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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_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA, 00002 $ AF, LDAF, IPIV, COLEQU, C, B, LDB, 00003 $ 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 3.2.2) -- 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 DOUBLE PRECISION RTHRESH, DZ_UB 00025 * .. 00026 * .. Array Arguments .. 00027 INTEGER IPIV( * ) 00028 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00029 $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * ) 00030 DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), 00031 $ ERR_BNDS_NORM( NRHS, * ), 00032 $ ERR_BNDS_COMP( NRHS, * ) 00033 * .. 00034 * 00035 * Purpose 00036 * ======= 00037 * 00038 * DLA_SYRFSX_EXTENDED improves the computed solution to a system of 00039 * linear equations by performing extra-precise iterative refinement 00040 * and provides error bounds and backward error estimates for the solution. 00041 * This subroutine is called by DSYRFSX to perform iterative refinement. 00042 * In addition to normwise error bound, the code provides maximum 00043 * componentwise error bound if possible. See comments for ERR_BNDS_NORM 00044 * and ERR_BNDS_COMP for details of the error bounds. Note that this 00045 * subroutine is only resonsible for setting the second fields of 00046 * ERR_BNDS_NORM and ERR_BNDS_COMP. 00047 * 00048 * Arguments 00049 * ========= 00050 * 00051 * PREC_TYPE (input) INTEGER 00052 * Specifies the intermediate precision to be used in refinement. 00053 * The value is defined by ILAPREC(P) where P is a CHARACTER and 00054 * P = 'S': Single 00055 * = 'D': Double 00056 * = 'I': Indigenous 00057 * = 'X', 'E': Extra 00058 * 00059 * UPLO (input) CHARACTER*1 00060 * = 'U': Upper triangle of A is stored; 00061 * = 'L': Lower triangle of A is stored. 00062 * 00063 * N (input) INTEGER 00064 * The number of linear equations, i.e., the order of the 00065 * matrix A. N >= 0. 00066 * 00067 * NRHS (input) INTEGER 00068 * The number of right-hand-sides, i.e., the number of columns of the 00069 * matrix B. 00070 * 00071 * A (input) DOUBLE PRECISION array, dimension (LDA,N) 00072 * On entry, the N-by-N matrix A. 00073 * 00074 * LDA (input) INTEGER 00075 * The leading dimension of the array A. LDA >= max(1,N). 00076 * 00077 * AF (input) DOUBLE PRECISION array, dimension (LDAF,N) 00078 * The block diagonal matrix D and the multipliers used to 00079 * obtain the factor U or L as computed by DSYTRF. 00080 * 00081 * LDAF (input) INTEGER 00082 * The leading dimension of the array AF. LDAF >= max(1,N). 00083 * 00084 * IPIV (input) INTEGER array, dimension (N) 00085 * Details of the interchanges and the block structure of D 00086 * as determined by DSYTRF. 00087 * 00088 * COLEQU (input) LOGICAL 00089 * If .TRUE. then column equilibration was done to A before calling 00090 * this routine. This is needed to compute the solution and error 00091 * bounds correctly. 00092 * 00093 * C (input) DOUBLE PRECISION array, dimension (N) 00094 * The column scale factors for A. If COLEQU = .FALSE., C 00095 * is not accessed. If C is input, each element of C should be a power 00096 * of the radix to ensure a reliable solution and error estimates. 00097 * Scaling by powers of the radix does not cause rounding errors unless 00098 * the result underflows or overflows. Rounding errors during scaling 00099 * lead to refining with a matrix that is not equivalent to the 00100 * input matrix, producing error estimates that may not be 00101 * reliable. 00102 * 00103 * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) 00104 * The right-hand-side matrix B. 00105 * 00106 * LDB (input) INTEGER 00107 * The leading dimension of the array B. LDB >= max(1,N). 00108 * 00109 * Y (input/output) DOUBLE PRECISION array, dimension 00110 * (LDY,NRHS) 00111 * On entry, the solution matrix X, as computed by DSYTRS. 00112 * On exit, the improved solution matrix Y. 00113 * 00114 * LDY (input) INTEGER 00115 * The leading dimension of the array Y. LDY >= max(1,N). 