sgtts2.c

Go to the documentation of this file.

/* sgtts2.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 sgtts2_(integer *itrans, integer *n, integer *nrhs, real 
        *dl, real *d__, real *du, real *du2, integer *ipiv, real *b, integer *
        ldb)
{
    /* System generated locals */
    integer b_dim1, b_offset, i__1, i__2;

    /* Local variables */
    integer i__, j, ip;
    real temp;


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

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

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

/*  SGTTS2 solves one of the systems of equations */
/*     A*X = B  or  A'*X = B, */
/*  with a tridiagonal matrix A using the LU factorization computed */
/*  by SGTTRF. */

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

/*  ITRANS  (input) INTEGER */
/*          Specifies the form of the system of equations. */
/*          = 0:  A * X = B  (No transpose) */
/*          = 1:  A'* X = B  (Transpose) */
/*          = 2:  A'* X = B  (Conjugate transpose = Transpose) */

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

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

/*  DL      (input) REAL array, dimension (N-1) */
/*          The (n-1) multipliers that define the matrix L from the */
/*          LU factorization of A. */

/*  D       (input) REAL array, dimension (N) */
/*          The n diagonal elements of the upper triangular matrix U from */
/*          the LU factorization of A. */

/*  DU      (input) REAL array, dimension (N-1) */
/*          The (n-1) elements of the first super-diagonal of U. */

/*  DU2     (input) REAL array, dimension (N-2) */
/*          The (n-2) elements of the second super-diagonal of U. */

/*  IPIV    (input) 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. */

/*  B       (input/output) REAL array, dimension (LDB,NRHS) */
/*          On entry, the matrix of right hand side vectors B. */
/*          On exit, B is overwritten by the solution vectors X. */

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

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

/*     .. Local Scalars .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick return if possible */

    /* Parameter adjustments */
    --dl;
    --d__;
    --du;
    --du2;
    --ipiv;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    if (*n == 0 || *nrhs == 0) {
        return 0;
    }

    if (*itrans == 0) {

/*        Solve A*X = B using the LU factorization of A, */
/*        overwriting each right hand side vector with its solution. */

        if (*nrhs <= 1) {
            j = 1;
L10:

/*           Solve L*x = b. */

            i__1 = *n - 1;
            for (i__ = 1; i__ <= i__1; ++i__) {
                ip = ipiv[i__];
                temp = b[i__ + 1 - ip + i__ + j * b_dim1] - dl[i__] * b[ip + 
                        j * b_dim1];
                b[i__ + j * b_dim1] = b[ip + j * b_dim1];
                b[i__ + 1 + j * b_dim1] = temp;
/* L20: */
            }

/*           Solve U*x = b. */

            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] - du2[i__] * b[i__ + 2 + j * b_dim1]
                        ) / d__[i__];
/* L30: */
            }
            if (j < *nrhs) {
                ++j;
                goto L10;
            }
        } else {
            i__1 = *nrhs;
            for (j = 1; j <= i__1; ++j) {

/*              Solve L*x = b. */

                i__2 = *n - 1;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    if (ipiv[i__] == i__) {
                        b[i__ + 1 + j * b_dim1] -= dl[i__] * b[i__ + j * 
                                b_dim1];
                    } else {
                        temp = b[i__ + j * b_dim1];
                        b[i__ + j * b_dim1] = b[i__ + 1 + j * b_dim1];
                        b[i__ + 1 + j * b_dim1] = temp - dl[i__] * b[i__ + j *
                                 b_dim1];
                    }
/* L40: */
                }

/*              Solve U*x = b. */

                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] - du2[i__] * b[i__ + 2 + j *
                             b_dim1]) / d__[i__];
/* L50: */
                }
/* L60: */
            }
        }
    } else {

/*        Solve A' * X = B. */

        if (*nrhs <= 1) {

/*           Solve U'*x = b. */

            j = 1;
L70:
            b[j * b_dim1 + 1] /= d__[1];
            if (*n > 1) {
                b[j * b_dim1 + 2] = (b[j * b_dim1 + 2] - du[1] * b[j * b_dim1 
                        + 1]) / d__[2];
            }
            i__1 = *n;
            for (i__ = 3; i__ <= i__1; ++i__) {
                b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__ - 1] * b[
                        i__ - 1 + j * b_dim1] - du2[i__ - 2] * b[i__ - 2 + j *
                         b_dim1]) / d__[i__];
/* L80: */
            }

/*           Solve L'*x = b. */

            for (i__ = *n - 1; i__ >= 1; --i__) {
                ip = ipiv[i__];
                temp = b[i__ + j * b_dim1] - dl[i__] * b[i__ + 1 + j * b_dim1]
                        ;
                b[i__ + j * b_dim1] = b[ip + j * b_dim1];
                b[ip + j * b_dim1] = temp;
/* L90: */
            }
            if (j < *nrhs) {
                ++j;
                goto L70;
            }

        } else {
            i__1 = *nrhs;
            for (j = 1; j <= i__1; ++j) {

/*              Solve U'*x = b. */

                b[j * b_dim1 + 1] /= d__[1];
                if (*n > 1) {
                    b[j * b_dim1 + 2] = (b[j * b_dim1 + 2] - du[1] * b[j * 
                            b_dim1 + 1]) / d__[2];
                }
                i__2 = *n;
                for (i__ = 3; i__ <= i__2; ++i__) {
                    b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__ - 1] *
                             b[i__ - 1 + j * b_dim1] - du2[i__ - 2] * b[i__ - 
                            2 + j * b_dim1]) / d__[i__];
/* L100: */
                }
                for (i__ = *n - 1; i__ >= 1; --i__) {
                    if (ipiv[i__] == i__) {
                        b[i__ + j * b_dim1] -= dl[i__] * b[i__ + 1 + j * 
                                b_dim1];
                    } else {
                        temp = b[i__ + 1 + j * b_dim1];
                        b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - dl[
                                i__] * temp;
                        b[i__ + j * b_dim1] = temp;
                    }
/* L110: */
                }
/* L120: */
            }
        }
    }

/*     End of SGTTS2 */

    return 0;
} /* sgtts2_ */