*> \brief \b SPORFSX * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SPORFSX + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B, * LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, * ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, * WORK, IWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO, EQUED * INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, * $ N_ERR_BNDS * REAL RCOND * .. * .. Array Arguments .. * INTEGER IWORK( * ) * REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), * $ X( LDX, * ), WORK( * ) * REAL S( * ), PARAMS( * ), BERR( * ), * $ ERR_BNDS_NORM( NRHS, * ), * $ ERR_BNDS_COMP( NRHS, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SPORFSX improves the computed solution to a system of linear *> equations when the coefficient matrix is symmetric positive *> definite, and provides error bounds and backward error estimates *> for the solution. In addition to normwise error bound, the code *> provides maximum componentwise error bound if possible. See *> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the *> error bounds. *> *> The original system of linear equations may have been equilibrated *> before calling this routine, as described by arguments EQUED and S *> below. In this case, the solution and error bounds returned are *> for the original unequilibrated system. *> \endverbatim * * Arguments: * ========== * *> \verbatim *> Some optional parameters are bundled in the PARAMS array. These *> settings determine how refinement is performed, but often the *> defaults are acceptable. If the defaults are acceptable, users *> can pass NPARAMS = 0 which prevents the source code from accessing *> the PARAMS argument. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] EQUED *> \verbatim *> EQUED is CHARACTER*1 *> Specifies the form of equilibration that was done to A *> before calling this routine. This is needed to compute *> the solution and error bounds correctly. *> = 'N': No equilibration *> = 'Y': Both row and column equilibration, i.e., A has been *> replaced by diag(S) * A * diag(S). *> The right hand side B has been changed accordingly. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrices B and X. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> The symmetric matrix A. If UPLO = 'U', the leading N-by-N *> upper triangular part of A contains the upper triangular part *> of the matrix A, and the strictly lower triangular part of A *> is not referenced. If UPLO = 'L', the leading N-by-N lower *> triangular part of A contains the lower triangular part of *> the matrix A, and the strictly upper triangular part of A is *> not referenced. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] AF *> \verbatim *> AF is REAL array, dimension (LDAF,N) *> The triangular factor U or L from the Cholesky factorization *> A = U**T*U or A = L*L**T, as computed by SPOTRF. *> \endverbatim *> *> \param[in] LDAF *> \verbatim *> LDAF is INTEGER *> The leading dimension of the array AF. LDAF >= max(1,N). *> \endverbatim *> *> \param[in,out] S *> \verbatim *> S is REAL array, dimension (N) *> The row scale factors for A. If EQUED = 'Y', A is multiplied on *> the left and right by diag(S). S is an input argument if FACT = *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED *> = 'Y', each element of S must be positive. If S is output, each *> element of S is a power of the radix. If S is input, each element *> of S should be a power of the radix to ensure a reliable solution *> and error estimates. Scaling by powers of the radix does not cause *> rounding errors unless the result underflows or overflows. *> Rounding errors during scaling lead to refining with a matrix that *> is not equivalent to the input matrix, producing error estimates *> that may not be reliable. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is REAL array, dimension (LDB,NRHS) *> The right hand side matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is REAL array, dimension (LDX,NRHS) *> On entry, the solution matrix X, as computed by SGETRS. *> On exit, the improved solution matrix X. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(1,N). *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is REAL *> Reciprocal scaled condition number. This is an estimate of the *> reciprocal Skeel condition number of the matrix A after *> equilibration (if done). If this is less than the machine *> precision (in particular, if it is zero), the matrix is singular *> to working precision. Note that the error may still be small even *> if this number is very small and the matrix appears ill- *> conditioned. *> \endverbatim *> *> \param[out] BERR *> \verbatim *> BERR is REAL array, dimension (NRHS) *> Componentwise relative backward error. This is the *> componentwise relative backward error of each solution vector X(j) *> (i.e., the smallest relative change in any element of A or B that *> makes X(j) an exact solution). *> \endverbatim *> *> \param[in] N_ERR_BNDS *> \verbatim *> N_ERR_BNDS is INTEGER *> Number of error bounds to return for each right hand side *> and each type (normwise or componentwise). See ERR_BNDS_NORM and *> ERR_BNDS_COMP below. *> \endverbatim *> *> \param[out] ERR_BNDS_NORM *> \verbatim *> ERR_BNDS_NORM is REAL array, dimension (NRHS, N_ERR_BNDS) *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: *> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) *> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. *> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. *> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). *> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. *> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error *> estimate is "guaranteed". These reciprocal condition *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. *> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim *> *> \param[out] ERR_BNDS_COMP *> \verbatim *> ERR_BNDS_COMP is REAL array, dimension (NRHS, N_ERR_BNDS) *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: *> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) *> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three *> pieces of information returned for each right-hand side. If *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. *> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. *> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). *> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. *> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error *> estimate is "guaranteed". These reciprocal condition *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some *> appropriately scaled matrix Z. *> Let Z = S*(A*diag(x)), where x is the solution for the *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. *> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim *> *> \param[in] NPARAMS *> \verbatim *> NPARAMS is INTEGER *> Specifies the number of parameters set in PARAMS. If .LE. 0, the *> PARAMS array is never referenced and default values are used. *> \endverbatim *> *> \param[in,out] PARAMS *> \verbatim *> PARAMS is REAL array, dimension NPARAMS *> Specifies algorithm parameters. If an entry is .LT. 0.0, then *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. *> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 *> = 0.0 : No refinement is performed, and no error bounds are *> computed. *> = 1.0 : Use the double-precision refinement algorithm, *> possibly with doubled-single computations if the *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) *> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 *> Aggressive: Set to 100 to permit convergence using approximate *> factorizations or factorizations other than LU. If *> the factorization uses a technique other than *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. *> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive *> is true, 0.0 is false. *> Default: 1.0 (attempt componentwise convergence) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (4*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: Successful exit. The solution to every right-hand side is *> guaranteed. *> < 0: If INFO = -i, the i-th argument had an illegal value *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization *> has been completed, but the factor U is exactly singular, so *> the solution and error bounds could not be computed. RCOND = 0 *> is returned. *> = N+J: The solution corresponding to the Jth right-hand side is *> not guaranteed. The solutions corresponding to other right- *> hand sides K with K > J may not be guaranteed as well, but *> only the first such right-hand side is reported. If a small *> componentwise error is not requested (PARAMS(3) = 0.0) then *> the Jth right-hand side is the first with a normwise error *> bound that is not guaranteed (the smallest J such *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) *> the Jth right-hand side is the first with either a normwise or *> componentwise error bound that is not guaranteed (the smallest *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information *> about all of the right-hand sides check ERR_BNDS_NORM or *> ERR_BNDS_COMP. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date April 2012 * *> \ingroup realPOcomputational * * ===================================================================== SUBROUTINE SPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B, $ LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, $ WORK, IWORK, INFO ) * * -- LAPACK computational routine (version 3.4.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * April 2012 * * .. Scalar Arguments .. CHARACTER UPLO, EQUED INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, $ N_ERR_BNDS REAL RCOND * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), $ X( LDX, * ), WORK( * ) REAL S( * ), PARAMS( * ), BERR( * ), $ ERR_BNDS_NORM( NRHS, * ), $ ERR_BNDS_COMP( NRHS, * ) * .. * * ================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) REAL ITREF_DEFAULT, ITHRESH_DEFAULT, $ COMPONENTWISE_DEFAULT REAL RTHRESH_DEFAULT, DZTHRESH_DEFAULT PARAMETER ( ITREF_DEFAULT = 1.0 ) PARAMETER ( ITHRESH_DEFAULT = 10.0 ) PARAMETER ( COMPONENTWISE_DEFAULT = 1.0 ) PARAMETER ( RTHRESH_DEFAULT = 0.5 ) PARAMETER ( DZTHRESH_DEFAULT = 0.25 ) INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I, $ LA_LINRX_CWISE_I PARAMETER ( LA_LINRX_ITREF_I = 1, $ LA_LINRX_ITHRESH_I = 2 ) PARAMETER ( LA_LINRX_CWISE_I = 3 ) INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I, $ LA_LINRX_RCOND_I PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 ) PARAMETER ( LA_LINRX_RCOND_I = 3 ) * .. * .. Local Scalars .. CHARACTER(1) NORM LOGICAL RCEQU INTEGER J, PREC_TYPE, REF_TYPE INTEGER N_NORMS REAL ANORM, RCOND_TMP REAL ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG LOGICAL IGNORE_CWISE INTEGER ITHRESH REAL RTHRESH, UNSTABLE_THRESH * .. * .. External Subroutines .. EXTERNAL XERBLA, SPOCON, SLA_PORFSX_EXTENDED * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. External Functions .. EXTERNAL LSAME, ILAPREC