LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cla_gerfsx_extended.f
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00001 *> \brief \b CLA_GERFSX_EXTENDED
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLA_GERFSX_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/cla_gerfsx_extended.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
00022 *                                       LDA, AF, LDAF, IPIV, COLEQU, C, B,
00023 *                                       LDB, Y, LDY, BERR_OUT, N_NORMS,
00024 *                                       ERRS_N, ERRS_C, RES, AYB, DY,
00025 *                                       Y_TAIL, RCOND, ITHRESH, RTHRESH,
00026 *                                       DZ_UB, IGNORE_CWISE, INFO )
00027 * 
00028 *       .. Scalar Arguments ..
00029 *       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
00030 *      $                   TRANS_TYPE, N_NORMS
00031 *       LOGICAL            COLEQU, IGNORE_CWISE
00032 *       INTEGER            ITHRESH
00033 *       REAL               RTHRESH, DZ_UB
00034 *       ..
00035 *       .. Array Arguments
00036 *       INTEGER            IPIV( * )
00037 *       COMPLEX            A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00038 *      $                   Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
00039 *       REAL               C( * ), AYB( * ), RCOND, BERR_OUT( * ),
00040 *      $                   ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
00041 *       ..
00042 *  
00043 *
00044 *> \par Purpose:
00045 *  =============
00046 *>
00047 *> \verbatim
00048 *>
00049 *> 
00050 *> CLA_GERFSX_EXTENDED improves the computed solution to a system of
00051 *> linear equations by performing extra-precise iterative refinement
00052 *> and provides error bounds and backward error estimates for the solution.
00053 *> This subroutine is called by CGERFSX to perform iterative refinement.
00054 *> In addition to normwise error bound, the code provides maximum
00055 *> componentwise error bound if possible. See comments for ERRS_N
00056 *> and ERRS_C for details of the error bounds. Note that this
00057 *> subroutine is only resonsible for setting the second fields of
00058 *> ERRS_N and ERRS_C.
00059 *> \endverbatim
00060 *
00061 *  Arguments:
00062 *  ==========
00063 *
00064 *> \param[in] PREC_TYPE
00065 *> \verbatim
00066 *>          PREC_TYPE is INTEGER
00067 *>     Specifies the intermediate precision to be used in refinement.
00068 *>     The value is defined by ILAPREC(P) where P is a CHARACTER and
00069 *>     P    = 'S':  Single
00070 *>          = 'D':  Double
00071 *>          = 'I':  Indigenous
00072 *>          = 'X', 'E':  Extra
00073 *> \endverbatim
00074 *>
00075 *> \param[in] TRANS_TYPE
00076 *> \verbatim
00077 *>          TRANS_TYPE is INTEGER
00078 *>     Specifies the transposition operation on A.
00079 *>     The value is defined by ILATRANS(T) where T is a CHARACTER and
00080 *>     T    = 'N':  No transpose
00081 *>          = 'T':  Transpose
00082 *>          = 'C':  Conjugate transpose
00083 *> \endverbatim
00084 *>
00085 *> \param[in] N
00086 *> \verbatim
00087 *>          N is INTEGER
00088 *>     The number of linear equations, i.e., the order of the
00089 *>     matrix A.  N >= 0.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] NRHS
00093 *> \verbatim
00094 *>          NRHS is INTEGER
00095 *>     The number of right-hand-sides, i.e., the number of columns of the
00096 *>     matrix B.
00097 *> \endverbatim
00098 *>
00099 *> \param[in] A
00100 *> \verbatim
00101 *>          A is COMPLEX array, dimension (LDA,N)
00102 *>     On entry, the N-by-N matrix A.
00103 *> \endverbatim
00104 *>
00105 *> \param[in] LDA
00106 *> \verbatim
00107 *>          LDA is INTEGER
00108 *>     The leading dimension of the array A.  LDA >= max(1,N).
00109 *> \endverbatim
00110 *>
00111 *> \param[in] AF
00112 *> \verbatim
00113 *>          AF is COMPLEX array, dimension (LDAF,N)
00114 *>     The factors L and U from the factorization
00115 *>     A = P*L*U as computed by CGETRF.
00116 *> \endverbatim
00117 *>
00118 *> \param[in] LDAF
00119 *> \verbatim
00120 *>          LDAF is INTEGER
00121 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00122 *> \endverbatim
00123 *>
00124 *> \param[in] IPIV
00125 *> \verbatim
00126 *>          IPIV is INTEGER array, dimension (N)
00127 *>     The pivot indices from the factorization A = P*L*U
00128 *>     as computed by CGETRF; row i of the matrix was interchanged
00129 *>     with row IPIV(i).
