add project license

.clang-format

@@ -7,6 +7,8 @@ ConstructorInitializerAllOnOneLineOrOnePerLine: true
 PointerAlignment: Left
 SortIncludes: true
 SpacesBeforeTrailingComments: 2
+SeparateDefinitionBlocks: Always
+SpaceBeforeCpp11BracedList: true
 UseTab: Always
 MaxEmptyLinesToKeep: 5
 

.gitea/workflows/ubuntu.yaml

@@ -0,0 +1,40 @@
+name: Linux arm64
+run-name: Build And Test
+
+on: [push]
+
+jobs:
+  Build:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Install opengl
+        run: |
+          apt update
+          apt install libgl-dev -y
+
+      - name: Check out repository code
+        uses: actions/checkout@v3
+
+      - name: Prepare Xmake
+        uses: xmake-io/github-action-setup-xmake@v1
+        with:
+          xmake-version: latest
+          actions-cache-folder: '.xmake-cache'
+          actions-cache-key: 'ubuntu-xmake'
+
+      - name: Cache
+        uses: actions/cache@v4
+        with:
+          path: ~/.xmake
+          key: 'ubuntu'
+
+      - name: XMake config
+        run: xmake f -p linux -y --root
+
+      - name: Build
+        run: xmake --root
+
+      - name: Test
+        run: |
+          xmake f -m debug --root
+          xmake test --root

.gitignore

@@ -5,4 +5,8 @@ build/
 # MacOS Cache
 .DS_Store
 
+# VsCode
+.vscode
 
+#ImGui
+imgui.ini

.gitmodules

@@ -0,0 +1,3 @@
+[submodule "doc/doxygen-awesome-css"]
+	path = doc/doxygen-awesome-css
+	url = https://github.com/jothepro/doxygen-awesome-css

.vscode/c_cpp_properties.json

@@ -0,0 +1,11 @@
+{
+    "configurations": [
+        {
+            "name": "Pivot",
+            "cppStandard": "c++20",
+            "includePath": ["include"],
+            "compileCommands": "${workspaceFolder}/.vscode/compile_commands.json"
+        }
+    ],
+    "version": 4
+}

LICENSE.txt

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Simon Pribylski, Thibaut Alessi, Houssem Zammali, Julien Chataigner
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

@@ -0,0 +1,23 @@
+# Projet MAM Pivot
+
+
+# Cahier des charges
+![imagecdc](projet.jpg)
+
+# Build ⚙️
+
+```
+xmake
+```
+
+# Run 🏃
+
+```
+xmake run
+```
+
+# Test 🛠
+
+```
+xmake test
+```

include/Gauss.h

@@ -0,0 +1,20 @@
+#pragma once
+
+/**
+ * \file Gauss.h
+ * \brief Contient la définition de l'algorithme de Gauss
+ */
+
+class Matrix;
+
+namespace Gauss {
+
+/**
+ * \brief Echelonne une matrice en ligne en utilisant l'algorithme de Gauss-Jordan
+ * \param a_Matrix La matrice à échelonner
+ * \param a_Reduite Mets des 0 au dessus des pivots
+ * \param a_Normalise Mets les pivots à 1
+ */
+void GaussJordan(Matrix& a_Matrix, bool a_Reduite, bool a_Normalise);
+
+}  // namespace Gauss

include/IO.h

@@ -0,0 +1,52 @@
+#pragma once
+
+/**
+ * \file IO.h
+ * \brief Contient des fonctions utiles pour travailler avec les systèmes d'entrée et de sortie
+ */
+
+#include <string>
+
+class Matrix;
+class Vect;
+class VectAffine;
+
+std::ostream& operator<<(std::ostream& stream, const Matrix& mat);
+std::istream& operator>>(std::istream& stream, Matrix& mat);
+
+/**
+ * \brief Charge une matrice à partir d'un fichier
+ * \param fileName Le chemin du fichier à charger
+ * \return Une matrice de taille nulle si une erreur intervient
+ */
+Matrix LoadMatrix(const std::string& fileName);
+
+/**
+ * \brief Sauvegarde une matrice dans un fichier
+ * \param mat La matrice à sauver
+ * \param fileName Le chemin du fichier à écrire
+ */
+void SaveMatrix(const Matrix& mat, const std::string& fileName);
+
+/**
+ * \brief Permet de saisir une matrice à partir de la console
+ */
+Matrix InsertMatrix();
+
+/**
+ * \brief Affiche une matrice dans la console
+ * \param mat La matrice à afficher
+ */
+void Print(const Matrix& mat);
+
+/**
+ * \brief Affiche un espace vectoriel dans la console
+ * \param vect L'espace vectoriel à afficher
+ */
+void Print(const Vect& vect);
+
+/**
+ * \brief Affiche un espace affine dans la console
+ * \param vect L'espace affine à afficher
+ */
+void Print(const VectAffine& vect);

