LAPACK 3.3.1
Linear Algebra PACKage

zporfsx.f

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00001       SUBROUTINE ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
00002      $                    LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
00003      $                    ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
00004      $                    WORK, RWORK, INFO )
00005 *
00006 *     -- LAPACK routine (version 3.2.2)                                 --
00007 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
00008 *     -- Jason Riedy of Univ. of California Berkeley.                 --
00009 *     -- June 2010                                                    --
00010 *
00011 *     -- LAPACK is a software package provided by Univ. of Tennessee, --
00012 *     -- Univ. of California Berkeley and NAG Ltd.                    --
00013 *
00014       IMPLICIT NONE
00015 *     ..
00016 *     .. Scalar Arguments ..
00017       CHARACTER          UPLO, EQUED
00018       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
00019      $                   N_ERR_BNDS
00020       DOUBLE PRECISION   RCOND
00021 *     ..
00022 *     .. Array Arguments ..
00023       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00024      $                   X( LDX, * ), WORK( * )
00025       DOUBLE PRECISION   RWORK( * ), S( * ), PARAMS(*), BERR( * ),
00026      $                   ERR_BNDS_NORM( NRHS, * ),
00027      $                   ERR_BNDS_COMP( NRHS, * )
00028 *     ..
00029 *
00030 *     Purpose
00031 *     =======
00032 *
00033 *     ZPORFSX improves the computed solution to a system of linear
00034 *     equations when the coefficient matrix is symmetric positive
00035 *     definite, and provides error bounds and backward error estimates
00036 *     for the solution.  In addition to normwise error bound, the code
00037 *     provides maximum componentwise error bound if possible.  See
00038 *     comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
00039 *     error bounds.
00040 *
00041 *     The original system of linear equations may have been equilibrated
00042 *     before calling this routine, as described by arguments EQUED and S
00043 *     below. In this case, the solution and error bounds returned are
00044 *     for the original unequilibrated system.
00045 *
00046 *     Arguments
00047 *     =========
00048 *
00049 *     Some optional parameters are bundled in the PARAMS array.  These
00050 *     settings determine how refinement is performed, but often the
00051 *     defaults are acceptable.  If the defaults are acceptable, users
00052 *     can pass NPARAMS = 0 which prevents the source code from accessing
00053 *     the PARAMS argument.
00054 *
00055 *     UPLO    (input) CHARACTER*1
00056 *       = 'U':  Upper triangle of A is stored;
00057 *       = 'L':  Lower triangle of A is stored.
00058 *
00059 *     EQUED   (input) CHARACTER*1
00060 *     Specifies the form of equilibration that was done to A
00061 *     before calling this routine. This is needed to compute
00062 *     the solution and error bounds correctly.
00063 *       = 'N':  No equilibration
00064 *       = 'Y':  Both row and column equilibration, i.e., A has been
00065 *               replaced by diag(S) * A * diag(S).
00066 *               The right hand side B has been changed accordingly.
00067 *
00068 *     N       (input) INTEGER
00069 *     The order of the matrix A.  N >= 0.
00070 *
00071 *     NRHS    (input) INTEGER
00072 *     The number of right hand sides, i.e., the number of columns
00073 *     of the matrices B and X.  NRHS >= 0.
00074 *
00075 *     A       (input) COMPLEX*16 array, dimension (LDA,N)
00076 *     The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
00077 *     upper triangular part of A contains the upper triangular part
00078 *     of the matrix A, and the strictly lower triangular part of A
00079 *     is not referenced.  If UPLO = 'L', the leading N-by-N lower
00080 *     triangular part of A contains the lower triangular part of
00081 *     the matrix A, and the strictly upper triangular part of A is
00082 *     not referenced.
00083 *
00084 *     LDA     (input) INTEGER
00085 *     The leading dimension of the array A.  LDA >= max(1,N).
00086 *
00087 *     AF      (input) COMPLEX*16 array, dimension (LDAF,N)
00088 *     The triangular factor U or L from the Cholesky factorization
00089 *     A = U**T*U or A = L*L**T, as computed by DPOTRF.
00090 *
00091 *     LDAF    (input) INTEGER
00092 *     The leading dimension of the array AF.  LDAF >= max(1,N).
