * radix so all absolute row sums of Z are approximately 1. 00176 * 00177 * This subroutine is only responsible for setting the second field 00178 * above. 00179 * See Lapack Working Note 165 for further details and extra 00180 * cautions. 00181 * 00182 * ERR_BNDS_COMP (input/output) REAL array, dimension 00183 * (NRHS, N_ERR_BNDS) 00184 * For each right-hand side, this array contains information about 00185 * various error bounds and condition numbers corresponding to the 00186 * componentwise relative error, which is defined as follows: 00187 * 00188 * Componentwise relative error in the ith solution vector: 00189 * abs(XTRUE(j,i) - X(j,i)) 00190 * max_j ---------------------- 00191 * abs(X(j,i)) 00192 * 00193 * The array is indexed by the right-hand side i (on which the 00194 * componentwise relative error depends), and the type of error 00195 * information as described below. There currently are up to three 00196 * pieces of information returned for each right-hand side. If 00197 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00198 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00199 * the first (:,N_ERR_BNDS) entries are returned. 00200 * 00201 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00202 * right-hand side. 00203 * 00204 * The second index in ERR_BNDS_COMP(:,err) contains the following 00205 * three fields: 00206 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00207 * reciprocal condition number is less than the threshold 00208 * sqrt(n) * slamch('Epsilon'). 00209 * 00210 * err = 2 "Guaranteed" error bound: The estimated forward error, 00211 * almost certainly within a factor of 10 of the true error 00212 * so long as the next entry is greater than the threshold 00213 * sqrt(n) * slamch('Epsilon'). This error bound should only 00214 * be trusted if the previous boolean is true. 00215 * 00216 * err = 3 Reciprocal condition number: Estimated componentwise 00217 * reciprocal condition number. Compared with the threshold 00218 * sqrt(n) * slamch('Epsilon') to determine if the error 00219 * estimate is "guaranteed". These reciprocal condition 00220 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00221 * appropriately scaled matrix Z. 00222 * Let Z = S*(A*diag(x)), where x is the solution for the 00223 * current right-hand side and S scales each row of 00224 * A*diag(x) by a power of the radix so all absolute row 00225 * sums of Z are approximately 1. 00226 * 00227 * This subroutine is only responsible for setting the second field 00228 * above. 00229 * See Lapack Working Note 165 for further details and extra 00230 * cautions. 00231 * 00232 * RES (input) REAL array, dimension (N) 00233 * Workspace to hold the intermediate residual. 00234 * 00235 * AYB (input) REAL array, dimension (N) 00236 * Workspace. This can be the same workspace passed for Y_TAIL. 00237 * 00238 * DY (input) REAL array, dimension (N) 00239 * Workspace to hold the intermediate solution. 00240 * 00241 * Y_TAIL (input) REAL array, dimension (N) 00242 * Workspace to hold the trailing bits of the intermediate solution. 00243 * 00244 * RCOND (input) REAL 00245 * Reciprocal scaled condition number. This is an estimate of the 00246 * reciprocal Skeel condition number of the matrix A after 00247 * equilibration (if done). If this is less than the machine 00248 * precision (in particular, if it is zero), the matrix is singular 00249 * to working precision. Note that the error may still be small even 00250 * if this number is very small and the matrix appears ill- 00251 * conditioned. 00252 * 00253 * ITHRESH (input) INTEGER 00254 * The maximum number of residual computations allowed for 00255 * refinement. The default is 10. For 'aggressive' set to 100 to 00256 * permit convergence using approximate factorizations or 00257 * factorizations other than LU. If the factorization uses a 00258 * technique other than Gaussian elimination, the guarantees in 00259 * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00260 * 00261 * RTHRESH (input) REAL 00262 * Determines when to stop refinement if the error estimate stops 00263 * decreasing. Refinement will stop when the next solution no longer 00264 * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00265 * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00266 * default value is 0.5. For 'aggressive' set to 0.9 to permit 00267 * convergence on extremely ill-conditioned matrices. See LAWN 165 00268 * for more details. 00269 * 00270 * DZ_UB (input) REAL 00271 * Determines when to start considering componentwise convergence. 