LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dla_syrfsx_extended.f
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00001 *> \brief \b DLA_SYRFSX_EXTENDED
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DLA_SYRFSX_EXTENDED + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrfsx_extended.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
00022 *                                       AF, LDAF, IPIV, COLEQU, C, B, LDB,
00023 *                                       Y, LDY, BERR_OUT, N_NORMS,
00024 *                                       ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
00025 *                                       AYB, DY, Y_TAIL, RCOND, ITHRESH,
00026 *                                       RTHRESH, DZ_UB, IGNORE_CWISE,
00027 *                                       INFO )
00028 * 
00029 *       .. Scalar Arguments ..
00030 *       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
00031 *      $                   N_NORMS, ITHRESH
00032 *       CHARACTER          UPLO
00033 *       LOGICAL            COLEQU, IGNORE_CWISE
00034 *       DOUBLE PRECISION   RTHRESH, DZ_UB
00035 *       ..
00036 *       .. Array Arguments ..
00037 *       INTEGER            IPIV( * )
00038 *       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00039 *      $                   Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
00040 *       DOUBLE PRECISION   C( * ), AYB( * ), RCOND, BERR_OUT( * ),
00041 *      $                   ERR_BNDS_NORM( NRHS, * ),
00042 *      $                   ERR_BNDS_COMP( NRHS, * )
00043 *       ..
00044 *  
00045 *
00046 *> \par Purpose:
00047 *  =============
00048 *>
00049 *> \verbatim
00050 *>
00051 *> 
00052 *> DLA_SYRFSX_EXTENDED improves the computed solution to a system of
00053 *> linear equations by performing extra-precise iterative refinement
00054 *> and provides error bounds and backward error estimates for the solution.
00055 *> This subroutine is called by DSYRFSX to perform iterative refinement.
00056 *> In addition to normwise error bound, the code provides maximum
00057 *> componentwise error bound if possible. See comments for ERR_BNDS_NORM
00058 *> and ERR_BNDS_COMP for details of the error bounds. Note that this
00059 *> subroutine is only resonsible for setting the second fields of
00060 *> ERR_BNDS_NORM and ERR_BNDS_COMP.
00061 *> \endverbatim
00062 *
00063 *  Arguments:
00064 *  ==========
00065 *
00066 *> \param[in] PREC_TYPE
00067 *> \verbatim
00068 *>          PREC_TYPE is INTEGER
00069 *>     Specifies the intermediate precision to be used in refinement.
00070 *>     The value is defined by ILAPREC(P) where P is a CHARACTER and
00071 *>     P    = 'S':  Single
00072 *>          = 'D':  Double
00073 *>          = 'I':  Indigenous
00074 *>          = 'X', 'E':  Extra
00075 *> \endverbatim
00076 *>
00077 *> \param[in] UPLO
00078 *> \verbatim
00079 *>          UPLO is CHARACTER*1
00080 *>       = 'U':  Upper triangle of A is stored;
00081 *>       = 'L':  Lower triangle of A is stored.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] N
00085 *> \verbatim
00086 *>          N is INTEGER
00087 *>     The number of linear equations, i.e., the order of the
00088 *>     matrix A.  N >= 0.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] NRHS
00092 *> \verbatim
00093 *>          NRHS is INTEGER
00094 *>     The number of right-hand-sides, i.e., the number of columns of the
00095 *>     matrix B.
00096 *> \endverbatim
00097 *>
00098 *> \param[in] A
00099 *> \verbatim
00100 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
00101 *>     On entry, the N-by-N matrix A.
00102 *> \endverbatim
00103 *>
00104 *> \param[in] LDA
00105 *> \verbatim
00106 *>          LDA is INTEGER
00107 *>     The leading dimension of the array A.  LDA >= max(1,N).
00108 *> \endverbatim
00109 *>
00110 *> \param[in] AF
00111 *> \verbatim
00112 *>          AF is DOUBLE PRECISION array, dimension (LDAF,N)
00113 *>     The block diagonal matrix D and the multipliers used to
00114 *>     obtain the factor U or L as computed by DSYTRF.
