LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sla_syrfsx_extended.f
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00001 *> \brief \b SLA_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 SLA_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/sla_syrfsx_extended.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SLA_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 *       REAL               RTHRESH, DZ_UB
00035 *       ..
00036 *       .. Array Arguments ..
00037 *       INTEGER            IPIV( * )
00038 *       REAL               A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00039 *      $                   Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
00040 *       REAL               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 *> SLA_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 SSYRFSX 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 REAL 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 REAL 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 SSYTRF.
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 SSYTRF.
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 REAL 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 REAL 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 REAL array, dimension (LDY,NRHS)
00166 *>     On entry, the solution matrix X, as computed by SSYTRS.
00167 *>     On exit, the improved solution matrix Y.
00168 *> \endverbatim
00169 *>
00170 *> \param[in] LDY
00171 *> \verbatim
00172 *>          LDY is INTEGER
00173 *>     The leading dimension of the array Y.  LDY >= max(1,N).
00174 *> \endverbatim
00175 *>
00176 *> \param[out] BERR_OUT
00177 *> \verbatim
00178 *>          BERR_OUT is REAL array, dimension (NRHS)
00179 *>     On exit, BERR_OUT(j) contains the componentwise relative backward
00180 *>     error for right-hand-side j from the formula
00181 *>         max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00182 *>     where abs(Z) is the componentwise absolute value of the matrix
00183 *>     or vector Z. This is computed by SLA_LIN_BERR.
00184 *> \endverbatim
00185 *>
00186 *> \param[in] N_NORMS
00187 *> \verbatim
00188 *>          N_NORMS is INTEGER
00189 *>     Determines which error bounds to return (see ERR_BNDS_NORM
00190 *>     and ERR_BNDS_COMP).
00191 *>     If N_NORMS >= 1 return normwise error bounds.
00192 *>     If N_NORMS >= 2 return componentwise error bounds.
00193 *> \endverbatim
00194 *>
00195 *> \param[in,out] ERR_BNDS_NORM
00196 *> \verbatim
00197 *>          ERR_BNDS_NORM is REAL array, dimension (NRHS, N_ERR_BNDS)
00198 *>     For each right-hand side, this array contains information about
00199 *>     various error bounds and condition numbers corresponding to the
00200 *>     normwise relative error, which is defined as follows:
00201 *>
00202 *>     Normwise relative error in the ith solution vector:
00203 *>             max_j (abs(XTRUE(j,i) - X(j,i)))
00204 *>            ------------------------------
00205 *>                  max_j abs(X(j,i))
00206 *>
00207 *>     The array is indexed by the type of error information as described
00208 *>     below. There currently are up to three pieces of information
00209 *>     returned.
00210 *>
00211 *>     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
00212 *>     right-hand side.
00213 *>
00214 *>     The second index in ERR_BNDS_NORM(:,err) contains the following
00215 *>     three fields:
00216 *>     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00217 *>              reciprocal condition number is less than the threshold
00218 *>              sqrt(n) * slamch('Epsilon').
00219 *>
00220 *>     err = 2 "Guaranteed" error bound: The estimated forward error,
00221 *>              almost certainly within a factor of 10 of the true error
00222 *>              so long as the next entry is greater than the threshold
00223 *>              sqrt(n) * slamch('Epsilon'). This error bound should only
00224 *>              be trusted if the previous boolean is true.
00225 *>
00226 *>     err = 3  Reciprocal condition number: Estimated normwise
00227 *>              reciprocal condition number.  Compared with the threshold
00228 *>              sqrt(n) * slamch('Epsilon') to determine if the error
00229 *>              estimate is "guaranteed". These reciprocal condition
00230 *>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00231 *>              appropriately scaled matrix Z.
00232 *>              Let Z = S*A, where S scales each row by a power of the
00233 *>              radix so all absolute row sums of Z are approximately 1.
