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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE SLA_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 $ ERR_BNDS_NORM, ERR_BNDS_COMP, RES, 00005 $ AYB, DY, Y_TAIL, RCOND, ITHRESH, 00006 $ RTHRESH, DZ_UB, IGNORE_CWISE, 00007 $ 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, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE, 00021 $ TRANS_TYPE, N_NORMS, ITHRESH 00022 LOGICAL COLEQU, IGNORE_CWISE 00023 REAL RTHRESH, DZ_UB 00024 * .. 00025 * .. Array Arguments .. 00026 INTEGER IPIV( * ) 00027 REAL A( LDA, * ), AF( LDAF, * ), 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_GERFSX_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 SGERFSX 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 * NRHS (input) INTEGER 00070 * The number of right-hand-sides, i.e., the number of columns of the 00071 * matrix B. 00072 * 00073 * A (input) REAL array, dimension (LDA,N) 00074 * On entry, the N-by-N matrix A. 00075 * 00076 * LDA (input) INTEGER 00077 * The leading dimension of the array A. LDA >= max(1,N). 00078 * 00079 * AF (input) REAL array, dimension (LDAF,N) 00080 * The factors L and U from the factorization 00081 * A = P*L*U as computed by SGETRF. 00082 * 00083 * LDAF (input) INTEGER 00084 * The leading dimension of the array AF. LDAF >= max(1,N). 00085 * 00086 * IPIV (input) INTEGER array, dimension (N) 00087 * The pivot indices from the factorization A = P*L*U 00088 * as computed by SGETRF; row i of the matrix was interchanged 00089 * with row IPIV(i). 00090 * 00091 * COLEQU (input) LOGICAL 00092 * If .TRUE. then column equilibration was done to A before calling 00093 * this routine. This is needed to compute the solution and error 00094 * bounds correctly. 00095 * 00096 * C (input) REAL array, dimension (N) 00097 * The column scale factors for A. If COLEQU = .FALSE., C 00098 * is not accessed. If C is input, each element of C should be a power 00099 * of the radix to ensure a reliable solution and error estimates. 00100 * Scaling by powers of the radix does not cause rounding errors unless 00101 * the result underflows or overflows. Rounding errors during scaling 00102 * lead to refining with a matrix that is not equivalent to the 00103 * input matrix, producing error estimates that may not be 00104 * reliable. 00105 * 00106 * B (input) REAL array, dimension (LDB,NRHS) 00107 * The right-hand-side matrix B. 00108 * 00109 * LDB (input) INTEGER 00110 * The leading dimension of the array B. LDB >= max(1,N). 00111 * 00112 * Y (input/output) REAL array, dimension (LDY,NRHS) 00113 * On entry, the solution matrix X, as computed by SGETRS. 00114 * On exit, the improved solution matrix Y. 00115 * 00116 * LDY (input) INTEGER 00117 * The leading dimension of the array Y. LDY >= max(1,N). 00118 * 00119 * BERR_OUT (output) REAL array, dimension (NRHS) 00120 * On exit, BERR_OUT(j) contains the componentwise relative backward 00121 * error for right-hand-side j from the formula 00122 * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00123 * where abs(Z) is the componentwise absolute value of the matrix 00124 * or vector Z. This is computed by SLA_LIN_BERR. 00125 * 00126 * N_NORMS (input) INTEGER 00127 * Determines which error bounds to return (see ERR_BNDS_NORM 00128 * and ERR_BNDS_COMP). 00129 * If N_NORMS >= 1 return normwise error bounds. 00130 * If N_NORMS >= 2 return componentwise error bounds. 00131 * 00132 * ERR_BNDS_NORM (input/output) REAL array, dimension (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) REAL array, dimension (NRHS, N_ERR_BNDS) 00176 * For each right-hand side, this array contains information about 00177 * various error bounds and condition numbers corresponding to the 00178 * componentwise relative error, which is defined as follows: 00179 * 00180 * Componentwise relative error in the ith solution vector: 00181 * abs(XTRUE(j,i) - X(j,i)) 00182 * max_j ---------------------- 00183 * abs(X(j,i)) 00184 * 00185 * The array is indexed by the right-hand side i (on which the 00186 * componentwise relative error depends), and the type of error 00187 * information as described below. There currently are up to three 00188 * pieces of information returned for each right-hand side. If 00189 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00190 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00191 * the first (:,N_ERR_BNDS) entries are returned. 