00093 *
00094 *     S       (input or output) DOUBLE PRECISION array, dimension (N)
00095 *     The row scale factors for A.  If EQUED = 'Y', A is multiplied on
00096 *     the left and right by diag(S).  S is an input argument if FACT =
00097 *     'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
00098 *     = 'Y', each element of S must be positive.  If S is output, each
00099 *     element of S is a power of the radix. If S is input, each element
00100 *     of S should be a power of the radix to ensure a reliable solution
00101 *     and error estimates. Scaling by powers of the radix does not cause
00102 *     rounding errors unless the result underflows or overflows.
00103 *     Rounding errors during scaling lead to refining with a matrix that
00104 *     is not equivalent to the input matrix, producing error estimates
00105 *     that may not be reliable.
00106 *
00107 *     B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
00108 *     The right hand side matrix B.
00109 *
00110 *     LDB     (input) INTEGER
00111 *     The leading dimension of the array B.  LDB >= max(1,N).
00112 *
00113 *     X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
00114 *     On entry, the solution matrix X, as computed by DGETRS.
00115 *     On exit, the improved solution matrix X.
00116 *
00117 *     LDX     (input) INTEGER
00118 *     The leading dimension of the array X.  LDX >= max(1,N).
00119 *
00120 *     RCOND   (output) DOUBLE PRECISION
00121 *     Reciprocal scaled condition number.  This is an estimate of the
00122 *     reciprocal Skeel condition number of the matrix A after
00123 *     equilibration (if done).  If this is less than the machine
00124 *     precision (in particular, if it is zero), the matrix is singular
00125 *     to working precision.  Note that the error may still be small even
00126 *     if this number is very small and the matrix appears ill-
00127 *     conditioned.
00128 *
00129 *     BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
00130 *     Componentwise relative backward error.  This is the
00131 *     componentwise relative backward error of each solution vector X(j)
00132 *     (i.e., the smallest relative change in any element of A or B that
00133 *     makes X(j) an exact solution).
00134 *
00135 *     N_ERR_BNDS (input) INTEGER
00136 *     Number of error bounds to return for each right hand side
00137 *     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
00138 *     ERR_BNDS_COMP below.
00139 *
00140 *     ERR_BNDS_NORM  (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
00141 *     For each right-hand side, this array contains information about
00142 *     various error bounds and condition numbers corresponding to the
00143 *     normwise relative error, which is defined as follows:
00144 *
00145 *     Normwise relative error in the ith solution vector:
00146 *             max_j (abs(XTRUE(j,i) - X(j,i)))
00147 *            ------------------------------
00148 *                  max_j abs(X(j,i))
00149 *
00150 *     The array is indexed by the type of error information as described
00151 *     below. There currently are up to three pieces of information
00152 *     returned.
00153 *
00154 *     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
00155 *     right-hand side.
00156 *
00157 *     The second index in ERR_BNDS_NORM(:,err) contains the following
00158 *     three fields:
00159 *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00160 *              reciprocal condition number is less than the threshold
00161 *              sqrt(n) * dlamch('Epsilon').
00162 *
00163 *     err = 2 "Guaranteed" error bound: The estimated forward error,
00164 *              almost certainly within a factor of 10 of the true error
00165 *              so long as the next entry is greater than the threshold
00166 *              sqrt(n) * dlamch('Epsilon'). This error bound should only
00167 *              be trusted if the previous boolean is true.
00168 *
00169 *     err = 3  Reciprocal condition number: Estimated normwise
00170 *              reciprocal condition number.  Compared with the threshold
00171 *              sqrt(n) * dlamch('Epsilon') to determine if the error
00172 *              estimate is "guaranteed". These reciprocal condition
00173 *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00174 *              appropriately scaled matrix Z.
00175 *              Let Z = S*A, where S scales each row by a power of the
00176 *              radix so all absolute row sums of Z are approximately 1.
00177 *
00178 *     See Lapack Working Note 165 for further details and extra
00179 *     cautions.
00180 *
00181 *     ERR_BNDS_COMP  (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
00182 *     For each right-hand side, this array contains information about
00183 *     various error bounds and condition numbers corresponding to the
00184 *     componentwise relative error, which is defined as follows:
00185 *
00186 *     Componentwise relative error in the ith solution vector:
00187 *                    abs(XTRUE(j,i) - X(j,i))
00188 *             max_j ----------------------
00189 *                         abs(X(j,i))
00190 *
00191 *     The array is indexed by the right-hand side i (on which the
00192 *     componentwise relative error depends), and the type of error
00193 *     information as described below. There currently are up to three
00194 *     pieces of information returned for each right-hand side. If
00195 *     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
00196 *     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
00197 *     the first (:,N_ERR_BNDS) entries are returned.