00234 *>
00235 *>     This subroutine is only responsible for setting the second field
00236 *>     above.
00237 *>     See Lapack Working Note 165 for further details and extra
00238 *>     cautions.
00239 *> \endverbatim
00240 *>
00241 *> \param[in,out] ERR_BNDS_COMP
00242 *> \verbatim
00243 *>          ERR_BNDS_COMP is REAL array, dimension (NRHS, N_ERR_BNDS)
00244 *>     For each right-hand side, this array contains information about
00245 *>     various error bounds and condition numbers corresponding to the
00246 *>     componentwise relative error, which is defined as follows:
00247 *>
00248 *>     Componentwise relative error in the ith solution vector:
00249 *>                    abs(XTRUE(j,i) - X(j,i))
00250 *>             max_j ----------------------
00251 *>                         abs(X(j,i))
00252 *>
00253 *>     The array is indexed by the right-hand side i (on which the
00254 *>     componentwise relative error depends), and the type of error
00255 *>     information as described below. There currently are up to three
00256 *>     pieces of information returned for each right-hand side. If
00257 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
00258 *>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
00259 *>     the first (:,N_ERR_BNDS) entries are returned.
00260 *>
00261 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
00262 *>     right-hand side.
00263 *>
00264 *>     The second index in ERR_BNDS_COMP(:,err) contains the following
00265 *>     three fields:
00266 *>     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00267 *>              reciprocal condition number is less than the threshold
00268 *>              sqrt(n) * slamch('Epsilon').
00269 *>
00270 *>     err = 2 "Guaranteed" error bound: The estimated forward error,
00271 *>              almost certainly within a factor of 10 of the true error
00272 *>              so long as the next entry is greater than the threshold
00273 *>              sqrt(n) * slamch('Epsilon'). This error bound should only
00274 *>              be trusted if the previous boolean is true.
00275 *>
00276 *>     err = 3  Reciprocal condition number: Estimated componentwise
00277 *>              reciprocal condition number.  Compared with the threshold
00278 *>              sqrt(n) * slamch('Epsilon') to determine if the error
00279 *>              estimate is "guaranteed". These reciprocal condition
00280 *>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00281 *>              appropriately scaled matrix Z.
00282 *>              Let Z = S*(A*diag(x)), where x is the solution for the
00283 *>              current right-hand side and S scales each row of
00284 *>              A*diag(x) by a power of the radix so all absolute row
00285 *>              sums of Z are approximately 1.
00286 *>
00287 *>     This subroutine is only responsible for setting the second field
00288 *>     above.
00289 *>     See Lapack Working Note 165 for further details and extra
00290 *>     cautions.
00291 *> \endverbatim
00292 *>
00293 *> \param[in] RES
00294 *> \verbatim
00295 *>          RES is REAL array, dimension (N)
00296 *>     Workspace to hold the intermediate residual.
00297 *> \endverbatim
00298 *>
00299 *> \param[in] AYB
00300 *> \verbatim
00301 *>          AYB is REAL array, dimension (N)
00302 *>     Workspace. This can be the same workspace passed for Y_TAIL.
00303 *> \endverbatim
00304 *>
00305 *> \param[in] DY
00306 *> \verbatim
00307 *>          DY is REAL array, dimension (N)
00308 *>     Workspace to hold the intermediate solution.
00309 *> \endverbatim
00310 *>
00311 *> \param[in] Y_TAIL
00312 *> \verbatim
00313 *>          Y_TAIL is REAL array, dimension (N)
00314 *>     Workspace to hold the trailing bits of the intermediate solution.
00315 *> \endverbatim
00316 *>
00317 *> \param[in] RCOND
00318 *> \verbatim
00319 *>          RCOND is REAL
00320 *>     Reciprocal scaled condition number.  This is an estimate of the
00321 *>     reciprocal Skeel condition number of the matrix A after
00322 *>     equilibration (if done).  If this is less than the machine
00323 *>     precision (in particular, if it is zero), the matrix is singular
00324 *>     to working precision.  Note that the error may still be small even
00325 *>     if this number is very small and the matrix appears ill-
00326 *>     conditioned.