00115 *> \endverbatim
00116 *>
00117 *> \param[in] LDAF
00118 *> \verbatim
00119 *>          LDAF is INTEGER
00120 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00121 *> \endverbatim
00122 *>
00123 *> \param[in] IPIV
00124 *> \verbatim
00125 *>          IPIV is INTEGER array, dimension (N)
00126 *>     Details of the interchanges and the block structure of D
00127 *>     as determined by DSYTRF.
00128 *> \endverbatim
00129 *>
00130 *> \param[in] COLEQU
00131 *> \verbatim
00132 *>          COLEQU is LOGICAL
00133 *>     If .TRUE. then column equilibration was done to A before calling
00134 *>     this routine. This is needed to compute the solution and error
00135 *>     bounds correctly.
00136 *> \endverbatim
00137 *>
00138 *> \param[in] C
00139 *> \verbatim
00140 *>          C is DOUBLE PRECISION array, dimension (N)
00141 *>     The column scale factors for A. If COLEQU = .FALSE., C
00142 *>     is not accessed. If C is input, each element of C should be a power
00143 *>     of the radix to ensure a reliable solution and error estimates.
00144 *>     Scaling by powers of the radix does not cause rounding errors unless
00145 *>     the result underflows or overflows. Rounding errors during scaling
00146 *>     lead to refining with a matrix that is not equivalent to the
00147 *>     input matrix, producing error estimates that may not be
00148 *>     reliable.
00149 *> \endverbatim
00150 *>
00151 *> \param[in] B
00152 *> \verbatim
00153 *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
00154 *>     The right-hand-side matrix B.
00155 *> \endverbatim
00156 *>
00157 *> \param[in] LDB
00158 *> \verbatim
00159 *>          LDB is INTEGER
00160 *>     The leading dimension of the array B.  LDB >= max(1,N).
00161 *> \endverbatim
00162 *>
00163 *> \param[in,out] Y
00164 *> \verbatim
00165 *>          Y is DOUBLE PRECISION array, dimension
00166 *>                    (LDY,NRHS)
00167 *>     On entry, the solution matrix X, as computed by DSYTRS.
00168 *>     On exit, the improved solution matrix Y.
00169 *> \endverbatim
00170 *>
00171 *> \param[in] LDY
00172 *> \verbatim
00173 *>          LDY is INTEGER
00174 *>     The leading dimension of the array Y.  LDY >= max(1,N).
00175 *> \endverbatim
00176 *>
00177 *> \param[out] BERR_OUT
00178 *> \verbatim
00179 *>          BERR_OUT is DOUBLE PRECISION array, dimension (NRHS)
00180 *>     On exit, BERR_OUT(j) contains the componentwise relative backward
00181 *>     error for right-hand-side j from the formula
00182 *>         max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00183 *>     where abs(Z) is the componentwise absolute value of the matrix
00184 *>     or vector Z. This is computed by DLA_LIN_BERR.
00185 *> \endverbatim
00186 *>
00187 *> \param[in] N_NORMS
00188 *> \verbatim
00189 *>          N_NORMS is INTEGER
00190 *>     Determines which error bounds to return (see ERR_BNDS_NORM
00191 *>     and ERR_BNDS_COMP).
00192 *>     If N_NORMS >= 1 return normwise error bounds.
00193 *>     If N_NORMS >= 2 return componentwise error bounds.
00194 *> \endverbatim
00195 *>
00196 *> \param[in,out] ERR_BNDS_NORM
00197 *> \verbatim
00198 *>          ERR_BNDS_NORM is DOUBLE PRECISION array, dimension
00199 *>                    (NRHS, N_ERR_BNDS)
00200 *>     For each right-hand side, this array contains information about
00201 *>     various error bounds and condition numbers corresponding to the
00202 *>     normwise relative error, which is defined as follows:
00203 *>
00204 *>     Normwise relative error in the ith solution vector:
00205 *>             max_j (abs(XTRUE(j,i) - X(j,i)))
00206 *>            ------------------------------
00207 *>                  max_j abs(X(j,i))
00208 *>
00209 *>     The array is indexed by the type of error information as described
00210 *>     below. There currently are up to three pieces of information
00211 *>     returned.
