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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 SLA_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 REAL RTHRESH, DZ_UB 00025 * .. 00026 * .. Array Arguments .. 00027 INTEGER IPIV( * ) 00028 REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00029 $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * ) 00030 REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), 00031 $ ERR_BNDS_NORM( NRHS, * ), 00032 $ ERR_BNDS_COMP( NRHS, * ) 00033 * .. 00034 * 00035 * Purpose 00036 * ======= 00037 * 00038 * SLA_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 SSYRFSX 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) REAL 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) REAL 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 SSYTRF. 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 SSYTRF. 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) REAL 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) REAL 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) REAL array, dimension (LDY,NRHS) 00110 * On entry, the solution matrix X, as computed by SSYTRS. 00111 * On exit, the improved solution matrix Y. 00112 * 00113 * LDY (input) INTEGER 00114 * The leading dimension of the array Y. LDY >= max(1,N). 00115 * 00116 * BERR_OUT (output) REAL array, dimension (NRHS) 00117 * On exit, BERR_OUT(j) contains the componentwise relative backward 00118 * error for right-hand-side j from the formula 00119 * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00120 * where abs(Z) is the componentwise absolute value of the matrix 00121 * or vector Z. This is computed by SLA_LIN_BERR. 00122 * 00123 * N_NORMS (input) INTEGER 00124 * Determines which error bounds to return (see ERR_BNDS_NORM 00125 * and ERR_BNDS_COMP). 00126 * If N_NORMS >= 1 return normwise error bounds. 00127 * If N_NORMS >= 2 return componentwise error bounds. 00128 * 00129 * ERR_BNDS_NORM (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) 00130 * For each right-hand side, this array contains information about 00131 * various error bounds and condition numbers corresponding to the 00132 * normwise relative error, which is defined as follows: 00133 * 00134 * Normwise relative error in the ith solution vector: 00135 * max_j (abs(XTRUE(j,i) - X(j,i))) 00136 * ------------------------------ 00137 * max_j abs(X(j,i)) 00138 * 00139 * The array is indexed by the type of error information as described 00140 * below. There currently are up to three pieces of information 00141 * returned. 00142 * 00143 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00144 * right-hand side. 00145 * 00146 * The second index in ERR_BNDS_NORM(:,err) contains the following 00147 * three fields: 00148 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00149 * reciprocal condition number is less than the threshold 00150 * sqrt(n) * slamch('Epsilon'). 00151 * 00152 * err = 2 "Guaranteed" error bound: The estimated forward error, 00153 * almost certainly within a factor of 10 of the true error 00154 * so long as the next entry is greater than the threshold 00155 * sqrt(n) * slamch('Epsilon'). This error bound should only 00156 * be trusted if the previous boolean is true. 00157 * 00158 * err = 3 Reciprocal condition number: Estimated normwise 00159 * reciprocal condition number. Compared with the threshold 00160 * sqrt(n) * slamch('Epsilon') to determine if the error 00161 * estimate is "guaranteed". These reciprocal condition 00162 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00163 * appropriately scaled matrix Z. 00164 * Let Z = S*A, where S scales each row by a power of the 00165 * radix so all absolute row sums of Z are approximately 1. 00166 * 00167 * This subroutine is only responsible for setting the second field 00168 * above. 00169 * See Lapack Working Note 165 for further details and extra 00170 * cautions. 