include/Matrix.h

@@ -0,0 +1,176 @@
+#pragma once
+
+/**
+ * \file Matrix.h
+ * \brief Contient la définition d'une matrice
+ */
+
+#include <cmath>
+#include <cstddef>
+#include <string>
+#include <vector>
+
+#include "NR.h"
+
+/**
+ * \class Matrix
+ * \brief Représente une matrice d'éléments
+ */
+class Matrix {
+  public:
+	typedef NR Element;
+	typedef std::vector<Element>::iterator iterator;
+
+  private:
+	std::size_t m_Raws;
+	std::size_t m_Columns;
+	std::vector<Element> m_Data;
+
+  public:
+	/**
+	 * \brief Constructeur par défaut. Crée une matrice de taille nulle
+	 */
+	Matrix() : m_Raws(0), m_Columns(0) {}
+
+	/**
+	 * \brief Construit une matrice de taille donnée remplie de données aléatoires (et peut-être invalides !)
+	 * \param a_Raws Le nombre de lignes
+	 * \param a_Columns Le nombre de colonne
+	 */
+	Matrix(std::size_t a_Raws, std::size_t a_Columns);
+
+	/**
+	 * \brief Construit une matrice de taille donnée avec des éléments donnés.\n
+	 * Exemple :
+	 * \code Matrix(2, 2, {1, 2, 3, 4}) \endcode construit la matrice \n
+	 * [1, 2]\n
+	 * [3, 4]
+	 * \param a_Raws Le nombre de lignes
+	 * \param a_Columns Le nombre de colonne
+	 * \param a_Elements Les élements à mettre
+	 */
+	Matrix(std::size_t a_Raws, std::size_t a_Columns, std::initializer_list<Element>&& a_Elements);
+
+	~Matrix() {}
+
+	/**
+	 * \brief Retourne le nombre de lignes de la matrice
+	 */
+	std::size_t GetRawCount() const;
+
+	/**
+	 * \brief Retourne le nombre de colonnes de la matrice
+	 */
+	std::size_t GetColumnCount() const;
+
+	/**
+	 * \brief Transpose la matrice
+	 */
+	void Transpose();
+
+	/**
+	 * \brief Augmente la matrice actuelle à droite avec une autre
+	 * \param a_Right Une matrice avec le bon nombre de lignes
+	 * \pre Les deux matrices doivent avoir le même nombre de lignes
+	 */
+	void Augment(const Matrix& a_Right);
+
+	/**
+	 * \brief Augmente la matrice actuelle en dessous avec une autre
+	 * \param a_Bottom Une matrice avec le bon nombre de colonnes
+	 * \pre Les deux matrices doivent avoir le même nombre de colonnes
+	 */
+	void AugmentBottom(const Matrix& a_Bottom);
+
+	/**
+	 * \brief Affecte tous les coefficients de la matrice à un élément
+	 * \param a_Element L'élément à affecter
+	 */
+	void Fill(Element a_Element);
+
+	/**
+	 * \brief Retourne la sous-matrice spécifiée
+	 * \param a_RawOrigin L'indice de la première ligne de la matrice à récupérer
+	 * \param a_ColumnOrigin L'indice de la première colonne de la matrice à récupérer
+	 * \param a_RawCount Le nombre de lignes de la sous-matrice
+	 * \param a_ColumnCount Le nombre de colonnes de la sous-matrice
+	 * \pre a_RawOrigin + a_RawCount <= GetRawCount()
+	 * \pre a_ColumnOrigin + a_ColumnCount <= GetColumnCount()
+	 */
+	Matrix SubMatrix(std::size_t a_RawOrigin, std::size_t a_ColumnOrigin, std::size_t a_RawCount, std::size_t a_ColumnCount) const;
+
+	Matrix operator+(const Matrix& a_Other) const;
+	Matrix operator-(const Matrix& a_Other) const;
+
+	bool operator==(const Matrix& a_Other) const;
+
+	/**
+	 * \brief Effectue un produit matriciel
+	 */
+	Matrix operator*(const Matrix& a_Other) const;
+
+	/**
+	 * \brief Retourne l'élément à l'indice recherché
+	 * \param a_Raw L'indice de la ligne
+	 * \param a_Column L'indice de la colonne
+	 */
+	Element& at(std::size_t a_Raw, std::size_t a_Column);
+
+	/**
+	 * \brief Retourne l'élément à l'indice recherché (version constante)
+	 * \param a_Raw L'indice de la ligne
+	 * \param a_Column L'indice de la colonne
+	 */
+	Element at(std::size_t a_Raw, std::size_t a_Column) const;
+
+	/**
+	 * \brief Construit une matrice identité de taille donnée
+	 * \param a_Size La taille de la matrice carrée
+	 */
+	static Matrix Identity(std::size_t a_Size);
+
+	/**
+	 * \brief Construit une matrice colonne à partir de données existantes.\n
+	 * Exemple :
+	 * \code
+	 * Matrix::ColumnVector({1, 2, 3, 4});
+	 * \endcode
+	 * construit une matrice de 4 lignes et 1 colonne de coordonnées (1, 2, 3, 4)
+	 */
+	static Matrix ColumnVector(std::initializer_list<Element>&& a_Elements);
+
+	/**
+	 * \brief Construit une matrice ligne à partir de données existantes.\n
+	 * Exemple :
+	 * \code
+	 * Matrix::RawVector({1, 2, 3, 4});
+	 * \endcode
+	 * construit une matrice de 1 ligne et 4 colonnes de coordonnées (1, 2, 3, 4)
+	 */
+	static Matrix RawVector(std::initializer_list<Element>&& a_Elements);
+
+	iterator begin();
+	iterator end();
+
+	iterator GetLineIterator(std::size_t a_Raw);
+};
+
+template <typename T>
+bool IsEqualZero(const T& var) {
+	return std::abs(var) < std::pow(10, -5);
+}
+
+template <>
+inline bool IsEqualZero(const int& var) {
+	return var == 0;
+}
+
+template <>
+inline bool IsEqualZero(const long& var) {
+	return var == 0;
+}
+
+template <>
+inline bool IsEqualZero(const NR& var) {
+	return var == 0;
+}

include/NR.h

@@ -0,0 +1,48 @@
+#pragma once
+
+#include <iostream>
+
+class NR {
+  public:
+	using Int = long long;
+
+  private:
+	Int m_Numerator;
+	Int m_Denominator;	// has to be > 0, sign is carried by the numerator
+
+  public:
+	NR();
+	NR(Int entier);
+	NR(Int numerator, Int denominator);	 // check if denominator != 0
+
+	Int GetNumerator() const;
+	Int GetDenominator() const;
+
+	bool operator==(const NR& opNR) const;
+	bool operator<(const NR& opNR) const;
+	bool operator>(const NR& opNR) const;
+
+	bool operator!=(const NR& opNR) const;
+	bool operator<=(const NR& opNR) const;
+	bool operator>=(const NR& opNR) const;
+
+	NR operator+(const NR& opNR) const;
+	NR operator-(const NR& opNR) const;
+	NR operator*(const NR& opNR) const;
+	NR operator/(const NR& opNR) const;
+
+	NR& operator+=(const NR& opNR);
+	NR& operator-=(const NR& opNR);
+	NR& operator*=(const NR& opNR);
+	NR& operator/=(const NR& opNR);
+
+	NR operator-() const;
+
+	NR Inverse() const;
+
+	friend std::ostream& operator<<(std::ostream& os, const NR& opNR);
+	friend std::istream& operator>>(std::istream& os, NR& opNR);
+
+  private:
+	void Reduce();
+};

include/Solver.h

@@ -0,0 +1,44 @@
+#pragma once
+
+/**
+ * \file Solver.h
+ * \brief Contient la définition du solutionneur
+ */
+
+#include "Vect.h"
+
+/**
+ * \class Solver
+ * \brief Permet d'obtenir différentes propriétés d'une matrice comme l'image ou le noyau
+ */
+class Solver {
+  public:
+	/**
+	 * \brief Calcule l'image d'une matrice
+	 * \param a_Matrix La matrice à traiter
+	 * \return L'espace vectoriel correspondant
+	 */
+	Vect Image(Matrix&& a_Matrix) const;
+
+	/**
+	 * \brief Calcule le noyau d'une matrice
+	 * \param a_Matrix La matrice à traiter
+	 * \return L'espace vectoriel correspondant
+	 */
+	Vect Kernel(Matrix&& a_Matrix) const;
+
+	/**
+	 * \brief Résout le système rectangulaire de la forme AX=B, avec X et B, des vecteurs colonne.
+	 * \param a_MatrixA La matrice jouant le rôle de A
+	 * \param a_VectorB La matrice colonne jouant le rôle de B
+	 * \return L'espace affine associé
+	 */
+	VectAffine RectangularSystem(Matrix&& a_MatrixA, const Matrix& a_VectorB) const;
+
+	/**
+	 * \brief Calcule le rang d'une matrice
+	 * \param a_Matrix La matrice à traiter
+	 * \note Ceci équivaut à \code Image(a_Matrix).GetCardinal() \endcode
+	 */
+	std::size_t Rank(Matrix&& a_Matrix) const;
+};

