image et noyau

src/Solver.cpp

@@ -0,0 +1,31 @@
+#include "Solver.h"
+
+Solver::Solver(const Matrix& mat) : m_Matrix(mat) {}
+
+Vect Solver::Image() const {
+	Matrix result = m_Matrix;
+	result.Transpose();
+	result.GaussJordan(true);
+	result.Transpose();
+	return {result};
+}
+
+// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
+Vect Solver::Noyau() const {
+	Matrix result = m_Matrix;
+	result.Transpose();
+	result.Augmenter(Matrix::Identity(result.GetRawCount()));
+	result.GaussJordan(true);
+	result.Transpose();
+
+	// nombre de colonnes non nulles
+	std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, m_Matrix.GetRawCount(), m_Matrix.GetColumnCount())).GetDimension();
+
+	return {result.SubMatrix(m_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - m_Matrix.GetRawCount(),
+		result.GetColumnCount() - origine_colonne)};
+}
+
+std::size_t Solver::Rang() const {
+	Vect image = Image();
+	return image.GetDimension();
+}