• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

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

SYNOPSIS

  SUBROUTINE DGBTRF( M, N, NSUB, NSUPER, A, LDA, IPIVOT, INFO)
  INTEGER M, N, NSUB, NSUPER, LDA, INFO
  INTEGER IPIVOT(*)
  DOUBLE PRECISION A(LDA,*)

  SUBROUTINE DGBTRF_64( M, N, NSUB, NSUPER, A, LDA, IPIVOT, INFO)
  INTEGER*8 M, N, NSUB, NSUPER, LDA, INFO
  INTEGER*8 IPIVOT(*)
  DOUBLE PRECISION A(LDA,*)

F95 INTERFACE

  SUBROUTINE GBTRF( [M], [N], NSUB, NSUPER, A, [LDA], IPIVOT, [INFO])
  INTEGER :: M, N, NSUB, NSUPER, LDA, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:,:) :: A

  SUBROUTINE GBTRF_64( [M], [N], NSUB, NSUPER, A, [LDA], IPIVOT, [INFO])
  INTEGER(8) :: M, N, NSUB, NSUPER, LDA, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void dgbtrf(int m, int n, int nsub, int nsuper, double *a, int lda, int *ipivot, int *info);

void dgbtrf_64(long m, long n, long nsub, long nsuper, double *a, long lda, long *ipivot, long *info);

PURPOSE

dgbtrf 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)
  The number of rows of the matrix A. M > = 0.

• N (input)
  The number of columns of the matrix A. N > = 0.

• NSUB (input)
  The number of subdiagonals within the band of A. NSUB > = 0.

• NSUPER (input)
  The number of superdiagonals within the band of A. NSUPER > = 0.

• A (input/output)
  On entry, the matrix A in band storage, in rows NSUB+1 to 2*NSUB+NSUPER+1; rows 1 to NSUB of the array need not be set. The j-th column of A is stored in the j-th column of the array A as follows: A(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 NSUB+NSUPER superdiagonals in rows 1 to NSUB+NSUPER+1, and the multipliers used during the factorization are stored in rows NSUB+NSUPER+2 to 2*NSUB+NSUPER+1. See below for further details.

• LDA (input)
  The leading dimension of the array A. LDA > = 2*NSUB+NSUPER+1.

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

• INFO (output)
  

   = 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, NSUB = 2, NSUPER = 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.