LAPACK 3.3.0

dla_porfsx_extended.f

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00001       SUBROUTINE DLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
00002      $                                AF, LDAF, COLEQU, C, B, LDB, Y,
00003      $                                LDY, BERR_OUT, N_NORMS,
00004      $                                ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
00005      $                                AYB, DY, Y_TAIL, RCOND, ITHRESH,
00006      $                                RTHRESH, DZ_UB, IGNORE_CWISE,
00007      $                                INFO )
00008 *
00009 *     -- LAPACK routine (version 3.2.2)                                 --
00010 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
00011 *     -- Jason Riedy of Univ. of California Berkeley.                 --
00012 *     -- June 2010                                                    --
00013 *
00014 *     -- LAPACK is a software package provided by Univ. of Tennessee, --
00015 *     -- Univ. of California Berkeley and NAG Ltd.                    --
00016 *
00017       IMPLICIT NONE
00018 *     ..
00019 *     .. Scalar Arguments ..
00020       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
00021      $                   N_NORMS, ITHRESH
00022       CHARACTER          UPLO
00023       LOGICAL            COLEQU, IGNORE_CWISE
00024       DOUBLE PRECISION   RTHRESH, DZ_UB
00025 *     ..
00026 *     .. Array Arguments ..
00027       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00028      $                   Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
00029       DOUBLE PRECISION   C( * ), AYB(*), RCOND, BERR_OUT( * ),
00030      $                   ERR_BNDS_NORM( NRHS, * ),
00031      $                   ERR_BNDS_COMP( NRHS, * )
00032 *     ..
00033 *
00034 *  Purpose
00035 *  =======
00036 *
00037 *  DLA_PORFSX_EXTENDED improves the computed solution to a system of
00038 *  linear equations by performing extra-precise iterative refinement
00039 *  and provides error bounds and backward error estimates for the solution.
00040 *  This subroutine is called by DPORFSX to perform iterative refinement.
00041 *  In addition to normwise error bound, the code provides maximum
00042 *  componentwise error bound if possible. See comments for ERR_BNDS_NORM
00043 *  and ERR_BNDS_COMP for details of the error bounds. Note that this
00044 *  subroutine is only resonsible for setting the second fields of
00045 *  ERR_BNDS_NORM and ERR_BNDS_COMP.
00046 *
00047 *  Arguments
00048 *  =========
00049 *
00050 *     PREC_TYPE      (input) INTEGER
00051 *     Specifies the intermediate precision to be used in refinement.
00052 *     The value is defined by ILAPREC(P) where P is a CHARACTER and
00053 *     P    = 'S':  Single
00054 *          = 'D':  Double
00055 *          = 'I':  Indigenous
00056 *          = 'X', 'E':  Extra
00057 *
00058 *     UPLO    (input) CHARACTER*1
00059 *       = 'U':  Upper triangle of A is stored;
00060 *       = 'L':  Lower triangle of A is stored.
00061 *
00062 *     N              (input) INTEGER
00063 *     The number of linear equations, i.e., the order of the
00064 *     matrix A.  N >= 0.
00065 *
00066 *     NRHS           (input) INTEGER
00067 *     The number of right-hand-sides, i.e., the number of columns of the
00068 *     matrix B.
00069 *
00070 *     A              (input) DOUBLE PRECISION array, dimension (LDA,N)
00071 *     On entry, the N-by-N matrix A.
00072 *
00073 *     LDA            (input) INTEGER
00074 *     The leading dimension of the array A.  LDA >= max(1,N).
00075 *
00076 *     AF             (input) DOUBLE PRECISION array, dimension (LDAF,N)
00077 *     The triangular factor U or L from the Cholesky factorization
00078 *     A = U**T*U or A = L*L**T, as computed by DPOTRF.
00079 *
00080 *     LDAF           (input) INTEGER
00081 *     The leading dimension of the array AF.  LDAF >= max(1,N).