00212 *>
00213 *>     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
00214 *>     right-hand side.
00215 *>
00216 *>     The second index in ERR_BNDS_NORM(:,err) contains the following
00217 *>     three fields:
00218 *>     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00219 *>              reciprocal condition number is less than the threshold
00220 *>              sqrt(n) * slamch('Epsilon').
00221 *>
00222 *>     err = 2 "Guaranteed" error bound: The estimated forward error,
00223 *>              almost certainly within a factor of 10 of the true error
00224 *>              so long as the next entry is greater than the threshold
00225 *>              sqrt(n) * slamch('Epsilon'). This error bound should only
00226 *>              be trusted if the previous boolean is true.
00227 *>
00228 *>     err = 3  Reciprocal condition number: Estimated normwise
00229 *>              reciprocal condition number.  Compared with the threshold
00230 *>              sqrt(n) * slamch('Epsilon') to determine if the error
00231 *>              estimate is "guaranteed". These reciprocal condition
00232 *>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00233 *>              appropriately scaled matrix Z.
00234 *>              Let Z = S*A, where S scales each row by a power of the
00235 *>              radix so all absolute row sums of Z are approximately 1.
00236 *>
00237 *>     This subroutine is only responsible for setting the second field
00238 *>     above.
00239 *>     See Lapack Working Note 165 for further details and extra
00240 *>     cautions.
00241 *> \endverbatim
00242 *>
00243 *> \param[in,out] ERR_BNDS_COMP
00244 *> \verbatim
00245 *>          ERR_BNDS_COMP is DOUBLE PRECISION array, dimension
00246 *>                    (NRHS, N_ERR_BNDS)
00247 *>     For each right-hand side, this array contains information about
00248 *>     various error bounds and condition numbers corresponding to the
00249 *>     componentwise relative error, which is defined as follows:
00250 *>
00251 *>     Componentwise relative error in the ith solution vector:
00252 *>                    abs(XTRUE(j,i) - X(j,i))
00253 *>             max_j ----------------------
00254 *>                         abs(X(j,i))
00255 *>
00256 *>     The array is indexed by the right-hand side i (on which the
00257 *>     componentwise relative error depends), and the type of error
00258 *>     information as described below. There currently are up to three
00259 *>     pieces of information returned for each right-hand side. If
00260 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
00261 *>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
00262 *>     the first (:,N_ERR_BNDS) entries are returned.
00263 *>
00264 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
00265 *>     right-hand side.
00266 *>
00267 *>     The second index in ERR_BNDS_COMP(:,err) contains the following
00268 *>     three fields:
00269 *>     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00270 *>              reciprocal condition number is less than the threshold
00271 *>              sqrt(n) * slamch('Epsilon').
00272 *>
00273 *>     err = 2 "Guaranteed" error bound: The estimated forward error,
00274 *>              almost certainly within a factor of 10 of the true error
00275 *>              so long as the next entry is greater than the threshold
00276 *>              sqrt(n) * slamch('Epsilon'). This error bound should only
00277 *>              be trusted if the previous boolean is true.
00278 *>
00279 *>     err = 3  Reciprocal condition number: Estimated componentwise
00280 *>              reciprocal condition number.  Compared with the threshold
00281 *>              sqrt(n) * slamch('Epsilon') to determine if the error
00282 *>              estimate is "guaranteed". These reciprocal condition
00283 *>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00284 *>              appropriately scaled matrix Z.
00285 *>              Let Z = S*(A*diag(x)), where x is the solution for the
00286 *>              current right-hand side and S scales each row of
00287 *>              A*diag(x) by a power of the radix so all absolute row
00288 *>              sums of Z are approximately 1.
00289 *>
00290 *>     This subroutine is only responsible for setting the second field
00291 *>     above.
00292 *>     See Lapack Working Note 165 for further details and extra
00293 *>     cautions.
