#include <LU.h>
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 |
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
![\[M = L \times U\]](form_49.png)
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.
| Precision TooN::LU< Size, Precision >::determinant | ( | ) | const [inline] |
| int TooN::LU< Size, Precision >::get_info | ( | ) | const [inline] |
| const Matrix<Size,Size,Precision>& 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.
| int TooN::LU< Size, Precision >::get_sign | ( | ) | const [inline, private] |
, this calculates 
by back substitution (i.e. without explictly calculating the inverse). 
, this calculates 
by back substitution (i.e. without explictly calculating the inverse).