From 54798d0ff2889fdecafaa0c72b4b0023fe772e17 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 21 Feb 2024 22:01:31 +0100
Subject: [PATCH] resolve rectangular systems

---
 src/Solver.cpp | 12 ++++++++++++
 src/Solver.h   |  3 +++
 src/Vect.cpp   | 13 ++++++++++++-
 src/Vect.h     | 20 ++++++++++++++++++++
 src/main.cpp   |  3 +++
 5 files changed, 50 insertions(+), 1 deletion(-)

diff --git a/src/Solver.cpp b/src/Solver.cpp
index 336711d..ca71ef7 100644
--- a/src/Solver.cpp
+++ b/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();
diff --git a/src/Solver.h b/src/Solver.h
index aded7b5..f299f2e 100644
--- a/src/Solver.h
+++ b/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;
 };
\ No newline at end of file
diff --git a/src/Vect.cpp b/src/Vect.cpp
index 17c06d9..5ec21af 100644
--- a/src/Vect.cpp
+++ b/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();
-}
\ No newline at end of file
+}
+
+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();
+}
diff --git a/src/Vect.h b/src/Vect.h
index 6d5c759..9dbee22 100644
--- a/src/Vect.h
+++ b/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;
+	}
 };
\ No newline at end of file
diff --git a/src/main.cpp b/src/main.cpp
index 39d5061..d4a1693 100644
--- a/src/main.cpp
+++ b/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() {