00130 *> \endverbatim
00131 *>
00132 *> \param[in] COLEQU
00133 *> \verbatim
00134 *>          COLEQU is LOGICAL
00135 *>     If .TRUE. then column equilibration was done to A before calling
00136 *>     this routine. This is needed to compute the solution and error
00137 *>     bounds correctly.
00138 *> \endverbatim
00139 *>
00140 *> \param[in] C
00141 *> \verbatim
00142 *>          C is REAL array, dimension (N)
00143 *>     The column scale factors for A. If COLEQU = .FALSE., C
00144 *>     is not accessed. If C is input, each element of C should be a power
00145 *>     of the radix to ensure a reliable solution and error estimates.
00146 *>     Scaling by powers of the radix does not cause rounding errors unless
00147 *>     the result underflows or overflows. Rounding errors during scaling
00148 *>     lead to refining with a matrix that is not equivalent to the
00149 *>     input matrix, producing error estimates that may not be
00150 *>     reliable.
00151 *> \endverbatim
00152 *>
00153 *> \param[in] B
00154 *> \verbatim
00155 *>          B is COMPLEX array, dimension (LDB,NRHS)
00156 *>     The right-hand-side matrix B.
00157 *> \endverbatim
00158 *>
00159 *> \param[in] LDB
00160 *> \verbatim
00161 *>          LDB is INTEGER
00162 *>     The leading dimension of the array B.  LDB >= max(1,N).
00163 *> \endverbatim
00164 *>
00165 *> \param[in,out] Y
00166 *> \verbatim
00167 *>          Y is COMPLEX array, dimension (LDY,NRHS)
00168 *>     On entry, the solution matrix X, as computed by CGETRS.
00169 *>     On exit, the improved solution matrix Y.
00170 *> \endverbatim
00171 *>
00172 *> \param[in] LDY
00173 *> \verbatim
00174 *>          LDY is INTEGER
00175 *>     The leading dimension of the array Y.  LDY >= max(1,N).
00176 *> \endverbatim
00177 *>
00178 *> \param[out] BERR_OUT
00179 *> \verbatim
00180 *>          BERR_OUT is REAL array, dimension (NRHS)
00181 *>     On exit, BERR_OUT(j) contains the componentwise relative backward
00182 *>     error for right-hand-side j from the formula
00183 *>         max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00184 *>     where abs(Z) is the componentwise absolute value of the matrix
00185 *>     or vector Z. This is computed by CLA_LIN_BERR.
00186 *> \endverbatim
00187 *>
00188 *> \param[in] N_NORMS
00189 *> \verbatim
00190 *>          N_NORMS is INTEGER
00191 *>     Determines which error bounds to return (see ERRS_N
00192 *>     and ERRS_C).
00193 *>     If N_NORMS >= 1 return normwise error bounds.
00194 *>     If N_NORMS >= 2 return componentwise error bounds.
00195 *> \endverbatim
00196 *>
00197 *> \param[in,out] ERRS_N
00198 *> \verbatim
00199 *>          ERRS_N is REAL array, dimension (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 ERRS_N(i,:) corresponds to the ith
00214 *>     right-hand side.
00215 *>
00216 *>     The second index in ERRS_N(:,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] ERRS_C
00244 *> \verbatim
00245 *>          ERRS_C is REAL array, dimension (NRHS, N_ERR_BNDS)
00246 *>     For each right-hand side, this array contains information about
00247 *>     various error bounds and condition numbers corresponding to the
00248 *>     componentwise relative error, which is defined as follows:
00249 *>
00250 *>     Componentwise relative error in the ith solution vector:
00251 *>                    abs(XTRUE(j,i) - X(j,i))
00252 *>             max_j ----------------------
00253 *>                         abs(X(j,i))
00254 *>
00255 *>     The array is indexed by the right-hand side i (on which the
00256 *>     componentwise relative error depends), and the type of error
00257 *>     information as described below. There currently are up to three
00258 *>     pieces of information returned for each right-hand side. If
00259 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
00260 *>     ERRS_C is not accessed.  If N_ERR_BNDS .LT. 3, then at most
00261 *>     the first (:,N_ERR_BNDS) entries are returned.
