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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 DSYRFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV, 00002 $ S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, 00003 $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, 00004 $ WORK, IWORK, INFO ) 00005 * 00006 * -- LAPACK routine (version 3.2.2) -- 00007 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 00008 * -- Jason Riedy of Univ. of California Berkeley. -- 00009 * -- June 2010 -- 00010 * 00011 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00012 * -- Univ. of California Berkeley and NAG Ltd. -- 00013 * 00014 IMPLICIT NONE 00015 * .. 00016 * .. Scalar Arguments .. 00017 CHARACTER UPLO, EQUED 00018 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, 00019 $ N_ERR_BNDS 00020 DOUBLE PRECISION RCOND 00021 * .. 00022 * .. Array Arguments .. 00023 INTEGER IPIV( * ), IWORK( * ) 00024 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), 00025 $ X( LDX, * ), WORK( * ) 00026 DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ), 00027 $ ERR_BNDS_NORM( NRHS, * ), 00028 $ ERR_BNDS_COMP( NRHS, * ) 00029 * .. 00030 * 00031 * Purpose 00032 * ======= 00033 * 00034 * DSYRFSX improves the computed solution to a system of linear 00035 * equations when the coefficient matrix is symmetric indefinite, and 00036 * provides error bounds and backward error estimates for the 00037 * solution. In addition to normwise error bound, the code provides 00038 * maximum componentwise error bound if possible. See comments for 00039 * ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds. 00040 * 00041 * The original system of linear equations may have been equilibrated 00042 * before calling this routine, as described by arguments EQUED and S 00043 * below. In this case, the solution and error bounds returned are 00044 * for the original unequilibrated system. 00045 * 00046 * Arguments 00047 * ========= 00048 * 00049 * Some optional parameters are bundled in the PARAMS array. These 00050 * settings determine how refinement is performed, but often the 00051 * defaults are acceptable. If the defaults are acceptable, users 00052 * can pass NPARAMS = 0 which prevents the source code from accessing 00053 * the PARAMS argument. 00054 * 00055 * UPLO (input) CHARACTER*1 00056 * = 'U': Upper triangle of A is stored; 00057 * = 'L': Lower triangle of A is stored. 00058 * 00059 * EQUED (input) CHARACTER*1 00060 * Specifies the form of equilibration that was done to A 00061 * before calling this routine. This is needed to compute 00062 * the solution and error bounds correctly. 00063 * = 'N': No equilibration 00064 * = 'Y': Both row and column equilibration, i.e., A has been 00065 * replaced by diag(S) * A * diag(S). 00066 * The right hand side B has been changed accordingly. 00067 * 00068 * N (input) INTEGER 00069 * The order of the matrix A. N >= 0. 00070 * 00071 * NRHS (input) INTEGER 00072 * The number of right hand sides, i.e., the number of columns 00073 * of the matrices B and X. NRHS >= 0. 00074 * 00075 * A (input) DOUBLE PRECISION array, dimension (LDA,N) 00076 * The symmetric matrix A. If UPLO = 'U', the leading N-by-N 00077 * upper triangular part of A contains the upper triangular 00078 * part of the matrix A, and the strictly lower triangular 00079 * part of A is not referenced. If UPLO = 'L', the leading 00080 * N-by-N lower triangular part of A contains the lower 00081 * triangular part of the matrix A, and the strictly upper 00082 * triangular part of A is not referenced. 00083 * 00084 * LDA (input) INTEGER 00085 * The leading dimension of the array A. LDA >= max(1,N). 00086 * 00087 * AF (input) DOUBLE PRECISION array, dimension (LDAF,N) 00088 * The factored form of the matrix A. AF contains the block 00089 * diagonal matrix D and the multipliers used to obtain the 00090 * factor U or L from the factorization A = U*D*U**T or A = 00091 * L*D*L**T as computed by DSYTRF. 00092 * 00093 * LDAF (input) INTEGER 00094 * The leading dimension of the array AF. LDAF >= max(1,N). 00095 * 00096 * IPIV (input) INTEGER array, dimension (N) 00097 * Details of the interchanges and the block structure of D 00098 * as determined by DSYTRF. 00099 * 00100 * S (input or output) DOUBLE PRECISION array, dimension (N) 00101 * The scale factors for A. If EQUED = 'Y', A is multiplied on 00102 * the left and right by diag(S). S is an input argument if FACT = 00103 * 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED 00104 * = 'Y', each element of S must be positive. If S is output, each 00105 * element of S is a power of the radix. If S is input, each element 00106 * of S should be a power of the radix to ensure a reliable solution 00107 * and error estimates. Scaling by powers of the radix does not cause 00108 * rounding errors unless the result underflows or overflows. 