00082 *
00083 *     COLEQU         (input) LOGICAL
00084 *     If .TRUE. then column equilibration was done to A before calling
00085 *     this routine. This is needed to compute the solution and error
00086 *     bounds correctly.
00087 *
00088 *     C              (input) DOUBLE PRECISION array, dimension (N)
00089 *     The column scale factors for A. If COLEQU = .FALSE., C
00090 *     is not accessed. If C is input, each element of C should be a power
00091 *     of the radix to ensure a reliable solution and error estimates.
00092 *     Scaling by powers of the radix does not cause rounding errors unless
00093 *     the result underflows or overflows. Rounding errors during scaling
00094 *     lead to refining with a matrix that is not equivalent to the
00095 *     input matrix, producing error estimates that may not be
00096 *     reliable.
00097 *
00098 *     B              (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
00099 *     The right-hand-side matrix B.
00100 *
00101 *     LDB            (input) INTEGER
00102 *     The leading dimension of the array B.  LDB >= max(1,N).
00103 *
00104 *     Y              (input/output) DOUBLE PRECISION array, dimension
00105 *                    (LDY,NRHS)
00106 *     On entry, the solution matrix X, as computed by DPOTRS.
00107 *     On exit, the improved solution matrix Y.
00108 *
00109 *     LDY            (input) INTEGER
00110 *     The leading dimension of the array Y.  LDY >= max(1,N).
00111 *
00112 *     BERR_OUT       (output) DOUBLE PRECISION array, dimension (NRHS)
00113 *     On exit, BERR_OUT(j) contains the componentwise relative backward
00114 *     error for right-hand-side j from the formula
00115 *         max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00116 *     where abs(Z) is the componentwise absolute value of the matrix
00117 *     or vector Z. This is computed by DLA_LIN_BERR.
00118 *
00119 *     N_NORMS        (input) INTEGER
00120 *     Determines which error bounds to return (see ERR_BNDS_NORM
00121 *     and ERR_BNDS_COMP).
00122 *     If N_NORMS >= 1 return normwise error bounds.
00123 *     If N_NORMS >= 2 return componentwise error bounds.
00124 *
00125 *     ERR_BNDS_NORM  (input/output) DOUBLE PRECISION array, dimension
00126 *                    (NRHS, N_ERR_BNDS)
00127 *     For each right-hand side, this array contains information about
00128 *     various error bounds and condition numbers corresponding to the
00129 *     normwise relative error, which is defined as follows:
00130 *
00131 *     Normwise relative error in the ith solution vector:
00132 *             max_j (abs(XTRUE(j,i) - X(j,i)))
00133 *            ------------------------------
00134 *                  max_j abs(X(j,i))
00135 *
00136 *     The array is indexed by the type of error information as described
00137 *     below. There currently are up to three pieces of information
00138 *     returned.
00139 *
00140 *     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
00141 *     right-hand side.
00142 *
00143 *     The second index in ERR_BNDS_NORM(:,err) contains the following
00144 *     three fields:
00145 *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00146 *              reciprocal condition number is less than the threshold
00147 *              sqrt(n) * slamch('Epsilon').
00148 *
00149 *     err = 2 "Guaranteed" error bound: The estimated forward error,
00150 *              almost certainly within a factor of 10 of the true error
00151 *              so long as the next entry is greater than the threshold
00152 *              sqrt(n) * slamch('Epsilon'). This error bound should only
00153 *              be trusted if the previous boolean is true.
00154 *
00155 *     err = 3  Reciprocal condition number: Estimated normwise
00156 *              reciprocal condition number.  Compared with the threshold
00157 *              sqrt(n) * slamch('Epsilon') to determine if the error
00158 *              estimate is "guaranteed". These reciprocal condition
00159 *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00160 *              appropriately scaled matrix Z.