00192 * 00193 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00194 * right-hand side. 00195 * 00196 * The second index in ERR_BNDS_COMP(:,err) contains the following 00197 * three fields: 00198 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00199 * reciprocal condition number is less than the threshold 00200 * sqrt(n) * slamch('Epsilon'). 00201 * 00202 * err = 2 "Guaranteed" error bound: The estimated forward error, 00203 * almost certainly within a factor of 10 of the true error 00204 * so long as the next entry is greater than the threshold 00205 * sqrt(n) * slamch('Epsilon'). This error bound should only 00206 * be trusted if the previous boolean is true. 00207 * 00208 * err = 3 Reciprocal condition number: Estimated componentwise 00209 * reciprocal condition number. Compared with the threshold 00210 * sqrt(n) * slamch('Epsilon') to determine if the error 00211 * estimate is "guaranteed". These reciprocal condition 00212 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00213 * appropriately scaled matrix Z. 00214 * Let Z = S*(A*diag(x)), where x is the solution for the 00215 * current right-hand side and S scales each row of 00216 * A*diag(x) by a power of the radix so all absolute row 00217 * sums of Z are approximately 1. 00218 * 00219 * This subroutine is only responsible for setting the second field 00220 * above. 00221 * See Lapack Working Note 165 for further details and extra 00222 * cautions. 00223 * 00224 * RES (input) REAL array, dimension (N) 00225 * Workspace to hold the intermediate residual. 00226 * 00227 * AYB (input) REAL array, dimension (N) 00228 * Workspace. This can be the same workspace passed for Y_TAIL. 00229 * 00230 * DY (input) REAL array, dimension (N) 00231 * Workspace to hold the intermediate solution. 00232 * 00233 * Y_TAIL (input) REAL array, dimension (N) 00234 * Workspace to hold the trailing bits of the intermediate solution. 00235 * 00236 * RCOND (input) REAL 00237 * Reciprocal scaled condition number. This is an estimate of the 00238 * reciprocal Skeel condition number of the matrix A after 00239 * equilibration (if done). If this is less than the machine 00240 * precision (in particular, if it is zero), the matrix is singular 00241 * to working precision. Note that the error may still be small even 00242 * if this number is very small and the matrix appears ill- 00243 * conditioned. 00244 * 00245 * ITHRESH (input) INTEGER 00246 * The maximum number of residual computations allowed for 00247 * refinement. The default is 10. For 'aggressive' set to 100 to 00248 * permit convergence using approximate factorizations or 00249 * factorizations other than LU. If the factorization uses a 00250 * technique other than Gaussian elimination, the guarantees in 00251 * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00252 * 00253 * RTHRESH (input) REAL 00254 * Determines when to stop refinement if the error estimate stops 00255 * decreasing. Refinement will stop when the next solution no longer 00256 * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00257 * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00258 * default value is 0.5. For 'aggressive' set to 0.9 to permit 00259 * convergence on extremely ill-conditioned matrices. See LAWN 165 00260 * for more details. 00261 * 00262 * DZ_UB (input) REAL 00263 * Determines when to start considering componentwise convergence. 00264 * Componentwise convergence is only considered after each component 00265 * of the solution Y is stable, which we definte as the relative 00266 * change in each component being less than DZ_UB. The default value 00267 * is 0.25, requiring the first bit to be stable. See LAWN 165 for 00268 * more details. 00269 * 00270 * IGNORE_CWISE (input) LOGICAL 00271 * If .TRUE. then ignore componentwise convergence. Default value 00272 * is .FALSE.. 