00109 * Rounding errors during scaling lead to refining with a matrix that 00110 * is not equivalent to the input matrix, producing error estimates 00111 * that may not be reliable. 00112 * 00113 * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) 00114 * The right hand side matrix B. 00115 * 00116 * LDB (input) INTEGER 00117 * The leading dimension of the array B. LDB >= max(1,N). 00118 * 00119 * X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS) 00120 * On entry, the solution matrix X, as computed by DGETRS. 00121 * On exit, the improved solution matrix X. 00122 * 00123 * LDX (input) INTEGER 00124 * The leading dimension of the array X. LDX >= max(1,N). 00125 * 00126 * RCOND (output) DOUBLE PRECISION 00127 * Reciprocal scaled condition number. This is an estimate of the 00128 * reciprocal Skeel condition number of the matrix A after 00129 * equilibration (if done). If this is less than the machine 00130 * precision (in particular, if it is zero), the matrix is singular 00131 * to working precision. Note that the error may still be small even 00132 * if this number is very small and the matrix appears ill- 00133 * conditioned. 00134 * 00135 * BERR (output) DOUBLE PRECISION array, dimension (NRHS) 00136 * Componentwise relative backward error. This is the 00137 * componentwise relative backward error of each solution vector X(j) 00138 * (i.e., the smallest relative change in any element of A or B that 00139 * makes X(j) an exact solution). 00140 * 00141 * N_ERR_BNDS (input) INTEGER 00142 * Number of error bounds to return for each right hand side 00143 * and each type (normwise or componentwise). See ERR_BNDS_NORM and 00144 * ERR_BNDS_COMP below. 00145 * 00146 * ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) 00147 * For each right-hand side, this array contains information about 00148 * various error bounds and condition numbers corresponding to the 00149 * normwise relative error, which is defined as follows: 00150 * 00151 * Normwise relative error in the ith solution vector: 00152 * max_j (abs(XTRUE(j,i) - X(j,i))) 00153 * ------------------------------ 00154 * max_j abs(X(j,i)) 00155 * 00156 * The array is indexed by the type of error information as described 00157 * below. There currently are up to three pieces of information 00158 * returned. 00159 * 00160 * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith 00161 * right-hand side. 00162 * 00163 * The second index in ERR_BNDS_NORM(:,err) contains the following 00164 * three fields: 00165 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00166 * reciprocal condition number is less than the threshold 00167 * sqrt(n) * dlamch('Epsilon'). 00168 * 00169 * err = 2 "Guaranteed" error bound: The estimated forward error, 00170 * almost certainly within a factor of 10 of the true error 00171 * so long as the next entry is greater than the threshold 00172 * sqrt(n) * dlamch('Epsilon'). This error bound should only 00173 * be trusted if the previous boolean is true. 00174 * 00175 * err = 3 Reciprocal condition number: Estimated normwise 00176 * reciprocal condition number. Compared with the threshold 00177 * sqrt(n) * dlamch('Epsilon') to determine if the error 00178 * estimate is "guaranteed". These reciprocal condition 00179 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00180 * appropriately scaled matrix Z. 00181 * Let Z = S*A, where S scales each row by a power of the 00182 * radix so all absolute row sums of Z are approximately 1. 00183 * 00184 * See Lapack Working Note 165 for further details and extra 00185 * cautions. 00186 * 00187 * ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) 00188 * For each right-hand side, this array contains information about 00189 * various error bounds and condition numbers corresponding to the 00190 * componentwise relative error, which is defined as follows: 00191 * 00192 * Componentwise relative error in the ith solution vector: 00193 * abs(XTRUE(j,i) - X(j,i)) 00194 * max_j ---------------------- 00195 * abs(X(j,i)) 00196 * 00197 * The array is indexed by the right-hand side i (on which the 00198 * componentwise relative error depends), and the type of error 00199 * information as described below. There currently are up to three 00200 * pieces of information returned for each right-hand side. If 00201 * componentwise accuracy is not requested (PARAMS(3) = 0.0), then 00202 * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most 00203 * the first (:,N_ERR_BNDS) entries are returned. 