
sgbtf2.f(3) LAPACK sgbtf2.f(3)
NAME
sgbtf2.f 
SYNOPSIS
Functions/Subroutines
subroutine sgbtf2 (M, N, KL, KU, AB, LDAB, IPIV, INFO)
SGBTF2 computes the LU factorization of a general band matrix using the unblocked
version of the algorithm.
Function/Subroutine Documentation
subroutine sgbtf2 (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB,
integerLDAB, integer, dimension( * )IPIV, integerINFO)
SGBTF2 computes the LU factorization of a general band matrix using the unblocked version
of the algorithm.
Purpose:
SGBTF2 computes an LU factorization of a real mbyn band matrix A
using partial pivoting with row interchanges.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
AB
AB is 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 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
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV
IPIV is 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
INFO is 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
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 fillin resulting from the row
interchanges.
Definition at line 146 of file sgbtf2.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgbtf2.f(3) 
