# TooN::LU< Size, Precision > Class Template Reference [Matrix decompositions]

#include <LU.h>

List of all members.

## Public Member Functions

template<int Rows, class Base >
Vector< Size, Precision > backsub (const Vector< Rows, Precision, Base > &rhs)
template<int Rows, int NRHS, class Base >
Matrix< Size, NRHS, Precision > backsub (const Matrix< Rows, NRHS, Precision, Base > &rhs)
template<int S1, int S2, class Base >
void compute (const Matrix< S1, S2, Precision, Base > &m)
Perform the LU decompsition of another matrix.
Precision determinant () const
Calculate the determinant of the matrix.
int get_info () const
Get the LAPACK info.
Matrix< Size, Size, Precision > get_inverse ()
const Matrix< Size, Size,
Precision > &
get_lu () const
template<int S1, int S2, class Base >
LU (const Matrix< S1, S2, Precision, Base > &m)

## Private Member Functions

int get_sign () const

## Private Attributes

int my_info
Vector< Size, int > my_IPIV
Matrix< Size, Size, Precision > my_lu

## Detailed Description

### template<int Size = -1, class Precision = double> class TooN::LU< Size, Precision >

Performs LU decomposition and back substitutes to solve equations. The LU decomposition is the fastest way of solving the equation m, but it becomes unstable when is (nearly) singular (in which cases the SymEigen or SVD decompositions are better). It decomposes a matrix into

where is a lower-diagonal matrix with unit diagonal and is an upper-diagonal matrix. The library only supports the decomposition of square matrices. It can be used as follows to solve the problem as follows:

  // construct M
Matrix<3> M;
M[0] = makeVector(1,2,3);
M[1] = makeVector(3,2,1);
M[2] = makeVector(1,0,1);
// construct c
Vector<3> c = makeVector(2,3,4);
// create the LU decomposition of M
LU<3> luM(M);
// compute x = M^-1 * c
Vector<3> x = luM.backsub(c);


The convention LU<> (=LU<-1>) is used to create an LU decomposition whose size is determined at runtime.

Definition at line 69 of file LU.h.

## Constructor & Destructor Documentation

template<int Size = -1, class Precision = double>
template<int S1, int S2, class Base >
 TooN::LU< Size, Precision >::LU ( const Matrix< S1, S2, Precision, Base > & m )  [inline]

Construct the LU decomposition of a matrix. This initialises the class, and performs the decomposition immediately.

Definition at line 75 of file LU.h.

## Member Function Documentation

template<int Size = -1, class Precision = double>
template<int Rows, class Base >
 Vector TooN::LU< Size, Precision >::backsub ( const Vector< Rows, Precision, Base > & rhs )  [inline]

Calculate result of multiplying the inverse of M by a vector. For a vector , this calculates by back substitution (i.e. without explictly calculating the inverse).

Definition at line 132 of file LU.h.

template<int Size = -1, class Precision = double>
template<int Rows, int NRHS, class Base >
 Matrix TooN::LU< Size, Precision >::backsub ( const Matrix< Rows, NRHS, Precision, Base > & rhs )  [inline]

Calculate result of multiplying the inverse of M by another matrix. For a matrix , this calculates by back substitution (i.e. without explictly calculating the inverse).

Definition at line 103 of file LU.h.

template<int Size = -1, class Precision = double>
template<int S1, int S2, class Base >
 void TooN::LU< Size, Precision >::compute ( const Matrix< S1, S2, Precision, Base > & m )  [inline]

Perform the LU decompsition of another matrix.

Definition at line 82 of file LU.h.

template<int Size = -1, class Precision = double>
 Precision TooN::LU< Size, Precision >::determinant ( ) const [inline]

Calculate the determinant of the matrix.

Definition at line 192 of file LU.h.

template<int Size = -1, class Precision = double>
 int TooN::LU< Size, Precision >::get_info ( ) const [inline]

Get the LAPACK info.

Definition at line 201 of file LU.h.

template<int Size = -1, class Precision = double>
 Matrix TooN::LU< Size, Precision >::get_inverse ( )  [inline]

Calculate inverse of the matrix. This is not usually needed: if you need the inverse just to multiply it by a matrix or a vector, use one of the backsub() functions, which will be faster.

Definition at line 158 of file LU.h.

template<int Size = -1, class Precision = double>
 const Matrix& TooN::LU< Size, Precision >::get_lu ( ) const [inline]

Returns the L and U matrices. The permutation matrix is not returned. Since L is lower-triangular (with unit diagonal) and U is upper-triangular, these are returned conflated into one matrix, where the diagonal and above parts of the matrix are U and the below-diagonal part, plus a unit diagonal, are L.

Definition at line 177 of file LU.h.

template<int Size = -1, class Precision = double>
 int TooN::LU< Size, Precision >::get_sign ( ) const [inline, private]

Definition at line 180 of file LU.h.

## Member Data Documentation

template<int Size = -1, class Precision = double>
 int TooN::LU< Size, Precision >::my_info [private]

Definition at line 206 of file LU.h.

template<int Size = -1, class Precision = double>
 Vector TooN::LU< Size, Precision >::my_IPIV [private]

Definition at line 207 of file LU.h.

template<int Size = -1, class Precision = double>
 Matrix TooN::LU< Size, Precision >::my_lu [private]

Definition at line 205 of file LU.h.

The documentation for this class was generated from the following file:

libtoon
Author(s): Florian Weisshardt
autogenerated on Fri Jan 11 10:09:49 2013