include/Vect.h

@@ -0,0 +1,111 @@
+#pragma once
+
+/**
+ * \file Vect.h
+ * \brief Contient la définition d'un espace affine et d'un espace vectoriel
+ */
+
+#include "Matrix.h"
+
+/**
+ * \class Vect
+ * \brief Représente une base d'un espace vectoriel de dimension finie
+ */
+class Vect {
+  private:
+	Matrix m_Data;
+
+  public:
+	/**
+	 * \brief Construit une base d'un espace vectoriel à partir des colonnes d'une matrice.
+	 * Les colonnes de 0 sont ignorées
+	 * \param a_Matrix Une matrice échelonnée.
+	 */
+	Vect(Matrix&& a_Matrix);
+
+	/**
+	 * \brief Permet d'obtenir le ieme vecteur de la base
+	 * \param a_Index l'index du vecteur souhaité
+	 * \return Une matrice colonne
+	 */
+	Matrix GetVector(std::size_t a_Index) const;
+
+	/**
+	 * \brief Retourne le nombre de coordonnées des vecteurs de la base (leur nombre de colonne)
+	 */
+	std::size_t GetDimension() const;
+
+	/**
+	 * \brief Retourne le nombre de vecteur de la base
+	 */
+	std::size_t GetCardinal() const;
+
+	/**
+	 * \brief Exprime l'espace vectoriel comme les solutions d'un système linéaire des coordonnées des vecteurs
+	 * \return Une matrice représentant le système linéaire
+	 */
+	Matrix GetLinearSystem() const;
+
+	/**
+	 * \brief Concatène la base actuelle avec un nouveau vecteur
+	 * \param a_Vector Une matrice colonne de taille GetDimension()
+	 */
+	void AddVector(const Matrix& a_Vector);
+
+	/**
+	 * \brief Vérifie si le vecteur spécifié appartient au sous-espace vectoriel
+	 * \param a_Vector Une matrice colonne représentant le vecteur à tester
+	 */
+	bool IsElementOf(const Matrix& a_Vector) const;
+
+	bool operator==(const Vect& a_Other) const;
+	bool operator!=(const Vect& a_Other) const;
+
+  private:
+	void Simplify();
+
+	friend class VectAffine;
+};
+
+/**
+ * \class VectAffine
+ * \brief Représente un espace affine
+ */
+class VectAffine {
+  private:
+	Vect m_Base;
+	Matrix m_Origin;
+
+  public:
+	/**
+	 * \brief Construit un espace affine à partir d'un espace vectoriel et d'une origine
+	 * \param a_Base La base de l'espace vectoriel
+	 * \param a_Origin Le vecteur d'origine (matrice colonne)
+	 */
+	VectAffine(const Vect& a_Base, const Matrix& a_Origin);
+
+	/**
+	 * \brief Retourne l'espace vectoriel correspondant
+	 */
+	const Vect& GetBase() const {
+		return m_Base;
+	}
+
+	/**
+	 * \brief Retourne l'origine de l'espace affine
+	 * \return Un vecteur colonne
+	 */
+	const Matrix& GetOrigin() const {
+		return m_Origin;
+	}
+
+	/**
+	 * \brief Vérifie si le vecteur spécifié appartient à l'espace affine
+	 * \param a_Vector Une matrice colonne représentant le vecteur à tester
+	 */
+	bool IsElementOf(const Matrix& a_Vector) const;
+
+	bool operator==(const VectAffine& a_VectAffine) const {
+		return m_Origin == a_VectAffine.GetOrigin() && m_Base == a_VectAffine.GetBase();
+	};
+};

matricies/test/matrice1.test

@@ -0,0 +1,12 @@
+2 3
+1 2 3
+4 5 6
+
+2 2
+0 1
+1 0
+
+3 1
+1
+-2
+1

matricies/test/matrice2.test

@@ -0,0 +1,11 @@
+3 3
+1 0 1
+0 1 3
+0 4 4
+
+3 3
+1 0 0
+0 1 0
+0 0 1
+
+3 0

matricies/test/matrice3.test

@@ -0,0 +1,16 @@
+4 3
+1 -1 0
+2 1 3
+1 2 3
+2 -2 0
+
+4 2
+1 0
+1 1
+0 1
+2 0
+
+3 1
+1
+1
+-1

matricies/test/matrice4.test

@@ -0,0 +1,17 @@
+4 4
+5 2 3 0
+9 0 -9 0
+1 0 -1 0
+0 0 3 -3
+
+4 3
+1 0 0
+0 0 9
+0 0 1
+0 -3 0
+
+4 1
+1
+-4
+1
+1

matricies/test/matrice5.test

@@ -0,0 +1,14 @@
+5 4
+0 0 0 0
+0 0 0 0
+0 0 0 0
+0 0 0 0
+0 0 0 0
+
+5 0
+
+4 4
+1 0 0 0
+0 1 0 0
+0 0 1 0
+0 0 0 1

matricies/test/matrice6.test

@@ -0,0 +1,19 @@
+5 4
+0 0 0 0
+0 0 0 1
+0 0 0 0
+0 0 0 0
+0 0 0 0
+
+5 1
+0
+1
+0
+0
+0
+
+4 3
+1 0 0
+0 1 0
+0 0 1
+0 0 0

src/Gauss.cpp

@@ -0,0 +1,113 @@
+#include "Gauss.h"
+
+#include "Matrix.h"
+
+#include <algorithm>
+#include <execution>
+#include <ranges>
+
+namespace Gauss {
+
+static void SwapLines(Matrix& mat, std::size_t line1, std::size_t line2) {
+	std::swap_ranges(
+		std::execution::par_unseq, mat.GetLineIterator(line1), mat.GetLineIterator(line1 + 1), mat.GetLineIterator(line2));
+}
+
+static void DivideLine(Matrix& mat, std::size_t line, Matrix::Element number) {
+	std::transform(std::execution::par_unseq, mat.GetLineIterator(line), mat.GetLineIterator(line + 1), mat.GetLineIterator(line),
+		[number](Matrix::Element e) { return e /= number; });
+}
+
+static int FirstNotNullElementIndexOnColumn(Matrix& mat, std::size_t column, std::size_t startLine = 0) {
+	for (std::size_t i = startLine; i < mat.GetRawCount(); i++) {
+		if (!IsEqualZero(mat.at(i, column))) {
+			return i;
+		}
+	}
+	return -1;
+}
+
+static void SimplifyLine(Matrix& mat, std::size_t line, std::size_t pivot_line, std::size_t pivot_column) {
+	const Matrix::Element pivot = mat.at(pivot_line, pivot_column);
+	const Matrix::Element anul = mat.at(line, pivot_column);
+
+	auto range = std::views::iota(static_cast<std::size_t>(0), mat.GetColumnCount());
+
+	std::for_each(std::execution::par_unseq, range.begin(), range.end(), [&mat, pivot, anul, line, pivot_line](std::size_t j) {
+		mat.at(line, j) = mat.at(line, j) * pivot - mat.at(pivot_line, j) * anul;
+	});
+}
+
+static void GaussJordanReduced(Matrix& a_Matrix, bool a_Normalise) {
+	int indice_ligne_pivot = -1;
+
+	for (std::size_t j = 0; j < a_Matrix.GetColumnCount(); j++) {
+
+		int indice_ligne_pivot_trouve = FirstNotNullElementIndexOnColumn(a_Matrix, j, indice_ligne_pivot + 1);
+
+		if (indice_ligne_pivot_trouve < 0)	// colonne de 0
+			continue;						// on regarde la prochaine colonne
+
+		indice_ligne_pivot++;
+
+		if (indice_ligne_pivot_trouve != indice_ligne_pivot) {
+			SwapLines(a_Matrix, indice_ligne_pivot_trouve, indice_ligne_pivot);
+		}
+
+		Matrix::Element pivot = a_Matrix.at(indice_ligne_pivot, j);
+
+		if (a_Normalise) {
+			DivideLine(a_Matrix, indice_ligne_pivot, pivot);
+		}
+
+		auto range = std::views::iota(static_cast<std::size_t>(0), a_Matrix.GetRawCount());
+
+		// On simplifie les autres lignes
+		std::for_each(std::execution::par_unseq, range.begin(), range.end(), [&a_Matrix, j, indice_ligne_pivot](std::size_t i) {
+			if (i != static_cast<std::size_t>(indice_ligne_pivot)) {
+				SimplifyLine(a_Matrix, i, indice_ligne_pivot, j);
+			}
+		});
+	}
+}
+
+static void GaussJordanTriangular(Matrix& a_Matrix, bool a_Normalise) {
+	int indice_ligne_pivot = -1;
+
+	for (std::size_t j = 0; j < a_Matrix.GetColumnCount(); j++) {
+
+		int indice_ligne_pivot_trouve = FirstNotNullElementIndexOnColumn(a_Matrix, j, indice_ligne_pivot + 1);
+
+		if (indice_ligne_pivot_trouve < 0)	// colonne de 0
+			continue;						// on regarde la prochaine colonne
+
+		indice_ligne_pivot++;
+
+		if (indice_ligne_pivot_trouve != indice_ligne_pivot) {
+			SwapLines(a_Matrix, indice_ligne_pivot_trouve, indice_ligne_pivot);
+		}
+
+		Matrix::Element pivot = a_Matrix.at(indice_ligne_pivot, j);
+
+		if (a_Normalise) {
+			DivideLine(a_Matrix, indice_ligne_pivot, pivot);
+		}
+
+		auto range = std::views::iota(static_cast<std::size_t>(indice_ligne_pivot + 1), a_Matrix.GetRawCount());
+
+		// On simplifie les autres lignes après la ligne du pivot
+		std::for_each(std::execution::par_unseq, range.begin(), range.end(),
+			[&a_Matrix, indice_ligne_pivot, j](std::size_t i) { 
+				SimplifyLine(a_Matrix, i, indice_ligne_pivot, j); 
+			});
+	}
+}
+
+void GaussJordan(Matrix& a_Matrix, bool a_Reduite, bool a_Normalise) {
+	if (a_Reduite)
+		GaussJordanReduced(a_Matrix, a_Normalise);
+	else
+		GaussJordanTriangular(a_Matrix, a_Normalise);
+}
+
+}  // namespace Gauss