00204 * 00205 * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith 00206 * right-hand side. 00207 * 00208 * The second index in ERR_BNDS_COMP(:,err) contains the following 00209 * three fields: 00210 * err = 1 "Trust/don't trust" boolean. Trust the answer if the 00211 * reciprocal condition number is less than the threshold 00212 * sqrt(n) * dlamch('Epsilon'). 00213 * 00214 * err = 2 "Guaranteed" error bound: The estimated forward error, 00215 * almost certainly within a factor of 10 of the true error 00216 * so long as the next entry is greater than the threshold 00217 * sqrt(n) * dlamch('Epsilon'). This error bound should only 00218 * be trusted if the previous boolean is true. 00219 * 00220 * err = 3 Reciprocal condition number: Estimated componentwise 00221 * reciprocal condition number. Compared with the threshold 00222 * sqrt(n) * dlamch('Epsilon') to determine if the error 00223 * estimate is "guaranteed". These reciprocal condition 00224 * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some 00225 * appropriately scaled matrix Z. 00226 * Let Z = S*(A*diag(x)), where x is the solution for the 00227 * current right-hand side and S scales each row of 00228 * A*diag(x) by a power of the radix so all absolute row 00229 * sums of Z are approximately 1. 00230 * 00231 * See Lapack Working Note 165 for further details and extra 00232 * cautions. 00233 * 00234 * NPARAMS (input) INTEGER 00235 * Specifies the number of parameters set in PARAMS. If .LE. 0, the 00236 * PARAMS array is never referenced and default values are used. 00237 * 00238 * PARAMS (input / output) DOUBLE PRECISION array, dimension (NPARAMS) 00239 * Specifies algorithm parameters. If an entry is .LT. 0.0, then 00240 * that entry will be filled with default value used for that 00241 * parameter. Only positions up to NPARAMS are accessed; defaults 00242 * are used for higher-numbered parameters. 00243 * 00244 * PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative 00245 * refinement or not. 00246 * Default: 1.0D+0 00247 * = 0.0 : No refinement is performed, and no error bounds are 00248 * computed. 00249 * = 1.0 : Use the double-precision refinement algorithm, 00250 * possibly with doubled-single computations if the 00251 * compilation environment does not support DOUBLE 00252 * PRECISION. 00253 * (other values are reserved for future use) 00254 * 00255 * PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual 00256 * computations allowed for refinement. 00257 * Default: 10 00258 * Aggressive: Set to 100 to permit convergence using approximate 00259 * factorizations or factorizations other than LU. If 00260 * the factorization uses a technique other than 00261 * Gaussian elimination, the guarantees in 00262 * err_bnds_norm and err_bnds_comp may no longer be 00263 * trustworthy. 00264 * 00265 * PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code 00266 * will attempt to find a solution with small componentwise 00267 * relative error in the double-precision algorithm. Positive 00268 * is true, 0.0 is false. 00269 * Default: 1.0 (attempt componentwise convergence) 00270 * 00271 * WORK (workspace) DOUBLE PRECISION array, dimension (4*N) 00272 * 00273 * IWORK (workspace) INTEGER array, dimension (N) 00274 * 00275 * INFO (output) INTEGER 00276 * = 0: Successful exit. The solution to every right-hand side is 00277 * guaranteed. 00278 * < 0: If INFO = -i, the i-th argument had an illegal value 00279 * > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization 00280 * has been completed, but the factor U is exactly singular, so 00281 * the solution and error bounds could not be computed. RCOND = 0 00282 * is returned. 00283 * = N+J: The solution corresponding to the Jth right-hand side is 00284 * not guaranteed. The solutions corresponding to other right- 00285 * hand sides K with K > J may not be guaranteed as well, but 00286 * only the first such right-hand side is reported. If a small 00287 * componentwise error is not requested (PARAMS(3) = 0.0) then 00288 * the Jth right-hand side is the first with a normwise error 00289 * bound that is not guaranteed (the smallest J such 00290 * that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) 00291 * the Jth right-hand side is the first with either a normwise or 00292 * componentwise error bound that is not guaranteed (the smallest 00293 * J such that either ERR_BNDS_NORM(J,1) = 0.0 or 00294 * ERR_BNDS_COMP(J,1) = 0.0). See the definition of 00295 * ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information 00296 * about all of the right-hand sides check ERR_BNDS_NORM or 00297 * ERR_BNDS_COMP. 00298 * 00299 * ================================================================== 00300 * 00301 * .. Parameters .. 