spbsv.c

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/* spbsv.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 spbsv_(char *uplo, integer *n, integer *kd, integer *
        nrhs, real *ab, integer *ldab, real *b, integer *ldb, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;

    /* Local variables */
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int xerbla_(char *, integer *), spbtrf_(
            char *, integer *, integer *, real *, integer *, integer *), spbtrs_(char *, integer *, integer *, integer *, real *, 
            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 */
/*  ======= */

/*  SPBSV computes the solution to a real system of linear equations */
/*     A * X = B, */
/*  where A is an N-by-N symmetric positive definite band matrix and X */
/*  and B are N-by-NRHS matrices. */

/*  The Cholesky decomposition is used to factor A as */
/*     A = U**T * U,  if UPLO = 'U', or */
/*     A = L * L**T,  if UPLO = 'L', */
/*  where U is an upper triangular band matrix, and L is a lower */
/*  triangular band matrix, with the same number of superdiagonals or */
/*  subdiagonals as A.  The factored form of A is then used to solve the */
/*  system of equations A * X = B. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

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

/*  KD      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'.  KD >= 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 upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first KD+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD). */
/*          See below for further details. */

/*          On exit, if INFO = 0, the triangular factor U or L from the */
/*          Cholesky factorization A = U**T*U or A = L*L**T of the band */
/*          matrix A, in the same storage format as A. */

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

/*  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, the leading minor of order i of A is not */
/*                positive definite, so the factorization could not be */
/*                completed, and the solution has not been computed. */

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

/*  The band storage scheme is illustrated by the following example, when */
/*  N = 6, KD = 2, and UPLO = 'U': */

/*  On entry:                       On exit: */

/*      *    *   a13  a24  a35  a46      *    *   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 */

/*  Similarly, if UPLO = 'L' the format of A is as follows: */

/*  On entry:                       On exit: */

/*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66 */
/*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   * */
/*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    * */

/*  Array elements marked * are not used by the routine. */

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

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

/*     Test the input parameters. */

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

    /* Function Body */
    *info = 0;
    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*kd < 0) {
        *info = -3;
    } else if (*nrhs < 0) {
        *info = -4;
    } else if (*ldab < *kd + 1) {
        *info = -6;
    } else if (*ldb < max(1,*n)) {
        *info = -8;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("SPBSV ", &i__1);
        return 0;
    }

/*     Compute the Cholesky factorization A = U'*U or A = L*L'. */

    spbtrf_(uplo, n, kd, &ab[ab_offset], ldab, info);
    if (*info == 0) {

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

        spbtrs_(uplo, n, kd, nrhs, &ab[ab_offset], ldab, &b[b_offset], ldb, 
                info);

    }
    return 0;

/*     End of SPBSV */

} /* spbsv_ */