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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE DLA_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 DOUBLE PRECISION RTHRESH, DZ_UB 00024 * .. 00025 * .. Array Arguments .. 00026 INTEGER IPIV( * ) 00027 DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), 00028 $ Y( LDY, * ), RES(*), DY(*), Y_TAIL(*) 00029 DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT(*), 00030 $ ERR_BNDS_NORM( NRHS, * ), 00031 $ ERR_BNDS_COMP( NRHS, * ) 00032 * .. 00033 * 00034 * Purpose 00035 * ======= 00036 * 00037 * DLA_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 DGBRFSX 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDAF,N) 00086 * The factors L and U from the factorization 00087 * A = P*L*U as computed by DGBTRF. 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 DGBTRF; 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension 00119 * (LDY,NRHS) 00120 * On entry, the solution matrix X, as computed by DGBTRS. 00121 * On exit, the improved solution matrix Y. 00122 * 00123 * LDY (input) INTEGER 00124 * The leading dimension of the array Y. LDY >= max(1,N). 00125 * 00126 * BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS) 00127 * On exit, BERR_OUT(j) contains the componentwise relative backward 00128 * error for right-hand-side j from the formula 00129 * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00130 * where abs(Z) is the componentwise absolute value of the matrix 00131 * or vector Z. This is computed by DLA_LIN_BERR. 00132 * 00133 * N_NORMS (input) INTEGER 00134 * Determines which error bounds to return (see ERR_BNDS_NORM 00135 * and ERR_BNDS_COMP). 00136 * If N_NORMS >= 1 return normwise error bounds. 00137 * If N_NORMS >= 2 return componentwise error bounds. 00138 * 00139 * ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension 00140 * (NRHS, N_ERR_BNDS) 00141 * For each right-hand side, this array contains information about 00142 * various error bounds and condition numbers corresponding to the 00143 * normwise relative error, which is defined as follows: 00144 * 00145 * Normwise relative error in the ith solution vector: 00146 * max_j (abs(XTRUE(j,i) - X(j,i))) 00147 * ------------------------------ 00148 * max_j abs(X(j,i)) 00149 * 00150 * The array is indexed by the type of error information as described 00151 * below. There currently are up to three pieces of information 00152 * returned. 00153 * 00154 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00155 * right-hand side. 00156 * 00157 * The second index in ERR_BNDS_NORM(:,err) contains the following 00158 * three fields: 00159 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00160 * reciprocal condition number is less than the threshold 00161 * sqrt(n) * slamch('Epsilon'). 00162 * 00163 * err = 2 "Guaranteed" error bound: The estimated forward error, 00164 * almost certainly within a factor of 10 of the true error 00165 * so long as the next entry is greater than the threshold 00166 * sqrt(n) * slamch('Epsilon'). This error bound should only 00167 * be trusted if the previous boolean is true. 00168 * 00169 * err = 3 Reciprocal condition number: Estimated normwise 00170 * reciprocal condition number. Compared with the threshold 00171 * sqrt(n) * slamch('Epsilon') to determine if the error 00172 * estimate is "guaranteed". These reciprocal condition 00173 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00174 * appropriately scaled matrix Z. 00175 * Let Z = S*A, where S scales each row by a power of the 00176 * radix so all absolute row sums of Z are approximately 1. 00177 * 00178 * This subroutine is only responsible for setting the second field 00179 * above. 00180 * See Lapack Working Note 165 for further details and extra 00181 * cautions. 00182 * 00183 * ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension 00184 * (NRHS, N_ERR_BNDS) 00185 * For each right-hand side, this array contains information about 00186 * various error bounds and condition numbers corresponding to the 00187 * componentwise relative error, which is defined as follows: 00188 * 00189 * Componentwise relative error in the ith solution vector: 00190 * abs(XTRUE(j,i) - X(j,i)) 00191 * max_j ---------------------- 00192 * abs(X(j,i)) 00193 * 00194 * The array is indexed by the right-hand side i (on which the 00195 * componentwise relative error depends), and the type of error 00196 * information as described below. There currently are up to three 00197 * pieces of information returned for each right-hand side. If 00198 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00199 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00200 * the first (:,N_ERR_BNDS) entries are returned. 