00294 *> \endverbatim
00295 *>
00296 *> \param[in] RES
00297 *> \verbatim
00298 *>          RES is DOUBLE PRECISION array, dimension (N)
00299 *>     Workspace to hold the intermediate residual.
00300 *> \endverbatim
00301 *>
00302 *> \param[in] AYB
00303 *> \verbatim
00304 *>          AYB is DOUBLE PRECISION array, dimension (N)
00305 *>     Workspace. This can be the same workspace passed for Y_TAIL.
00306 *> \endverbatim
00307 *>
00308 *> \param[in] DY
00309 *> \verbatim
00310 *>          DY is DOUBLE PRECISION array, dimension (N)
00311 *>     Workspace to hold the intermediate solution.
00312 *> \endverbatim
00313 *>
00314 *> \param[in] Y_TAIL
00315 *> \verbatim
00316 *>          Y_TAIL is DOUBLE PRECISION array, dimension (N)
00317 *>     Workspace to hold the trailing bits of the intermediate solution.
00318 *> \endverbatim
00319 *>
00320 *> \param[in] RCOND
00321 *> \verbatim
00322 *>          RCOND is DOUBLE PRECISION
00323 *>     Reciprocal scaled condition number.  This is an estimate of the
00324 *>     reciprocal Skeel condition number of the matrix A after
00325 *>     equilibration (if done).  If this is less than the machine
00326 *>     precision (in particular, if it is zero), the matrix is singular
00327 *>     to working precision.  Note that the error may still be small even
00328 *>     if this number is very small and the matrix appears ill-
00329 *>     conditioned.
00330 *> \endverbatim
00331 *>
00332 *> \param[in] ITHRESH
00333 *> \verbatim
00334 *>          ITHRESH is INTEGER
00335 *>     The maximum number of residual computations allowed for
00336 *>     refinement. The default is 10. For 'aggressive' set to 100 to
00337 *>     permit convergence using approximate factorizations or
00338 *>     factorizations other than LU. If the factorization uses a
00339 *>     technique other than Gaussian elimination, the guarantees in
00340 *>     ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
00341 *> \endverbatim
00342 *>
00343 *> \param[in] RTHRESH
00344 *> \verbatim
00345 *>          RTHRESH is DOUBLE PRECISION
00346 *>     Determines when to stop refinement if the error estimate stops
00347 *>     decreasing. Refinement will stop when the next solution no longer
00348 *>     satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
00349 *>     the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
00350 *>     default value is 0.5. For 'aggressive' set to 0.9 to permit
00351 *>     convergence on extremely ill-conditioned matrices. See LAWN 165
00352 *>     for more details.
00353 *> \endverbatim
00354 *>
00355 *> \param[in] DZ_UB
00356 *> \verbatim
00357 *>          DZ_UB is DOUBLE PRECISION
00358 *>     Determines when to start considering componentwise convergence.
00359 *>     Componentwise convergence is only considered after each component
00360 *>     of the solution Y is stable, which we definte as the relative
00361 *>     change in each component being less than DZ_UB. The default value
00362 *>     is 0.25, requiring the first bit to be stable. See LAWN 165 for
00363 *>     more details.
00364 *> \endverbatim
00365 *>
00366 *> \param[in] IGNORE_CWISE
00367 *> \verbatim
00368 *>          IGNORE_CWISE is LOGICAL
00369 *>     If .TRUE. then ignore componentwise convergence. Default value
00370 *>     is .FALSE..
00371 *> \endverbatim
00372 *>
00373 *> \param[out] INFO
00374 *> \verbatim
00375 *>          INFO is INTEGER
00376 *>       = 0:  Successful exit.
00377 *>       < 0:  if INFO = -i, the ith argument to DLA_SYRFSX_EXTENDED had an illegal
00378 *>             value
00379 *> \endverbatim
00380 *
00381 *  Authors:
00382 *  ========
00383 *
00384 *> \author Univ. of Tennessee 
00385 *> \author Univ. of California Berkeley 
00386 *> \author Univ. of Colorado Denver 
00387 *> \author NAG Ltd. 