00171 * 00172 * ERR_BNDS_COMP (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) 00173 * For each right-hand side, this array contains information about 00174 * various error bounds and condition numbers corresponding to the 00175 * componentwise relative error, which is defined as follows: 00176 * 00177 * Componentwise relative error in the ith solution vector: 00178 * abs(XTRUE(j,i) - X(j,i)) 00179 * max_j ---------------------- 00180 * abs(X(j,i)) 00181 * 00182 * The array is indexed by the right-hand side i (on which the 00183 * componentwise relative error depends), and the type of error 00184 * information as described below. There currently are up to three 00185 * pieces of information returned for each right-hand side. If 00186 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00187 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00188 * the first (:,N_ERR_BNDS) entries are returned. 00189 * 00190 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00191 * right-hand side. 00192 * 00193 * The second index in ERR_BNDS_COMP(:,err) contains the following 00194 * three fields: 00195 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00196 * reciprocal condition number is less than the threshold 00197 * sqrt(n) * slamch('Epsilon'). 00198 * 00199 * err = 2 "Guaranteed" error bound: The estimated forward error, 00200 * almost certainly within a factor of 10 of the true error 00201 * so long as the next entry is greater than the threshold 00202 * sqrt(n) * slamch('Epsilon'). This error bound should only 00203 * be trusted if the previous boolean is true. 00204 * 00205 * err = 3 Reciprocal condition number: Estimated componentwise 00206 * reciprocal condition number. Compared with the threshold 00207 * sqrt(n) * slamch('Epsilon') to determine if the error 00208 * estimate is "guaranteed". These reciprocal condition 00209 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00210 * appropriately scaled matrix Z. 00211 * Let Z = S*(A*diag(x)), where x is the solution for the 00212 * current right-hand side and S scales each row of 00213 * A*diag(x) by a power of the radix so all absolute row 00214 * sums of Z are approximately 1. 00215 * 00216 * This subroutine is only responsible for setting the second field 00217 * above. 00218 * See Lapack Working Note 165 for further details and extra 00219 * cautions. 00220 * 00221 * RES (input) REAL array, dimension (N) 00222 * Workspace to hold the intermediate residual. 00223 * 00224 * AYB (input) REAL array, dimension (N) 00225 * Workspace. This can be the same workspace passed for Y_TAIL. 00226 * 00227 * DY (input) REAL array, dimension (N) 00228 * Workspace to hold the intermediate solution. 00229 * 00230 * Y_TAIL (input) REAL array, dimension (N) 00231 * Workspace to hold the trailing bits of the intermediate solution. 00232 * 00233 * RCOND (input) REAL 00234 * Reciprocal scaled condition number. This is an estimate of the 00235 * reciprocal Skeel condition number of the matrix A after 00236 * equilibration (if done). If this is less than the machine 00237 * precision (in particular, if it is zero), the matrix is singular 00238 * to working precision. Note that the error may still be small even 00239 * if this number is very small and the matrix appears ill- 00240 * conditioned. 00241 * 00242 * ITHRESH (input) INTEGER 00243 * The maximum number of residual computations allowed for 00244 * refinement. The default is 10. For 'aggressive' set to 100 to 00245 * permit convergence using approximate factorizations or 00246 * factorizations other than LU. If the factorization uses a 00247 * technique other than Gaussian elimination, the guarantees in 00248 * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. 00249 * 00250 * RTHRESH (input) REAL 00251 * Determines when to stop refinement if the error estimate stops 00252 * decreasing. Refinement will stop when the next solution no longer 00253 * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is 00254 * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The 00255 * default value is 0.5. For 'aggressive' set to 0.9 to permit 00256 * convergence on extremely ill-conditioned matrices. See LAWN 165 00257 * for more details. 00258 * 00259 * DZ_UB (input) REAL 00260 * Determines when to start considering componentwise convergence. 00261 * Componentwise convergence is only considered after each component 00262 * of the solution Y is stable, which we definte as the relative 00263 * change in each component being less than DZ_UB. The default value 00264 * is 0.25, requiring the first bit to be stable. See LAWN 165 for 00265 * more details. 