dgbtf2 (l) - Linux Manuals

dgbtf2: computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

NAME

DGBTF2 - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

SYNOPSIS

SUBROUTINE DGBTF2(
M, N, KL, KU, AB, LDAB, IPIV, INFO )

    
INTEGER INFO, KL, KU, LDAB, M, N

    
INTEGER IPIV( * )

    
DOUBLE PRECISION AB( LDAB, * )

PURPOSE

DGBTF2 computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 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) DOUBLE PRECISION 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.

Pages related to dgbtf2

  • dgbtf2 (3)
  • dgbtrf (l) - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
  • dgbtrs (l) - solves a system of linear equations A * X = B or Aaq * X = B with a general band matrix A using the LU factorization computed by DGBTRF
  • dgbbrd (l) - reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
  • dgbcon (l) - estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
  • dgbequ (l) - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
  • dgbequb (l) - computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number
  • dgbmv (l) - performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*Aaq*x + beta*y,