SDBTRF(3)     ScaLAPACK routine of NEC Numeric Library Collection    SDBTRF(3)



NAME
       SDBTRF  -  compute  an  LU factorization of a real m-by-n band matrix A
       without using partial pivoting or row interchanges

SYNOPSIS
       SUBROUTINE SDBTRF( M, N, KL, KU, AB, LDAB, INFO )

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

           REAL           AB( LDAB, * )

PURPOSE
       Sdbtrf computes an LU factorization of a  real  m-by-n  band  matrix  A
       without  using  partial  pivoting  or  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.

       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:

           *   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.




ScaLAPACK routine               31 October 2017                      SDBTRF(3)