00161 *              Let Z = S*A, where S scales each row by a power of the
00162 *              radix so all absolute row sums of Z are approximately 1.
00163 *
00164 *     This subroutine is only responsible for setting the second field
00165 *     above.
00166 *     See Lapack Working Note 165 for further details and extra
00167 *     cautions.
00168 *
00169 *     ERR_BNDS_COMP  (input/output) DOUBLE PRECISION array, dimension
00170 *                    (NRHS, N_ERR_BNDS)
00171 *     For each right-hand side, this array contains information about
00172 *     various error bounds and condition numbers corresponding to the
00173 *     componentwise relative error, which is defined as follows:
00174 *
00175 *     Componentwise relative error in the ith solution vector:
00176 *                    abs(XTRUE(j,i) - X(j,i))
00177 *             max_j ----------------------
00178 *                         abs(X(j,i))
00179 *
00180 *     The array is indexed by the right-hand side i (on which the
00181 *     componentwise relative error depends), and the type of error
00182 *     information as described below. There currently are up to three
00183 *     pieces of information returned for each right-hand side. If
00184 *     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
00185 *     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
00186 *     the first (:,N_ERR_BNDS) entries are returned.
00187 *
00188 *     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
00189 *     right-hand side.
00190 *
00191 *     The second index in ERR_BNDS_COMP(:,err) contains the following
00192 *     three fields:
00193 *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00194 *              reciprocal condition number is less than the threshold
00195 *              sqrt(n) * slamch('Epsilon').
00196 *
00197 *     err = 2 "Guaranteed" error bound: The estimated forward error,
00198 *              almost certainly within a factor of 10 of the true error
00199 *              so long as the next entry is greater than the threshold
00200 *              sqrt(n) * slamch('Epsilon'). This error bound should only
00201 *              be trusted if the previous boolean is true.
00202 *
00203 *     err = 3  Reciprocal condition number: Estimated componentwise
00204 *              reciprocal condition number.  Compared with the threshold
00205 *              sqrt(n) * slamch('Epsilon') to determine if the error
00206 *              estimate is "guaranteed". These reciprocal condition
00207 *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00208 *              appropriately scaled matrix Z.
00209 *              Let Z = S*(A*diag(x)), where x is the solution for the
00210 *              current right-hand side and S scales each row of
00211 *              A*diag(x) by a power of the radix so all absolute row
00212 *              sums of Z are approximately 1.
00213 *
00214 *     This subroutine is only responsible for setting the second field
00215 *     above.
00216 *     See Lapack Working Note 165 for further details and extra
00217 *     cautions.
00218 *
00219 *     RES            (input) DOUBLE PRECISION array, dimension (N)
00220 *     Workspace to hold the intermediate residual.
00221 *
00222 *     AYB            (input) DOUBLE PRECISION array, dimension (N)
00223 *     Workspace. This can be the same workspace passed for Y_TAIL.
00224 *
00225 *     DY             (input) DOUBLE PRECISION array, dimension (N)
00226 *     Workspace to hold the intermediate solution.
00227 *
00228 *     Y_TAIL         (input) DOUBLE PRECISION array, dimension (N)
00229 *     Workspace to hold the trailing bits of the intermediate solution.
00230 *
00231 *     RCOND          (input) DOUBLE PRECISION
00232 *     Reciprocal scaled condition number.  This is an estimate of the
00233 *     reciprocal Skeel condition number of the matrix A after
00234 *     equilibration (if done).  If this is less than the machine
00235 *     precision (in particular, if it is zero), the matrix is singular
00236 *     to working precision.  Note that the error may still be small even
00237 *     if this number is very small and the matrix appears ill-
00238 *     conditioned.