00262 *>
00263 *>     The first index in ERRS_C(i,:) corresponds to the ith
00264 *>     right-hand side.
00265 *>
00266 *>     The second index in ERRS_C(:,err) contains the following
00267 *>     three fields:
00268 *>     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00269 *>              reciprocal condition number is less than the threshold
00270 *>              sqrt(n) * slamch('Epsilon').
00271 *>
00272 *>     err = 2 "Guaranteed" error bound: The estimated forward error,
00273 *>              almost certainly within a factor of 10 of the true error
00274 *>              so long as the next entry is greater than the threshold
00275 *>              sqrt(n) * slamch('Epsilon'). This error bound should only
00276 *>              be trusted if the previous boolean is true.
00277 *>
00278 *>     err = 3  Reciprocal condition number: Estimated componentwise
00279 *>              reciprocal condition number.  Compared with the threshold
00280 *>              sqrt(n) * slamch('Epsilon') to determine if the error
00281 *>              estimate is "guaranteed". These reciprocal condition
00282 *>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00283 *>              appropriately scaled matrix Z.
00284 *>              Let Z = S*(A*diag(x)), where x is the solution for the
00285 *>              current right-hand side and S scales each row of
00286 *>              A*diag(x) by a power of the radix so all absolute row
00287 *>              sums of Z are approximately 1.
00288 *>
00289 *>     This subroutine is only responsible for setting the second field
00290 *>     above.
00291 *>     See Lapack Working Note 165 for further details and extra
00292 *>     cautions.
00293 *> \endverbatim
00294 *>
00295 *> \param[in] RES
00296 *> \verbatim
00297 *>          RES is COMPLEX array, dimension (N)
00298 *>     Workspace to hold the intermediate residual.
00299 *> \endverbatim
00300 *>
00301 *> \param[in] AYB
00302 *> \verbatim
00303 *>          AYB is REAL array, dimension (N)
00304 *>     Workspace.
00305 *> \endverbatim
00306 *>
00307 *> \param[in] DY
00308 *> \verbatim
00309 *>          DY is COMPLEX array, dimension (N)
00310 *>     Workspace to hold the intermediate solution.
00311 *> \endverbatim
00312 *>
00313 *> \param[in] Y_TAIL
00314 *> \verbatim
00315 *>          Y_TAIL is COMPLEX array, dimension (N)
00316 *>     Workspace to hold the trailing bits of the intermediate solution.
00317 *> \endverbatim
00318 *>
00319 *> \param[in] RCOND
00320 *> \verbatim
00321 *>          RCOND is REAL
00322 *>     Reciprocal scaled condition number.  This is an estimate of the
00323 *>     reciprocal Skeel condition number of the matrix A after
00324 *>     equilibration (if done).  If this is less than the machine
00325 *>     precision (in particular, if it is zero), the matrix is singular
00326 *>     to working precision.  Note that the error may still be small even
00327 *>     if this number is very small and the matrix appears ill-
00328 *>     conditioned.
00329 *> \endverbatim
00330 *>
00331 *> \param[in] ITHRESH
00332 *> \verbatim
00333 *>          ITHRESH is INTEGER
00334 *>     The maximum number of residual computations allowed for
00335 *>     refinement. The default is 10. For 'aggressive' set to 100 to
00336 *>     permit convergence using approximate factorizations or
00337 *>     factorizations other than LU. If the factorization uses a
00338 *>     technique other than Gaussian elimination, the guarantees in
00339 *>     ERRS_N and ERRS_C may no longer be trustworthy.
00340 *> \endverbatim
00341 *>
00342 *> \param[in] RTHRESH
00343 *> \verbatim
00344 *>          RTHRESH is REAL
00345 *>     Determines when to stop refinement if the error estimate stops
00346 *>     decreasing. Refinement will stop when the next solution no longer
00347 *>     satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
00348 *>     the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
00349 *>     default value is 0.5. For 'aggressive' set to 0.9 to permit
00350 *>     convergence on extremely ill-conditioned matrices. See LAWN 165
00351 *>     for more details.
00352 *> \endverbatim
00353 *>
00354 *> \param[in] DZ_UB
00355 *> \verbatim
00356 *>          DZ_UB is REAL
00357 *>     Determines when to start considering componentwise convergence.
00358 *>     Componentwise convergence is only considered after each component
00359 *>     of the solution Y is stable, which we definte as the relative
00360 *>     change in each component being less than DZ_UB. The default value
00361 *>     is 0.25, requiring the first bit to be stable. See LAWN 165 for
00362 *>     more details.
