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cgbtrf (3)
  • >> cgbtrf (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         cgbtrf - compute an LU factorization  of  a  complex  m-by-n
         band matrix A using partial pivoting with row interchanges
    
    SYNOPSIS
         SUBROUTINE CGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
    
         INTEGER INFO, KL, KU, LDAB, M, N
    
         INTEGER IPIV( * )
    
         COMPLEX AB( LDAB, * )
    
    
    
         #include <sunperf.h>
    
         void cgbtrf(int m, int n, int kl, int ku, complex *cab,  int
                   ldab, int *ipivot, int *info) ;
    
    PURPOSE
         CGBTRF computes an LU factorization of a complex 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) COMPLEX 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  mul-
                   tipliers  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  ille-
                   gal 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 equa-
                   tions.
    
    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;  ele-
         ments 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.
    
    
    
    


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