00201 * 00202 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00203 * right-hand side. 00204 * 00205 * The second index in ERR_BNDS_COMP(:,err) contains the following 00206 * three fields: 00207 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00208 * reciprocal condition number is less than the threshold 00209 * sqrt(n) * slamch('Epsilon'). 00210 * 00211 * err = 2 "Guaranteed" error bound: The estimated forward error, 00212 * almost certainly within a factor of 10 of the true error 00213 * so long as the next entry is greater than the threshold 00214 * sqrt(n) * slamch('Epsilon'). This error bound should only 00215 * be trusted if the previous boolean is true. 00216 * 00217 * err = 3 Reciprocal condition number: Estimated componentwise 00218 * reciprocal condition number. Compared with the threshold 00219 * sqrt(n) * slamch('Epsilon') to determine if the error 00220 * estimate is "guaranteed". These reciprocal condition 00221 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00222 * appropriately scaled matrix Z. 00223 * Let Z = S*(A*diag(x)), where x is the solution for the 00224 * current right-hand side and S scales each row of 00225 * A*diag(x) by a power of the radix so all absolute row 00226 * sums of Z are approximately 1. 00227 * 00228 * This subroutine is only responsible for setting the second field 00229 * above. 00230 * See Lapack Working Note 165 for further details and extra 00231 * cautions. 00232 * 00233 * RES (input) DOUBLE PRECISION array, dimension (N) 00234 * Workspace to hold the intermediate residual. 00235 * 00236 * AYB (input) DOUBLE PRECISION array, dimension (N) 00237 * Workspace. This can be the same workspace passed for Y_TAIL. 00238 * 00239 * DY (input) DOUBLE PRECISION array, dimension (N) 00240 * Workspace to hold the intermediate solution. 00241 * 00242 * Y_TAIL (input) DOUBLE PRECISION array, dimension (N) 00243 * Workspace to hold the trailing bits of the intermediate solution. 00244 * 00245 * RCOND (input) DOUBLE PRECISION 00246 * Reciprocal scaled condition number. This is an estimate of the 00247 * reciprocal Skeel condition number of the matrix A after 00248 * equilibration (if done). If this is less than the machine 00249 * precision (in particular, if it is zero), the matrix is singular 00250 * to working precision. Note that the error may still be small even 00251 * if this number is very small and the matrix appears ill- 00252 * conditioned. 00253 * 00254 * ITHRESH (input) INTEGER 00255 * The maximum number of residual computations allowed for 00256 * refinement. The default is 10. For 'aggressive' set to 100 to 00257 * permit convergence using approximate factorizations or 00258 * factorizations other than LU. If the factorization uses a 00259 * technique other than Gaussian elimination, the guarantees in 00260 * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00261 * 00262 * RTHRESH (input) DOUBLE PRECISION 00263 * Determines when to stop refinement if the error estimate stops 00264 * decreasing. Refinement will stop when the next solution no longer 00265 * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00266 * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00267 * default value is 0.5. For 'aggressive' set to 0.9 to permit 00268 * convergence on extremely ill-conditioned matrices. See LAWN 165 00269 * for more details. 00270 * 00271 * DZ_UB (input) DOUBLE PRECISION 00272 * Determines when to start considering componentwise convergence. 00273 * Componentwise convergence is only considered after each component 00274 * of the solution Y is stable, which we definte as the relative 00275 * change in each component being less than DZ_UB. The default value 00276 * is 0.25, requiring the first bit to be stable. See LAWN 165 for 00277 * more details. 00278 * 00279 * IGNORE_CWISE (input) LOGICAL 00280 * If .TRUE. then ignore componentwise convergence. Default value 00281 * is .FALSE.. 