00327 *> \endverbatim
00328 *>
00329 *> \param[in] ITHRESH
00330 *> \verbatim
00331 *>          ITHRESH is INTEGER
00332 *>     The maximum number of residual computations allowed for
00333 *>     refinement. The default is 10. For 'aggressive' set to 100 to
00334 *>     permit convergence using approximate factorizations or
00335 *>     factorizations other than LU. If the factorization uses a
00336 *>     technique other than Gaussian elimination, the guarantees in
00337 *>     ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
00338 *> \endverbatim
00339 *>
00340 *> \param[in] RTHRESH
00341 *> \verbatim
00342 *>          RTHRESH is REAL
00343 *>     Determines when to stop refinement if the error estimate stops
00344 *>     decreasing. Refinement will stop when the next solution no longer
00345 *>     satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
00346 *>     the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
00347 *>     default value is 0.5. For 'aggressive' set to 0.9 to permit
00348 *>     convergence on extremely ill-conditioned matrices. See LAWN 165
00349 *>     for more details.
00350 *> \endverbatim
00351 *>
00352 *> \param[in] DZ_UB
00353 *> \verbatim
00354 *>          DZ_UB is REAL
00355 *>     Determines when to start considering componentwise convergence.
00356 *>     Componentwise convergence is only considered after each component
00357 *>     of the solution Y is stable, which we definte as the relative
00358 *>     change in each component being less than DZ_UB. The default value
00359 *>     is 0.25, requiring the first bit to be stable. See LAWN 165 for
00360 *>     more details.
00361 *> \endverbatim
00362 *>
00363 *> \param[in] IGNORE_CWISE
00364 *> \verbatim
00365 *>          IGNORE_CWISE is LOGICAL
00366 *>     If .TRUE. then ignore componentwise convergence. Default value
00367 *>     is .FALSE..
00368 *> \endverbatim
00369 *>
00370 *> \param[out] INFO
00371 *> \verbatim
00372 *>          INFO is INTEGER
00373 *>       = 0:  Successful exit.
00374 *>       < 0:  if INFO = -i, the ith argument to SLA_SYRFSX_EXTENDED had an illegal
00375 *>             value
00376 *> \endverbatim
00377 *
00378 *  Authors:
00379 *  ========
00380 *
00381 *> \author Univ. of Tennessee 
00382 *> \author Univ. of California Berkeley 
00383 *> \author Univ. of Colorado Denver 
00384 *> \author NAG Ltd. 
00385 *
00386 *> \date November 2011
00387 *
00388 *> \ingroup realSYcomputational
00389 *
00390 *  =====================================================================
00391       SUBROUTINE SLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
00392      $                                AF, LDAF, IPIV, COLEQU, C, B, LDB,
00393      $                                Y, LDY, BERR_OUT, N_NORMS,
00394      $                                ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
00395      $                                AYB, DY, Y_TAIL, RCOND, ITHRESH,
00396      $                                RTHRESH, DZ_UB, IGNORE_CWISE,
00397      $                                INFO )
00398 *
00399 *  -- LAPACK computational routine (version 3.4.0) --
00400 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00401 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00402 *     November 2011
00403 *
00404 *     .. Scalar Arguments ..
00405       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
00406      $                   N_NORMS, ITHRESH
00407       CHARACTER          UPLO
00408       LOGICAL            COLEQU, IGNORE_CWISE
00409       REAL               RTHRESH, DZ_UB
00410 *     ..
00411 *     .. Array Arguments ..
00412       INTEGER            IPIV( * )
00413       REAL               A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00414      $                   Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
00415       REAL               C( * ), AYB( * ), RCOND, BERR_OUT( * ),
00416      $                   ERR_BNDS_NORM( NRHS, * ),
00417      $                   ERR_BNDS_COMP( NRHS, * )
00418 *     ..