00239 *
00240 *     ITHRESH        (input) INTEGER
00241 *     The maximum number of residual computations allowed for
00242 *     refinement. The default is 10. For 'aggressive' set to 100 to
00243 *     permit convergence using approximate factorizations or
00244 *     factorizations other than LU. If the factorization uses a
00245 *     technique other than Gaussian elimination, the guarantees in
00246 *     ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
00247 *
00248 *     RTHRESH        (input) DOUBLE PRECISION
00249 *     Determines when to stop refinement if the error estimate stops
00250 *     decreasing. Refinement will stop when the next solution no longer
00251 *     satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
00252 *     the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
00253 *     default value is 0.5. For 'aggressive' set to 0.9 to permit
00254 *     convergence on extremely ill-conditioned matrices. See LAWN 165
00255 *     for more details.
00256 *
00257 *     DZ_UB          (input) DOUBLE PRECISION
00258 *     Determines when to start considering componentwise convergence.
00259 *     Componentwise convergence is only considered after each component
00260 *     of the solution Y is stable, which we definte as the relative
00261 *     change in each component being less than DZ_UB. The default value
00262 *     is 0.25, requiring the first bit to be stable. See LAWN 165 for
00263 *     more details.
00264 *
00265 *     IGNORE_CWISE   (input) LOGICAL
00266 *     If .TRUE. then ignore componentwise convergence. Default value
00267 *     is .FALSE..
00268 *
00269 *     INFO           (output) INTEGER
00270 *       = 0:  Successful exit.
00271 *       < 0:  if INFO = -i, the ith argument to DPOTRS had an illegal
00272 *             value
00273 *
00274 *  =====================================================================
00275 *
00276 *     .. Local Scalars ..
00277       INTEGER            UPLO2, CNT, I, J, X_STATE, Z_STATE
00278       DOUBLE PRECISION   YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
00279      $                   DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
00280      $                   DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
00281      $                   EPS, HUGEVAL, INCR_THRESH
00282       LOGICAL            INCR_PREC
00283 *     ..
00284 *     .. Parameters ..
00285       INTEGER           UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
00286      $                  NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
00287      $                  EXTRA_RESIDUAL, EXTRA_Y
00288       PARAMETER         ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
00289      $                  CONV_STATE = 2, NOPROG_STATE = 3 )
00290       PARAMETER         ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
00291      $                  EXTRA_Y = 2 )
00292       INTEGER            FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
00293       INTEGER            RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
00294       INTEGER            CMP_ERR_I, PIV_GROWTH_I
00295       PARAMETER          ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
00296      $                   BERR_I = 3 )
00297       PARAMETER          ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
00298       PARAMETER          ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
00299      $                   PIV_GROWTH_I = 9 )
00300       INTEGER            LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
00301      $                   LA_LINRX_CWISE_I
00302       PARAMETER          ( LA_LINRX_ITREF_I = 1,
00303      $                   LA_LINRX_ITHRESH_I = 2 )
00304       PARAMETER          ( LA_LINRX_CWISE_I = 3 )
00305       INTEGER            LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
00306      $                   LA_LINRX_RCOND_I
00307       PARAMETER          ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
00308       PARAMETER          ( LA_LINRX_RCOND_I = 3 )
00309 *     ..
00310 *     .. External Functions ..
00311       LOGICAL            LSAME
00312       EXTERNAL           ILAUPLO
00313       INTEGER            ILAUPLO
00314 *     ..
00315 *     .. External Subroutines ..
00316       EXTERNAL          DAXPY, DCOPY, DPOTRS, DSYMV, BLAS_DSYMV_X,
00317      $                  BLAS_DSYMV2_X, DLA_SYAMV, DLA_WWADDW,
00318      $                  DLA_LIN_BERR
00319       DOUBLE PRECISION   DLAMCH
00320 *     ..
00321 *     .. Intrinsic Functions ..
00322       INTRINSIC         ABS, MAX, MIN
00323 *     ..
00324 *     .. Executable Statements ..
