Computes an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges.
Namespace: Extreme.Mathematics.LinearAlgebra.ImplementationAssembly: Extreme.Numerics.SinglePrecision.Net40 (in Extreme.Numerics.SinglePrecision.Net40.dll) Version: 6.0.16073.0 (6.0.16096.0)
public override void BandLUDecompose(
int m,
int n,
int kl,
int ku,
Array2D<float> ab,
Array1D<int> ipiv,
out int info
)
Public Overrides Sub BandLUDecompose (
m As Integer,
n As Integer,
kl As Integer,
ku As Integer,
ab As Array2D(Of Single),
ipiv As Array1D(Of Integer),
<OutAttribute> ByRef info As Integer
)
public:
virtual void BandLUDecompose(
int m,
int n,
int kl,
int ku,
Array2D<float> ab,
Array1D<int> ipiv,
[OutAttribute] int% info
) override
abstract BandLUDecompose :
m : int *
n : int *
kl : int *
ku : int *
ab : Array2D<float32> *
ipiv : Array1D<int> *
info : int byref -> unit
override BandLUDecompose :
m : int *
n : int *
kl : int *
ku : int *
ab : Array2D<float32> *
ipiv : Array1D<int> *
info : int byref -> unit
Parameters
- m
- Type: SystemInt32
The number of rows of the matrix A. M >= 0.
- n
- Type: SystemInt32
The number of columns of the matrix A. N >= 0.
- kl
- Type: SystemInt32
The number of subdiagonals within the band of A. KL >= 0.
- ku
- Type: SystemInt32
The number of superdiagonals within the band of A. KU >= 0.
- ab
- Type: Extreme.CollectionsArray2DSingle
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.
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
- ipiv
- Type: Extreme.CollectionsArray1DInt32
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
- Type: SystemInt32
= 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.
This is the blocked version of the algorithm, calling Level 3 BLAS.
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.
This method corresponds to the LAPACK routine ?GBTRF.
Numerical Libraries
Supported in: 6.0
Reference