#include <LU.h>
Public Member Functions | |
template<int S1, int S2, class Base > | |
LU (const Matrix< S1, S2, Precision, Base > &m) | |
template<int S1, int S2, class Base > | |
void | compute (const Matrix< S1, S2, Precision, Base > &m) |
template<int Rows, int NRHS, class Base > | |
Matrix< Size, NRHS, Precision > | backsub (const Matrix< Rows, NRHS, Precision, Base > &rhs) |
template<int Rows, class Base > | |
Vector< Size, Precision > | backsub (const Vector< Rows, Precision, Base > &rhs) |
Matrix< Size, Size, Precision > | get_inverse () |
const Matrix< Size, Size, Precision > & | get_lu () const |
Precision | determinant () const |
int | get_info () const |
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);
Construct the LU decomposition of a matrix.
This initialises the class, and performs the decomposition immediately.
References LU< Size, Precision >::compute().
void compute | ( | const Matrix< S1, S2, Precision, Base > & | m | ) |
Perform the LU decompsition of another matrix.
References Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().
Referenced by LU< Size, Precision >::LU().
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).
References Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().
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).
References Matrix< Rows, Cols, Precision, Layout >::num_rows(), and Vector< Size, Precision, Base >::size().
Matrix<Size,Size,Precision> get_inverse | ( | ) |
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.
References Matrix< Rows, Cols, Precision, Layout >::num_rows().
const Matrix<Size,Size,Precision>& get_lu | ( | ) | const |
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.
Precision determinant | ( | ) | const |
Calculate the determinant of the matrix.
References Matrix< Rows, Cols, Precision, Layout >::num_rows().
int get_info | ( | ) | const |
Get the LAPACK info.