floatMatrixAlgorithms.hpp File Reference

#include <vector>
#include <stdexcept>
#include <iostream>
#include "capd/basicalg/minmax.h"
#include "capd/basicalg/power.h"
#include "capd/matrixAlgorithms/floatMatrixAlgorithms.h"
#include "capd/basicalg/TypeTraits.h"
#include "capd/basicalg/doubleFun.h"
#include "capd/vectalg/Matrix.hpp"
#include "capd/vectalg/Norm.h"

Classes
class	capd::matrixAlgorithms::Gershgorin< MatrixType, isInterval >
class	capd::matrixAlgorithms::Gershgorin< MatrixType, false >
	Specialization for non-rigorous types. More...
class	capd::matrixAlgorithms::Gershgorin< MatrixType, true >
	Specialization for rigorous (interval) types. More...
struct	capd::matrixAlgorithms::GetExpRemainder< T, true >
struct	capd::matrixAlgorithms::GetExpRemainder< T, false >

Namespaces
	capd
	capd::matrixAlgorithms
	Matrix algorithms: Gauss elimination, orthonormalization, QR decomposition etc.

Functions
template<typename MatrixType >
MatrixType::ScalarType	capd::matrixAlgorithms::det (MatrixType A)
	Computes determinant of a matrix A by LU decomposition. More...
template<typename MatrixType , typename ResultType >
void	capd::matrixAlgorithms::gauss (MatrixType a, ResultType b, ResultType &result)
template<typename MatrixType , typename VectorType >
VectorType	capd::matrixAlgorithms::gauss (const MatrixType &A, const VectorType &b)
	Gauss elimination. More...
template<typename MatrixType , typename VectorType , typename IntVectorType >
void	capd::matrixAlgorithms::computeSortingPermutation (const MatrixType &Q, const VectorType &v, IntVectorType &permutation)
	computes sorting permutation according to sizes of the set in the direction of the base vectors More...
template<typename MatrixType >
void	capd::matrixAlgorithms::orthonormalize (MatrixType &Q, const typename MatrixType::RowVectorType &v)
template<typename MatrixType >
void	capd::matrixAlgorithms::orthonormalize (MatrixType &Q, const MatrixType &R)
template<typename MatrixType >
void	capd::matrixAlgorithms::orthonormalize (MatrixType &Q)
template<typename MatrixType >
void	capd::matrixAlgorithms::QR_decompose (const MatrixType &A, MatrixType &Q, MatrixType &R)
template<typename MatrixType , typename IntVectorType >
void	capd::matrixAlgorithms::QRdecomposeWithPivoting (const MatrixType &A, const typename MatrixType::RowVectorType &v, MatrixType &Q, MatrixType &R, typename MatrixType::RowVectorType &sizes, IntVectorType &p)
template<typename MatrixType >
int	capd::matrixAlgorithms::symMatrixDiagonalize (const MatrixType &A, MatrixType &D, typename MatrixType::ScalarType diagonalizingRelTolerance=capd::TypeTraits< typename MatrixType::ScalarType >::epsilon())
template<typename MatrixType >
MatrixType::ScalarType	capd::matrixAlgorithms::spectralRadiusOfSymMatrix (const MatrixType &A, typename MatrixType::ScalarType diagonalizingRelTolerance=capd::TypeTraits< typename MatrixType::ScalarType >::epsilon())
	this function computes bound for spectral radius of a symmetric matrix first it computes matrix which has the same eigenvalues and which is close to diagonal, next bound is computed from Gerschgorin theorem More...
template<typename MatrixType >
MatrixType::ScalarType	capd::matrixAlgorithms::maxEigenValueOfSymMatrix (const MatrixType &A, typename MatrixType::ScalarType diagonalizingRelTolerance=capd::TypeTraits< typename MatrixType::ScalarType >::epsilon())
	this function computes bound for maximal eigenvalue of a symmetric matrix first it computes matrix which has the same eigenvalues and which is close to diagonal, next bound is computed from Gerschgorin theorem More...
template<typename MatrixType >
void	capd::matrixAlgorithms::croutDecomposition (const MatrixType &A, MatrixType &D, MatrixType &G)
	Crout Decomposition of a matrix As a result matrix D is a lower triangle and G is an upper triangle with 1 on diagonal. More...
template<typename MatrixType >
MatrixType	capd::matrixAlgorithms::invLowerTriangleMatrix (const MatrixType &A)
template<typename MatrixType >
MatrixType	capd::matrixAlgorithms::invUpperTriangleMatrix (const MatrixType &A)
template<typename MatrixType >
MatrixType	capd::matrixAlgorithms::inverseMatrix (const MatrixType &A)
template<typename MatrixType >
MatrixType	capd::matrixAlgorithms::gaussInverseMatrix (const MatrixType &A)
template<typename MatrixType >
MatrixType	capd::matrixAlgorithms::matrixExp (const MatrixType &M, typename MatrixType::ScalarType tolerance=capd::TypeTraits< typename MatrixType::ScalarType >::epsilon())

Detailed Description

Author

The CAPD Group