00325 *
00326       IF (INFO.NE.0) RETURN
00327       EPS = DLAMCH( 'Epsilon' )
00328       HUGEVAL = DLAMCH( 'Overflow' )
00329 *     Force HUGEVAL to Inf
00330       HUGEVAL = HUGEVAL * HUGEVAL
00331 *     Using HUGEVAL may lead to spurious underflows.
00332       INCR_THRESH = DBLE( N ) * EPS
00333 
00334       IF ( LSAME ( UPLO, 'L' ) ) THEN
00335          UPLO2 = ILAUPLO( 'L' )
00336       ELSE
00337          UPLO2 = ILAUPLO( 'U' )
00338       ENDIF
00339 
00340       DO J = 1, NRHS
00341          Y_PREC_STATE = EXTRA_RESIDUAL
00342          IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
00343             DO I = 1, N
00344                Y_TAIL( I ) = 0.0D+0
00345             END DO
00346          END IF
00347 
00348          DXRAT = 0.0D+0
00349          DXRATMAX = 0.0D+0
00350          DZRAT = 0.0D+0
00351          DZRATMAX = 0.0D+0
00352          FINAL_DX_X = HUGEVAL
00353          FINAL_DZ_Z = HUGEVAL
00354          PREVNORMDX = HUGEVAL
00355          PREV_DZ_Z = HUGEVAL
00356          DZ_Z = HUGEVAL
00357          DX_X = HUGEVAL
00358 
00359          X_STATE = WORKING_STATE
00360          Z_STATE = UNSTABLE_STATE
00361          INCR_PREC = .FALSE.
00362 
00363          DO CNT = 1, ITHRESH
00364 *
00365 *         Compute residual RES = B_s - op(A_s) * Y,
00366 *             op(A) = A, A**T, or A**H depending on TRANS (and type).
00367 *
00368             CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
00369             IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
00370                CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1,
00371      $              1.0D+0, RES, 1 )
00372             ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN
00373                CALL BLAS_DSYMV_X( UPLO2, N, -1.0D+0, A, LDA,
00374      $              Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE )
00375             ELSE
00376                CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,
00377      $              Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)
00378             END IF
00379 
00380 !         XXX: RES is no longer needed.
00381             CALL DCOPY( N, RES, 1, DY, 1 )
00382             CALL DPOTRS( UPLO, N, 1, AF, LDAF, DY, N, INFO )
00383 *
00384 *         Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
00385 *
00386             NORMX = 0.0D+0
00387             NORMY = 0.0D+0
00388             NORMDX = 0.0D+0
00389             DZ_Z = 0.0D+0
00390             YMIN = HUGEVAL
00391 
00392             DO I = 1, N
00393                YK = ABS( Y( I, J ) )
00394                DYK = ABS( DY( I ) )
00395 
00396                IF ( YK .NE. 0.0D+0 ) THEN
00397                   DZ_Z = MAX( DZ_Z, DYK / YK )
00398                ELSE IF ( DYK .NE. 0.0D+0 ) THEN
00399                   DZ_Z = HUGEVAL
00400                END IF
00401 
00402                YMIN = MIN( YMIN, YK )
00403 
00404                NORMY = MAX( NORMY, YK )
00405 
00406                IF ( COLEQU ) THEN
00407                   NORMX = MAX( NORMX, YK * C( I ) )
00408                   NORMDX = MAX( NORMDX, DYK * C( I ) )
00409                ELSE
00410                   NORMX = NORMY
00411                   NORMDX = MAX( NORMDX, DYK )
00412                END IF
00413             END DO
00414 
00415             IF ( NORMX .NE. 0.0D+0 ) THEN
00416                DX_X = NORMDX / NORMX
00417             ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
00418                DX_X = 0.0D+0
00419             ELSE
00420                DX_X = HUGEVAL
00421             END IF
00422 
00423             DXRAT = NORMDX / PREVNORMDX
00424             DZRAT = DZ_Z / PREV_DZ_Z
00425 *
00426 *         Check termination criteria.