00419 *
00420 *  =====================================================================
00421 *
00422 *     .. Local Scalars ..
00423       INTEGER            UPLO2, CNT, I, J, X_STATE, Z_STATE
00424       REAL               YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
00425      $                   DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
00426      $                   DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
00427      $                   EPS, HUGEVAL, INCR_THRESH
00428       LOGICAL            INCR_PREC, UPPER
00429 *     ..
00430 *     .. Parameters ..
00431       INTEGER            UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
00432      $                   NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
00433      $                   EXTRA_RESIDUAL, EXTRA_Y
00434       PARAMETER          ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
00435      $                   CONV_STATE = 2, NOPROG_STATE = 3 )
00436       PARAMETER          ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
00437      $                   EXTRA_Y = 2 )
00438       INTEGER            FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
00439       INTEGER            RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
00440       INTEGER            CMP_ERR_I, PIV_GROWTH_I
00441       PARAMETER          ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
00442      $                   BERR_I = 3 )
00443       PARAMETER          ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
00444       PARAMETER          ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
00445      $                   PIV_GROWTH_I = 9 )
00446       INTEGER            LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
00447      $                   LA_LINRX_CWISE_I
00448       PARAMETER          ( LA_LINRX_ITREF_I = 1,
00449      $                   LA_LINRX_ITHRESH_I = 2 )
00450       PARAMETER          ( LA_LINRX_CWISE_I = 3 )
00451       INTEGER            LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
00452      $                   LA_LINRX_RCOND_I
00453       PARAMETER          ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
00454       PARAMETER          ( LA_LINRX_RCOND_I = 3 )
00455 *     ..
00456 *     .. External Functions ..
00457       LOGICAL            LSAME
00458       EXTERNAL           ILAUPLO
00459       INTEGER            ILAUPLO
00460 *     ..
00461 *     .. External Subroutines ..
00462       EXTERNAL           SAXPY, SCOPY, SSYTRS, SSYMV, BLAS_SSYMV_X,
00463      $                   BLAS_SSYMV2_X, SLA_SYAMV, SLA_WWADDW,
00464      $                   SLA_LIN_BERR
00465       REAL               SLAMCH
00466 *     ..
00467 *     .. Intrinsic Functions ..
00468       INTRINSIC          ABS, MAX, MIN
00469 *     ..
00470 *     .. Executable Statements ..
00471 *
00472       INFO = 0
00473       UPPER = LSAME( UPLO, 'U' )
00474       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00475          INFO = -2
00476       ELSE IF( N.LT.0 ) THEN
00477          INFO = -3
00478       ELSE IF( NRHS.LT.0 ) THEN
00479          INFO = -4
00480       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00481          INFO = -6
00482       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00483          INFO = -8
00484       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00485          INFO = -13
00486       ELSE IF( LDY.LT.MAX( 1, N ) ) THEN
00487          INFO = -15
00488       END IF
00489       IF( INFO.NE.0 ) THEN
00490          CALL XERBLA( 'SLA_SYRFSX_EXTENDED', -INFO )
00491          RETURN
00492       END IF
00493       EPS = SLAMCH( 'Epsilon' )
00494       HUGEVAL = SLAMCH( 'Overflow' )
00495 *     Force HUGEVAL to Inf
00496       HUGEVAL = HUGEVAL * HUGEVAL
00497 *     Using HUGEVAL may lead to spurious underflows.