00272 * Componentwise convergence is only considered after each component 00273 * of the solution Y is stable, which we definte as the relative 00274 * change in each component being less than DZ_UB. The default value 00275 * is 0.25, requiring the first bit to be stable. See LAWN 165 for 00276 * more details. 00277 * 00278 * IGNORE_CWISE (input) LOGICAL 00279 * If .TRUE. then ignore componentwise convergence. Default value 00280 * is .FALSE.. 00281 * 00282 * INFO (output) INTEGER 00283 * = 0: Successful exit. 00284 * < 0: if INFO = -i, the ith argument to SGBTRS had an illegal 00285 * value 00286 * 00287 * ===================================================================== 00288 * 00289 * .. Local Scalars .. 00290 CHARACTER TRANS 00291 INTEGER CNT, I, J, M, X_STATE, Z_STATE, Y_PREC_STATE 00292 REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00293 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00294 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00295 $ EPS, HUGEVAL, INCR_THRESH 00296 LOGICAL INCR_PREC 00297 * .. 00298 * .. Parameters .. 00299 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00300 $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL, 00301 $ EXTRA_Y 00302 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00303 $ CONV_STATE = 2, NOPROG_STATE = 3 ) 00304 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00305 $ EXTRA_Y = 2 ) 00306 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00307 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00308 INTEGER CMP_ERR_I, PIV_GROWTH_I 00309 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00310 $ BERR_I = 3 ) 00311 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00312 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00313 $ PIV_GROWTH_I = 9 ) 00314 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00315 $ LA_LINRX_CWISE_I 00316 PARAMETER ( LA_LINRX_ITREF_I = 1, 00317 $ LA_LINRX_ITHRESH_I = 2 ) 00318 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00319 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00320 $ LA_LINRX_RCOND_I 00321 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00322 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00323 * .. 00324 * .. External Subroutines .. 00325 EXTERNAL SAXPY, SCOPY, SGBTRS, SGBMV, BLAS_SGBMV_X, 00326 $ BLAS_SGBMV2_X, SLA_GBAMV, SLA_WWADDW, SLAMCH, 00327 $ CHLA_TRANSTYPE, SLA_LIN_BERR 00328 REAL SLAMCH 00329 CHARACTER CHLA_TRANSTYPE 00330 * .. 00331 * .. Intrinsic Functions .. 00332 INTRINSIC ABS, MAX, MIN 00333 * .. 00334 * .. Executable Statements .. 00335 * 00336 IF (INFO.NE.0) RETURN 00337 TRANS = CHLA_TRANSTYPE(TRANS_TYPE) 00338 EPS = SLAMCH( 'Epsilon' ) 00339 HUGEVAL = SLAMCH( 'Overflow' ) 00340 * Force HUGEVAL to Inf 00341 HUGEVAL = HUGEVAL * HUGEVAL 00342 * Using HUGEVAL may lead to spurious underflows. 00343 INCR_THRESH = REAL( N ) * EPS 00344 M = KL+KU+1 00345 00346 DO J = 1, NRHS 00347 Y_PREC_STATE = EXTRA_RESIDUAL 00348 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00349 DO I = 1, N 00350 Y_TAIL( I ) = 0.0 00351 END DO 00352 END IF 00353 00354 DXRAT = 0.0 00355 DXRATMAX = 0.0 00356 DZRAT = 0.0 00357 DZRATMAX = 0.0 00358 FINAL_DX_X = HUGEVAL 00359 FINAL_DZ_Z = HUGEVAL 00360 PREVNORMDX = HUGEVAL 00361 PREV_DZ_Z = HUGEVAL 00362 DZ_Z = HUGEVAL 00363 DX_X = HUGEVAL 00364 00365 X_STATE = WORKING_STATE 00366 Z_STATE = UNSTABLE_STATE 00367 INCR_PREC = .FALSE. 00368 00369 DO CNT = 1, ITHRESH 00370 * 00371 * Compute residual RES = B_s - op(A_s) * Y, 00372 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00373 * 00374 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00375 IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN 00376 CALL SGBMV( TRANS, M, N, KL, KU, -1.0, AB, LDAB, 00377 $ Y( 1, J ), 1, 1.0, RES, 1 ) 00378 ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN 00379 CALL BLAS_SGBMV_X( TRANS_TYPE, N, N, KL, KU, 00380 $ -1.0, AB, LDAB, Y( 1, J ), 1, 1.0, RES, 1, 00381 $ PREC_TYPE ) 00382 ELSE 00383 CALL BLAS_SGBMV2_X( TRANS_TYPE, N, N, KL, KU, -1.0, 00384 $ AB, LDAB, Y( 1, J ), Y_TAIL, 1, 1.0, RES, 1, 00385 $ PREC_TYPE ) 00386 END IF 00387 00388 ! XXX: RES is no longer needed. 