src/IO.cpp

@@ -0,0 +1,101 @@
+#include "IO.h"
+
+#include "Vect.h"
+#include <fstream>
+#include <iostream>
+
+std::ostream& operator<<(std::ostream& stream, const Matrix& mat) {
+	stream << mat.GetRawCount() << " " << mat.GetColumnCount() << "\n";
+	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
+			stream << mat.at(i, j) << " ";
+		}
+		stream << "\n";
+	}
+	return stream;
+}
+
+std::istream& operator>>(std::istream& stream, Matrix& mat) {
+	std::size_t raw, column;
+	stream >> raw >> column;
+
+	Matrix result {raw, column};
+	mat = result;
+
+	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
+			stream >> mat.at(i, j);
+		}
+	}
+
+	return stream;
+}
+
+Matrix LoadMatrix(const std::string& fileName) {
+	std::ifstream in {fileName};
+	if (!in) {
+		std::cerr << "Impossible de charger la matrice !\n";
+		return {};
+	}
+	Matrix result;
+	in >> result;
+
+	return result;
+}
+
+void SaveMatrix(const Matrix& mat, const std::string& fileName) {
+	std::ofstream out {fileName};
+	if (!out) {
+		std::cerr << "Impossible de sauvegarder la matrice !\n";
+		return;
+	}
+	out << mat;
+}
+
+Matrix InsertMatrix() {
+	std::cout << "Quelle est le nombre de lignes de votre matrice ?" << std::endl;
+	std::size_t lignes;
+	std::cin >> lignes;
+	std::cout << "Quelle est le nombre de colonnes de votre matrice ?" << std::endl;
+	std::size_t colonnes;
+	std::cin >> colonnes;
+	std::cout << "Rentrez les coefficients de la matrice" << std::endl;
+	Matrix result(lignes, colonnes);
+	for (size_t i = 0; i < result.GetRawCount(); ++i) {
+		for (size_t j = 0; j < result.GetColumnCount(); ++j) {
+			std::cin >> result.at(i, j);
+		}
+		std::cout << std::endl;
+	}
+
+	return result;
+}
+
+void Print(const Matrix& mat) {
+	for (size_t i = 0; i < mat.GetRawCount(); ++i) {
+		std::cout << "[ ";
+		for (size_t j = 0; j < mat.GetColumnCount(); ++j) {
+			std::cout << mat.at(i, j) << " ";
+		}
+		std::cout << "]";
+		std::cout << std::endl;
+	}
+}
+
+void Print(const Vect& vect) {
+	std::cout << "Espace vectoriel de dimension " << vect.GetCardinal() << " de base :\n\n";
+	for (std::size_t i = 0; i < vect.GetDimension(); i++) {
+		for (std::size_t j = 0; j < vect.GetCardinal(); j++) {
+			Matrix vector = vect.GetVector(j);
+			std::cout << "[ " << vector.at(i, 0) << " ]\t";
+		}
+		std::cout << "\n";
+	}
+}
+
+void Print(const VectAffine& vect) {
+	std::cout << "\tEspace Affine :\n\n";
+	Print(vect.GetBase());
+	std::cout << "\nOrigine :\n\n";
+	Print(vect.GetOrigin());
+}