00498       INCR_THRESH = REAL( N )*EPS
00499 
00500       IF ( LSAME ( UPLO, 'L' ) ) THEN
00501          UPLO2 = ILAUPLO( 'L' )
00502       ELSE
00503          UPLO2 = ILAUPLO( 'U' )
00504       ENDIF
00505 
00506       DO J = 1, NRHS
00507          Y_PREC_STATE = EXTRA_RESIDUAL
00508          IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
00509             DO I = 1, N
00510                Y_TAIL( I ) = 0.0
00511             END DO
00512          END IF
00513 
00514          DXRAT = 0.0
00515          DXRATMAX = 0.0
00516          DZRAT = 0.0
00517          DZRATMAX = 0.0
00518          FINAL_DX_X = HUGEVAL
00519          FINAL_DZ_Z = HUGEVAL
00520          PREVNORMDX = HUGEVAL
00521          PREV_DZ_Z = HUGEVAL
00522          DZ_Z = HUGEVAL
00523          DX_X = HUGEVAL
00524 
00525          X_STATE = WORKING_STATE
00526          Z_STATE = UNSTABLE_STATE
00527          INCR_PREC = .FALSE.
00528 
00529          DO CNT = 1, ITHRESH
00530 *
00531 *        Compute residual RES = B_s - op(A_s) * Y,
00532 *            op(A) = A, A**T, or A**H depending on TRANS (and type).
00533 *
00534             CALL SCOPY( N, B( 1, J ), 1, RES, 1 )
00535             IF (Y_PREC_STATE .EQ. BASE_RESIDUAL) THEN
00536                CALL SSYMV( UPLO, N, -1.0, A, LDA, Y(1,J), 1,
00537      $              1.0, RES, 1 )
00538             ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
00539                CALL BLAS_SSYMV_X( UPLO2, N, -1.0, A, LDA,
00540      $              Y( 1, J ), 1, 1.0, RES, 1, PREC_TYPE )
00541             ELSE
00542                CALL BLAS_SSYMV2_X(UPLO2, N, -1.0, A, LDA,
00543      $              Y(1, J), Y_TAIL, 1, 1.0, RES, 1, PREC_TYPE)
00544             END IF
00545             
00546 !         XXX: RES is no longer needed.
00547             CALL SCOPY( N, RES, 1, DY, 1 )
00548             CALL SSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )
00549 *
00550 *         Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
00551 *
00552             NORMX = 0.0
00553             NORMY = 0.0
00554             NORMDX = 0.0
00555             DZ_Z = 0.0
00556             YMIN = HUGEVAL
00557             
00558             DO I = 1, N
00559                YK = ABS( Y( I, J ) )
00560                DYK = ABS( DY( I ) )
00561                
00562                IF ( YK .NE. 0.0 ) THEN
00563                   DZ_Z = MAX( DZ_Z, DYK / YK )
00564                ELSE IF ( DYK .NE. 0.0 ) THEN
00565                   DZ_Z = HUGEVAL
00566                END IF
00567 
00568                YMIN = MIN( YMIN, YK )
00569 
00570                NORMY = MAX( NORMY, YK )
00571 
00572                IF ( COLEQU ) THEN
00573                   NORMX = MAX( NORMX, YK * C( I ) )
00574                   NORMDX = MAX( NORMDX, DYK * C( I ) )
00575                ELSE
00576                   NORMX = NORMY
00577                   NORMDX = MAX(NORMDX, DYK)
00578                END IF
00579             END DO
00580 
00581             IF ( NORMX .NE. 0.0 ) THEN
00582                DX_X = NORMDX / NORMX
00583             ELSE IF ( NORMDX .EQ. 0.0 ) THEN
00584                DX_X = 0.0
00585             ELSE
00586                DX_X = HUGEVAL
00587             END IF
00588 
00589             DXRAT = NORMDX / PREVNORMDX
00590             DZRAT = DZ_Z / PREV_DZ_Z
00591 *
00592 *         Check termination criteria.
00593 *
00594             IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
00595      $           .AND. Y_PREC_STATE .LT. EXTRA_Y )
00596      $           INCR_PREC = .TRUE.