00116 * 00117 * BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS) 00118 * On exit, BERR_OUT(j) contains the componentwise relative backward 00119 * error for right-hand-side j from the formula 00120 * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00121 * where abs(Z) is the componentwise absolute value of the matrix 00122 * or vector Z. This is computed by DLA_LIN_BERR. 00123 * 00124 * N_NORMS (input) INTEGER 00125 * Determines which error bounds to return (see ERR_BNDS_NORM 00126 * and ERR_BNDS_COMP). 00127 * If N_NORMS >= 1 return normwise error bounds. 00128 * If N_NORMS >= 2 return componentwise error bounds. 00129 * 00130 * ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension 00131 * (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) DOUBLE PRECISION array, dimension 00175 * (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) DOUBLE PRECISION array, dimension (N) 00225 * Workspace to hold the intermediate residual. 00226 * 00227 * AYB (input) DOUBLE PRECISION array, dimension (N) 00228 * Workspace. This can be the same workspace passed for Y_TAIL. 00229 * 00230 * DY (input) DOUBLE PRECISION array, dimension (N) 00231 * Workspace to hold the intermediate solution. 00232 * 00233 * Y_TAIL (input) DOUBLE PRECISION array, dimension (N) 00234 * Workspace to hold the trailing bits of the intermediate solution. 00235 * 00236 * RCOND (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DSYTRS had an illegal 00277 * value 00278 * 00279 * ===================================================================== 00280 * 00281 * .. Local Scalars .. 00282 INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE 00283 DOUBLE PRECISION 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 * .. 00289 * .. Parameters .. 00290 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00291 $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL, 00292 $ EXTRA_RESIDUAL, EXTRA_Y 00293 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00294 $ CONV_STATE = 2, NOPROG_STATE = 3 ) 00295 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00296 $ EXTRA_Y = 2 ) 00297 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00298 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00299 INTEGER CMP_ERR_I, PIV_GROWTH_I 00300 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00301 $ BERR_I = 3 ) 00302 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00303 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00304 $ PIV_GROWTH_I = 9 ) 00305 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00306 $ LA_LINRX_CWISE_I 00307 PARAMETER ( LA_LINRX_ITREF_I = 1, 00308 $ LA_LINRX_ITHRESH_I = 2 ) 00309 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00310 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00311 $ LA_LINRX_RCOND_I 00312 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00313 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00314 * .. 00315 * .. External Functions .. 00316 LOGICAL LSAME 00317 EXTERNAL ILAUPLO 00318 INTEGER ILAUPLO 00319 * .. 00320 * .. External Subroutines .. 00321 EXTERNAL DAXPY, DCOPY, DSYTRS, DSYMV, BLAS_DSYMV_X, 00322 $ BLAS_DSYMV2_X, DLA_SYAMV, DLA_WWADDW, 00323 $ DLA_LIN_BERR 00324 DOUBLE PRECISION DLAMCH 00325 * .. 00326 * .. Intrinsic Functions .. 00327 INTRINSIC ABS, MAX, MIN 00328 * .. 00329 * .. Executable Statements .. 00330 * 00331 IF ( INFO.NE.0 ) RETURN 00332 EPS = DLAMCH( 'Epsilon' ) 00333 HUGEVAL = DLAMCH( 'Overflow' ) 00334 * Force HUGEVAL to Inf 00335 HUGEVAL = HUGEVAL * HUGEVAL 00336 * Using HUGEVAL may lead to spurious underflows. 00337 INCR_THRESH = DBLE( N )*EPS 00338 00339 IF ( LSAME ( UPLO, 'L' ) ) THEN 00340 UPLO2 = ILAUPLO( 'L' ) 00341 ELSE 00342 UPLO2 = ILAUPLO( 'U' ) 00343 ENDIF 00344 00345 DO J = 1, NRHS 00346 Y_PREC_STATE = EXTRA_RESIDUAL 00347 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00348 DO I = 1, N 00349 Y_TAIL( I ) = 0.0D+0 00350 END DO 00351 END IF 00352 00353 DXRAT = 0.0D+0 00354 DXRATMAX = 0.0D+0 00355 DZRAT = 0.0D+0 00356 DZRATMAX = 0.0D+0 00357 FINAL_DX_X = HUGEVAL 00358 FINAL_DZ_Z = HUGEVAL 00359 PREVNORMDX = HUGEVAL 00360 PREV_DZ_Z = HUGEVAL 00361 DZ_Z = HUGEVAL 00362 DX_X = HUGEVAL 00363 00364 X_STATE = WORKING_STATE 00365 Z_STATE = UNSTABLE_STATE 00366 INCR_PREC = .FALSE. 