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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE SLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA, 00002 $ AF, LDAF, COLEQU, C, B, LDB, Y, 00003 $ 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 3.2.2) -- 00010 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 00011 * -- Jason Riedy of Univ. of California Berkeley. -- 00012 * -- June 2010 -- 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 $ N_NORMS, ITHRESH 00022 CHARACTER UPLO 00023 LOGICAL COLEQU, IGNORE_CWISE 00024 REAL RTHRESH, DZ_UB 00025 * .. 00026 * .. Array Arguments .. 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_PORFSX_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 SPORFSX 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 * UPLO (input) CHARACTER*1 00059 * = 'U': Upper triangle of A is stored; 00060 * = 'L': Lower triangle of A is stored. 00061 * 00062 * N (input) INTEGER 00063 * The number of linear equations, i.e., the order of the 00064 * matrix A. N >= 0. 00065 * 00066 * NRHS (input) INTEGER 00067 * The number of right-hand-sides, i.e., the number of columns of the 00068 * matrix B. 00069 * 00070 * A (input) REAL array, dimension (LDA,N) 00071 * On entry, the N-by-N matrix A. 00072 * 00073 * LDA (input) INTEGER 00074 * The leading dimension of the array A. LDA >= max(1,N). 00075 * 00076 * AF (input) REAL array, dimension (LDAF,N) 00077 * The triangular factor U or L from the Cholesky factorization 00078 * A = U**T*U or A = L*L**T, as computed by SPOTRF. 00079 * 00080 * LDAF (input) INTEGER 00081 * The leading dimension of the array AF. LDAF >= max(1,N). 00082 * 00083 * COLEQU (input) LOGICAL 00084 * If .TRUE. then column equilibration was done to A before calling 00085 * this routine. This is needed to compute the solution and error 00086 * bounds correctly. 00087 * 00088 * C (input) REAL array, dimension (N) 00089 * The column scale factors for A. If COLEQU = .FALSE., C 00090 * is not accessed. If C is input, each element of C should be a power 00091 * of the radix to ensure a reliable solution and error estimates. 00092 * Scaling by powers of the radix does not cause rounding errors unless 00093 * the result underflows or overflows. Rounding errors during scaling 00094 * lead to refining with a matrix that is not equivalent to the 00095 * input matrix, producing error estimates that may not be 00096 * reliable. 00097 * 00098 * B (input) REAL array, dimension (LDB,NRHS) 00099 * The right-hand-side matrix B. 00100 * 00101 * LDB (input) INTEGER 00102 * The leading dimension of the array B. LDB >= max(1,N). 00103 * 00104 * Y (input/output) REAL array, dimension (LDY,NRHS) 00105 * On entry, the solution matrix X, as computed by SPOTRS. 00106 * On exit, the improved solution matrix Y. 00107 * 00108 * LDY (input) INTEGER 00109 * The leading dimension of the array Y. LDY >= max(1,N). 00110 * 00111 * BERR_OUT (output) REAL array, dimension (NRHS) 00112 * On exit, BERR_OUT(j) contains the componentwise relative backward 00113 * error for right-hand-side j from the formula 00114 * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00115 * where abs(Z) is the componentwise absolute value of the matrix 00116 * or vector Z. This is computed by SLA_LIN_BERR. 00117 * 00118 * N_NORMS (input) INTEGER 00119 * Determines which error bounds to return (see ERR_BNDS_NORM 00120 * and ERR_BNDS_COMP). 00121 * If N_NORMS >= 1 return normwise error bounds. 00122 * If N_NORMS >= 2 return componentwise error bounds. 00123 * 00124 * ERR_BNDS_NORM (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) 00125 * For each right-hand side, this array contains information about 00126 * various error bounds and condition numbers corresponding to the 00127 * normwise relative error, which is defined as follows: 00128 * 00129 * Normwise relative error in the ith solution vector: 00130 * max_j (abs(XTRUE(j,i) - X(j,i))) 00131 * ------------------------------ 00132 * max_j abs(X(j,i)) 00133 * 00134 * The array is indexed by the type of error information as described 00135 * below. There currently are up to three pieces of information 00136 * returned. 