sgtsv.c

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/* sgtsv.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 sgtsv_(integer *n, integer *nrhs, real *dl, real *d__, 
        real *du, real *b, integer *ldb, integer *info)
{
    /* System generated locals */
    integer b_dim1, b_offset, i__1, i__2;
    real r__1, r__2;

    /* Local variables */
    integer i__, j;
    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 */
/*  ======= */

/*  SGTSV  solves the equation */

/*     A*X = B, */

/*  where A is an n by n tridiagonal matrix, by Gaussian elimination with */
/*  partial pivoting. */

/*  Note that the equation  A'*X = B  may be solved by interchanging the */
/*  order of the arguments DU and DL. */

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

/*  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 matrix B.  NRHS >= 0. */

/*  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-2) elements of the */
/*          second super-diagonal of the upper triangular matrix U from */
/*          the LU factorization of A, in DL(1), ..., DL(n-2). */

/*  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 U. */

/*  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. */

/*  B       (input/output) REAL array, dimension (LDB,NRHS) */
/*          On entry, the N by NRHS matrix of right hand side matrix B. */
/*          On exit, if INFO = 0, the N by NRHS solution matrix X. */

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

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -i, the i-th argument had an illegal value */
/*          > 0: if INFO = i, U(i,i) is exactly zero, and the solution */
/*               has not been computed.  The factorization has not been */
/*               completed unless i = N. */

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

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

    /* Parameter adjustments */
    --dl;
    --d__;
    --du;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    *info = 0;
    if (*n < 0) {
        *info = -1;
    } else if (*nrhs < 0) {
        *info = -2;
    } else if (*ldb < max(1,*n)) {
        *info = -7;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("SGTSV ", &i__1);
        return 0;
    }

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

    if (*nrhs == 1) {
        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 */

                if (d__[i__] != 0.f) {
                    fact = dl[i__] / d__[i__];
                    d__[i__ + 1] -= fact * du[i__];
                    b[i__ + 1 + b_dim1] -= fact * b[i__ + b_dim1];
                } else {
                    *info = i__;
                    return 0;
                }
                dl[i__] = 0.f;
            } else {

/*              Interchange rows I and I+1 */

                fact = d__[i__] / dl[i__];
                d__[i__] = dl[i__];
                temp = d__[i__ + 1];
                d__[i__ + 1] = du[i__] - fact * temp;
                dl[i__] = du[i__ + 1];
                du[i__ + 1] = -fact * dl[i__];
                du[i__] = temp;
                temp = b[i__ + b_dim1];
                b[i__ + b_dim1] = b[i__ + 1 + b_dim1];
                b[i__ + 1 + b_dim1] = temp - fact * b[i__ + 1 + b_dim1];
            }
/* L10: */
        }
        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__];
                    d__[i__ + 1] -= fact * du[i__];
                    b[i__ + 1 + b_dim1] -= fact * b[i__ + b_dim1];
                } else {
                    *info = i__;
                    return 0;
                }
            } else {
                fact = d__[i__] / dl[i__];
                d__[i__] = dl[i__];
                temp = d__[i__ + 1];
                d__[i__ + 1] = du[i__] - fact * temp;
                du[i__] = temp;
                temp = b[i__ + b_dim1];
                b[i__ + b_dim1] = b[i__ + 1 + b_dim1];
                b[i__ + 1 + b_dim1] = temp - fact * b[i__ + 1 + b_dim1];
            }
        }
        if (d__[*n] == 0.f) {
            *info = *n;
            return 0;
        }
    } else {
        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 */

                if (d__[i__] != 0.f) {
                    fact = dl[i__] / d__[i__];
                    d__[i__ + 1] -= fact * du[i__];
                    i__2 = *nrhs;
                    for (j = 1; j <= i__2; ++j) {
                        b[i__ + 1 + j * b_dim1] -= fact * b[i__ + j * b_dim1];
/* L20: */
                    }
                } else {
                    *info = i__;
                    return 0;
                }
                dl[i__] = 0.f;
            } else {

/*              Interchange rows I and I+1 */

                fact = d__[i__] / dl[i__];
                d__[i__] = dl[i__];
                temp = d__[i__ + 1];
                d__[i__ + 1] = du[i__] - fact * temp;
                dl[i__] = du[i__ + 1];
                du[i__ + 1] = -fact * dl[i__];
                du[i__] = temp;
                i__2 = *nrhs;
                for (j = 1; j <= i__2; ++j) {
                    temp = b[i__ + j * b_dim1];
                    b[i__ + j * b_dim1] = b[i__ + 1 + j * b_dim1];
                    b[i__ + 1 + j * b_dim1] = temp - fact * b[i__ + 1 + j * 
                            b_dim1];
/* L30: */
                }
            }
/* L40: */
        }
        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__];
                    d__[i__ + 1] -= fact * du[i__];
                    i__1 = *nrhs;
                    for (j = 1; j <= i__1; ++j) {
                        b[i__ + 1 + j * b_dim1] -= fact * b[i__ + j * b_dim1];
/* L50: */
                    }
                } else {
                    *info = i__;
                    return 0;
                }
            } else {
                fact = d__[i__] / dl[i__];
                d__[i__] = dl[i__];
                temp = d__[i__ + 1];
                d__[i__ + 1] = du[i__] - fact * temp;
                du[i__] = temp;
                i__1 = *nrhs;
                for (j = 1; j <= i__1; ++j) {
                    temp = b[i__ + j * b_dim1];
                    b[i__ + j * b_dim1] = b[i__ + 1 + j * b_dim1];
                    b[i__ + 1 + j * b_dim1] = temp - fact * b[i__ + 1 + j * 
                            b_dim1];
/* L60: */
                }
            }
        }
        if (d__[*n] == 0.f) {
            *info = *n;
            return 0;
        }
    }

/*     Back solve with the matrix U from the factorization. */

    if (*nrhs <= 2) {
        j = 1;
L70:
        b[*n + j * b_dim1] /= d__[*n];
        if (*n > 1) {
            b[*n - 1 + j * b_dim1] = (b[*n - 1 + j * b_dim1] - du[*n - 1] * b[
                    *n + j * b_dim1]) / d__[*n - 1];
        }
        for (i__ = *n - 2; i__ >= 1; --i__) {
            b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__] * b[i__ + 1 
                    + j * b_dim1] - dl[i__] * b[i__ + 2 + j * b_dim1]) / d__[
                    i__];
/* L80: */
        }
        if (j < *nrhs) {
            ++j;
            goto L70;
        }
    } else {
        i__1 = *nrhs;
        for (j = 1; j <= i__1; ++j) {
            b[*n + j * b_dim1] /= d__[*n];
            if (*n > 1) {
                b[*n - 1 + j * b_dim1] = (b[*n - 1 + j * b_dim1] - du[*n - 1] 
                        * b[*n + j * b_dim1]) / d__[*n - 1];
            }
            for (i__ = *n - 2; i__ >= 1; --i__) {
                b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__] * b[i__ 
                        + 1 + j * b_dim1] - dl[i__] * b[i__ + 2 + j * b_dim1])
                         / d__[i__];
/* L90: */
            }
/* L100: */
        }
    }

    return 0;

/*     End of SGTSV */

} /* sgtsv_ */