LU.h File Reference

#include "../../Matrix.h"
#include <cmath>
#include <vector>

Go to the source code of this file.

Functions
std::pair< Matrix< double >, std::vector< unsigned int > >	LU (const Matrix< double > &A)

Detailed Description

implements LU decomposition, places L and U in resulting matrix

$$ A = L \cdot U $$ $$ L = \begin{pmatrix} 1& 0& 0& ... \\ l_{2,1}& 1& 0& ... \\ l_{3,1}& l_{3,2}& 1, ... \\ ... \\ l_{m,1}& ... \end{pmatrix} $$ $$ U = \begin{pmatrix} 0& u_{1,2}& u_{1,3}& ...& u_{1,n}\\ 0& 0& u_{2,3}& ...& u_{2,n}\\ 0& ...& 0& u_{m-1, n}\\ 0& ...& 0 \end{pmatrix} $$ Result: $$L + U$$ LU decomposition

Requires:

#include <math/numerics/lin_alg/LU.h>

Function Documentation

LU()

std::pair< Matrix< double >, std::vector< unsigned int > > LU

(

const Matrix< double > &

A

)

LU-decomposition of A

Parameters

A	matrix to decompose

Returns

in-place decomposed matrix L+U

Examples

numerics/lin_alg/TestLU.cpp.