00363 *> \endverbatim
00364 *>
00365 *> \param[in] IGNORE_CWISE
00366 *> \verbatim
00367 *>          IGNORE_CWISE is LOGICAL
00368 *>     If .TRUE. then ignore componentwise convergence. Default value
00369 *>     is .FALSE..
00370 *> \endverbatim
00371 *>
00372 *> \param[out] INFO
00373 *> \verbatim
00374 *>          INFO is INTEGER
00375 *>       = 0:  Successful exit.
00376 *>       < 0:  if INFO = -i, the ith argument to CGETRS had an illegal
00377 *>             value
00378 *> \endverbatim
00379 *
00380 *  Authors:
00381 *  ========
00382 *
00383 *> \author Univ. of Tennessee 
00384 *> \author Univ. of California Berkeley 
00385 *> \author Univ. of Colorado Denver 
00386 *> \author NAG Ltd. 
00387 *
00388 *> \date November 2011
00389 *
00390 *> \ingroup complexGEcomputational
00391 *
00392 *  =====================================================================
00393       SUBROUTINE CLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, NRHS, A,
00394      $                                LDA, AF, LDAF, IPIV, COLEQU, C, B,
00395      $                                LDB, Y, LDY, BERR_OUT, N_NORMS,
00396      $                                ERRS_N, ERRS_C, RES, AYB, DY,
00397      $                                Y_TAIL, RCOND, ITHRESH, RTHRESH,
00398      $                                DZ_UB, IGNORE_CWISE, INFO )
00399 *
00400 *  -- LAPACK computational routine (version 3.4.0) --
00401 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00402 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00403 *     November 2011
00404 *
00405 *     .. Scalar Arguments ..
00406       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
00407      $                   TRANS_TYPE, N_NORMS
00408       LOGICAL            COLEQU, IGNORE_CWISE
00409       INTEGER            ITHRESH
00410       REAL               RTHRESH, DZ_UB
00411 *     ..
00412 *     .. Array Arguments
00413       INTEGER            IPIV( * )
00414       COMPLEX            A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00415      $                   Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
00416       REAL               C( * ), AYB( * ), RCOND, BERR_OUT( * ),
00417      $                   ERRS_N( NRHS, * ), ERRS_C( NRHS, * )
00418 *     ..
00419 *
00420 *  =====================================================================
00421 *
00422 *     .. Local Scalars ..
00423       CHARACTER          TRANS
00424       INTEGER            CNT, I, J,  X_STATE, Z_STATE, Y_PREC_STATE
00425       REAL               YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
00426      $                   DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
00427      $                   DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
00428      $                   EPS, HUGEVAL, INCR_THRESH
00429       LOGICAL            INCR_PREC
00430       COMPLEX            ZDUM
00431 *     ..
00432 *     .. Parameters ..
00433       INTEGER            UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
00434      $                   NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
00435      $                   EXTRA_Y
00436       PARAMETER          ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
00437      $                   CONV_STATE = 2,
00438      $                   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 Subroutines ..
00460       EXTERNAL           CAXPY, CCOPY, CGETRS, CGEMV, BLAS_CGEMV_X,
00461      $                   BLAS_CGEMV2_X, CLA_GEAMV, CLA_WWADDW, SLAMCH,
00462      $                   CHLA_TRANSTYPE, CLA_LIN_BERR
00463       REAL               SLAMCH
00464       CHARACTER          CHLA_TRANSTYPE
00465 *     ..
00466 *     .. Intrinsic Functions ..
00467       INTRINSIC          ABS, MAX, MIN
00468 *     ..
00469 *     .. Statement Functions ..
00470       REAL               CABS1
00471 *     ..
00472 *     .. Statement Function Definitions ..
00473       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00474 *     ..
00475 *     .. Executable Statements ..
00476 *
00477       IF ( INFO.NE.0 ) RETURN
00478       TRANS = CHLA_TRANSTYPE(TRANS_TYPE)
00479       EPS = SLAMCH( 'Epsilon' )
00480       HUGEVAL = SLAMCH( 'Overflow' )
00481 *     Force HUGEVAL to Inf
00482       HUGEVAL = HUGEVAL * HUGEVAL
00483 *     Using HUGEVAL may lead to spurious underflows.
