resolve rectangular systems

src/Solver.cpp

@@ -25,6 +25,18 @@ Vect Solver::Noyau() const {
 		result.GetColumnCount() - origine_colonne)};
 }
 
+VectAffine Solver::SystemeTriangulaire() const {
+	Matrix mat = m_Matrix;
+	mat.GaussJordan(true);
+
+	Solver solver{mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};
+
+	Vect noyau = solver.Noyau();
+	Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
+
+	return {noyau, origin};
+}
+
 std::size_t Solver::Rang() const {
 	Vect image = Image();
 	return image.GetCardinal();

src/Solver.h

@@ -5,6 +5,7 @@
 class Solver {
   private:
 	Matrix m_Matrix;
+
   public:
 	Solver(const Matrix& mat);
 	~Solver() {}
@@ -12,5 +13,7 @@ class Solver {
 	Vect Image() const;
 	Vect Noyau() const;
 
+	VectAffine SystemeTriangulaire() const;
+
 	std::size_t Rang() const;
 };

src/Vect.cpp

@@ -1,6 +1,7 @@
 #include "Vect.h"
 
 #include "Solver.h"
+#include <cassert>
 #include <iostream>
 
 Vect::Vect(const Matrix& mat) : m_Data(mat) {
@@ -75,4 +76,14 @@ void Vect::Print() const {
 
 std::size_t Vect::GetDimension() const {
 	return m_Data.GetRawCount();
-}
+}
+
+VectAffine::VectAffine(const Vect& base, const Matrix& origine) :
+	m_Base(base), m_Origin(origine.SubMatrix(0, 0, m_Base.GetDimension(), 1)) {}
+
+void VectAffine::Print() const {
+	std::cout << "\tEspace Affine :\n\n";
+	m_Base.Print();
+	std::cout << "\nOrigine :\n\n";
+	m_Origin.Print();
+}

src/Vect.h

@@ -36,4 +36,24 @@ class Vect {
 
   private:
 	void Simplify();
+};
+
+
+class VectAffine {
+  private:
+	Vect m_Base;
+	Matrix m_Origin;
+
+  public:
+	VectAffine(const Vect& base, const Matrix& origin);
+
+	void Print() const;
+
+	const Vect& GetBase() const {
+		return m_Base;
+	}
+
+	const Matrix& GetOrigin() const {
+		return m_Origin;
+	}
 };

src/main.cpp

@@ -32,6 +32,9 @@ void test() {
 	noyau.Print();
 	std::cout << "Système :\n";
 	noyau.GetLinearSystem().Print();
+
+	std::cout << "\n\n";
+	solver.SystemeTriangulaire().Print();
 }
 
 void prompt() {