path: root/contrib/libs/clapack/sporfsx.c

/* sporfsx.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
	on Microsoft Windows system, link with libf2c.lib;
	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
	or, if you install libf2c.a in a standard place, with -lf2c -lm
	-- in that order, at the end of the command line, as in
		cc *.o -lf2c -lm
	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

		http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c_n1 = -1;
static integer c__0 = 0;
static integer c__1 = 1;

/* Subroutine */ int sporfsx_(char *uplo, char *equed, integer *n, integer *
	nrhs, real *a, integer *lda, real *af, integer *ldaf, real *s, real *
	b, integer *ldb, real *x, integer *ldx, real *rcond, real *berr, 
	integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, 
	integer *nparams, real *params, real *work, integer *iwork, integer *
	info)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 
	    x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 
	    err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
    real r__1, r__2;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    real illrcond_thresh__, unstable_thresh__, err_lbnd__;
    integer ref_type__, j;
    real rcond_tmp__;
    integer prec_type__;
    extern doublereal sla_porcond__(char *, integer *, real *, integer *, 
	    real *, integer *, integer *, real *, integer *, real *, integer *
	    , ftnlen);
    real cwise_wrong__;
    extern /* Subroutine */ int sla_porfsx_extended__(integer *, char *, 
	    integer *, integer *, real *, integer *, real *, integer *, 
	    logical *, real *, real *, integer *, real *, integer *, real *, 
	    integer *, real *, real *, real *, real *, real *, real *, real *,
	     integer *, real *, real *, logical *, integer *, ftnlen);
    char norm[1];
    logical ignore_cwise__;
    extern logical lsame_(char *, char *);
    real anorm;
    logical rcequ;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *), spocon_(
	    char *, integer *, real *, integer *, real *, real *, real *, 
	    integer *, integer *);
    extern doublereal slansy_(char *, char *, integer *, real *, integer *, 
	    real *);
    extern integer ilaprec_(char *);
    integer ithresh, n_norms__;
    real rthresh;


/*  -- LAPACK routine (version 3.2.1)                                  -- */
/*  -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and    -- */
/*  -- Jason Riedy of Univ. of California Berkeley.                    -- */
/*  -- April 2009                                                      -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     .. */
/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*     Purpose */
/*     ======= */

/*     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. */

/*     Arguments */
/*     ========= */

/*     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. */

/*     UPLO    (input) CHARACTER*1 */
/*       = 'U':  Upper triangle of A is stored; */
/*       = 'L':  Lower triangle of A is stored. */

/*     EQUED   (input) 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. */

/*     N       (input) INTEGER */
/*     The order of the matrix A.  N >= 0. */

/*     NRHS    (input) INTEGER */
/*     The number of right hand sides, i.e., the number of columns */
/*     of the matrices B and X.  NRHS >= 0. */

/*     A       (input) 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. */

/*     LDA     (input) INTEGER */
/*     The leading dimension of the array A.  LDA >= max(1,N). */

/*     AF      (input) 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. */

/*     LDAF    (input) INTEGER */
/*     The leading dimension of the array AF.  LDAF >= max(1,N). */

/*     S       (input or output) 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. */

/*     B       (input) REAL array, dimension (LDB,NRHS) */
/*     The right hand side matrix B. */

/*     LDB     (input) INTEGER */
/*     The leading dimension of the array B.  LDB >= max(1,N). */

/*     X       (input/output) REAL array, dimension (LDX,NRHS) */
/*     On entry, the solution matrix X, as computed by SGETRS. */
/*     On exit, the improved solution matrix X. */

/*     LDX     (input) INTEGER */
/*     The leading dimension of the array X.  LDX >= max(1,N). */

/*     RCOND   (output) 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. */

/*     BERR    (output) 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). */

/*     N_ERR_BNDS (input) 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. */

/*     ERR_BNDS_NORM  (output) 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. */

/*     ERR_BNDS_COMP  (output) 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. */

/*     NPARAMS (input) INTEGER */
/*     Specifies the number of parameters set in PARAMS.  If .LE. 0, the */
/*     PARAMS array is never referenced and default values are used. */

/*     PARAMS  (input / output) 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) */

/*     WORK    (workspace) REAL array, dimension (4*N) */

/*     IWORK   (workspace) INTEGER array, dimension (N) */

/*     INFO    (output) 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. */

/*     ================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Check the input parameters. */

    /* Parameter adjustments */
    err_bnds_comp_dim1 = *nrhs;
    err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
    err_bnds_comp__ -= err_bnds_comp_offset;
    err_bnds_norm_dim1 = *nrhs;
    err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
    err_bnds_norm__ -= err_bnds_norm_offset;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    af_dim1 = *ldaf;
    af_offset = 1 + af_dim1;
    af -= af_offset;
    --s;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    --berr;
    --params;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    ref_type__ = 1;
    if (*nparams >= 1) {
	if (params[1] < 0.f) {
	    params[1] = 1.f;
	} else {
	    ref_type__ = params[1];
	}
    }

