sgttrf.c

Go to the documentation of this file.

/* sgttrf.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"

/* Subroutine */ int sgttrf_(integer *n, real *dl, real *d__, real *du, real *
        du2, integer *ipiv, integer *info)
{
    /* System generated locals */
    integer i__1;
    real r__1, r__2;

    /* Local variables */
    integer i__;
    real fact, temp;
    extern /* Subroutine */ int xerbla_(char *, integer *);


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

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

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

/*  SGTTRF computes an LU factorization of a real tridiagonal matrix A */
/*  using elimination with partial pivoting and row interchanges. */

/*  The factorization has the form */
/*     A = L * U */
/*  where L is a product of permutation and unit lower bidiagonal */
/*  matrices and U is upper triangular with nonzeros in only the main */
/*  diagonal and first two superdiagonals. */

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

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

/*  DL      (input/output) REAL array, dimension (N-1) */
/*          On entry, DL must contain the (n-1) sub-diagonal elements of */
/*          A. */

/*          On exit, DL is overwritten by the (n-1) multipliers that */
/*          define the matrix L from the LU factorization of A. */

/*  D       (input/output) REAL array, dimension (N) */
/*          On entry, D must contain the diagonal elements of A. */

/*          On exit, D is overwritten by the n diagonal elements of the */
/*          upper triangular matrix U from the LU factorization of A. */

/*  DU      (input/output) REAL array, dimension (N-1) */
/*          On entry, DU must contain the (n-1) super-diagonal elements */
/*          of A. */

/*          On exit, DU is overwritten by the (n-1) elements of the first */
/*          super-diagonal of U. */

/*  DU2     (output) REAL array, dimension (N-2) */
/*          On exit, DU2 is overwritten by the (n-2) elements of the */
/*          second super-diagonal of U. */

/*  IPIV    (output) INTEGER array, dimension (N) */
/*          The pivot indices; for 1 <= i <= n, row i of the matrix was */
/*          interchanged with row IPIV(i).  IPIV(i) will always be either */
/*          i or i+1; IPIV(i) = i indicates a row interchange was not */
/*          required. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -k, the k-th argument had an illegal value */
/*          > 0:  if INFO = k, U(k,k) is exactly zero. The factorization */
/*                has been completed, but the factor U is exactly */
/*                singular, and division by zero will occur if it is used */
/*                to solve a system of equations. */

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

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

    /* Parameter adjustments */
    --ipiv;
    --du2;
    --du;
    --d__;
    --dl;

    /* Function Body */
    *info = 0;
    if (*n < 0) {
        *info = -1;
        i__1 = -(*info);
        xerbla_("SGTTRF", &i__1);
        return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }

/*     Initialize IPIV(i) = i and DU2(I) = 0 */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        ipiv[i__] = i__;
/* L10: */
    }
    i__1 = *n - 2;
    for (i__ = 1; i__ <= i__1; ++i__) {
        du2[i__] = 0.f;
/* L20: */
    }

    i__1 = *n - 2;
    for (i__ = 1; i__ <= i__1; ++i__) {
        if ((r__1 = d__[i__], dabs(r__1)) >= (r__2 = dl[i__], dabs(r__2))) {

/*           No row interchange required, eliminate DL(I) */

            if (d__[i__] != 0.f) {
                fact = dl[i__] / d__[i__];
                dl[i__] = fact;
                d__[i__ + 1] -= fact * du[i__];
            }
        } else {

/*           Interchange rows I and I+1, eliminate DL(I) */

            fact = d__[i__] / dl[i__];
            d__[i__] = dl[i__];
            dl[i__] = fact;
            temp = du[i__];
            du[i__] = d__[i__ + 1];
            d__[i__ + 1] = temp - fact * d__[i__ + 1];
            du2[i__] = du[i__ + 1];
            du[i__ + 1] = -fact * du[i__ + 1];
            ipiv[i__] = i__ + 1;
        }
/* L30: */
    }
    if (*n > 1) {
        i__ = *n - 1;
        if ((r__1 = d__[i__], dabs(r__1)) >= (r__2 = dl[i__], dabs(r__2))) {
            if (d__[i__] != 0.f) {
                fact = dl[i__] / d__[i__];
                dl[i__] = fact;
                d__[i__ + 1] -= fact * du[i__];
            }
        } else {
            fact = d__[i__] / dl[i__];
            d__[i__] = dl[i__];
            dl[i__] = fact;
            temp = du[i__];
            du[i__] = d__[i__ + 1];
            d__[i__ + 1] = temp - fact * d__[i__ + 1];
            ipiv[i__] = i__ + 1;
        }
    }

/*     Check for a zero on the diagonal of U. */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        if (d__[i__] == 0.f) {
            *info = i__;
            goto L50;
        }
/* L40: */
    }
L50:

    return 0;

/*     End of SGTTRF */

} /* sgttrf_ */