00282 * 00283 * INFO (output) INTEGER 00284 * = 0: Successful exit. 00285 * < 0: if INFO = -i, the ith argument to DGBTRS had an illegal 00286 * value 00287 * 00288 * ===================================================================== 00289 * 00290 * .. Local Scalars .. 00291 CHARACTER TRANS 00292 INTEGER CNT, I, J, M, X_STATE, Z_STATE, Y_PREC_STATE 00293 DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00294 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00295 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00296 $ EPS, HUGEVAL, INCR_THRESH 00297 LOGICAL INCR_PREC 00298 * .. 00299 * .. Parameters .. 00300 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00301 $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL, 00302 $ EXTRA_Y 00303 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00304 $ CONV_STATE = 2, NOPROG_STATE = 3 ) 00305 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00306 $ EXTRA_Y = 2 ) 00307 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00308 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00309 INTEGER CMP_ERR_I, PIV_GROWTH_I 00310 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00311 $ BERR_I = 3 ) 00312 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00313 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00314 $ PIV_GROWTH_I = 9 ) 00315 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00316 $ LA_LINRX_CWISE_I 00317 PARAMETER ( LA_LINRX_ITREF_I = 1, 00318 $ LA_LINRX_ITHRESH_I = 2 ) 00319 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00320 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00321 $ LA_LINRX_RCOND_I 00322 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00323 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00324 * .. 00325 * .. External Subroutines .. 00326 EXTERNAL DAXPY, DCOPY, DGBTRS, DGBMV, BLAS_DGBMV_X, 00327 $ BLAS_DGBMV2_X, DLA_GBAMV, DLA_WWADDW, DLAMCH, 00328 $ CHLA_TRANSTYPE, DLA_LIN_BERR 00329 DOUBLE PRECISION DLAMCH 00330 CHARACTER CHLA_TRANSTYPE 00331 * .. 00332 * .. Intrinsic Functions .. 00333 INTRINSIC ABS, MAX, MIN 00334 * .. 00335 * .. Executable Statements .. 00336 * 00337 IF (INFO.NE.0) RETURN 00338 TRANS = CHLA_TRANSTYPE(TRANS_TYPE) 00339 EPS = DLAMCH( 'Epsilon' ) 00340 HUGEVAL = DLAMCH( 'Overflow' ) 00341 * Force HUGEVAL to Inf 00342 HUGEVAL = HUGEVAL * HUGEVAL 00343 * Using HUGEVAL may lead to spurious underflows. 00344 INCR_THRESH = DBLE( N ) * EPS 00345 M = KL+KU+1 00346 00347 DO J = 1, NRHS 00348 Y_PREC_STATE = EXTRA_RESIDUAL 00349 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00350 DO I = 1, N 00351 Y_TAIL( I ) = 0.0D+0 00352 END DO 00353 END IF 00354 00355 DXRAT = 0.0D+0 00356 DXRATMAX = 0.0D+0 00357 DZRAT = 0.0D+0 00358 DZRATMAX = 0.0D+0 00359 FINAL_DX_X = HUGEVAL 00360 FINAL_DZ_Z = HUGEVAL 00361 PREVNORMDX = HUGEVAL 00362 PREV_DZ_Z = HUGEVAL 00363 DZ_Z = HUGEVAL 00364 DX_X = HUGEVAL 00365 00366 X_STATE = WORKING_STATE 00367 Z_STATE = UNSTABLE_STATE 00368 INCR_PREC = .FALSE. 00369 00370 DO CNT = 1, ITHRESH 00371 * 00372 * Compute residual RES = B_s - op(A_s) * Y, 00373 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00374 * 00375 CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) 00376 IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN 00377 CALL DGBMV( TRANS, M, N, KL, KU, -1.0D+0, AB, LDAB, 00378 $ Y( 1, J ), 1, 1.0D+0, RES, 1 ) 00379 ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN 00380 CALL BLAS_DGBMV_X( TRANS_TYPE, N, N, KL, KU, 00381 $ -1.0D+0, AB, LDAB, Y( 1, J ), 1, 1.0D+0, RES, 1, 00382 $ PREC_TYPE ) 00383 ELSE 00384 CALL BLAS_DGBMV2_X( TRANS_TYPE, N, N, KL, KU, -1.0D+0, 00385 $ AB, LDAB, Y( 1, J ), Y_TAIL, 1, 1.0D+0, RES, 1, 00386 $ PREC_TYPE ) 00387 END IF 00388 00389 ! XXX: RES is no longer needed. 00390 CALL DCOPY( N, RES, 1, DY, 1 ) 00391 CALL DGBTRS( TRANS, N, KL, KU, 1, AFB, LDAFB, IPIV, DY, N, 00392 $ INFO ) 00393 * 00394 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00395 * 00396 NORMX = 0.0D+0 00397 NORMY = 0.0D+0 00398 NORMDX = 0.0D+0 00399 DZ_Z = 0.0D+0 00400 YMIN = HUGEVAL 00401 00402 DO I = 1, N 00403 YK = ABS( Y( I, J ) ) 00404 DYK = ABS( DY( I ) ) 00405 00406 IF ( YK .NE. 0.0D+0 ) THEN 00407 DZ_Z = MAX( DZ_Z, DYK / YK ) 00408 ELSE IF ( DYK .NE. 0.0D+0 ) THEN 00409 DZ_Z = HUGEVAL 00410 END IF 00411 00412 YMIN = MIN( YMIN, YK ) 00413 00414 NORMY = MAX( NORMY, YK ) 00415 00416 IF ( COLEQU ) THEN 00417 NORMX = MAX( NORMX, YK * C( I ) ) 00418 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00419 ELSE 00420 NORMX = NORMY 00421 NORMDX = MAX( NORMDX, DYK ) 00422 END IF 00423 END DO 00424 00425 IF ( NORMX .NE. 0.0D+0 ) THEN 00426 DX_X = NORMDX / NORMX 00427 ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN 00428 DX_X = 0.0D+0 00429 ELSE 00430 DX_X = HUGEVAL 00431 END IF 00432 00433 DXRAT = NORMDX / PREVNORMDX 00434 DZRAT = DZ_Z / PREV_DZ_Z 00435 * 00436 * Check termination criteria. 