SGBTRF (3lapack)

compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

SYNOPSIS

  SUBROUTINE SGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )

      INTEGER        INFO, KL, KU, LDAB, M, N

      INTEGER        IPIV( * )

      REAL           AB( LDAB, * )

PURPOSE

  SGBTRF computes an LU factorization of a real m-by-n band matrix A using
  partial pivoting with row interchanges.

  This is the blocked version of the algorithm, calling Level 3 BLAS.

ARGUMENTS

  M       (input) INTEGER
          The number of rows of the matrix A.  M >= 0.

  N       (input) INTEGER
          The number of columns 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.

  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(m,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 (min(M,N))
          The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was
          interchanged with row IPIV(i).

  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 division
          by zero will occur if it is used to solve a system of equations.

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.