00389 CALL SCOPY( N, RES, 1, DY, 1 ) 00390 CALL SGBTRS( TRANS, N, KL, KU, 1, AFB, LDAFB, IPIV, DY, N, 00391 $ INFO ) 00392 * 00393 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00394 * 00395 NORMX = 0.0 00396 NORMY = 0.0 00397 NORMDX = 0.0 00398 DZ_Z = 0.0 00399 YMIN = HUGEVAL 00400 00401 DO I = 1, N 00402 YK = ABS( Y( I, J ) ) 00403 DYK = ABS( DY( I ) ) 00404 00405 IF ( YK .NE. 0.0 ) THEN 00406 DZ_Z = MAX( DZ_Z, DYK / YK ) 00407 ELSE IF ( DYK .NE. 0.0 ) THEN 00408 DZ_Z = HUGEVAL 00409 END IF 00410 00411 YMIN = MIN( YMIN, YK ) 00412 00413 NORMY = MAX( NORMY, YK ) 00414 00415 IF ( COLEQU ) THEN 00416 NORMX = MAX( NORMX, YK * C( I ) ) 00417 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00418 ELSE 00419 NORMX = NORMY 00420 NORMDX = MAX( NORMDX, DYK ) 00421 END IF 00422 END DO 00423 00424 IF ( NORMX .NE. 0.0 ) THEN 00425 DX_X = NORMDX / NORMX 00426 ELSE IF ( NORMDX .EQ. 0.0 ) THEN 00427 DX_X = 0.0 00428 ELSE 00429 DX_X = HUGEVAL 00430 END IF 00431 00432 DXRAT = NORMDX / PREVNORMDX 00433 DZRAT = DZ_Z / PREV_DZ_Z 00434 * 00435 * Check termination criteria. 00436 * 00437 IF ( .NOT.IGNORE_CWISE 00438 $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY 00439 $ .AND. Y_PREC_STATE .LT. EXTRA_Y ) 00440 $ INCR_PREC = .TRUE. 00441 00442 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00443 $ X_STATE = WORKING_STATE 00444 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00445 IF ( DX_X .LE. EPS ) THEN 00446 X_STATE = CONV_STATE 00447 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00448 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00449 INCR_PREC = .TRUE. 00450 ELSE 00451 X_STATE = NOPROG_STATE 00452 END IF 00453 ELSE 00454 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00455 END IF 00456 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00457 END IF 00458 00459 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00460 $ Z_STATE = WORKING_STATE 00461 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00462 $ Z_STATE = WORKING_STATE 00463 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00464 IF ( DZ_Z .LE. EPS ) THEN 00465 Z_STATE = CONV_STATE 00466 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00467 Z_STATE = UNSTABLE_STATE 00468 DZRATMAX = 0.0 00469 FINAL_DZ_Z = HUGEVAL 00470 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00471 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00472 INCR_PREC = .TRUE. 00473 ELSE 00474 Z_STATE = NOPROG_STATE 00475 END IF 00476 ELSE 00477 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00478 END IF 00479 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00480 END IF 00481 * 00482 * Exit if both normwise and componentwise stopped working, 00483 * but if componentwise is unstable, let it go at least two 00484 * iterations. 00485 * 00486 IF ( X_STATE.NE.WORKING_STATE ) THEN 00487 IF ( IGNORE_CWISE ) GOTO 666 00488 IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE ) 00489 $ GOTO 666 00490 IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666 00491 END IF 00492 00493 IF ( INCR_PREC ) THEN 00494 INCR_PREC = .FALSE. 00495 Y_PREC_STATE = Y_PREC_STATE + 1 00496 DO I = 1, N 00497 Y_TAIL( I ) = 0.0 00498 END DO 00499 END IF 00500 00501 PREVNORMDX = NORMDX 00502 PREV_DZ_Z = DZ_Z 00503 * 00504 * Update soluton. 00505 * 00506 IF (Y_PREC_STATE .LT. EXTRA_Y) THEN 00507 CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 ) 00508 ELSE 00509 CALL SLA_WWADDW( N, Y(1,J), Y_TAIL, DY ) 00510 END IF 00511 00512 END DO 00513 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00514 666 CONTINUE 00515 * 00516 * Set final_* when cnt hits ithresh. 00517 * 00518 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00519 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00520 * 00521 * Compute error bounds. 00522 * 00523 IF ( N_NORMS .GE. 1 ) THEN 00524 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 00525 $ FINAL_DX_X / (1 - DXRATMAX) 00526 END IF 00527 IF (N_NORMS .GE. 2) THEN 00528 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 00529 $ FINAL_DZ_Z / (1 - DZRATMAX) 00530 END IF 00531 * 00532 * Compute componentwise relative backward error from formula 00533 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00534 * where abs(Z) is the componentwise absolute value of the matrix 00535 * or vector Z. 00536 * 00537 * Compute residual RES = B_s - op(A_s) * Y, 00538 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00539 * 00540 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00541 CALL SGBMV(TRANS, N, N, KL, KU, -1.0, AB, LDAB, Y(1,J), 00542 $ 1, 1.0, RES, 1 ) 00543 00544 DO I = 1, N 00545 AYB( I ) = ABS( B( I, J ) ) 00546 END DO 00547 * 00548 * Compute abs(op(A_s))*abs(Y) + abs(B_s). 00549 * 00550 CALL SLA_GBAMV( TRANS_TYPE, N, N, KL, KU, 1.0, 00551 $ AB, LDAB, Y(1, J), 1, 1.0, AYB, 1 ) 00552 00553 CALL SLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) ) 00554 * 00555 * End of loop for each RHS 00556 * 00557 END DO 00558 * 00559 RETURN 00560 END
1.7.2