00198 *
00199 *     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
00200 *     right-hand side.
00201 *
00202 *     The second index in ERR_BNDS_COMP(:,err) contains the following
00203 *     three fields:
00204 *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00205 *              reciprocal condition number is less than the threshold
00206 *              sqrt(n) * dlamch('Epsilon').
00207 *
00208 *     err = 2 "Guaranteed" error bound: The estimated forward error,
00209 *              almost certainly within a factor of 10 of the true error
00210 *              so long as the next entry is greater than the threshold
00211 *              sqrt(n) * dlamch('Epsilon'). This error bound should only
00212 *              be trusted if the previous boolean is true.
00213 *
00214 *     err = 3  Reciprocal condition number: Estimated componentwise
00215 *              reciprocal condition number.  Compared with the threshold
00216 *              sqrt(n) * dlamch('Epsilon') to determine if the error
00217 *              estimate is "guaranteed". These reciprocal condition
00218 *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00219 *              appropriately scaled matrix Z.
00220 *              Let Z = S*(A*diag(x)), where x is the solution for the
00221 *              current right-hand side and S scales each row of
00222 *              A*diag(x) by a power of the radix so all absolute row
00223 *              sums of Z are approximately 1.
00224 *
00225 *     See Lapack Working Note 165 for further details and extra
00226 *     cautions.
00227 *
00228 *     NPARAMS (input) INTEGER
00229 *     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
00230 *     PARAMS array is never referenced and default values are used.
00231 *
00232 *     PARAMS  (input / output) DOUBLE PRECISION array, dimension NPARAMS
00233 *     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
00234 *     that entry will be filled with default value used for that
00235 *     parameter.  Only positions up to NPARAMS are accessed; defaults
00236 *     are used for higher-numbered parameters.
00237 *
00238 *       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
00239 *            refinement or not.
00240 *         Default: 1.0D+0
00241 *            = 0.0 : No refinement is performed, and no error bounds are
00242 *                    computed.
00243 *            = 1.0 : Use the double-precision refinement algorithm,
00244 *                    possibly with doubled-single computations if the
00245 *                    compilation environment does not support DOUBLE
00246 *                    PRECISION.
00247 *              (other values are reserved for future use)
00248 *
00249 *       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
00250 *            computations allowed for refinement.
00251 *         Default: 10
00252 *         Aggressive: Set to 100 to permit convergence using approximate
00253 *                     factorizations or factorizations other than LU. If
00254 *                     the factorization uses a technique other than
00255 *                     Gaussian elimination, the guarantees in
00256 *                     err_bnds_norm and err_bnds_comp may no longer be
00257 *                     trustworthy.
00258 *
00259 *       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
00260 *            will attempt to find a solution with small componentwise
00261 *            relative error in the double-precision algorithm.  Positive
00262 *            is true, 0.0 is false.
00263 *         Default: 1.0 (attempt componentwise convergence)
00264 *
00265 *     WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00266 *
00267 *     RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)
00268 *
00269 *     INFO    (output) INTEGER
00270 *       = 0:  Successful exit. The solution to every right-hand side is
00271 *         guaranteed.
00272 *       < 0:  If INFO = -i, the i-th argument had an illegal value
00273 *       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
00274 *         has been completed, but the factor U is exactly singular, so
00275 *         the solution and error bounds could not be computed. RCOND = 0
00276 *         is returned.
00277 *       = N+J: The solution corresponding to the Jth right-hand side is
00278 *         not guaranteed. The solutions corresponding to other right-
00279 *         hand sides K with K > J may not be guaranteed as well, but
00280 *         only the first such right-hand side is reported. If a small
00281 *         componentwise error is not requested (PARAMS(3) = 0.0) then
00282 *         the Jth right-hand side is the first with a normwise error
00283 *         bound that is not guaranteed (the smallest J such
00284 *         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
00285 *         the Jth right-hand side is the first with either a normwise or
00286 *         componentwise error bound that is not guaranteed (the smallest
00287 *         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
00288 *         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
00289 *         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
00290 *         about all of the right-hand sides check ERR_BNDS_NORM or
00291 *         ERR_BNDS_COMP.
00292 *
00293 *     ==================================================================
00294 *
00295 *     .. Parameters ..