00273 * 00274 * INFO (output) INTEGER 00275 * = 0: Successful exit. 00276 * < 0: if INFO = -i, the ith argument to SGETRS had an illegal 00277 * value 00278 * 00279 * ===================================================================== 00280 * 00281 * .. Local Scalars .. 00282 CHARACTER TRANS 00283 INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE 00284 REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00285 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00286 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00287 $ EPS, HUGEVAL, INCR_THRESH 00288 LOGICAL INCR_PREC 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, NOPROG_STATE = 3 ) 00296 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00297 $ EXTRA_Y = 2 ) 00298 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00299 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00300 INTEGER CMP_ERR_I, PIV_GROWTH_I 00301 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00302 $ BERR_I = 3 ) 00303 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00304 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00305 $ PIV_GROWTH_I = 9 ) 00306 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00307 $ LA_LINRX_CWISE_I 00308 PARAMETER ( LA_LINRX_ITREF_I = 1, 00309 $ LA_LINRX_ITHRESH_I = 2 ) 00310 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00311 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00312 $ LA_LINRX_RCOND_I 00313 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00314 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00315 * .. 00316 * .. External Subroutines .. 00317 EXTERNAL SAXPY, SCOPY, SGETRS, SGEMV, BLAS_SGEMV_X, 00318 $ BLAS_SGEMV2_X, SLA_GEAMV, SLA_WWADDW, SLAMCH, 00319 $ CHLA_TRANSTYPE, SLA_LIN_BERR 00320 REAL SLAMCH 00321 CHARACTER CHLA_TRANSTYPE 00322 * .. 00323 * .. Intrinsic Functions .. 00324 INTRINSIC ABS, MAX, MIN 00325 * .. 00326 * .. Executable Statements .. 00327 * 00328 IF ( INFO.NE.0 ) RETURN 00329 TRANS = CHLA_TRANSTYPE(TRANS_TYPE) 00330 EPS = SLAMCH( 'Epsilon' ) 00331 HUGEVAL = SLAMCH( 'Overflow' ) 00332 * Force HUGEVAL to Inf 00333 HUGEVAL = HUGEVAL * HUGEVAL 00334 * Using HUGEVAL may lead to spurious underflows. 00335 INCR_THRESH = REAL( N ) * EPS 00336 * 00337 DO J = 1, NRHS 00338 Y_PREC_STATE = EXTRA_RESIDUAL 00339 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00340 DO I = 1, N 00341 Y_TAIL( I ) = 0.0 00342 END DO 00343 END IF 00344 00345 DXRAT = 0.0 00346 DXRATMAX = 0.0 00347 DZRAT = 0.0 00348 DZRATMAX = 0.0 00349 FINAL_DX_X = HUGEVAL 00350 FINAL_DZ_Z = HUGEVAL 00351 PREVNORMDX = HUGEVAL 00352 PREV_DZ_Z = HUGEVAL 00353 DZ_Z = HUGEVAL 00354 DX_X = HUGEVAL 00355 00356 X_STATE = WORKING_STATE 00357 Z_STATE = UNSTABLE_STATE 00358 INCR_PREC = .FALSE. 00359 00360 DO CNT = 1, ITHRESH 00361 * 00362 * Compute residual RES = B_s - op(A_s) * Y, 00363 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00364 * 00365 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00366 IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN 00367 CALL SGEMV( TRANS, N, N, -1.0, A, LDA, Y( 1, J ), 1, 00368 $ 1.0, RES, 1 ) 00369 ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN 00370 CALL BLAS_SGEMV_X( TRANS_TYPE, N, N, -1.0, A, LDA, 00371 $ Y( 1, J ), 1, 1.0, RES, 1, PREC_TYPE ) 00372 ELSE 00373 CALL BLAS_SGEMV2_X( TRANS_TYPE, N, N, -1.0, A, LDA, 00374 $ Y( 1, J ), Y_TAIL, 1, 1.0, RES, 1, PREC_TYPE ) 00375 END IF 00376 00377 ! XXX: RES is no longer needed. 00378 CALL SCOPY( N, RES, 1, DY, 1 ) 00379 CALL SGETRS( TRANS, N, 1, AF, LDAF, IPIV, DY, N, INFO ) 00380 * 00381 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00382 * 00383 NORMX = 0.0 00384 NORMY = 0.0 00385 NORMDX = 0.0 00386 DZ_Z = 0.0 00387 YMIN = HUGEVAL 00388 * 00389 DO I = 1, N 00390 YK = ABS( Y( I, J ) ) 00391 DYK = ABS( DY( I ) ) 00392 00393 IF ( YK .NE. 0.0 ) THEN 00394 DZ_Z = MAX( DZ_Z, DYK / YK ) 00395 ELSE IF ( DYK .NE. 0.0 ) THEN 00396 DZ_Z = HUGEVAL 00397 END IF 00398 00399 YMIN = MIN( YMIN, YK ) 00400 00401 NORMY = MAX( NORMY, YK ) 00402 00403 IF ( COLEQU ) THEN 00404 NORMX = MAX( NORMX, YK * C( I ) ) 00405 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00406 ELSE 00407 NORMX = NORMY 00408 NORMDX = MAX( NORMDX, DYK ) 00409 END IF 00410 END DO 00411 00412 IF ( NORMX .NE. 0.0 ) THEN 00413 DX_X = NORMDX / NORMX 00414 ELSE IF ( NORMDX .EQ. 0.0 ) THEN 00415 DX_X = 0.0 00416 ELSE 00417 DX_X = HUGEVAL 00418 END IF 00419 00420 DXRAT = NORMDX / PREVNORMDX 00421 DZRAT = DZ_Z / PREV_DZ_Z 00422 * 00423 * Check termination criteria 00424 * 00425 IF (.NOT.IGNORE_CWISE 00426 $ .