00437 * 00438 IF ( .NOT.IGNORE_CWISE 00439 $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY 00440 $ .AND. Y_PREC_STATE .LT. EXTRA_Y ) 00441 $ INCR_PREC = .TRUE. 00442 00443 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00444 $ X_STATE = WORKING_STATE 00445 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00446 IF ( DX_X .LE. EPS ) THEN 00447 X_STATE = CONV_STATE 00448 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00449 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00450 INCR_PREC = .TRUE. 00451 ELSE 00452 X_STATE = NOPROG_STATE 00453 END IF 00454 ELSE 00455 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00456 END IF 00457 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00458 END IF 00459 00460 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00461 $ Z_STATE = WORKING_STATE 00462 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00463 $ Z_STATE = WORKING_STATE 00464 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00465 IF ( DZ_Z .LE. EPS ) THEN 00466 Z_STATE = CONV_STATE 00467 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00468 Z_STATE = UNSTABLE_STATE 00469 DZRATMAX = 0.0D+0 00470 FINAL_DZ_Z = HUGEVAL 00471 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00472 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00473 INCR_PREC = .TRUE. 00474 ELSE 00475 Z_STATE = NOPROG_STATE 00476 END IF 00477 ELSE 00478 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00479 END IF 00480 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00481 END IF 00482 * 00483 * Exit if both normwise and componentwise stopped working, 00484 * but if componentwise is unstable, let it go at least two 00485 * iterations. 00486 * 00487 IF ( X_STATE.NE.WORKING_STATE ) THEN 00488 IF ( IGNORE_CWISE ) GOTO 666 00489 IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE ) 00490 $ GOTO 666 00491 IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666 00492 END IF 00493 00494 IF ( INCR_PREC ) THEN 00495 INCR_PREC = .FALSE. 00496 Y_PREC_STATE = Y_PREC_STATE + 1 00497 DO I = 1, N 00498 Y_TAIL( I ) = 0.0D+0 00499 END DO 00500 END IF 00501 00502 PREVNORMDX = NORMDX 00503 PREV_DZ_Z = DZ_Z 00504 * 00505 * Update soluton. 00506 * 00507 IF (Y_PREC_STATE .LT. EXTRA_Y) THEN 00508 CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 ) 00509 ELSE 00510 CALL DLA_WWADDW( N, Y(1,J), Y_TAIL, DY ) 00511 END IF 00512 00513 END DO 00514 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00515 666 CONTINUE 00516 * 00517 * Set final_* when cnt hits ithresh. 00518 * 00519 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00520 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00521 * 00522 * Compute error bounds. 00523 * 00524 IF ( N_NORMS .GE. 1 ) THEN 00525 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 00526 $ FINAL_DX_X / (1 - DXRATMAX) 00527 END IF 00528 IF (N_NORMS .GE. 2) THEN 00529 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 00530 $ FINAL_DZ_Z / (1 - DZRATMAX) 00531 END IF 00532 * 00533 * Compute componentwise relative backward error from formula 00534 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00535 * where abs(Z) is the componentwise absolute value of the matrix 00536 * or vector Z. 00537 * 00538 * Compute residual RES = B_s - op(A_s) * Y, 00539 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00540 * 00541 CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) 00542 CALL DGBMV(TRANS, N, N, KL, KU, -1.0D+0, AB, LDAB, Y(1,J), 00543 $ 1, 1.0D+0, RES, 1 ) 00544 00545 DO I = 1, N 00546 AYB( I ) = ABS( B( I, J ) ) 00547 END DO 00548 * 00549 * Compute abs(op(A_s))*abs(Y) + abs(B_s). 00550 * 00551 CALL DLA_GBAMV( TRANS_TYPE, N, N, KL, KU, 1.0D+0, 00552 $ AB, LDAB, Y(1, J), 1, 1.0D+0, AYB, 1 ) 00553 00554 CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) ) 00555 * 00556 * End of loop for each RHS 00557 * 00558 END DO 00559 * 00560 RETURN 00561 END
1.7.3 