00296       DOUBLE PRECISION   ZERO, ONE
00297       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00298       DOUBLE PRECISION   ITREF_DEFAULT, ITHRESH_DEFAULT
00299       DOUBLE PRECISION   COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
00300       DOUBLE PRECISION   DZTHRESH_DEFAULT
00301       PARAMETER          ( ITREF_DEFAULT = 1.0D+0 )
00302       PARAMETER          ( ITHRESH_DEFAULT = 10.0D+0 )
00303       PARAMETER          ( COMPONENTWISE_DEFAULT = 1.0D+0 )
00304       PARAMETER          ( RTHRESH_DEFAULT = 0.5D+0 )
00305       PARAMETER          ( DZTHRESH_DEFAULT = 0.25D+0 )
00306       INTEGER            LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
00307      $                   LA_LINRX_CWISE_I
00308       PARAMETER          ( LA_LINRX_ITREF_I = 1,
00309      $                   LA_LINRX_ITHRESH_I = 2 )
00310       PARAMETER          ( LA_LINRX_CWISE_I = 3 )
00311       INTEGER            LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
00312      $                   LA_LINRX_RCOND_I
00313       PARAMETER          ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
00314       PARAMETER          ( LA_LINRX_RCOND_I = 3 )
00315 *     ..
00316 *     .. Local Scalars ..
00317       CHARACTER(1)       NORM
00318       LOGICAL            RCEQU
00319       INTEGER            J, PREC_TYPE, REF_TYPE
00320       INTEGER            N_NORMS
00321       DOUBLE PRECISION   ANORM, RCOND_TMP
00322       DOUBLE PRECISION   ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
00323       LOGICAL            IGNORE_CWISE
00324       INTEGER            ITHRESH
00325       DOUBLE PRECISION   RTHRESH, UNSTABLE_THRESH
00326 *     ..
00327 *     .. External Subroutines ..
00328       EXTERNAL           XERBLA, ZPOCON, ZLA_PORFSX_EXTENDED
00329 *     ..
00330 *     .. Intrinsic Functions ..
00331       INTRINSIC          MAX, SQRT, TRANSFER
00332 *     ..
00333 *     .. External Functions ..
00334       EXTERNAL           LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
00335       EXTERNAL           DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
00336       DOUBLE PRECISION   DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
00337       LOGICAL            LSAME
00338       INTEGER            BLAS_FPINFO_X
00339       INTEGER            ILATRANS, ILAPREC
00340 *     ..
00341 *     .. Executable Statements ..
00342 *
00343 *     Check the input parameters.
00344 *
00345       INFO = 0
00346       REF_TYPE = INT( ITREF_DEFAULT )
00347       IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
00348          IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
00349             PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
00350          ELSE
00351             REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
00352          END IF
00353       END IF
00354 *
00355 *     Set default parameters.
00356 *
00357       ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
00358       ITHRESH = INT( ITHRESH_DEFAULT )
00359       RTHRESH = RTHRESH_DEFAULT
00360       UNSTABLE_THRESH = DZTHRESH_DEFAULT
00361       IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
00362 *
00363       IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
00364          IF ( PARAMS(LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
00365             PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
00366          ELSE
00367             ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
00368          END IF
00369       END IF
00370       IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
00371          IF ( PARAMS(LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
00372             IF ( IGNORE_CWISE ) THEN
00373                PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
00374             ELSE
00375                PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
00376             END IF
00377          ELSE
00378             IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
00379          END IF
00380       END IF
00381       IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
00382          N_NORMS = 0
00383       ELSE IF ( IGNORE_CWISE ) THEN
00384          N_NORMS = 1
00385       ELSE
00386          N_NORMS = 2
00387       END IF
00388 *
00389       RCEQU = LSAME( EQUED, 'Y' )
00390 *
00391 *     Test input parameters.
00392 *
00393       IF (.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00394         INFO = -1
00395       ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
00396         INFO = -2
00397       ELSE IF( N.LT.0 ) THEN
00398         INFO = -3
00399       ELSE IF( NRHS.LT.0 ) THEN
00400         INFO = -4
00401       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00402         INFO = -6
00403       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00404         INFO = -8
00405       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00406         INFO = -11
00407       ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
00408         INFO = -13
00409       END IF
00410       IF( INFO.NE.0 ) THEN
00411         CALL XERBLA( 'ZPORFSX', -INFO )
00412         RETURN
00413       END IF
00414 *
00415 *     Quick return if possible.