00266 * 00267 * IGNORE_CWISE (input) LOGICAL 00268 * If .TRUE. then ignore componentwise convergence. Default value 00269 * is .FALSE.. 00270 * 00271 * INFO (output) INTEGER 00272 * = 0: Successful exit. 00273 * < 0: if INFO = -i, the ith argument to SSYTRS had an illegal 00274 * value 00275 * 00276 * ===================================================================== 00277 * 00278 * .. Local Scalars .. 00279 INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE 00280 REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, 00281 $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX, 00282 $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z, 00283 $ EPS, HUGEVAL, INCR_THRESH 00284 LOGICAL INCR_PREC 00285 * .. 00286 * .. Parameters .. 00287 INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE, 00288 $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL, 00289 $ EXTRA_RESIDUAL, EXTRA_Y 00290 PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1, 00291 $ CONV_STATE = 2, NOPROG_STATE = 3 ) 00292 PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1, 00293 $ EXTRA_Y = 2 ) 00294 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I 00295 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I 00296 INTEGER CMP_ERR_I, PIV_GROWTH_I 00297 PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2, 00298 $ BERR_I = 3 ) 00299 PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 ) 00300 PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8, 00301 $ PIV_GROWTH_I = 9 ) 00302 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00303 $ LA_LINRX_CWISE_I 00304 PARAMETER ( LA_LINRX_ITREF_I = 1, 00305 $ LA_LINRX_ITHRESH_I = 2 ) 00306 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00307 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00308 $ LA_LINRX_RCOND_I 00309 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00310 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00311 * .. 00312 * .. External Functions .. 00313 LOGICAL LSAME 00314 EXTERNAL ILAUPLO 00315 INTEGER ILAUPLO 00316 * .. 00317 * .. External Subroutines .. 00318 EXTERNAL SAXPY, SCOPY, SSYTRS, SSYMV, BLAS_SSYMV_X, 00319 $ BLAS_SSYMV2_X, SLA_SYAMV, SLA_WWADDW, 00320 $ SLA_LIN_BERR 00321 REAL SLAMCH 00322 * .. 00323 * .. Intrinsic Functions .. 00324 INTRINSIC ABS, MAX, MIN 00325 * .. 00326 * .. Executable Statements .. 00327 * 00328 IF ( INFO.NE.0 ) RETURN 00329 EPS = SLAMCH( 'Epsilon' ) 00330 HUGEVAL = SLAMCH( 'Overflow' ) 00331 * Force HUGEVAL to Inf 00332 HUGEVAL = HUGEVAL * HUGEVAL 00333 * Using HUGEVAL may lead to spurious underflows. 00334 INCR_THRESH = REAL( N )*EPS 00335 00336 IF ( LSAME ( UPLO, 'L' ) ) THEN 00337 UPLO2 = ILAUPLO( 'L' ) 00338 ELSE 00339 UPLO2 = ILAUPLO( 'U' ) 00340 ENDIF 00341 00342 DO J = 1, NRHS 00343 Y_PREC_STATE = EXTRA_RESIDUAL 00344 IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN 00345 DO I = 1, N 00346 Y_TAIL( I ) = 0.0 00347 END DO 00348 END IF 00349 00350 DXRAT = 0.0 00351 DXRATMAX = 0.0 00352 DZRAT = 0.0 00353 DZRATMAX = 0.0 00354 FINAL_DX_X = HUGEVAL 00355 FINAL_DZ_Z = HUGEVAL 00356 PREVNORMDX = HUGEVAL 00357 PREV_DZ_Z = HUGEVAL 00358 DZ_Z = HUGEVAL 00359 DX_X = HUGEVAL 00360 00361 X_STATE = WORKING_STATE 00362 Z_STATE = UNSTABLE_STATE 00363 INCR_PREC = .FALSE. 00364 00365 DO CNT = 1, ITHRESH 00366 * 00367 * Compute residual RES = B_s - op(A_s) * Y, 00368 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00369 * 00370 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00371 IF (Y_PREC_STATE .EQ. BASE_RESIDUAL) THEN 00372 CALL SSYMV( UPLO, N, -1.0, A, LDA, Y(1,J), 1, 00373 $ 1.0, RES, 1 ) 00374 ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN 00375 CALL BLAS_SSYMV_X( UPLO2, N, -1.0, A, LDA, 00376 $ Y( 1, J ), 1, 1.0, RES, 1, PREC_TYPE ) 00377 ELSE 00378 CALL BLAS_SSYMV2_X(UPLO2, N, -1.0, A, LDA, 00379 $ Y(1, J), Y_TAIL, 1, 1.0, RES, 1, PREC_TYPE) 00380 END IF 00381 00382 ! XXX: RES is no longer needed. 00383 CALL SCOPY( N, RES, 1, DY, 1 ) 00384 CALL SSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO ) 00385 * 00386 * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. 