EXTERNAL SLAMCH, SLANSY, SLA_PORCOND REAL SLAMCH, SLANSY, SLA_PORCOND LOGICAL LSAME INTEGER ILAPREC * .. * .. Executable Statements .. * * Check the input parameters. * INFO = 0 REF_TYPE = INT( ITREF_DEFAULT ) IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0 ) THEN PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT ELSE REF_TYPE = PARAMS( LA_LINRX_ITREF_I ) END IF END IF * * Set default parameters. * ILLRCOND_THRESH = REAL( N ) * SLAMCH( 'Epsilon' ) ITHRESH = INT( ITHRESH_DEFAULT ) RTHRESH = RTHRESH_DEFAULT UNSTABLE_THRESH = DZTHRESH_DEFAULT IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0 * IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0 ) THEN PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH ELSE ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) ) END IF END IF IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0 ) THEN IF ( IGNORE_CWISE ) THEN PARAMS( LA_LINRX_CWISE_I ) = 0.0 ELSE PARAMS( LA_LINRX_CWISE_I ) = 1.0 END IF ELSE IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0 END IF END IF IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN N_NORMS = 0 ELSE IF ( IGNORE_CWISE ) THEN N_NORMS = 1 ELSE N_NORMS = 2 END IF * RCEQU = LSAME( EQUED, 'Y' ) * * Test input parameters. * IF (.NOT.LSAME(UPLO, 'U') .AND. .NOT.LSAME(UPLO, 'L')) THEN INFO = -1 ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( NRHS.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN INFO = -8 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -11 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN INFO = -13 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SPORFSX', -INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN RCOND = 1.0 DO J = 1, NRHS BERR( J ) = 0.0 IF ( N_ERR_BNDS .GE. 1 ) THEN ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0 END IF IF ( N_ERR_BNDS .GE. 2 ) THEN ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0 END IF IF ( N_ERR_BNDS .GE. 3 ) THEN ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0 END IF END DO RETURN END IF * * Default to failure. * RCOND = 0.0 DO J = 1, NRHS BERR( J ) = 1.0 IF ( N_ERR_BNDS .GE. 1 ) THEN ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0 END IF IF ( N_ERR_BNDS .GE. 2 ) THEN ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0 ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0 END IF IF ( N_ERR_BNDS .GE. 3 ) THEN ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0 ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0 END IF END DO * * Compute the norm of A and the reciprocal of the condition * number of A. * NORM = 'I' ANORM = SLANSY( NORM, UPLO, N, A, LDA, WORK ) CALL SPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK, $ IWORK, INFO ) * * Perform refinement on each right-hand side * IF ( REF_TYPE .NE. 0 ) THEN PREC_TYPE = ILAPREC( 'D' ) CALL SLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, $ NRHS, A, LDA, AF, LDAF, RCEQU, S, B, $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP, $ WORK( N+1 ), WORK( 1 ), WORK( 2*N+1 ), WORK( 1 ), RCOND, $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE, $ INFO ) END IF ERR_LBND = MAX( 10.0, SQRT( REAL( N ) ) ) * SLAMCH( 'Epsilon' ) IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN * * Compute scaled normwise condition number cond(A*C). * IF ( RCEQU ) THEN RCOND_TMP = SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, $ -1, S, INFO, WORK, IWORK ) ELSE RCOND_TMP = SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, $ 0, S, INFO, WORK, IWORK ) END IF DO J = 1, NRHS * * Cap the error at 1.0. * IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0 ) $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0 * * Threshold the error (see LAWN). * IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0 ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0 IF ( INFO .LE. N ) INFO = N + J ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND ) $ THEN ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0 END IF * * Save the condition number. * IF (N_ERR_BNDS .GE. LA_LINRX_RCOND_I) THEN ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP END IF END DO END IF IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN * * Compute componentwise condition number cond(A*diag(Y(:,J))) for * each right-hand side using the current solution as an estimate of * the true solution. If the componentwise error estimate is too * large, then the solution is a lousy estimate of truth and the * estimated RCOND may be too optimistic. To avoid misleading users, * the inverse condition number is set to 0.0 when the estimated * cwise error is at least CWISE_WRONG. * CWISE_WRONG = SQRT( SLAMCH( 'Epsilon' ) ) DO J = 1, NRHS IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG ) $ THEN RCOND_TMP = SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, 1, $ X( 1, J ), INFO, WORK, IWORK ) ELSE RCOND_TMP = 0.0 END IF * * Cap the error at 1.0. * IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0 ) $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0 * * Threshold the error (see LAWN). * IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0 ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0 IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0 $ .AND. INFO.LT.N + J ) INFO = N + J ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) $ .LT. ERR_LBND ) THEN ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0 END IF * * Save the condition number. * IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP END IF END DO END IF * RETURN * * End of SPORFSX * END