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY 00427 $ .AND. Y_PREC_STATE .LT. EXTRA_Y) 00428 $ INCR_PREC = .TRUE. 00429 00430 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00431 $ X_STATE = WORKING_STATE 00432 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00433 IF ( DX_X .LE. EPS ) THEN 00434 X_STATE = CONV_STATE 00435 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00436 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00437 INCR_PREC = .TRUE. 00438 ELSE 00439 X_STATE = NOPROG_STATE 00440 END IF 00441 ELSE 00442 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00443 END IF 00444 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00445 END IF 00446 00447 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00448 $ Z_STATE = WORKING_STATE 00449 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00450 $ Z_STATE = WORKING_STATE 00451 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00452 IF ( DZ_Z .LE. EPS ) THEN 00453 Z_STATE = CONV_STATE 00454 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00455 Z_STATE = UNSTABLE_STATE 00456 DZRATMAX = 0.0 00457 FINAL_DZ_Z = HUGEVAL 00458 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00459 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00460 INCR_PREC = .TRUE. 00461 ELSE 00462 Z_STATE = NOPROG_STATE 00463 END IF 00464 ELSE 00465 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00466 END IF 00467 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00468 END IF 00469 * 00470 * Exit if both normwise and componentwise stopped working, 00471 * but if componentwise is unstable, let it go at least two 00472 * iterations. 00473 * 00474 IF ( X_STATE.NE.WORKING_STATE ) THEN 00475 IF ( IGNORE_CWISE) GOTO 666 00476 IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE ) 00477 $ GOTO 666 00478 IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666 00479 END IF 00480 00481 IF ( INCR_PREC ) THEN 00482 INCR_PREC = .FALSE. 00483 Y_PREC_STATE = Y_PREC_STATE + 1 00484 DO I = 1, N 00485 Y_TAIL( I ) = 0.0 00486 END DO 00487 END IF 00488 00489 PREVNORMDX = NORMDX 00490 PREV_DZ_Z = DZ_Z 00491 * 00492 * Update soluton. 00493 * 00494 IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN 00495 CALL SAXPY( N, 1.0, DY, 1, Y( 1, J ), 1 ) 00496 ELSE 00497 CALL SLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY ) 00498 END IF 00499 00500 END DO 00501 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00502 666 CONTINUE 00503 * 00504 * Set final_* when cnt hits ithresh. 00505 * 00506 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00507 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00508 * 00509 * Compute error bounds 00510 * 00511 IF (N_NORMS .GE. 1) THEN 00512 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 00513 $ FINAL_DX_X / (1 - DXRATMAX) 00514 END IF 00515 IF ( N_NORMS .GE. 2 ) THEN 00516 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 00517 $ FINAL_DZ_Z / (1 - DZRATMAX) 00518 END IF 00519 * 00520 * Compute componentwise relative backward error from formula 00521 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00522 * where abs(Z) is the componentwise absolute value of the matrix 00523 * or vector Z. 00524 * 00525 * Compute residual RES = B_s - op(A_s) * Y, 00526 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00527 * 00528 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00529 CALL SGEMV( TRANS, N, N, -1.0, A, LDA, Y(1,J), 1, 1.0, 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 SLA_GEAMV ( TRANS_TYPE, N, N, 1.0, 00538 $ A, LDA, Y(1, J), 1, 1.0, AYB, 1 ) 00539 00540 CALL SLA_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
1.7.3 