src/Matrix.cpp

@@ -0,0 +1,199 @@
+#include "Matrix.h"
+
+#include "IO.h"
+#include <algorithm>
+#include <cassert>
+#include <cmath>
+#include <fstream>
+#include <iostream>
+
+Matrix::Matrix(std::size_t a_Raws, std::size_t a_Columns) : m_Raws(a_Raws), m_Columns(a_Columns) {
+	m_Data.resize(m_Raws * m_Columns);
+}
+
+Matrix::Matrix(std::size_t a_Raws, std::size_t a_Columns, std::initializer_list<Element>&& a_Elements) :
+	m_Raws(a_Raws), m_Columns(a_Columns) {
+	m_Data = a_Elements;
+	m_Data.resize(m_Raws * m_Columns);
+}
+
+Matrix Matrix::operator*(const Matrix& a_Other) const {
+	assert(m_Columns == a_Other.m_Raws);
+
+	Matrix result(m_Raws, a_Other.m_Columns);
+
+	for (std::size_t i = 0; i < m_Raws; ++i) {
+		for (std::size_t j = 0; j < a_Other.m_Columns; ++j) {
+			Element sum = 0;
+			for (std::size_t k = 0; k < m_Columns; k++) {
+				sum += at(i, k) * a_Other.at(k, j);
+			}
+			result.at(i, j) = sum;
+		}
+	}
+	return result;
+}
+
+void Matrix::Transpose() {
+	Matrix result {m_Columns, m_Raws};
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < m_Columns; j++) {
+			result.at(j, i) = at(i, j);
+		}
+	}
+	*this = result;
+}
+
+Matrix Matrix::Identity(std::size_t a_Size) {
+	Matrix id {a_Size, a_Size};
+	for (std::size_t i = 0; i < a_Size; i++) {
+		for (std::size_t j = i; j < a_Size; j++) {
+			id.at(i, j) = (i == j);
+		}
+	}
+	return id;
+}
+
+Matrix Matrix::ColumnVector(std::initializer_list<Element>&& a_Elements) {
+	Matrix result {a_Elements.size(), 1};
+
+	result.m_Data = a_Elements;
+
+	return result;
+}
+
+Matrix Matrix::RawVector(std::initializer_list<Element>&& a_Elements) {
+	Matrix result {1, a_Elements.size()};
+
+	result.m_Data = a_Elements;
+
+	return result;
+}
+
+void Matrix::Fill(Element a_Element) {
+	std::fill(GetLineIterator(0), GetLineIterator(m_Raws), a_Element);
+}
+
+void Matrix::Augment(const Matrix& a_Right) {
+	assert(a_Right.m_Raws == m_Raws);
+	Matrix temp {m_Raws, m_Columns + a_Right.m_Columns};
+
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < m_Columns; j++) {
+			temp.at(i, j) = at(i, j);
+		}
+	}
+
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < a_Right.m_Columns; j++) {
+			temp.at(i, j + m_Columns) = a_Right.at(i, j);
+		}
+	}
+
+	*this = temp;
+}
+
+void Matrix::AugmentBottom(const Matrix& a_Bottom) {
+	assert(a_Bottom.m_Columns == m_Columns);
+	Matrix temp {m_Raws + a_Bottom.GetRawCount(), m_Columns};
+
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < m_Columns; j++) {
+			temp.at(i, j) = at(i, j);
+		}
+	}
+
+	for (std::size_t i = 0; i < a_Bottom.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < GetColumnCount(); j++) {
+			temp.at(i + GetRawCount(), j) = a_Bottom.at(i, j);
+		}
+	}
+
+	*this = temp;
+}
+
+Matrix Matrix::operator+(const Matrix& a_Other) const {
+	assert(GetColumnCount() == a_Other.GetColumnCount() && GetRawCount() == a_Other.GetRawCount());
+
+	Matrix result = *this;
+
+	for (std::size_t i = 0; i < GetRawCount(); i++) {
+		for (std::size_t j = 0; j < GetColumnCount(); j++) {
+			result.at(i, j) += a_Other.at(i, j);
+		}
+	}
+
+	return result;
+}
+
+Matrix Matrix::operator-(const Matrix& a_Other) const {
+	assert(GetColumnCount() == a_Other.GetColumnCount() && GetRawCount() == a_Other.GetRawCount());
+
+	Matrix result = *this;
+
+	for (std::size_t i = 0; i < GetRawCount(); i++) {
+		for (std::size_t j = 0; j < GetColumnCount(); j++) {
+			result.at(i, j) -= a_Other.at(i, j);
+		}
+	}
+
+	return result;
+}
+
+bool Matrix::operator==(const Matrix& a_Other) const {
+	assert(m_Raws == a_Other.m_Raws && m_Columns == a_Other.m_Columns);
+
+	for (std::size_t i = 0; i < m_Raws; i++) {
+		for (std::size_t j = 0; j < m_Columns; j++) {
+			if (!IsEqualZero(at(i, j) - a_Other.at(i, j)))
+				return false;
+		}
+	}
+
+	return true;
+}
+
+Matrix::Element& Matrix::at(std::size_t a_Raw, std::size_t a_Column) {
+	assert(a_Raw < m_Raws && a_Column < m_Columns);
+	return m_Data[a_Raw * m_Columns + a_Column];
+}
+
+Matrix::Element Matrix::at(std::size_t a_Raw, std::size_t a_Column) const {
+	assert(a_Raw < m_Raws && a_Column < m_Columns);
+	return m_Data[a_Raw * m_Columns + a_Column];
+}
+
+std::size_t Matrix::GetRawCount() const {
+	return m_Raws;
+}
+
+std::size_t Matrix::GetColumnCount() const {
+	return m_Columns;
+}
+
+Matrix Matrix::SubMatrix(
+	std::size_t a_RawOrigin, std::size_t a_ColumnOrigin, std::size_t a_RawCount, std::size_t a_ColumnCount) const {
+	assert(m_Raws >= a_RawOrigin + a_RawCount && m_Columns >= a_ColumnOrigin + a_ColumnCount);
+
+	Matrix result {a_RawCount, a_ColumnCount};
+
+	for (std::size_t i = 0; i < result.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < result.GetColumnCount(); j++) {
+			result.at(i, j) = at(i + a_RawOrigin, j + a_ColumnOrigin);
+		}
+	}
+
+	return result;
+}
+
+Matrix::iterator Matrix::begin() {
+	return m_Data.begin();
+}
+
+Matrix::iterator Matrix::end() {
+	return m_Data.end();
+}
+
+Matrix::iterator Matrix::GetLineIterator(std::size_t a_Raw) {
+	return m_Data.begin() + a_Raw * GetColumnCount();
+}

