dgetc2.c

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/* dgetc2.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__1 = 1;
static doublereal c_b10 = -1.;

/* Subroutine */ int dgetc2_(integer *n, doublereal *a, integer *lda, integer 
        *ipiv, integer *jpiv, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    doublereal d__1;

    /* Local variables */
    integer i__, j, ip, jp;
    doublereal eps;
    integer ipv, jpv;
    extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *);
    doublereal smin, xmax;
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
            doublereal *, integer *), dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *);
    doublereal bignum, smlnum;


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  DGETC2 computes an LU factorization with complete pivoting of the */
/*  n-by-n matrix A. The factorization has the form A = P * L * U * Q, */
/*  where P and Q are permutation matrices, L is lower triangular with */
/*  unit diagonal elements and U is upper triangular. */

/*  This is the Level 2 BLAS algorithm. */

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

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

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N) */
/*          On entry, the n-by-n matrix A to be factored. */
/*          On exit, the factors L and U from the factorization */
/*          A = P*L*U*Q; the unit diagonal elements of L are not stored. */
/*          If U(k, k) appears to be less than SMIN, U(k, k) is given the */
/*          value of SMIN, i.e., giving a nonsingular perturbed system. */

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

/*  IPIV    (output) INTEGER array, dimension(N). */
/*          The pivot indices; for 1 <= i <= N, row i of the */
/*          matrix has been interchanged with row IPIV(i). */

/*  JPIV    (output) INTEGER array, dimension(N). */
/*          The pivot indices; for 1 <= j <= N, column j of the */
/*          matrix has been interchanged with column JPIV(j). */

/*  INFO    (output) INTEGER */
/*           = 0: successful exit */
/*           > 0: if INFO = k, U(k, k) is likely to produce owerflow if */
/*                we try to solve for x in Ax = b. So U is perturbed to */
/*                avoid the overflow. */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/*     Umea University, S-901 87 Umea, Sweden. */

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

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

/*     Set constants to control overflow */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --ipiv;
    --jpiv;

    /* Function Body */
    *info = 0;
    eps = dlamch_("P");
    smlnum = dlamch_("S") / eps;
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);

/*     Factorize A using complete pivoting. */
/*     Set pivots less than SMIN to SMIN. */

    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {

/*        Find max element in matrix A */

        xmax = 0.;
        i__2 = *n;
        for (ip = i__; ip <= i__2; ++ip) {
            i__3 = *n;
            for (jp = i__; jp <= i__3; ++jp) {
                if ((d__1 = a[ip + jp * a_dim1], abs(d__1)) >= xmax) {
                    xmax = (d__1 = a[ip + jp * a_dim1], abs(d__1));
                    ipv = ip;
                    jpv = jp;
                }
/* L10: */
            }
/* L20: */
        }
        if (i__ == 1) {
/* Computing MAX */
            d__1 = eps * xmax;
            smin = max(d__1,smlnum);
        }

/*        Swap rows */

        if (ipv != i__) {
            dswap_(n, &a[ipv + a_dim1], lda, &a[i__ + a_dim1], lda);
        }
        ipiv[i__] = ipv;

/*        Swap columns */

        if (jpv != i__) {
            dswap_(n, &a[jpv * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
                    c__1);
        }
        jpiv[i__] = jpv;

/*        Check for singularity */

        if ((d__1 = a[i__ + i__ * a_dim1], abs(d__1)) < smin) {
            *info = i__;
            a[i__ + i__ * a_dim1] = smin;
        }
        i__2 = *n;
        for (j = i__ + 1; j <= i__2; ++j) {
            a[j + i__ * a_dim1] /= a[i__ + i__ * a_dim1];
/* L30: */
        }
        i__2 = *n - i__;
        i__3 = *n - i__;
        dger_(&i__2, &i__3, &c_b10, &a[i__ + 1 + i__ * a_dim1], &c__1, &a[i__ 
                + (i__ + 1) * a_dim1], lda, &a[i__ + 1 + (i__ + 1) * a_dim1], 
                lda);
/* L40: */
    }

    if ((d__1 = a[*n + *n * a_dim1], abs(d__1)) < smin) {
        *info = *n;
        a[*n + *n * a_dim1] = smin;
    }

    return 0;

/*     End of DGETC2 */

} /* dgetc2_ */