00137 * 00138 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00139 * right-hand side. 00140 * 00141 * The second index in ERR_BNDS_NORM(:,err) contains the following 00142 * three fields: 00143 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00144 * reciprocal condition number is less than the threshold 00145 * sqrt(n) * slamch('Epsilon'). 00146 * 00147 * err = 2 "Guaranteed" error bound: The estimated forward error, 00148 * almost certainly within a factor of 10 of the true error 00149 * so long as the next entry is greater than the threshold 00150 * sqrt(n) * slamch('Epsilon'). This error bound should only 00151 * be trusted if the previous boolean is true. 00152 * 00153 * err = 3 Reciprocal condition number: Estimated normwise 00154 * reciprocal condition number. Compared with the threshold 00155 * sqrt(n) * slamch('Epsilon') to determine if the error 00156 * estimate is "guaranteed". These reciprocal condition 00157 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00158 * appropriately scaled matrix Z. 00159 * Let Z = S*A, where S scales each row by a power of the 00160 * radix so all absolute row sums of Z are approximately 1. 00161 * 00162 * This subroutine is only responsible for setting the second field 00163 * above. 00164 * See Lapack Working Note 165 for further details and extra 00165 * cautions. 00166 * 00167 * ERR_BNDS_COMP (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) 00168 * For each right-hand side, this array contains information about 00169 * various error bounds and condition numbers corresponding to the 00170 * componentwise relative error, which is defined as follows: 00171 * 00172 * Componentwise relative error in the ith solution vector: 00173 * abs(XTRUE(j,i) - X(j,i)) 00174 * max_j ---------------------- 00175 * abs(X(j,i)) 00176 * 00177 * The array is indexed by the right-hand side i (on which the 00178 * componentwise relative error depends), and the type of error 00179 * information as described below. There currently are up to three 00180 * pieces of information returned for each right-hand side. If 00181 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00182 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00183 * the first (:,N_ERR_BNDS) entries are returned. 00184 * 00185 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00186 * right-hand side. 00187 * 00188 * The second index in ERR_BNDS_COMP(:,err) contains the following 00189 * three fields: 00190 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00191 * reciprocal condition number is less than the threshold 00192 * sqrt(n) * slamch('Epsilon'). 00193 * 00194 * err = 2 "Guaranteed" error bound: The estimated forward error, 00195 * almost certainly within a factor of 10 of the true error 00196 * so long as the next entry is greater than the threshold 00197 * sqrt(n) * slamch('Epsilon'). This error bound should only 00198 * be trusted if the previous boolean is true. 00199 * 00200 * err = 3 Reciprocal condition number: Estimated componentwise 00201 * reciprocal condition number. Compared with the threshold 00202 * sqrt(n) * slamch('Epsilon') to determine if the error 00203 * estimate is "guaranteed". These reciprocal condition 00204 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00205 * appropriately scaled matrix Z. 00206 * Let Z = S*(A*diag(x)), where x is the solution for the 00207 * current right-hand side and S scales each row of 00208 * A*diag(x) by a power of the radix so all absolute row 00209 * sums of Z are approximately 1. 00210 * 00211 * This subroutine is only responsible for setting the second field 00212 * above. 00213 * See Lapack Working Note 165 for further details and extra 00214 * cautions. 00215 * 00216 * RES (input) REAL array, dimension (N) 00217 * Workspace to hold the intermediate residual. 00218 * 00219 * AYB (input) REAL array, dimension (N) 00220 * Workspace. This can be the same workspace passed for Y_TAIL. 00221 * 00222 * DY (input) REAL array, dimension (N) 00223 * Workspace to hold the intermediate solution. 00224 * 00225 * Y_TAIL (input) REAL array, dimension (N) 00226 * Workspace to hold the trailing bits of the intermediate solution. 