00302 DOUBLE PRECISION ZERO, ONE 00303 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00304 DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT 00305 DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT 00306 DOUBLE PRECISION DZTHRESH_DEFAULT 00307 PARAMETER ( ITREF_DEFAULT = 1.0D+0 ) 00308 PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 ) 00309 PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 ) 00310 PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 ) 00311 PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 ) 00312 INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, 00313 $ LA_LINRX_CWISE_I 00314 PARAMETER ( LA_LINRX_ITREF_I = 1, 00315 $ LA_LINRX_ITHRESH_I = 2 ) 00316 PARAMETER ( LA_LINRX_CWISE_I = 3 ) 00317 INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, 00318 $ LA_LINRX_RCOND_I 00319 PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) 00320 PARAMETER ( LA_LINRX_RCOND_I = 3 ) 00321 * .. 00322 * .. Local Scalars .. 00323 CHARACTER(1) NORM 00324 LOGICAL RCEQU 00325 INTEGER J, PREC_TYPE, REF_TYPE, N_NORMS 00326 DOUBLE PRECISION ANORM, RCOND_TMP 00327 DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG 00328 LOGICAL IGNORE_CWISE 00329 INTEGER ITHRESH 00330 DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH 00331 * .. 00332 * .. External Subroutines .. 00333 EXTERNAL XERBLA, DSYCON, DLA_SYRFSX_EXTENDED 00334 * .. 00335 * .. Intrinsic Functions .. 00336 INTRINSIC MAX, SQRT 00337 * .. 00338 * .. External Functions .. 00339 EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC 00340 EXTERNAL DLAMCH, DLANSY, DLA_SYRCOND 00341 DOUBLE PRECISION DLAMCH, DLANSY, DLA_SYRCOND 00342 LOGICAL LSAME 00343 INTEGER BLAS_FPINFO_X 00344 INTEGER ILATRANS, ILAPREC 00345 * .. 00346 * .. Executable Statements .. 00347 * 00348 * Check the input parameters. 00349 * 00350 INFO = 0 00351 REF_TYPE = INT( ITREF_DEFAULT ) 00352 IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN 00353 IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN 00354 PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT 00355 ELSE 00356 REF_TYPE = PARAMS( LA_LINRX_ITREF_I ) 00357 END IF 00358 END IF 00359 * 00360 * Set default parameters. 00361 * 00362 ILLRCOND_THRESH = DBLE( N )*DLAMCH( 'Epsilon' ) 00363 ITHRESH = INT( ITHRESH_DEFAULT ) 00364 RTHRESH = RTHRESH_DEFAULT 00365 UNSTABLE_THRESH = DZTHRESH_DEFAULT 00366 IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0 00367 * 00368 IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN 00369 IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN 00370 PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH 00371 ELSE 00372 ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) ) 00373 END IF 00374 END IF 00375 IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN 00376 IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN 00377 IF ( IGNORE_CWISE ) THEN 00378 PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0 00379 ELSE 00380 PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0 00381 END IF 00382 ELSE 00383 IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0 00384 END IF 00385 END IF 00386 IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN 00387 N_NORMS = 0 00388 ELSE IF ( IGNORE_CWISE ) THEN 00389 N_NORMS = 1 00390 ELSE 00391 N_NORMS = 2 00392 END IF 00393 * 00394 RCEQU = LSAME( EQUED, 'Y' ) 00395 * 00396 * Test input parameters. 00397 * 00398 IF ( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00399 INFO = -1 00400 ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN 00401 INFO = -2 00402 ELSE IF( N.LT.0 ) THEN 00403 INFO = -3 00404 ELSE IF( NRHS.LT.0 ) THEN 00405 INFO = -4 00406 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00407 INFO = -6 00408 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN 00409 INFO = -8 00410 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00411 INFO = -11 00412 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN 00413 INFO = -13 00414 END IF 00415 IF( INFO.NE.0 ) THEN 00416 CALL XERBLA( 'DSYRFSX', -INFO ) 00417 RETURN 00418 END IF 00419 * 00420 * Quick return if possible. 00421 * 00422 IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN 00423 RCOND = 1.0D+0 00424 DO J = 1, NRHS 00425 BERR( J ) = 0.0D+0 00426 IF ( N_ERR_BNDS .GE. 1 ) THEN 00427 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00428 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00429 END IF 00430 IF ( N_ERR_BNDS .GE. 2 ) THEN 00431 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0 00432 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0 00433 END IF 00434 IF ( N_ERR_BNDS .GE. 3 ) THEN 00435 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0 00436 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0 00437 END IF 00438 END DO 00439 RETURN 00440 END IF 00441 * 00442 * Default to failure. 