solver move matricies
This commit is contained in:
@@ -18,14 +18,14 @@ class Solver {
|
|||||||
* \param a_Matrix La matrice à traiter
|
* \param a_Matrix La matrice à traiter
|
||||||
* \return L'espace vectoriel correspondant
|
* \return L'espace vectoriel correspondant
|
||||||
*/
|
*/
|
||||||
Vect Image(const Matrix& a_Matrix) const;
|
Vect Image(Matrix&& a_Matrix) const;
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* \brief Calcule le noyau d'une matrice
|
* \brief Calcule le noyau d'une matrice
|
||||||
* \param a_Matrix La matrice à traiter
|
* \param a_Matrix La matrice à traiter
|
||||||
* \return L'espace vectoriel correspondant
|
* \return L'espace vectoriel correspondant
|
||||||
*/
|
*/
|
||||||
Vect Kernel(const Matrix& a_Matrix) const;
|
Vect Kernel(Matrix&& a_Matrix) const;
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* \brief Résout le système rectangulaire de la forme AX=B, avec X et B, des vecteurs colonne.
|
* \brief Résout le système rectangulaire de la forme AX=B, avec X et B, des vecteurs colonne.
|
||||||
@@ -33,12 +33,12 @@ class Solver {
|
|||||||
* \param a_VectorB La matrice colonne jouant le rôle de B
|
* \param a_VectorB La matrice colonne jouant le rôle de B
|
||||||
* \return L'espace affine associé
|
* \return L'espace affine associé
|
||||||
*/
|
*/
|
||||||
VectAffine RectangularSystem(const Matrix& a_MatrixA, const Matrix& a_VectorB) const;
|
VectAffine RectangularSystem(Matrix&& a_MatrixA, const Matrix& a_VectorB) const;
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* \brief Calcule le rang d'une matrice
|
* \brief Calcule le rang d'une matrice
|
||||||
* \param a_Matrix La matrice à traiter
|
* \param a_Matrix La matrice à traiter
|
||||||
* \note Ceci équivaut à \code Image(a_Matrix).GetCardinal() \endcode
|
* \note Ceci équivaut à \code Image(a_Matrix).GetCardinal() \endcode
|
||||||
*/
|
*/
|
||||||
std::size_t Rank(const Matrix& a_Matrix) const;
|
std::size_t Rank(Matrix&& a_Matrix) const;
|
||||||
};
|
};
|
||||||
@@ -2,37 +2,38 @@
|
|||||||
|
|
||||||
#include "Gauss.h"
|
#include "Gauss.h"
|
||||||
|
|
||||||
Vect Solver::Image(const Matrix& a_Matrix) const {
|
Vect Solver::Image(Matrix&& a_Matrix) const {
|
||||||
Matrix result = a_Matrix;
|
a_Matrix.Transpose();
|
||||||
result.Transpose();
|
Gauss::GaussJordan(a_Matrix, true, true);
|
||||||
Gauss::GaussJordan(result, true, true);
|
a_Matrix.Transpose();
|
||||||
result.Transpose();
|
return {a_Matrix};
|
||||||
return {result};
|
|
||||||
}
|
}
|
||||||
|
|
||||||
// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
|
// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
|
||||||
Vect Solver::Kernel(const Matrix& a_Matrix) const {
|
Vect Solver::Kernel(Matrix&& a_Matrix) const {
|
||||||
Matrix result = a_Matrix;
|
std::size_t matrixRawCount = a_Matrix.GetRawCount();
|
||||||
result.Transpose();
|
std::size_t matrixColumnCount = a_Matrix.GetColumnCount();
|
||||||
result.Augment(Matrix::Identity(result.GetRawCount()));
|
|
||||||
Gauss::GaussJordan(result, true, true);
|
a_Matrix.Transpose();
|
||||||
result.Transpose();
|
a_Matrix.Augment(Matrix::Identity(a_Matrix.GetRawCount()));
|
||||||
|
Gauss::GaussJordan(a_Matrix, true, true);
|
||||||
|
a_Matrix.Transpose();
|
||||||
|
|
||||||
// nombre de colonnes non nulles
|
// nombre de colonnes non nulles
|
||||||
std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, a_Matrix.GetRawCount(), a_Matrix.GetColumnCount())).GetCardinal();
|
std::size_t origine_colonne = Vect(a_Matrix.SubMatrix(0, 0, matrixRawCount, matrixColumnCount)).GetCardinal();
|
||||||
|
|
||||||
return {result.SubMatrix(a_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - a_Matrix.GetRawCount(),