00227 * 00228 * RCOND (input) REAL 00229 * Reciprocal scaled condition number. This is an estimate of the 00230 * reciprocal Skeel condition number of the matrix A after 00231 * equilibration (if done). If this is less than the machine 00232 * precision (in particular, if it is zero), the matrix is singular 00233 * to working precision. Note that the error may still be small even 00234 * if this number is very small and the matrix appears ill- 00235 * conditioned. 00236 * 00237 * ITHRESH (input) INTEGER 00238 * The maximum number of residual computations allowed for 00239 * refinement. The default is 10. For 'aggressive' set to 100 to 00240 * permit convergence using approximate factorizations or 00241 * factorizations other than LU. If the factorization uses a 00242 * technique other than Gaussian elimination, the guarantees in 00243 * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00244 * 00245 * RTHRESH (input) REAL 00246 * Determines when to stop refinement if the error estimate stops 00247 * decreasing. Refinement will stop when the next solution no longer 00248 * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00249 * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00250 * default value is 0.5. For 'aggressive' set to 0.9 to permit 00251 * convergence on extremely ill-conditioned matrices. See LAWN 165 00252 * for more details. 00253 * 00254 * DZ_UB (input) REAL 00255 * Determines when to start considering componentwise convergence. 00256 * Componentwise convergence is only considered after each component 00257 * of the solution Y is stable, which we definte as the relative 00258 * change in each component being less than DZ_UB. The default value 00259 * is 0.25, requiring the first bit to be stable. See LAWN 165 for 00260 * more details. 00261 * 00262 * IGNORE_CWISE (input) LOGICAL 00263 * If .TRUE. then ignore componentwise convergence. Default value 00264 * is .FALSE.. 00265 * 00266 * INFO (output) INTEGER 00267 * = 0: Successful exit. 00268 * < 0: if INFO = -i, the ith argument to SPOTRS had an illegal 00269 * value 00270 * 00271 * ===================================================================== 00272 * 00273 * .. Local Scalars .. 00274 INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE 00275 REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00276 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00277 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00278 $ EPS, HUGEVAL, INCR_THRESH 00279 LOGICAL INCR_PREC 00280 * .. 00281 * .. Parameters .. 00282 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00283 $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL, 00284 $ EXTRA_RESIDUAL, EXTRA_Y 00285 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00286 $ CONV_STATE = 2, NOPROG_STATE = 3 ) 00287 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00288 $ EXTRA_Y = 2 ) 00289 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00290 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00291 INTEGER CMP_ERR_I, PIV_GROWTH_I 00292 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00293 $ BERR_I = 3 ) 00294 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00295 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00296 $ PIV_GROWTH_I = 9 ) 00297 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00298 $ LA_LINRX_CWISE_I 00299 PARAMETER ( LA_LINRX_ITREF_I = 1, 00300 $ LA_LINRX_ITHRESH_I = 2 ) 00301 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00302 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00303 $ LA_LINRX_RCOND_I 00304 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00305 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00306 * .. 00307 * .. External Functions .. 00308 LOGICAL LSAME 00309 EXTERNAL ILAUPLO 00310 INTEGER ILAUPLO 00311 * .. 00312 * .. External Subroutines .. 00313 EXTERNAL SAXPY, SCOPY, SPOTRS, SSYMV, BLAS_SSYMV_X, 00314 $ BLAS_SSYMV2_X, SLA_SYAMV, SLA_WWADDW, 00315 $ SLA_LIN_BERR 00316 REAL SLAMCH 00317 * .. 00318 * .. Intrinsic Functions .. 00319 INTRINSIC ABS, MAX, MIN 00320 * .. 00321 * .. Executable Statements .. 00322 * 00323 IF (INFO.NE.0) RETURN 00324 EPS = SLAMCH( 'Epsilon' ) 00325 HUGEVAL = SLAMCH( 'Overflow' ) 00326 * Force HUGEVAL to Inf 00327 HUGEVAL = HUGEVAL * HUGEVAL 00328 * Using HUGEVAL may lead to spurious underflows. 