/*     Set default parameters. */

    illrcond_thresh__ = (real) (*n) * slamch_("Epsilon");
    ithresh = 10;
    rthresh = .5f;
    unstable_thresh__ = .25f;
    ignore_cwise__ = FALSE_;

    if (*nparams >= 2) {
	if (params[2] < 0.f) {
	    params[2] = (real) ithresh;
	} else {
	    ithresh = (integer) params[2];
	}
    }
    if (*nparams >= 3) {
	if (params[3] < 0.f) {
	    if (ignore_cwise__) {
		params[3] = 0.f;
	    } else {
		params[3] = 1.f;
	    }
	} else {
	    ignore_cwise__ = params[3] == 0.f;
	}
    }
    if (ref_type__ == 0 || *n_err_bnds__ == 0) {
	n_norms__ = 0;
    } else if (ignore_cwise__) {
	n_norms__ = 1;
    } else {
	n_norms__ = 2;
    }

    rcequ = lsame_(equed, "Y");

/*     Test input parameters. */

    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (! rcequ && ! lsame_(equed, "N")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldaf < max(1,*n)) {
	*info = -8;
    } else if (*ldb < max(1,*n)) {
	*info = -11;
    } else if (*ldx < max(1,*n)) {
	*info = -13;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SPORFSX", &i__1);
	return 0;
    }

/*     Quick return if possible. */

    if (*n == 0 || *nrhs == 0) {
	*rcond = 1.f;
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    berr[j] = 0.f;
	    if (*n_err_bnds__ >= 1) {
		err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
		err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
	    } else if (*n_err_bnds__ >= 2) {
		err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f;
		err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f;
	    } else if (*n_err_bnds__ >= 3) {
		err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f;
		err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f;
	    }
	}
	return 0;
    }

/*     Default to failure. */

    *rcond = 0.f;
    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
	berr[j] = 1.f;
	if (*n_err_bnds__ >= 1) {
	    err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
	    err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
	} else if (*n_err_bnds__ >= 2) {
	    err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
	    err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
	} else if (*n_err_bnds__ >= 3) {
	    err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f;
	    err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f;
	}
    }

/*     Compute the norm of A and the reciprocal of the condition */
/*     number of A. */

    *(unsigned char *)norm = 'I';
    anorm = slansy_(norm, uplo, n, &a[a_offset], lda, &work[1]);
    spocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1], 
	     info);

/*     Perform refinement on each right-hand side */

    if (ref_type__ != 0) {
	prec_type__ = ilaprec_("D");
	sla_porfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, 
		&af[af_offset], ldaf, &rcequ, &s[1], &b[b_offset], ldb, &x[
		x_offset], ldx, &berr[1], &n_norms__, &err_bnds_norm__[
		err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset],
		 &work[*n + 1], &work[1], &work[(*n << 1) + 1], &work[1], 
		rcond, &ithresh, &rthresh, &unstable_thresh__, &
		ignore_cwise__, info, (ftnlen)1);
    }
/* Computing MAX */
    r__1 = 10.f, r__2 = sqrt((real) (*n));
    err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon");
    if (*n_err_bnds__ >= 1 && n_norms__ >= 1) {

/*     Compute scaled normwise condition number cond(A*C). */

	if (rcequ) {
	    rcond_tmp__ = sla_porcond__(uplo, n, &a[a_offset], lda, &af[
		    af_offset], ldaf, &c_n1, &s[1], info, &work[1], &iwork[1],
		     (ftnlen)1);
	} else {
	    rcond_tmp__ = sla_porcond__(uplo, n, &a[a_offset], lda, &af[
		    af_offset], ldaf, &c__0, &s[1], info, &work[1], &iwork[1],
		     (ftnlen)1);
	}
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {

/*     Cap the error at 1.0. */

	    if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 
		    << 1)] > 1.f) {
		err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
	    }

/*     Threshold the error (see LAWN). */

	    if (rcond_tmp__ < illrcond_thresh__) {
		err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
		err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f;
		if (*info <= *n) {
		    *info = *n + j;
		}
	    } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < 
		    err_lbnd__) {
		err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__;
		err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
	    }

/*     Save the condition number. */

	    if (*n_err_bnds__ >= 3) {
		err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__;
	    }
	}
    }
    if (*n_err_bnds__ >= 1 && n_norms__ >= 2) {

/*     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"));
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 
		    cwise_wrong__) {
		rcond_tmp__ = sla_porcond__(uplo, n, &a[a_offset], lda, &af[
			af_offset], ldaf, &c__1, &x[j * x_dim1 + 1], info, &
			work[1], &iwork[1], (ftnlen)1);
	    } else {
		rcond_tmp__ = 0.f;
	    }

/*     Cap the error at 1.0. */

	    if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 
		    << 1)] > 1.f) {
		err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
	    }

/*     Threshold the error (see LAWN). */

	    if (rcond_tmp__ < illrcond_thresh__) {
		err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
		err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f;
		if (params[3] == 1.f && *info < *n + j) {
		    *info = *n + j;
		}
	    } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < 
		    err_lbnd__) {
		err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__;
		err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
	    }

/*     Save the condition number. */

	    if (*n_err_bnds__ >= 3) {
		err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__;
	    }
	}
    }

    return 0;

/*     End of SPORFSX */

} /* sporfsx_ */