00427 *
00428             IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
00429      $           .AND. Y_PREC_STATE .LT. EXTRA_Y )
00430      $           INCR_PREC = .TRUE.
00431 
00432             IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
00433      $           X_STATE = WORKING_STATE
00434             IF ( X_STATE .EQ. WORKING_STATE ) THEN
00435                IF ( DX_X .LE. EPS ) THEN
00436                   X_STATE = CONV_STATE
00437                ELSE IF ( DXRAT .GT. RTHRESH ) THEN
00438                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00439                      INCR_PREC = .TRUE.
00440                   ELSE
00441                      X_STATE = NOPROG_STATE
00442                   END IF
00443                ELSE
00444                   IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
00445                END IF
00446                IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
00447             END IF
00448 
00449             IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
00450      $           Z_STATE = WORKING_STATE
00451             IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
00452      $           Z_STATE = WORKING_STATE
00453             IF ( Z_STATE .EQ. WORKING_STATE ) THEN
00454                IF ( DZ_Z .LE. EPS ) THEN
00455                   Z_STATE = CONV_STATE
00456                ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
00457                   Z_STATE = UNSTABLE_STATE
00458                   DZRATMAX = 0.0D+0
00459                   FINAL_DZ_Z = HUGEVAL
00460                ELSE IF ( DZRAT .GT. RTHRESH ) THEN
00461                   IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
00462                      INCR_PREC = .TRUE.
00463                   ELSE
00464                      Z_STATE = NOPROG_STATE
00465                   END IF
00466                ELSE
00467                   IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
00468                END IF
00469                IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00470             END IF
00471 
00472             IF ( X_STATE.NE.WORKING_STATE.AND.
00473      $           ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
00474      $           GOTO 666
00475 
00476             IF ( INCR_PREC ) THEN
00477                INCR_PREC = .FALSE.
00478                Y_PREC_STATE = Y_PREC_STATE + 1
00479                DO I = 1, N
00480                   Y_TAIL( I ) = 0.0D+0
00481                END DO
00482             END IF
00483 
00484             PREVNORMDX = NORMDX
00485             PREV_DZ_Z = DZ_Z
00486 *
00487 *           Update soluton.
00488 *
00489             IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
00490                CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
00491             ELSE
00492                CALL DLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY )
00493             END IF
00494 
00495          END DO
00496 *        Target of "IF (Z_STOP .AND. X_STOP)".  Sun's f77 won't EXIT.
00497  666     CONTINUE
00498 *
00499 *     Set final_* when cnt hits ithresh.
00500 *
00501          IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
00502          IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
00503 *
00504 *     Compute error bounds.
00505 *
00506          IF ( N_NORMS .GE. 1 ) THEN
00507             ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
00508      $           FINAL_DX_X / (1 - DXRATMAX)
00509          END IF
00510          IF ( N_NORMS .GE. 2 ) THEN
00511             ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
00512      $           FINAL_DZ_Z / (1 - DZRATMAX)
00513          END IF
00514 *
00515 *     Compute componentwise relative backward error from formula
00516 *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00517 *     where abs(Z) is the componentwise absolute value of the matrix
00518 *     or vector Z.
00519 *
00520 *        Compute residual RES = B_s - op(A_s) * Y,
00521 *            op(A) = A, A**T, or A**H depending on TRANS (and type).
00522 *
00523          CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
00524          CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES,
00525      $     1 )
00526 
00527          DO I = 1, N
00528             AYB( I ) = ABS( B( I, J ) )
00529          END DO
00530 *
00531 *     Compute abs(op(A_s))*abs(Y) + abs(B_s).
00532 *
00533          CALL DLA_SYAMV( UPLO2, N, 1.0D+0,
00534      $        A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
00535 
00536          CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
00537 *
00538 *     End of loop for each RHS.
00539 *
00540       END DO
00541 *
00542       RETURN
00543       END
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