sgbsv.c

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/* sgbsv.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 sgbsv_(integer *n, integer *kl, integer *ku, integer *
        nrhs, real *ab, integer *ldab, integer *ipiv, real *b, integer *ldb, 
        integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;

    /* Local variables */
    extern /* Subroutine */ int xerbla_(char *, integer *), sgbtrf_(
            integer *, integer *, integer *, integer *, real *, integer *, 
            integer *, integer *), sgbtrs_(char *, integer *, integer *, 
            integer *, integer *, real *, integer *, integer *, real *, 
            integer *, integer *);


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

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

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

/*  SGBSV computes the solution to a real system of linear equations */
/*  A * X = B, where A is a band matrix of order N with KL subdiagonals */
/*  and KU superdiagonals, and X and B are N-by-NRHS matrices. */

/*  The LU decomposition with partial pivoting and row interchanges is */
/*  used to factor A as A = L * U, where L is a product of permutation */
/*  and unit lower triangular matrices with KL subdiagonals, and U is */
/*  upper triangular with KL+KU superdiagonals.  The factored form of A */
/*  is then used to solve the system of equations A * X = B. */

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

/*  N       (input) INTEGER */
/*          The number of linear equations, i.e., the order of the */
/*          matrix A.  N >= 0. */

/*  KL      (input) INTEGER */
/*          The number of subdiagonals within the band of A.  KL >= 0. */

/*  KU      (input) INTEGER */
/*          The number of superdiagonals within the band of A.  KU >= 0. */

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

/*  AB      (input/output) REAL array, dimension (LDAB,N) */
/*          On entry, the matrix A in band storage, in rows KL+1 to */
/*          2*KL+KU+1; rows 1 to KL of the array need not be set. */
/*          The j-th column of A is stored in the j-th column of the */
/*          array AB as follows: */
/*          AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) */
/*          On exit, details of the factorization: U is stored as an */
/*          upper triangular band matrix with KL+KU superdiagonals in */
/*          rows 1 to KL+KU+1, and the multipliers used during the */
/*          factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */
/*          See below for further details. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */

/*  IPIV    (output) INTEGER array, dimension (N) */
/*          The pivot indices that define the permutation matrix P; */
/*          row i of the matrix was interchanged with row IPIV(i). */

/*  B       (input/output) REAL array, dimension (LDB,NRHS) */
/*          On entry, the N-by-NRHS 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.  The factorization */
/*                has been completed, but the factor U is exactly */
/*                singular, and the solution has not been computed. */

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

/*  The band storage scheme is illustrated by the following example, when */
/*  M = N = 6, KL = 2, KU = 1: */

/*  On entry:                       On exit: */

/*      *    *    *    +    +    +       *    *    *   u14  u25  u36 */
/*      *    *    +    +    +    +       *    *   u13  u24  u35  u46 */
/*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56 */
/*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66 */
/*     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   * */
/*     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    * */

/*  Array elements marked * are not used by the routine; elements marked */
/*  + need not be set on entry, but are required by the routine to store */
/*  elements of U because of fill-in resulting from the row interchanges. */

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

/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    --ipiv;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    *info = 0;
    if (*n < 0) {
        *info = -1;
    } else if (*kl < 0) {
        *info = -2;
    } else if (*ku < 0) {
        *info = -3;
    } else if (*nrhs < 0) {
        *info = -4;
    } else if (*ldab < (*kl << 1) + *ku + 1) {
        *info = -6;
    } else if (*ldb < max(*n,1)) {
        *info = -9;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("SGBSV ", &i__1);
        return 0;
    }

/*     Compute the LU factorization of the band matrix A. */

    sgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
    if (*info == 0) {

/*        Solve the system A*X = B, overwriting B with X. */

        sgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[
                1], &b[b_offset], ldb, info);
    }
    return 0;

/*     End of SGBSV */

} /* sgbsv_ */