00387 * 00388 NORMX = 0.0 00389 NORMY = 0.0 00390 NORMDX = 0.0 00391 DZ_Z = 0.0 00392 YMIN = HUGEVAL 00393 00394 DO I = 1, N 00395 YK = ABS( Y( I, J ) ) 00396 DYK = ABS( DY( I ) ) 00397 00398 IF ( YK .NE. 0.0 ) THEN 00399 DZ_Z = MAX( DZ_Z, DYK / YK ) 00400 ELSE IF ( DYK .NE. 0.0 ) THEN 00401 DZ_Z = HUGEVAL 00402 END IF 00403 00404 YMIN = MIN( YMIN, YK ) 00405 00406 NORMY = MAX( NORMY, YK ) 00407 00408 IF ( COLEQU ) THEN 00409 NORMX = MAX( NORMX, YK * C( I ) ) 00410 NORMDX = MAX( NORMDX, DYK * C( I ) ) 00411 ELSE 00412 NORMX = NORMY 00413 NORMDX = MAX(NORMDX, DYK) 00414 END IF 00415 END DO 00416 00417 IF ( NORMX .NE. 0.0 ) THEN 00418 DX_X = NORMDX / NORMX 00419 ELSE IF ( NORMDX .EQ. 0.0 ) THEN 00420 DX_X = 0.0 00421 ELSE 00422 DX_X = HUGEVAL 00423 END IF 00424 00425 DXRAT = NORMDX / PREVNORMDX 00426 DZRAT = DZ_Z / PREV_DZ_Z 00427 * 00428 * Check termination criteria. 00429 * 00430 IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY 00431 $ .AND. Y_PREC_STATE .LT. EXTRA_Y ) 00432 $ INCR_PREC = .TRUE. 00433 00434 IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH ) 00435 $ X_STATE = WORKING_STATE 00436 IF ( X_STATE .EQ. WORKING_STATE ) THEN 00437 IF ( DX_X .LE. EPS ) THEN 00438 X_STATE = CONV_STATE 00439 ELSE IF ( DXRAT .GT. RTHRESH ) THEN 00440 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00441 INCR_PREC = .TRUE. 00442 ELSE 00443 X_STATE = NOPROG_STATE 00444 END IF 00445 ELSE 00446 IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT 00447 END IF 00448 IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X 00449 END IF 00450 00451 IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB ) 00452 $ Z_STATE = WORKING_STATE 00453 IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH ) 00454 $ Z_STATE = WORKING_STATE 00455 IF ( Z_STATE .EQ. WORKING_STATE ) THEN 00456 IF ( DZ_Z .LE. EPS ) THEN 00457 Z_STATE = CONV_STATE 00458 ELSE IF ( DZ_Z .GT. DZ_UB ) THEN 00459 Z_STATE = UNSTABLE_STATE 00460 DZRATMAX = 0.0 00461 FINAL_DZ_Z = HUGEVAL 00462 ELSE IF ( DZRAT .GT. RTHRESH ) THEN 00463 IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN 00464 INCR_PREC = .TRUE. 00465 ELSE 00466 Z_STATE = NOPROG_STATE 00467 END IF 00468 ELSE 00469 IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT 00470 END IF 00471 IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00472 END IF 00473 00474 IF ( X_STATE.NE.WORKING_STATE.AND. 00475 $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) ) 00476 $ GOTO 666 00477 00478 IF ( INCR_PREC ) THEN 00479 INCR_PREC = .FALSE. 00480 Y_PREC_STATE = Y_PREC_STATE + 1 00481 DO I = 1, N 00482 Y_TAIL( I ) = 0.0 00483 END DO 00484 END IF 00485 00486 PREVNORMDX = NORMDX 00487 PREV_DZ_Z = DZ_Z 00488 * 00489 * Update soluton. 00490 * 00491 IF (Y_PREC_STATE .LT. EXTRA_Y) THEN 00492 CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 ) 00493 ELSE 00494 CALL SLA_WWADDW( N, Y(1,J), Y_TAIL, DY ) 00495 END IF 00496 00497 END DO 00498 * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. 00499 666 CONTINUE 00500 * 00501 * Set final_* when cnt hits ithresh. 00502 * 00503 IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X 00504 IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z 00505 * 00506 * Compute error bounds. 00507 * 00508 IF ( N_NORMS .GE. 1 ) THEN 00509 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 00510 $ FINAL_DX_X / (1 - DXRATMAX) 00511 END IF 00512 IF ( N_NORMS .GE. 2 ) THEN 00513 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 00514 $ FINAL_DZ_Z / (1 - DZRATMAX) 00515 END IF 00516 * 00517 * Compute componentwise relative backward error from formula 00518 * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) 00519 * where abs(Z) is the componentwise absolute value of the matrix 00520 * or vector Z. 00521 * 00522 * Compute residual RES = B_s - op(A_s) * Y, 00523 * op(A) = A, A**T, or A**H depending on TRANS (and type). 00524 CALL SCOPY( N, B( 1, J ), 1, RES, 1 ) 00525 CALL SSYMV( UPLO, N, -1.0, A, LDA, Y(1,J), 1, 1.0, RES, 1 ) 00526 00527 DO I = 1, N 00528 AYB( I ) = ABS( B( I, J ) ) 00529 END DO 00530 * 00531 * Compute abs(op(A_s))*abs(Y) + abs(B_s). 00532 * 00533 CALL SLA_SYAMV( UPLO2, N, 1.0, 00534 $ A, LDA, Y(1, J), 1, 1.0, AYB, 1 ) 00535 00536 CALL SLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) ) 00537 * 00538 * End of loop for each RHS. 00539 * 00540 END DO 00541 * 00542 RETURN 00543 END
1.7.3 