|
return {a_Matrix.SubMatrix(matrixRawCount, origine_colonne, a_Matrix.GetRawCount() - matrixRawCount,
|
||||||
result.GetColumnCount() - origine_colonne)};
|
a_Matrix.GetColumnCount() - origine_colonne)};
|
||||||
}
|
}
|
||||||
|
|
||||||
VectAffine Solver::RectangularSystem(const Matrix& a_MatrixA, const Matrix& a_VectorB) const {
|
VectAffine Solver::RectangularSystem(Matrix&& a_MatrixA, const Matrix& a_VectorB) const {
|
||||||
Matrix mat = a_MatrixA;
|
Matrix mat = a_MatrixA;
|
||||||
mat.Augment(a_VectorB);
|
mat.Augment(a_VectorB);
|
||||||
Gauss::GaussJordan(mat, true, true);
|
Gauss::GaussJordan(mat, true, true);
|
||||||
|
|
||||||
Solver solver;
|
Solver solver;
|
||||||
|
|
||||||
Vect noyau = solver.Kernel(a_MatrixA);
|
Vect noyau = solver.Kernel(std::move(a_MatrixA));
|
||||||
Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
|
Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
|
||||||
|
|
||||||
// on rajoute des 0 si il faut
|
// on rajoute des 0 si il faut
|
||||||
@@ -49,6 +50,6 @@ VectAffine Solver::RectangularSystem(const Matrix& a_MatrixA, const Matrix& a_Ve
|
|||||||
return {noyau, fullOrigin};
|
return {noyau, fullOrigin};
|
||||||
}
|
}
|
||||||
|
|
||||||
std::size_t Solver::Rank(const Matrix& a_Matrix) const {
|
std::size_t Solver::Rank(Matrix&& a_Matrix) const {
|
||||||
return Image(a_Matrix).GetCardinal();
|
return Image(std::move(a_Matrix)).GetCardinal();
|
||||||
}
|
}
|
||||||
|
|||||||
@@ -75,9 +75,9 @@ Matrix Vect::GetLinearSystem() const {
|
|||||||
vect.Transpose();
|
vect.Transpose();
|
||||||
|
|
||||||
Solver solver;
|
Solver solver;
|
||||||
vect = solver.Kernel(vect).m_Data;
|
Matrix result = solver.Kernel(std::move(vect)).m_Data;
|
||||||
vect.Transpose();
|
result.Transpose();
|
||||||
return vect;
|
return result;
|
||||||
}
|
}
|
||||||
|
|
||||||
std::size_t Vect::GetDimension() const {
|
std::size_t Vect::GetDimension() const {
|
||||||
|
|||||||
@@ -25,8 +25,8 @@ void test() {
|
|||||||
|
|
||||||
Solver solver;
|
Solver solver;
|
||||||
|
|
||||||
Vect image = solver.Image(mat2);
|
Vect image = solver.Image(Matrix{mat2});
|
||||||
Vect noyau = solver.Kernel(mat2);
|
Vect noyau = solver.Kernel(Matrix{mat2});
|
||||||
|
|
||||||
std::cout << "\tImage :\n";
|
std::cout << "\tImage :\n";
|
||||||
Print(image);
|
Print(image);
|
||||||
|
|||||||
@@ -37,7 +37,9 @@ static void Test() {
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
Vect kernel = solver.Kernel(matrix);
|
Matrix copy = matrix;
|
||||||
|
|
||||||
|
Vect kernel = solver.Kernel(std::move(copy));
|
||||||
|
|
||||||
Matrix nullVector {matrix.GetRawCount(), 1};
|
Matrix nullVector {matrix.GetRawCount(), 1};
|
||||||
nullVector.Fill(0.0);
|
nullVector.Fill(0.0);
|
||||||
|
|||||||
@@ -18,7 +18,7 @@ void TestRectangular() {
|
|||||||
|
|
||||||
Solver solver;
|
Solver solver;
|
||||||
|
|
||||||
std::cout << solver.RectangularSystem(mat2, Matrix::ColumnVector({1, 2})).GetLinearSystem() << std::endl;
|
std::cout << solver.RectangularSystem(std::move(mat2), Matrix::ColumnVector({1, 2})).GetLinearSystem() << std::endl;
|
||||||
std::cout << aff.GetLinearSystem() << std::endl;
|
std::cout << aff.GetLinearSystem() << std::endl;
|
||||||
}
|
}
|
||||||
|
|
||||||
@@ -39,8 +39,10 @@ void TestKernelImage() {
|
|||||||
|
|
||||||
Solver solver;
|
Solver solver;
|
||||||
|
|
||||||
test_assert(solver.Image(mat) == image);
|
Matrix copy = mat;
|
||||||
test_assert(solver.Kernel(mat) == noyau);
|
|
||||||
|
test_assert(solver.Image(std::move(copy)) == image);
|
||||||
|
test_assert(solver.Kernel(std::move(mat)) == noyau);
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|||||||
Reference in New Issue
Block a user