00388 *
00389 *> \date November 2011
00390 *
00391 *> \ingroup doubleSYcomputational
00392 *
00393 *  =====================================================================
00394       SUBROUTINE DLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
00395      $                                AF, LDAF, IPIV, COLEQU, C, B, LDB,
00396      $                                Y, LDY, BERR_OUT, N_NORMS,
00397      $                                ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
00398      $                                AYB, DY, Y_TAIL, RCOND, ITHRESH,
00399      $                                RTHRESH, DZ_UB, IGNORE_CWISE,
00400      $                                INFO )
00401 *
00402 *  -- LAPACK computational routine (version 3.4.0) --
00403 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00404 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00405 *     November 2011
00406 *
00407 *     .. Scalar Arguments ..
00408       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
00409      $                   N_NORMS, ITHRESH
00410       CHARACTER          UPLO
00411       LOGICAL            COLEQU, IGNORE_CWISE
00412       DOUBLE PRECISION   RTHRESH, DZ_UB
00413 *     ..
00414 *     .. Array Arguments ..
00415       INTEGER            IPIV( * )
00416       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00417      $                   Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
00418       DOUBLE PRECISION   C( * ), AYB( * ), RCOND, BERR_OUT( * ),
00419      $                   ERR_BNDS_NORM( NRHS, * ),
00420      $                   ERR_BNDS_COMP( NRHS, * )
00421 *     ..
00422 *
00423 *  =====================================================================
00424 *
00425 *     .. Local Scalars ..
00426       INTEGER            UPLO2, CNT, I, J, X_STATE, Z_STATE
00427       DOUBLE PRECISION   YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
00428      $                   DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
00429      $                   DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
00430      $                   EPS, HUGEVAL, INCR_THRESH
00431       LOGICAL            INCR_PREC, UPPER
00432 *     ..
00433 *     .. Parameters ..
00434       INTEGER            UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
00435      $                   NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
00436      $                   EXTRA_RESIDUAL, EXTRA_Y
00437       PARAMETER          ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
00438      $                   CONV_STATE = 2, NOPROG_STATE = 3 )
00439       PARAMETER          ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
00440      $                   EXTRA_Y = 2 )
00441       INTEGER            FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
00442       INTEGER            RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
00443       INTEGER            CMP_ERR_I, PIV_GROWTH_I
00444       PARAMETER          ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
00445      $                   BERR_I = 3 )
00446       PARAMETER          ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
00447       PARAMETER          ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
00448      $                   PIV_GROWTH_I = 9 )
00449       INTEGER            LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
00450      $                   LA_LINRX_CWISE_I
00451       PARAMETER          ( LA_LINRX_ITREF_I = 1,
00452      $                   LA_LINRX_ITHRESH_I = 2 )
00453       PARAMETER          ( LA_LINRX_CWISE_I = 3 )
00454       INTEGER            LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
00455      $                   LA_LINRX_RCOND_I
00456       PARAMETER          ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
00457       PARAMETER          ( LA_LINRX_RCOND_I = 3 )
00458 *     ..
00459 *     .. External Functions ..
00460       LOGICAL            LSAME
00461       EXTERNAL           ILAUPLO
00462       INTEGER            ILAUPLO
00463 *     ..
00464 *     .. External Subroutines ..
00465       EXTERNAL           DAXPY, DCOPY, DSYTRS, DSYMV, BLAS_DSYMV_X,
00466      $                   BLAS_DSYMV2_X, DLA_SYAMV, DLA_WWADDW,
00467      $                   DLA_LIN_BERR
00468       DOUBLE PRECISION   DLAMCH
00469 *     ..
00470 *     .. Intrinsic Functions ..
00471       INTRINSIC          ABS, MAX, MIN
00472 *     ..
00473 *     .. Executable Statements ..