src/Matrix.h

@@ -1,256 +0,0 @@
-#pragma once
-
-#include <algorithm>
-#include <cmath>
-#include <fstream>
-#include <iostream>
-#include <vector>
-
-template <typename T>
-static bool EqualZero(T var) {
-	return std::abs(var) < std::pow(10, -5);
-}
-
-template <typename T>
-class Matrix {
-  private:
-	std::size_t m_Lignes;
-	std::size_t m_Colonnes;
-	std::size_t m_Dimension;
-	std::vector<T> m_Data;
-
-  public:
-	Matrix(const std::string& fileNameInput) {
-		Load(fileNameInput);
-	}
-	Matrix(std::size_t lignes, std::size_t colonnes) : m_Lignes(lignes), m_Colonnes(colonnes), m_Dimension(lignes * colonnes) {
-		m_Data.resize(m_Dimension);
-	}
-	Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<T>&& initList) :
-		m_Lignes(lignes), m_Colonnes(colonnes), m_Dimension(lignes * colonnes) {
-		m_Data = initList;
-		m_Data.resize(m_Dimension);
-	}
-	~Matrix() {}
-
-	Matrix operator*(const Matrix& other) const {
-		if (m_Colonnes != other.m_Lignes) {
-			std::cerr << "Mutiplication impossible car la dimensions des matrices est incompatible" << std::endl;
-		}
-
-		Matrix result(m_Lignes, other.m_Colonnes);
-
-		for (std::size_t i = 0; i < m_Lignes; ++i) {
-			for (std::size_t j = 0; j < other.m_Colonnes; ++j) {
-				T sum = 0;
-				for (std::size_t k = 0; k < m_Colonnes; k++) {
-					sum += at(i, k) * other.at(k, j);
-				}
-				result.at(i, j) = sum;
-			}
-		}
-		return result;
-	}
-
-	void Print() const {
-		for (size_t i = 0; i < m_Lignes; ++i) {
-			std::cout << "[ ";
-			for (size_t j = 0; j < m_Colonnes; ++j) {
-				std::size_t indice = i * m_Lignes + j;
-				std::cout << at(i, j) << " ";
-			}
-			std::cout << "]";
-			std::cout << std::endl;
-		}
-	}
-
-	void PrintDebug() {
-#ifndef NDEBUG
-		Print();
-		std::cout << "\n";
-#endif
-	}
-
-	void Insert() {
-		for (size_t i = 0; i < m_Lignes; ++i) {
-			for (size_t j = 0; j < m_Colonnes; ++j) {
-				std::cin >> at(i, j);
-			}
-			std::cout << std::endl;
-		}
-	}
-
-	void Save(const std::string& fileName) {
-		std::ofstream out{fileName};
-		if (!out) {
-			std::cerr << "Impossible de sauvegarder la matrice !\n";
-			return;
-		}
-		out << m_Lignes << " " << m_Colonnes << "\n";
-		for (std::size_t i = 0; i < m_Lignes; i++) {
-			for (std::size_t j = 0; j < m_Colonnes; j++) {
-				out << at(i, j) << " ";
-			}
-			out << "\n";
-		}
-	}
-
-	void Load(const std::string& filename) {
-		std::ifstream in{filename};
-		if (!in) {
-			std::cerr << "Impossible de charger la matrice !\n";
-			return;
-		}
-		in >> m_Lignes >> m_Colonnes;
-		m_Data.resize(m_Lignes * m_Colonnes);
-		for (std::size_t i = 0; i < m_Lignes; i++) {
-			for (std::size_t j = 0; j < m_Colonnes; j++) {
-				in >> at(i, j);
-			}
-		}
-	}
-
-	void Transpose() {
-		for (std::size_t i = 0; i < m_Lignes; i++) {
-			for (std::size_t j = i; j < m_Colonnes; j++) {
-				std::swap(at(i, j), at(j, i));
-			}
-		}
-	}
-
-	void Identity() {
-		for (std::size_t i = 0; i < m_Lignes; i++) {
-			for (std::size_t j = i; j < m_Colonnes; j++) {
-				if (i != j) {
-					at(i, j) = 0;
-				} else {
-					at(i, j) = 1;
-				}
-			}
-		}
-	}
-
-	bool IsInverse(const Matrix& mat, const Matrix& aug) const {
-		Matrix result = mat * aug;
-
-		for (std::size_t i = 0; i < m_Lignes; ++i) {
-			for (std::size_t j = 0; j < m_Colonnes; ++j) {
-				if ((i == j && !EqualZero(result.at(i, j) - 1.0)) || (i != j && EqualZero(result.at(i, j)))) {
-					return false;
-				}
-			}
-		}
-		return true;
-	}
-
-	Matrix GaussNonJordan(bool reduite, bool augmentee) {
-		Matrix<float> aug = Matrix(m_Lignes, m_Colonnes);
-		if (augmentee) {
-			std::size_t choix;
-			std::cout
-				<< "Entrez 1 pour rentrer la matrice augmentee que je vous voulez ou 2 pour la matrice augmentee Id pour trouver "
-				   "l'inverse si elle existe."
-				<< std::endl;
-			std::cin >> choix;
-			while (choix != 1 && choix != 2) {
-				std::cout
-					<< "Entrez 1 pour rentrer la matrice augmentee que je vous voulez ou 2 pour la matrice augmentee Id pour trouver "
-					   "l'inverse si elle existe."
-					<< std::endl;
-				std::cin >> choix;
-			}
-			if (choix == 1) {
-				std::cout << "Rentrez les coefficients de la matrice" << std::endl;
-				aug.Insert();
-			} else {
-				aug.Identity();
-			}
-		}
-		aug.Print();
-		int r = -1;
-		for (std::size_t j = 0; j < m_Colonnes; j++) {
-			std::size_t indice_ligne_maximum = r + 1;
-
-			// Recherche maximum
-			for (std::size_t i = r + 1; i < m_Lignes; i++) {
-				if (std::abs(at(i, j)) > std::abs(at(indice_ligne_maximum, j)))
-					indice_ligne_maximum = i;
-			}
-
-			// std::cout << "l'indice du maximum est : " << indice_ligne_maximum << "\n\n";
-
-			// Si A[k,j]≠0 alors    (A[k,j] désigne la valeur de la ligne k et de la colonne j)
-			if (at(indice_ligne_maximum, j) != 0) {
-				r++;
-
-				// PrintDebug();
-
-				// Si k≠r alors
-				if (indice_ligne_maximum != r) {
-					// Échanger les lignes k et r  (On place la ligne du pivot en position r)
-					// std::cout << "On échange les lignes " << indice_ligne_maximum << " et " << r << '\n';
-					for (std::size_t k = 0; k < m_Colonnes; k++) {
-						std::swap(at(indice_ligne_maximum, k), at(r, k));
-						// matrice augmentee
-						std::swap(aug.at(indice_ligne_maximum, k), aug.at(r, k));
-					}
-				}
-
-				// Pour i de 1 jusqu'à n               (On simplifie les autres lignes)
-				for (std::size_t i = (reduite ? 0 : j); i < m_Lignes; i++) {
-					// Si i≠r alors
-					if (i != r) {
-						// Soustraire à la ligne i la ligne r multipliée par A[i,j] (de façon à
-						// annuler A[i,j])
-						T anulid = at(i, j);
-						for (int k = m_Colonnes - 1; k >= 0; k--) {
-							T pivot = at(r, j);
-							T anul = at(i, j);
-							at(i, k) = at(i, k) * pivot - at(r, k) * anul;
-							// matrice augmentee
-							aug.at(i, k) = aug.at(i, k) * pivot - aug.at(r, k) * anulid;
-						}
-					}
-				}
-			}
-		}
-		return (aug);
-	}
-
-	Matrix GaussJordan(bool reduite, bool augmentee) {
-		Matrix<float> aug = GaussNonJordan(reduite, augmentee);
-		for (std::size_t i = 0; i < m_Lignes; i++) {
-			int k = -1;
-			int kaugmentee = -1;
-			for (std::size_t j = 0; j < m_Colonnes; j++) {
-				if (at(i, j) != 0) {
-					k = j;
-					break;
-				}
-			}
-			// ligne de 0
-			if (k == -1)
-				break;
-			// on divise la ligne par (i, k)
-			T annul = at(i, k);
-			for (int j = 0; j < m_Colonnes; j++) {
-				at(i, j) /= annul;
-				// augmentee
-				aug.at(i, j) /= annul;
-			}
-		}
-		return aug;
-	}
-
-	T& operator[](std::size_t indice) {
-		return at(indice);
-	}
-
-	T& at(std::size_t ligne, std::size_t colonne) {
-		return m_Data[ligne * m_Lignes + colonne];
-	}
-
-	T at(std::size_t ligne, std::size_t colonne) const {
-		return m_Data[ligne * m_Lignes + colonne];
-	}
-};

src/NR.cpp

@@ -0,0 +1,145 @@
+#include "NR.h"
+
+#include <cassert>
+#include <iostream>
+
+NR::Int PGCD(NR::Int x, NR::Int y) {
+	if (x == 0 || y == 0)
+		return 1;
+	else if (x % y == 0)
+		return std::abs(y);
+	else
+		return PGCD(y, x % y);
+}
+
+NR::NR() : m_Numerator(0), m_Denominator(1) {}
+
+NR::NR(NR::Int entier) : m_Numerator(entier), m_Denominator(1) {}
+
+NR::NR(NR::Int numerator, NR::Int denominator) :
+	m_Numerator((denominator > 0) ? numerator : -numerator), m_Denominator(std::abs(denominator)) {
+	Reduce();
+}
+
+void NR::Reduce() {
+	NR::Int divisor = PGCD(m_Denominator, m_Numerator);
+	m_Denominator /= divisor;
+	m_Numerator /= divisor;
+	assert(m_Denominator != 0);
+}
+
+NR NR::Inverse() const {
+	assert(*this != 0);
+	return {m_Denominator, m_Numerator};
+}
+
+NR::Int NR::GetNumerator() const {
+	return m_Numerator;
+}
+
+NR::Int NR::GetDenominator() const {
+	return m_Denominator;
+}
+
+bool NR::operator==(const NR& opNR) const {
+	return (m_Numerator * opNR.GetDenominator() == m_Denominator * opNR.GetNumerator());
+}
+
+bool NR::operator<(const NR& opNR) const {
+	return (m_Numerator * opNR.GetDenominator() < m_Denominator * opNR.GetNumerator());
+}
+
+bool NR::operator>(const NR& opNR) const {
+	return (m_Numerator * opNR.GetDenominator() > m_Denominator * opNR.GetNumerator());
+}
+
+bool NR::operator!=(const NR& opNR) const {
+	return !(*this == opNR);
+}
+
+bool NR::operator<=(const NR& opNR) const {
+	return !(*this > opNR);
+}
+
+bool NR::operator>=(const NR& opNR) const {
+	return !(*this < opNR);
+}
+
+std::ostream& operator<<(std::ostream& os, const NR& opNR) {
+	os << opNR.GetNumerator();
+	if (opNR.GetDenominator() != 1)
+		os << "/" << opNR.GetDenominator();
+	return os;
+}
+
+std::istream& operator>>(std::istream& is, NR& opNR) {
+	char slash;
+	is >> opNR.m_Numerator >> slash;
+	if (slash != '/') {
+		// on revient un charactère en arrière
+		is.seekg(is.tellg() - static_cast<std::streampos>(1));
+		opNR.m_Denominator = 1;
+	} else {
+		is >> opNR.m_Denominator;
+	}
+	opNR.Reduce();
+	return is;
+}
+
+NR NR::operator+(const NR& opNR) const {
+	Int num, den;
+	num = m_Numerator * opNR.GetDenominator();
+	den = m_Denominator * opNR.GetDenominator();
+	num += (opNR.GetNumerator() * m_Denominator);
+	NR result(num, num == 0 ? 1 : den);
+	return result;
+}
+
+NR NR::operator-(const NR& opNR) const {
+	Int num, den;
+	num = m_Numerator * opNR.GetDenominator();
+	den = m_Denominator * opNR.GetDenominator();
+	num -= (opNR.GetNumerator() * m_Denominator);
+	NR result(num, num == 0 ? 1 : den);
+	return result;
+}
+
+NR NR::operator*(const NR& opNR) const {
+	Int num, den;
+	num = m_Numerator * opNR.GetNumerator();
+	den = m_Denominator * opNR.GetDenominator();
+	NR result(num, num == 0 ? 1 : den);
+	return result;
+}
+
+NR NR::operator/(const NR& opNR) const {
+	Int num, den;
+	num = m_Numerator * opNR.GetDenominator();
+	den = m_Denominator * opNR.GetNumerator();
+	NR result(num, num == 0 ? 1 : den);
+	return result;
+}
+
+NR& NR::operator+=(const NR& opNR) {
+	*this = *this + opNR;
+	return *this;
+}
+
+NR& NR::operator-=(const NR& opNR) {
+	*this = *this - opNR;
+	return *this;
+}
+
+NR& NR::operator*=(const NR& opNR) {
+	*this = *this * opNR;
+	return *this;
+}
+
+NR& NR::operator/=(const NR& opNR) {
+	*this = *this / opNR;
+	return *this;
+}
+
+NR NR::operator-() const {
+	return {-m_Numerator, m_Denominator};
+}