00484       INCR_THRESH = REAL( N ) * EPS
00485 *
00486       DO J = 1, NRHS
00487          Y_PREC_STATE = EXTRA_RESIDUAL
00488          IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
00489             DO I = 1, N
00490                Y_TAIL( I ) = 0.0
00491             END DO
00492          END IF
00493 
00494          DXRAT = 0.0
00495          DXRATMAX = 0.0
00496          DZRAT = 0.0
00497          DZRATMAX = 0.0
00498          FINAL_DX_X = HUGEVAL
00499          FINAL_DZ_Z = HUGEVAL
00500          PREVNORMDX = HUGEVAL
00501          PREV_DZ_Z = HUGEVAL
00502          DZ_Z = HUGEVAL
00503          DX_X = HUGEVAL
00504 
00505          X_STATE = WORKING_STATE
00506          Z_STATE = UNSTABLE_STATE
00507          INCR_PREC = .FALSE.
00508 
00509          DO CNT = 1, ITHRESH
00510 *
00511 *         Compute residual RES = B_s - op(A_s) * Y,
00512 *             op(A) = A, A**T, or A**H depending on TRANS (and type).
00513 *
00514             CALL CCOPY( N, B( 1, J ), 1, RES, 1 )
00515             IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
00516                CALL CGEMV( TRANS, N, N, (-1.0E+0,0.0E+0), A, LDA,
00517      $              Y( 1, J ), 1, (1.0E+0,0.0E+0), RES, 1)
00518             ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
00519                CALL BLAS_CGEMV_X( TRANS_TYPE, N, N, (-1.0E+0,0.0E+0), A,
00520      $              LDA, Y( 1, J ), 1, (1.0E+0,0.0E+0),
00521      $              RES, 1, PREC_TYPE )
00522             ELSE
00523                CALL BLAS_CGEMV2_X( TRANS_TYPE, N, N, (-1.0E+0,0.0E+0),
00524      $              A, LDA, Y(1, J), Y_TAIL, 1, (1.0E+0,0.0E+0), RES, 1,
00525      $              PREC_TYPE)
00526             END IF
00527 
00528 !         XXX: RES is no longer needed.
00529             CALL CCOPY( N, RES, 1, DY, 1 )
00530             CALL CGETRS( TRANS, N, 1, AF, LDAF, IPIV, DY, N, INFO )
00531 *
00532 *         Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
00533 *
00534             NORMX = 0.0E+0
00535             NORMY = 0.0E+0
00536             NORMDX = 0.0E+0
00537             DZ_Z = 0.0E+0
00538             YMIN = HUGEVAL
00539 *
00540             DO I = 1, N
00541                YK = CABS1( Y( I, J ) )
00542                DYK = CABS1( DY( I ) )
00543 
00544                IF ( YK .NE. 0.0E+0 ) THEN
00545                   DZ_Z = MAX( DZ_Z, DYK / YK )
00546                ELSE IF ( DYK .NE. 0.0 ) THEN
00547                   DZ_Z = HUGEVAL
00548                END IF
00549 
00550                YMIN = MIN( YMIN, YK )
00551 
00552                NORMY = MAX( NORMY, YK )
00553 
00554                IF ( COLEQU ) THEN
00555                   NORMX = MAX( NORMX, YK * C( I ) )
00556                   NORMDX = MAX( NORMDX, DYK * C( I ) )
00557                ELSE
00558                   NORMX = NORMY
00559                   NORMDX = MAX(NORMDX, DYK)
00560                END IF
00561             END DO
00562 
00563             IF ( NORMX .NE. 0.0 ) THEN
00564                DX_X = NORMDX / NORMX
00565             ELSE IF ( NORMDX .EQ. 0.0 ) THEN
00566                DX_X = 0.0
00567             ELSE
00568                DX_X = HUGEVAL
00569             END IF
00570 
00571             DXRAT = NORMDX / PREVNORMDX
00572             DZRAT = DZ_Z / PREV_DZ_Z
00573 *
00574 *         Check termination criteria
00575 *
00576             IF (.NOT.IGNORE_CWISE
00577      $           .AND. YMIN*RCOND .LT. INCR_THRESH*NORMY
00578      $           .AND. Y_PREC_STATE .LT. EXTRA_Y )
00579      $           INCR_PREC = .TRUE.