00474 *
00475       INFO = 0
00476       UPPER = LSAME( UPLO, 'U' )
00477       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00478          INFO = -2
00479       ELSE IF( N.LT.0 ) THEN
00480          INFO = -3
00481       ELSE IF( NRHS.LT.0 ) THEN
00482          INFO = -4
00483       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00484          INFO = -6
00485       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00486          INFO = -8
00487       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00488          INFO = -13
00489       ELSE IF( LDY.LT.MAX( 1, N ) ) THEN
00490          INFO = -15
00491       END IF
00492       IF( INFO.NE.0 ) THEN
00493          CALL XERBLA( 'DLA_SYRFSX_EXTENDED', -INFO )
00494          RETURN
00495       END IF
00496       EPS = DLAMCH( 'Epsilon' )
00497       HUGEVAL = DLAMCH( 'Overflow' )
00498 *     Force HUGEVAL to Inf
00499       HUGEVAL = HUGEVAL * HUGEVAL
00500 *     Using HUGEVAL may lead to spurious underflows.
00501       INCR_THRESH = DBLE( N )*EPS
00502 
00503       IF ( LSAME ( UPLO, 'L' ) ) THEN
00504          UPLO2 = ILAUPLO( 'L' )
00505       ELSE
00506          UPLO2 = ILAUPLO( 'U' )
00507       ENDIF
00508 
00509       DO J = 1, NRHS
00510          Y_PREC_STATE = EXTRA_RESIDUAL
00511          IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
00512             DO I = 1, N
00513                Y_TAIL( I ) = 0.0D+0
00514             END DO
00515          END IF
00516 
00517          DXRAT = 0.0D+0
00518          DXRATMAX = 0.0D+0
00519          DZRAT = 0.0D+0
00520          DZRATMAX = 0.0D+0
00521          FINAL_DX_X = HUGEVAL
00522          FINAL_DZ_Z = HUGEVAL
00523          PREVNORMDX = HUGEVAL
00524          PREV_DZ_Z = HUGEVAL
00525          DZ_Z = HUGEVAL
00526          DX_X = HUGEVAL
00527 
00528          X_STATE = WORKING_STATE
00529          Z_STATE = UNSTABLE_STATE
00530          INCR_PREC = .FALSE.
00531 
00532          DO CNT = 1, ITHRESH
00533 *
00534 *        Compute residual RES = B_s - op(A_s) * Y,
00535 *            op(A) = A, A**T, or A**H depending on TRANS (and type).
00536 *
00537             CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
00538             IF (Y_PREC_STATE .EQ. BASE_RESIDUAL) THEN
00539                CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1,
00540      $              1.0D+0, RES, 1 )
00541             ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
00542                CALL BLAS_DSYMV_X( UPLO2, N, -1.0D+0, A, LDA,
00543      $              Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE )
00544             ELSE
00545                CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,
00546      $              Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)
00547             END IF
00548             
00549 !         XXX: RES is no longer needed.
00550             CALL DCOPY( N, RES, 1, DY, 1 )
00551             CALL DSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )
00552 *
00553 *         Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
00554 *
00555             NORMX = 0.0D+0
00556             NORMY = 0.0D+0
00557             NORMDX = 0.0D+0
00558             DZ_Z = 0.0D+0
00559             YMIN = HUGEVAL
00560             
00561             DO I = 1, N
00562                YK = ABS( Y( I, J ) )
00563                DYK = ABS( DY( I ) )
00564                
00565                IF ( YK .NE. 0.0D+0 ) THEN
00566                   DZ_Z = MAX( DZ_Z, DYK / YK )
00567                ELSE IF ( DYK .NE. 0.0D+0 ) THEN
00568                   DZ_Z = HUGEVAL
00569                END IF
00570 
00571                YMIN = MIN( YMIN, YK )
00572 
00573                NORMY = MAX( NORMY, YK )
00574 
00575                IF ( COLEQU ) THEN
00576                   NORMX = MAX( NORMX, YK * C( I ) )
00577                   NORMDX = MAX( NORMDX, DYK * C( I ) )
00578                ELSE
00579                   NORMX = NORMY
00580                   NORMDX = MAX(NORMDX, DYK)
00581                END IF
00582             END DO
00583 
00584             IF ( NORMX .NE. 0.0D+0 ) THEN
00585                DX_X = NORMDX / NORMX
00586             ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
00587                DX_X = 0.0D+0
00588             ELSE
00589                DX_X = HUGEVAL
00590             END IF
00591 
00592             DXRAT = NORMDX / PREVNORMDX
00593             DZRAT = DZ_Z / PREV_DZ_Z
00594 *
00595 *         Check termination criteria.