00367 00368 DO CNT = 1, ITHRESH 00369 * 00370 * Compute residual RES = B_s - op(A_s) * Y, 00371 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00372 * 00373 CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) 00374 IF (Y_PREC_STATE .EQ. BASE_RESIDUAL) THEN 00375 CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 00376 $ 1.0D+0, RES, 1 ) 00377 ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN 00378 CALL BLAS_DSYMV_X( UPLO2, N, -1.0D+0, A, LDA, 00379 $ Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE ) 00380 ELSE 00381 CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA, 00382 $ Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE) 00383 END IF 00384 00385 ! XXX: RES is no longer needed. 00386 CALL DCOPY( N, RES, 1, DY, 1 ) 00387 CALL DSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO ) 00388 * 00389 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00390 * 00391 NORMX = 0.0D+0 00392 NORMY = 0.0D+0 00393 NORMDX = 0.0D+0 00394 DZ_Z = 0.0D+0 00395 YMIN = HUGEVAL 00396 00397 DO I = 1, N 00398 YK = ABS( Y( I, J ) ) 00399 DYK = ABS( DY( I ) ) 00400 00401 IF ( YK .NE. 0.0D+0 ) THEN 00402 DZ_Z = MAX( DZ_Z, DYK / YK ) 00403 ELSE IF ( DYK .NE. 0.0D+0 ) THEN 00404 DZ_Z = HUGEVAL 00405 END IF 00406 00407 YMIN = MIN( YMIN, YK ) 00408 00409 NORMY = MAX( NORMY, YK ) 00410 00411 IF ( COLEQU ) THEN 00412 NORMX = MAX( NORMX, YK * C( I ) ) 00413 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00414 ELSE 00415 NORMX = NORMY 00416 NORMDX = MAX(NORMDX, DYK) 00417 END IF 00418 END DO 00419 00420 IF ( NORMX .NE. 0.0D+0 ) THEN 00421 DX_X = NORMDX / NORMX 00422 ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN 00423 DX_X = 0.0D+0 00424 ELSE 00425 DX_X = HUGEVAL 00426 END IF 00427 00428 DXRAT = NORMDX / PREVNORMDX 00429 DZRAT = DZ_Z / PREV_DZ_Z 00430 * 00431 * Check termination criteria. 00432 * 00433 IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY 00434 $ .AND. Y_PREC_STATE .LT. EXTRA_Y ) 00435 $ INCR_PREC = .TRUE. 00436 00437 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00438 $ X_STATE = WORKING_STATE 00439 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00440 IF ( DX_X .LE. EPS ) THEN 00441 X_STATE = CONV_STATE 00442 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00443 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00444 INCR_PREC = .TRUE. 00445 ELSE 00446 X_STATE = NOPROG_STATE 00447 END IF 00448 ELSE 00449 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00450 END IF 00451 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00452 END IF 00453 00454 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00455 $ Z_STATE = WORKING_STATE 00456 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00457 $ Z_STATE = WORKING_STATE 00458 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00459 IF ( DZ_Z .LE. EPS ) THEN 00460 Z_STATE = CONV_STATE 00461 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00462 Z_STATE = UNSTABLE_STATE 00463 DZRATMAX = 0.0D+0 00464 FINAL_DZ_Z = HUGEVAL 00465 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00466 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00467 INCR_PREC = .TRUE. 00468 ELSE 00469 Z_STATE = NOPROG_STATE 00470 END IF 00471 ELSE 00472 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00473 END IF 00474 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00475 END IF 00476 00477 IF ( X_STATE.NE.WORKING_STATE.AND. 00478 $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) ) 00479 $ GOTO 666 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 ) = 0.0D+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 DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 ) 00496 ELSE 00497 CALL DLA_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 CALL DCOPY( N, B( 1, J ), 1, RES, 1 ) 00528 CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES, 00529 $ 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 DLA_SYAMV( UPLO2, N, 1.0D+0, 00538 $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 ) 00539 00540 CALL DLA_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 