src/NR.h

@@ -1,12 +0,0 @@
-#pragma once
-
-class NR {
-  private:
-	int m_Numerator;
-	int m_Denominator;
-
-  public:
-	NR() : m_Numerator(0), m_Denominator(1) {}
-	NR(int entier) : m_Numerator(entier), m_Denominator(1) {}
-	NR(int numerator, int denominator) : m_Numerator(numerator), m_Denominator(denominator) {}
-};

src/Solver.cpp

@@ -0,0 +1,70 @@
+#include "Solver.h"
+
+#include "Gauss.h"
+
+static int FirstNotNullElementIndexOnLine(const Matrix& mat, std::size_t line) {
+	for (std::size_t i = 0; i < mat.GetColumnCount(); i++) {
+		if (!IsEqualZero(mat.at(line, i))) {
+			return i;
+		}
+	}
+	return -1;
+}
+
+Vect Solver::Image(Matrix&& a_Matrix) const {
+	a_Matrix.Transpose();
+	Gauss::GaussJordan(a_Matrix, false, false);
+	a_Matrix.Transpose();
+	return {std::move(a_Matrix)};
+}
+
+// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
+Vect Solver::Kernel(Matrix&& a_Matrix) const {
+	std::size_t matrixRawCount = a_Matrix.GetRawCount();
+	std::size_t matrixColumnCount = a_Matrix.GetColumnCount();
+
+	a_Matrix.Transpose();
+	a_Matrix.Augment(Matrix::Identity(a_Matrix.GetRawCount()));
+	Gauss::GaussJordan(a_Matrix, false, true);
+	a_Matrix.Transpose();
+
+	// nombre de colonnes non nulles
+	std::size_t origine_colonne = Vect(a_Matrix.SubMatrix(0, 0, matrixRawCount, matrixColumnCount)).GetCardinal();
+
+	return {a_Matrix.SubMatrix(
+		matrixRawCount, origine_colonne, a_Matrix.GetRawCount() - matrixRawCount, a_Matrix.GetColumnCount() - origine_colonne)};
+}
+
+VectAffine Solver::RectangularSystem(Matrix&& a_MatrixA, const Matrix& a_VectorB) const {
+	Matrix mat = a_MatrixA;
+	mat.Augment(a_VectorB);
+	Gauss::GaussJordan(mat, true, true);
+
+	Solver solver;
+
+	Vect noyau = solver.Kernel(std::move(a_MatrixA));
+	Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
+
+	// on calcule le vecteur qui dirige l'espace affine
+	Matrix fullOrigin {mat.GetColumnCount() - 1, 1};
+	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
+		int pivot_index = FirstNotNullElementIndexOnLine(mat, i);
+		
+		if (static_cast<std::size_t>(pivot_index) == mat.GetColumnCount() - 1) {
+			// on a une ligne du type 0 = n. Aucune solution !
+			return {Matrix {}, Matrix::ColumnVector({0})};
+		}
+
+		// ligne entière de 0
+		if (pivot_index < 0)
+			continue;
+
+		fullOrigin.at(pivot_index, 0) = origin.at(i, 0);
+	}
+
+	return {noyau, fullOrigin};
+}
+
+std::size_t Solver::Rank(Matrix&& a_Matrix) const {
+	return Image(std::move(a_Matrix)).GetCardinal();
+}

src/Vect.cpp

@@ -0,0 +1,90 @@
+#include "Vect.h"
+
+#include "Gauss.h"
+#include "Solver.h"
+
+static bool IsColumnNull(Matrix& mat, std::size_t column) {
+	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
+		if (!IsEqualZero(mat.at(i, column))) {
+			return false;
+		}
+	}
+	return true;
+}
+
+Vect::Vect(Matrix&& a_Matrix) : m_Data(std::move(a_Matrix)) {
+	m_Data.Transpose();
+	Gauss::GaussJordan(m_Data, false, true);
+	m_Data.Transpose();
+	Simplify();
+}
+
+void Vect::Simplify() {
+	Matrix mat = m_Data;
+	for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
+		if (IsColumnNull(mat, j)) {
+			m_Data = mat.SubMatrix(0, 0, mat.GetRawCount(), j);
+			return;
+		}
+	}
+	m_Data = mat;
+}
+
+Matrix Vect::GetVector(std::size_t a_Index) const {
+	return m_Data.SubMatrix(0, a_Index, m_Data.GetRawCount(), 1);
+}
+
+std::size_t Vect::GetCardinal() const {
+	return m_Data.GetColumnCount();
+}
+
+bool Vect::IsElementOf(const Matrix& a_Vector) const {
+	Vect base = *this;
+	base.AddVector(a_Vector);
+	return base.GetCardinal() == GetCardinal();
+}
+
+bool Vect::operator==(const Vect& a_Other) const {
+	if (GetDimension() != a_Other.GetDimension() || GetCardinal() != a_Other.GetCardinal())
+		return false;
+
+	// on vérifie si chaque vecteur de la deuxième base appartient à l'espace vectoriel engendré par la première base
+	for (std::size_t i = 0; i < GetCardinal(); i++) {
+		if (!IsElementOf(a_Other.GetVector(i)))
+			return false;
+	}
+	return true;
+}
+
+void Vect::AddVector(const Matrix& a_Vector) {
+	m_Data.Augment(a_Vector);
+	m_Data.Transpose();
+	Gauss::GaussJordan(m_Data, false, false);
+	m_Data.Transpose();
+	Simplify();
+}
+
+bool Vect::operator!=(const Vect& a_Other) const {
+	return !(*this == a_Other);
+}
+
+Matrix Vect::GetLinearSystem() const {
+	Matrix vect = m_Data;
+	vect.Transpose();
+
+	Solver solver;
+	Matrix result = solver.Kernel(std::move(vect)).m_Data;
+	result.Transpose();
+	return result;
+}
+
+std::size_t Vect::GetDimension() const {
+	return m_Data.GetRawCount();
+}
+
+VectAffine::VectAffine(const Vect& a_Base, const Matrix& a_Origin) :
+	m_Base(a_Base), m_Origin(a_Origin.SubMatrix(0, 0, m_Base.GetDimension(), 1)) {}
+
+bool VectAffine::IsElementOf(const Matrix& a_Vector) const {
+	return m_Base.IsElementOf(a_Vector - m_Origin);
+}