00580 
00581             IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
00582      $           X_STATE = WORKING_STATE
00583             IF ( X_STATE .EQ. WORKING_STATE ) THEN
00584                IF (DX_X .LE. EPS) THEN
00585                   X_STATE = CONV_STATE
00586                ELSE IF ( DXRAT .GT. RTHRESH ) THEN
00587                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00588                      INCR_PREC = .TRUE.
00589                   ELSE
00590                      X_STATE = NOPROG_STATE
00591                   END IF
00592                ELSE
00593                   IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
00594                END IF
00595                IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
00596             END IF
00597 
00598             IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
00599      $           Z_STATE = WORKING_STATE
00600             IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
00601      $           Z_STATE = WORKING_STATE
00602             IF ( Z_STATE .EQ. WORKING_STATE ) THEN
00603                IF ( DZ_Z .LE. EPS ) THEN
00604                   Z_STATE = CONV_STATE
00605                ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
00606                   Z_STATE = UNSTABLE_STATE
00607                   DZRATMAX = 0.0
00608                   FINAL_DZ_Z = HUGEVAL
00609                ELSE IF ( DZRAT .GT. RTHRESH ) THEN
00610                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00611                      INCR_PREC = .TRUE.
00612                   ELSE
00613                      Z_STATE = NOPROG_STATE
00614                   END IF
00615                ELSE
00616                   IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
00617                END IF
00618                IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00619             END IF
00620 *
00621 *           Exit if both normwise and componentwise stopped working,
00622 *           but if componentwise is unstable, let it go at least two
00623 *           iterations.
00624 *
00625             IF ( X_STATE.NE.WORKING_STATE ) THEN
00626                IF ( IGNORE_CWISE ) GOTO 666
00627                IF ( Z_STATE.EQ.NOPROG_STATE .OR. Z_STATE.EQ.CONV_STATE )
00628      $              GOTO 666
00629                IF ( Z_STATE.EQ.UNSTABLE_STATE .AND. CNT.GT.1 ) GOTO 666
00630             END IF
00631 
00632             IF ( INCR_PREC ) THEN
00633                INCR_PREC = .FALSE.
00634                Y_PREC_STATE = Y_PREC_STATE + 1
00635                DO I = 1, N
00636                   Y_TAIL( I ) = 0.0
00637                END DO
00638             END IF
00639 
00640             PREVNORMDX = NORMDX
00641             PREV_DZ_Z = DZ_Z
00642 *
00643 *           Update soluton.
00644 *
00645             IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
00646                CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 )
00647             ELSE
00648                CALL CLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY )
00649             END IF
00650 
00651          END DO
00652 *        Target of "IF (Z_STOP .AND. X_STOP)".  Sun's f77 won't EXIT.
00653  666     CONTINUE
00654 *
00655 *     Set final_* when cnt hits ithresh
00656 *
00657          IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
00658          IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00659 *
00660 *     Compute error bounds
00661 *
00662          IF (N_NORMS .GE. 1) THEN
00663             ERRS_N( J, LA_LINRX_ERR_I ) = FINAL_DX_X / (1 - DXRATMAX)
00664 
00665          END IF
00666          IF ( N_NORMS .GE. 2 ) THEN
00667             ERRS_C( J, LA_LINRX_ERR_I ) = FINAL_DZ_Z / (1 - DZRATMAX)
00668          END IF
00669 *
00670 *     Compute componentwise relative backward error from formula
00671 *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00672 *     where abs(Z) is the componentwise absolute value of the matrix
00673 *     or vector Z.
00674 *
00675 *        Compute residual RES = B_s - op(A_s) * Y,
00676 *            op(A) = A, A**T, or A**H depending on TRANS (and type).
00677 *
00678          CALL CCOPY( N, B( 1, J ), 1, RES, 1 )
00679          CALL CGEMV( TRANS, N, N, (-1.0E+0,0.0E+0), A, LDA, Y(1,J), 1,
00680      $        (1.0E+0,0.0E+0), RES, 1 )
00681 
00682          DO I = 1, N
00683             AYB( I ) = CABS1( B( I, J ) )
00684          END DO
00685 *
00686 *     Compute abs(op(A_s))*abs(Y) + abs(B_s).
00687 *
00688          CALL CLA_GEAMV ( TRANS_TYPE, N, N, 1.0E+0,
00689      $        A, LDA, Y(1, J), 1, 1.0E+0, AYB, 1 )
00690 
00691          CALL CLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) )
00692 *
00693 *     End of loop for each RHS.
00694 *
00695       END DO
00696 *
00697       RETURN
00698       END
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