00416 *
00417       IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
00418          RCOND = 1.0D+0
00419          DO J = 1, NRHS
00420             BERR( J ) = 0.0D+0
00421             IF ( N_ERR_BNDS .GE. 1 ) THEN
00422                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
00423                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
00424             END IF
00425             IF ( N_ERR_BNDS .GE. 2 ) THEN
00426                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0
00427                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
00428             END IF
00429             IF ( N_ERR_BNDS .GE. 3 ) THEN
00430                ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0
00431                ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
00432             END IF
00433          END DO
00434          RETURN
00435       END IF
00436 *
00437 *     Default to failure.
00438 *
00439       RCOND = 0.0D+0
00440       DO J = 1, NRHS
00441          BERR( J ) = 1.0D+0
00442          IF ( N_ERR_BNDS .GE. 1 ) THEN
00443             ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
00444             ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
00445          END IF
00446          IF ( N_ERR_BNDS .GE. 2 ) THEN
00447             ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
00448             ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
00449          END IF
00450          IF ( N_ERR_BNDS .GE. 3 ) THEN
00451             ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
00452             ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0
00453          END IF
00454       END DO
00455 *
00456 *     Compute the norm of A and the reciprocal of the condition
00457 *     number of A.
00458 *
00459       NORM = 'I'
00460       ANORM = ZLANHE( NORM, UPLO, N, A, LDA, RWORK )
00461       CALL ZPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK, RWORK,
00462      $     INFO )
00463 *
00464 *     Perform refinement on each right-hand side
00465 *
00466       IF ( REF_TYPE .NE. 0 ) THEN
00467 
00468          PREC_TYPE = ILAPREC( 'E' )
00469 
00470          CALL ZLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N,
00471      $        NRHS, A, LDA, AF, LDAF, RCEQU, S, B,
00472      $        LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
00473      $        WORK, RWORK, WORK(N+1),
00474      $        TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), RCOND,
00475      $        ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
00476      $        INFO )
00477       END IF
00478 
00479       ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' )
00480       IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
00481 *
00482 *     Compute scaled normwise condition number cond(A*C).
00483 *
00484          IF ( RCEQU ) THEN
00485             RCOND_TMP = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF,
00486      $           S, .TRUE., INFO, WORK, RWORK )
00487          ELSE
00488             RCOND_TMP = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF,
00489      $           S, .FALSE., INFO, WORK, RWORK )
00490          END IF
00491          DO J = 1, NRHS
00492 *
00493 *     Cap the error at 1.0.
00494 *
00495             IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
00496      $           .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
00497      $           ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
00498 *
00499 *     Threshold the error (see LAWN).
00500 *
00501             IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
00502                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
00503                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0
00504                IF ( INFO .LE. N ) INFO = N + J
00505             ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
00506      $     THEN
00507                ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
00508                ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
00509             END IF
00510 *
00511 *     Save the condition number.
00512 *
00513             IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
00514                ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
00515             END IF
00516 
00517          END DO
00518       END IF
00519 
00520       IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2) THEN
00521 *
00522 *     Compute componentwise condition number cond(A*diag(Y(:,J))) for
00523 *     each right-hand side using the current solution as an estimate of
00524 *     the true solution.  If the componentwise error estimate is too
00525 *     large, then the solution is a lousy estimate of truth and the
00526 *     estimated RCOND may be too optimistic.  To avoid misleading users,
00527 *     the inverse condition number is set to 0.0 when the estimated
00528 *     cwise error is at least CWISE_WRONG.
00529 *
00530          CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
00531          DO J = 1, NRHS
00532             IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
00533      $     THEN
00534                RCOND_TMP = ZLA_PORCOND_X( UPLO, N, A, LDA, AF, LDAF,
00535      $         X(1,J), INFO, WORK, RWORK )
00536             ELSE
00537                RCOND_TMP = 0.0D+0
00538             END IF
00539 *
00540 *     Cap the error at 1.0.
00541 *
00542             IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
00543      $           .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
00544      $           ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
00545 *
00546 *     Threshold the error (see LAWN).
00547 *
00548             IF (RCOND_TMP .LT. ILLRCOND_THRESH) THEN
00549                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
00550                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
00551                IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
00552      $              .AND. INFO.LT.N + J ) INFO = N + J
00553             ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
00554      $              .LT. ERR_LBND ) THEN
00555                ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
00556                ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
00557             END IF
00558 *
00559 *     Save the condition number.
00560 *
00561             IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
00562                ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
00563             END IF
00564 
00565          END DO
00566       END IF
00567 *
00568       RETURN
00569 *
00570 *     End of ZPORFSX
00571 *
00572       END
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