56 lines
1.5 KiB
C++
56 lines
1.5 KiB
C++
#include "Solver.h"
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#include "Gauss.h"
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Solver::Solver(const Matrix& mat) : m_Matrix(mat) {}
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Vect Solver::Image() const {
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Matrix result = m_Matrix;
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result.Transpose();
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Gauss::GaussJordan(result, true, true);
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result.Transpose();
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return {result};
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}
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// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
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Vect Solver::Kernel() const {
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Matrix result = m_Matrix;
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result.Transpose();
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result.Augment(Matrix::Identity(result.GetRawCount()));
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Gauss::GaussJordan(result, true, true);
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result.Transpose();
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// nombre de colonnes non nulles
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std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, m_Matrix.GetRawCount(), m_Matrix.GetColumnCount())).GetCardinal();
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return {result.SubMatrix(m_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - m_Matrix.GetRawCount(),
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result.GetColumnCount() - origine_colonne)};
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}
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VectAffine Solver::TriangularSystem() const {
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Matrix mat = m_Matrix;
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Gauss::GaussJordan(mat, true, true);
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Solver solver {mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};
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Vect noyau = solver.Kernel();
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Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
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// on rajoute des 0 si il faut
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Matrix fullOrigin {mat.GetColumnCount() - 1, 1};
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for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
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fullOrigin.at(i, 0) = origin.at(i, 0);
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}
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for (std::size_t i = mat.GetRawCount(); i < mat.GetColumnCount() - 1; i++) {
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fullOrigin.at(i, 0) = 0;
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}
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return {noyau, fullOrigin};
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}
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std::size_t Solver::Rank() const {
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return Image().GetCardinal();
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}
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