00596 *
00597             IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
00598      $           .AND. Y_PREC_STATE .LT. EXTRA_Y )
00599      $           INCR_PREC = .TRUE.
00600 
00601             IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
00602      $           X_STATE = WORKING_STATE
00603             IF ( X_STATE .EQ. WORKING_STATE ) THEN
00604                IF ( DX_X .LE. EPS ) THEN
00605                   X_STATE = CONV_STATE
00606                ELSE IF ( DXRAT .GT. RTHRESH ) THEN
00607                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00608                      INCR_PREC = .TRUE.
00609                   ELSE
00610                      X_STATE = NOPROG_STATE
00611                   END IF
00612                ELSE
00613                   IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
00614                END IF
00615                IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
00616             END IF
00617 
00618             IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
00619      $           Z_STATE = WORKING_STATE
00620             IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
00621      $           Z_STATE = WORKING_STATE
00622             IF ( Z_STATE .EQ. WORKING_STATE ) THEN
00623                IF ( DZ_Z .LE. EPS ) THEN
00624                   Z_STATE = CONV_STATE
00625                ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
00626                   Z_STATE = UNSTABLE_STATE
00627                   DZRATMAX = 0.0D+0
00628                   FINAL_DZ_Z = HUGEVAL
00629                ELSE IF ( DZRAT .GT. RTHRESH ) THEN
00630                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00631                      INCR_PREC = .TRUE.
00632                   ELSE
00633                      Z_STATE = NOPROG_STATE
00634                   END IF
00635                ELSE
00636                   IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
00637                END IF
00638                IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00639             END IF
00640 
00641             IF ( X_STATE.NE.WORKING_STATE.AND.
00642      $           ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
00643      $           GOTO 666
00644 
00645             IF ( INCR_PREC ) THEN
00646                INCR_PREC = .FALSE.
00647                Y_PREC_STATE = Y_PREC_STATE + 1
00648                DO I = 1, N
00649                   Y_TAIL( I ) = 0.0D+0
00650                END DO
00651             END IF
00652 
00653             PREVNORMDX = NORMDX
00654             PREV_DZ_Z = DZ_Z
00655 *
00656 *           Update soluton.
00657 *
00658             IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
00659                CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
00660             ELSE
00661                CALL DLA_WWADDW( N, Y(1,J), Y_TAIL, DY )
00662             END IF
00663             
00664          END DO
00665 *        Target of "IF (Z_STOP .AND. X_STOP)".  Sun's f77 won't EXIT.
00666  666     CONTINUE
00667 *
00668 *     Set final_* when cnt hits ithresh.
00669 *
00670          IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
00671          IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00672 *
00673 *     Compute error bounds.
00674 *
00675          IF ( N_NORMS .GE. 1 ) THEN
00676             ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
00677      $           FINAL_DX_X / (1 - DXRATMAX)
00678          END IF
00679          IF ( N_NORMS .GE. 2 ) THEN
00680             ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
00681      $           FINAL_DZ_Z / (1 - DZRATMAX)
00682          END IF
00683 *
00684 *     Compute componentwise relative backward error from formula
00685 *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00686 *     where abs(Z) is the componentwise absolute value of the matrix
00687 *     or vector Z.
00688 *
00689 *        Compute residual RES = B_s - op(A_s) * Y,
00690 *            op(A) = A, A**T, or A**H depending on TRANS (and type).
00691          CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
00692          CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES, 
00693      $     1 )
00694          
00695          DO I = 1, N
00696             AYB( I ) = ABS( B( I, J ) )
00697          END DO
00698 *
00699 *     Compute abs(op(A_s))*abs(Y) + abs(B_s).
00700 *
00701          CALL DLA_SYAMV( UPLO2, N, 1.0D+0,
00702      $        A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
00703          
00704          CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
00705 *
00706 *     End of loop for each RHS.
00707 *
00708       END DO
00709 *
00710       RETURN
00711       END
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