dgbtrf (l)  Linux Manuals
dgbtrf: computes an LU factorization of a real mbyn band matrix A using partial pivoting with row interchanges
NAME
DGBTRF  computes an LU factorization of a real mbyn band matrix A using partial pivoting with row interchangesSYNOPSIS
 SUBROUTINE DGBTRF(
 M, N, KL, KU, AB, LDAB, IPIV, INFO )
 INTEGER INFO, KL, KU, LDAB, M, N
 INTEGER IPIV( * )
 DOUBLE PRECISION AB( LDAB, * )
PURPOSE
DGBTRF computes an LU factorization of a real mbyn 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) 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 jth column of A is stored in the jth column of the array AB as follows: AB(kl+ku+1+ij,j) = A(i,j) for max(1,jku)<=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 ith 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:
a11
a21
a31