00329 INCR_THRESH = REAL( N ) * EPS 00330 00331 IF ( LSAME ( UPLO, 'L' ) ) THEN 00332 UPLO2 = ILAUPLO( 'L' ) 00333 ELSE 00334 UPLO2 = ILAUPLO( 'U' ) 00335 ENDIF 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 SSYMV( UPLO, 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_SSYMV_X( UPLO2, N, -1.0, A, LDA, 00371 $ Y( 1, J ), 1, 1.0, RES, 1, PREC_TYPE ) 00372 ELSE 00373 CALL BLAS_SSYMV2_X(UPLO2, 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 SPOTRS( UPLO, N, 1, AF, LDAF, 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 ( YMIN*RCOND .LT. INCR_THRESH*NORMY 00426 $ .AND. Y_PREC_STATE .LT. EXTRA_Y ) 00427 $ INCR_PREC = .TRUE. 00428 00429 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00430 $ X_STATE = WORKING_STATE 00431 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00432 IF ( DX_X .LE. EPS ) THEN 00433 X_STATE = CONV_STATE 00434 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00435 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00436 INCR_PREC = .TRUE. 00437 ELSE 00438 X_STATE = NOPROG_STATE 00439 END IF 00440 ELSE 00441 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00442 END IF 00443 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00444 END IF 00445 00446 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00447 $ Z_STATE = WORKING_STATE 00448 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00449 $ Z_STATE = WORKING_STATE 00450 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00451 IF ( DZ_Z .LE. EPS ) THEN 00452 Z_STATE = CONV_STATE 00453 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00454 Z_STATE = UNSTABLE_STATE 00455 DZRATMAX = 0.0 00456 FINAL_DZ_Z = HUGEVAL 00457 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00458 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00459 INCR_PREC = .TRUE. 00460 ELSE 00461 Z_STATE = NOPROG_STATE 00462 END IF 00463 ELSE 00464 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00465 END IF 00466 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00467 END IF 00468 00469 IF ( X_STATE.NE.WORKING_STATE.AND. 00470 $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) ) 00471 $ GOTO 666 00472 00473 IF ( INCR_PREC ) THEN 00474 INCR_PREC = .FALSE. 00475 Y_PREC_STATE = Y_PREC_STATE + 1 00476 DO I = 1, N 00477 Y_TAIL( I ) = 0.0 00478 END DO 00479 END IF 00480 00481 PREVNORMDX = NORMDX 00482 PREV_DZ_Z = DZ_Z 00483 * 00484 * Update soluton. 00485 * 00486 IF (Y_PREC_STATE .LT. EXTRA_Y) THEN 00487 CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 ) 00488 ELSE 00489 CALL SLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY ) 00490 END IF 00491 00492 END DO 00493 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00494 666 CONTINUE 00495 * 00496 * Set final_* when cnt hits ithresh. 00497 * 00498 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00499 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00500 * 00501 * Compute error bounds. 00502 * 00503 IF ( N_NORMS .GE. 1 ) THEN 00504 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 00505 $ FINAL_DX_X / (1 - DXRATMAX) 00506 END IF 00507 IF ( N_NORMS .GE. 2 ) THEN 00508 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 00509 $ FINAL_DZ_Z / (1 - DZRATMAX) 00510 END IF 00511 * 00512 * Compute componentwise relative backward error from formula 00513 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00514 * where abs(Z) is the componentwise absolute value of the matrix 00515 * or vector Z. 00516 * 00517 * Compute residual RES = B_s - op(A_s) * Y, 00518 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00519 * 00520 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00521 CALL SSYMV( UPLO, N, -1.0, A, LDA, Y(1,J), 1, 1.0, RES, 1 ) 00522 00523 DO I = 1, N 00524 AYB( I ) = ABS( B( I, J ) ) 00525 END DO 00526 * 00527 * Compute abs(op(A_s))*abs(Y) + abs(B_s). 00528 * 00529 CALL SLA_SYAMV( UPLO2, N, 1.0, 00530 $ A, LDA, Y(1, J), 1, 1.0, AYB, 1 ) 00531 00532 CALL SLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) ) 00533 * 00534 * End of loop for each RHS. 00535 * 00536 END DO 00537 * 00538 RETURN 00539 END
1.7.3 