00443 * 00444 RCOND = 0.0D+0 00445 DO J = 1, NRHS 00446 BERR( J ) = 1.0D+0 00447 IF ( N_ERR_BNDS .GE. 1 ) THEN 00448 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00449 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00450 END IF 00451 IF ( N_ERR_BNDS .GE. 2 ) THEN 00452 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00453 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00454 END IF 00455 IF ( N_ERR_BNDS .GE. 3 ) THEN 00456 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0 00457 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0 00458 END IF 00459 END DO 00460 * 00461 * Compute the norm of A and the reciprocal of the condition 00462 * number of A. 00463 * 00464 NORM = 'I' 00465 ANORM = DLANSY( NORM, UPLO, N, A, LDA, WORK ) 00466 CALL DSYCON( UPLO, N, AF, LDAF, IPIV, ANORM, RCOND, WORK, 00467 $ IWORK, INFO ) 00468 * 00469 * Perform refinement on each right-hand side 00470 * 00471 IF ( REF_TYPE .NE. 0 ) THEN 00472 00473 PREC_TYPE = ILAPREC( 'E' ) 00474 00475 CALL DLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, 00476 $ NRHS, A, LDA, AF, LDAF, IPIV, RCEQU, S, B, 00477 $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP, 00478 $ WORK( N+1 ), WORK( 1 ), WORK( 2*N+1 ), WORK( 1 ), RCOND, 00479 $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE, 00480 $ INFO ) 00481 END IF 00482 00483 ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) )*DLAMCH( 'Epsilon' ) 00484 IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1) THEN 00485 * 00486 * Compute scaled normwise condition number cond(A*C). 00487 * 00488 IF ( RCEQU ) THEN 00489 RCOND_TMP = DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, 00490 $ -1, S, INFO, WORK, IWORK ) 00491 ELSE 00492 RCOND_TMP = DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, 00493 $ 0, S, INFO, WORK, IWORK ) 00494 END IF 00495 DO J = 1, NRHS 00496 * 00497 * Cap the error at 1.0. 00498 * 00499 IF (N_ERR_BNDS .GE. LA_LINRX_ERR_I 00500 $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0) 00501 $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00502 * 00503 * Threshold the error (see LAWN). 00504 * 00505 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN 00506 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0 00507 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0 00508 IF ( INFO .LE. N ) INFO = N + J 00509 ELSE IF (ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND) 00510 $ THEN 00511 ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND 00512 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0 00513 END IF 00514 * 00515 * Save the condition number. 00516 * 00517 IF (N_ERR_BNDS .GE. LA_LINRX_RCOND_I) THEN 00518 ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00519 END IF 00520 END DO 00521 END IF 00522 00523 IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN 00524 * 00525 * Compute componentwise condition number cond(A*diag(Y(:,J))) for 00526 * each right-hand side using the current solution as an estimate of 00527 * the true solution. If the componentwise error estimate is too 00528 * large, then the solution is a lousy estimate of truth and the 00529 * estimated RCOND may be too optimistic. To avoid misleading users, 00530 * the inverse condition number is set to 0.0 when the estimated 00531 * cwise error is at least CWISE_WRONG. 00532 * 00533 CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) ) 00534 DO J = 1, NRHS 00535 IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG ) 00536 $ THEN 00537 RCOND_TMP = DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, 00538 $ 1, X(1,J), INFO, WORK, IWORK ) 00539 ELSE 00540 RCOND_TMP = 0.0D+0 00541 END IF 00542 * 00543 * Cap the error at 1.0. 00544 * 00545 IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I 00546 $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 ) 00547 $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00548 * 00549 * Threshold the error (see LAWN). 00550 * 00551 IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN 00552 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0 00553 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0 00554 IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0 00555 $ .AND. INFO.LT.N + J ) INFO = N + J 00556 ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) 00557 $ .LT. ERR_LBND ) THEN 00558 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND 00559 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0 00560 END IF 00561 * 00562 * Save the condition number. 00563 * 00564 IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN 00565 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP 00566 END IF 00567 00568 END DO 00569 END IF 00570 * 00571 RETURN 00572 * 00573 * End of DSYRFSX 00574 * 00575 END
1.7.3 