00597 
00598             IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
00599      $           X_STATE = WORKING_STATE
00600             IF ( X_STATE .EQ. WORKING_STATE ) THEN
00601                IF ( DX_X .LE. EPS ) THEN
00602                   X_STATE = CONV_STATE
00603                ELSE IF ( DXRAT .GT. RTHRESH ) THEN
00604                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00605                      INCR_PREC = .TRUE.
00606                   ELSE
00607                      X_STATE = NOPROG_STATE
00608                   END IF
00609                ELSE
00610                   IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
00611                END IF
00612                IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
00613             END IF
00614 
00615             IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
00616      $           Z_STATE = WORKING_STATE
00617             IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
00618      $           Z_STATE = WORKING_STATE
00619             IF ( Z_STATE .EQ. WORKING_STATE ) THEN
00620                IF ( DZ_Z .LE. EPS ) THEN
00621                   Z_STATE = CONV_STATE
00622                ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
00623                   Z_STATE = UNSTABLE_STATE
00624                   DZRATMAX = 0.0
00625                   FINAL_DZ_Z = HUGEVAL
00626                ELSE IF ( DZRAT .GT. RTHRESH ) THEN
00627                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00628                      INCR_PREC = .TRUE.
00629                   ELSE
00630                      Z_STATE = NOPROG_STATE
00631                   END IF
00632                ELSE
00633                   IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
00634                END IF
00635                IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00636             END IF
00637 
00638             IF ( X_STATE.NE.WORKING_STATE.AND.
00639      $           ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
00640      $           GOTO 666
00641 
00642             IF ( INCR_PREC ) THEN
00643                INCR_PREC = .FALSE.
00644                Y_PREC_STATE = Y_PREC_STATE + 1
00645                DO I = 1, N
00646                   Y_TAIL( I ) = 0.0
00647                END DO
00648             END IF
00649 
00650             PREVNORMDX = NORMDX
00651             PREV_DZ_Z = DZ_Z
00652 *
00653 *           Update soluton.
00654 *
00655             IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
00656                CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 )
00657             ELSE
00658                CALL SLA_WWADDW( N, Y(1,J), Y_TAIL, DY )
00659             END IF
00660             
00661          END DO
00662 *        Target of "IF (Z_STOP .AND. X_STOP)".  Sun's f77 won't EXIT.
00663  666     CONTINUE
00664 *
00665 *     Set final_* when cnt hits ithresh.
00666 *
00667          IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
00668          IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00669 *
00670 *     Compute error bounds.
00671 *
00672          IF ( N_NORMS .GE. 1 ) THEN
00673             ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
00674      $           FINAL_DX_X / (1 - DXRATMAX)
00675          END IF
00676          IF ( N_NORMS .GE. 2 ) THEN
00677             ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
00678      $           FINAL_DZ_Z / (1 - DZRATMAX)
00679          END IF
00680 *
00681 *     Compute componentwise relative backward error from formula
00682 *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00683 *     where abs(Z) is the componentwise absolute value of the matrix
00684 *     or vector Z.
00685 *
00686 *        Compute residual RES = B_s - op(A_s) * Y,
00687 *            op(A) = A, A**T, or A**H depending on TRANS (and type).
00688          CALL SCOPY( N, B( 1, J ), 1, RES, 1 )
00689          CALL SSYMV( UPLO, N, -1.0, A, LDA, Y(1,J), 1, 1.0, RES, 1 )
00690          
00691          DO I = 1, N
00692             AYB( I ) = ABS( B( I, J ) )
00693          END DO
00694 *
00695 *     Compute abs(op(A_s))*abs(Y) + abs(B_s).
00696 *
00697          CALL SLA_SYAMV( UPLO2, N, 1.0,
00698      $        A, LDA, Y(1, J), 1, 1.0, AYB, 1 )
00699          
00700          CALL SLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
00701 *
00702 *     End of loop for each RHS.
00703 *
00704       END DO
00705 *
00706       RETURN
00707       END
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