src/gui/PivotGui.cpp

@@ -0,0 +1,311 @@
+#include "PivotGui.h"
+
+#include "Gauss.h"
+#include "Matrix.h"
+#include "Solver.h"
+#include <imgui.h>
+#include <sstream>
+
+static std::string equationsResultImage;
+
+struct GuiMatrix {
+	std::vector<std::vector<int>> matrixValues;
+	int matrixSizeX = 4;
+	int matrixSizeY = 4;
+};
+
+static void ResizeGuiMatrix(bool refresh, GuiMatrix& guiMatrix) {
+	if (refresh) {
+		guiMatrix.matrixValues.resize(guiMatrix.matrixSizeY);
+		for (auto& row : guiMatrix.matrixValues) {
+			row.resize(guiMatrix.matrixSizeX, 0);
+		}
+	}
+}
+
+static void RenderMatrix(bool& refresh, GuiMatrix& guiMatrix) {
+	ResizeGuiMatrix(refresh, guiMatrix);
+
+	for (int y = 0; y < guiMatrix.matrixSizeY; y++) {
+		for (int x = 0; x < guiMatrix.matrixSizeX; x++) {
+			if (x > 0)
+				ImGui::SameLine();
+			ImGui::PushID((guiMatrix.matrixSizeX * 20 + guiMatrix.matrixSizeY * 50) + y * guiMatrix.matrixSizeX + x);
+			ImGui::PushItemWidth(60);  // Adjust this value to change the cell size
+			if (ImGui::InputInt("", &guiMatrix.matrixValues[y][x], 0, 0, ImGuiInputTextFlags_CharsDecimal))
+				refresh = true;
+			ImGui::PopItemWidth();
+			ImGui::PopID();
+		}
+	}
+}
+
+static Matrix LoadMatrixFromStdVect(const std::vector<std::vector<int>>& data) {
+	Matrix result {data.size(), data.empty() ? 0 : data[0].size()};
+	for (std::size_t i = 0; i < result.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < result.GetColumnCount(); j++) {
+			result.at(i, j) = static_cast<Matrix::Element>(data[i][j]);
+		}
+	}
+	return result;
+}
+
+static std::string ElementToString(Matrix::Element e) {
+	std::stringstream ss;
+	ss << e;
+	return ss.str();
+}
+
+static std::string PrintRawMatrix(const Matrix& mat) {
+	if (mat.GetRawCount() == 0)
+		return "";
+
+	std::string result = " ( ";
+	for (std::size_t j = 0; j < mat.GetRawCount(); j++) {
+		result += ElementToString(mat.at(j, 0)) + ", ";
+	}
+	result = result.substr(0, result.size() - 2);
+	result += " )";
+	return result;
+}
+
+static std::string PrintVect(const Vect& vect) {
+	if (vect.GetCardinal() == 0)
+		return "{0}";
+
+	std::string result = "Vect( ";
+	for (std::size_t i = 0; i < vect.GetCardinal(); i++) {
+		Matrix vector = vect.GetVector(i);
+		result += PrintRawMatrix(vector);
+		result += ", ";
+	}
+	result = result.substr(0, result.size() - 2);
+	result += "  )";
+	return result;
+}
+
+void PivotGui::Init() {}
+
+static void RenderLeftSystemChild(bool& refresh, GuiMatrix& system, GuiMatrix& origin) {
+	ImVec2 topLeftWindowSize(ImGui::GetContentRegionAvail().x * 0.5f, 0);
+
+	ImGui::BeginChild("Left Child", topLeftWindowSize, ImGuiChildFlags_Border);
+
+	ImGui::Text("Système de la forme AX=B");
+	ImGui::Separator();
+	ImGui::Text("Taille matrice A :");
+
+	if (ImGui::InputInt("##RowsMatriceInitiale", &system.matrixSizeY))
+		refresh = true;
+	system.matrixSizeY = std::max(1, system.matrixSizeY);
+	ImGui::SameLine();
+	ImGui::Text("Lignes");
+
+
+	if (ImGui::InputInt("##ColumnsMatriceInitiale", &system.matrixSizeX))
+		refresh = true;
+	system.matrixSizeX = std::max(1, system.matrixSizeX);
+	ImGui::SameLine();
+	ImGui::Text("Colonnes");
+
+	ImGui::NewLine();
+
+	RenderMatrix(refresh, system);
+
+	if (refresh) {
+		origin.matrixSizeX = 1;
+		origin.matrixSizeY = system.matrixSizeY;
+	}
+
+	ImGui::NewLine();
+	ImGui::Separator();
+	ImGui::Text("Matrice B :");
+	ImGui::NewLine();
+
+	RenderMatrix(refresh, origin);
+
+	ImGui::EndChild();
+}
+
+static void RenderRightSystemChild(bool& refresh, GuiMatrix& system, GuiMatrix& origin) {
+	ImGui::BeginChild("Right Child", {0, 0}, ImGuiChildFlags_Border);
+
+	static std::string result = "";
+
+	static Solver solver;
+
+	if (refresh) {
+		VectAffine solutions =
+			solver.RectangularSystem(LoadMatrixFromStdVect(system.matrixValues), LoadMatrixFromStdVect(origin.matrixValues));
+
+		result = "Solutions :\n";
+		result += PrintVect(solutions.GetBase());
+		result += "\n\n+\n\n";
+		result += PrintRawMatrix(solutions.GetOrigin());
+	}
+
+	ImGui::TextWrapped("%s", result.c_str());
+
+	ImGui::EndChild();
+}
+
+static void RenderSystemTab() {
+	static GuiMatrix guiMatrix, originMatrix;
+	static bool refresh = true;
+
+	RenderLeftSystemChild(refresh, guiMatrix, originMatrix);
+	ImGui::SameLine();
+	RenderRightSystemChild(refresh, guiMatrix, originMatrix);
+}
+
+static void RenderLeftGaussChild(bool& refresh, GuiMatrix& guiMatrix) {
+	// divisions des fenetres
+	ImVec2 topLeftWindowSize(ImGui::GetContentRegionAvail().x * 0.5f, 0);
+
+	// Begin fenetre top left
+	// ImGui::SetNextWindowPos(ImVec2(0, 0));	// Position at the top-left corner
+	ImGui::BeginChild("Left Top Window", topLeftWindowSize, ImGuiChildFlags_Border);
+	/*ImGui::Begin(, nullptr,
+		ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
+*/
+	// ImGui::BeginTabBar("MainMenu");
+
+	// Get window position
+	ImVec2 windowPos = ImGui::GetWindowPos();
+
+	ImGui::Text("Matrice initiale:");
+
+	if (ImGui::InputInt("##RowsMatriceInitiale", &guiMatrix.matrixSizeY))
+		refresh = true;
+	guiMatrix.matrixSizeY = std::max(1, guiMatrix.matrixSizeY);
+	ImGui::SameLine();
+	ImGui::Text("Lignes");
+
+
+	if (ImGui::InputInt("##ColumnsMatriceInitiale", &guiMatrix.matrixSizeX))
+		refresh = true;
+	guiMatrix.matrixSizeX = std::max(1, guiMatrix.matrixSizeX);
+	ImGui::SameLine();
+	ImGui::Text("Colonnes");
+
+	ImGui::NewLine();
+
+	// ImGui::BeginChild("MatriceInitiale", ImVec2(topLeftWindowSize.x, io.DisplaySize.y * 0.7f), false);
+
+	// Resize matrixValues and initialize new elements to 0
+
+	RenderMatrix(refresh, guiMatrix);
+
+	// ImGui::EndChild();	// End Matrice initiale
+
+	ImGui::NewLine();
+
+	ImGui::Text("Matrice échelonnée:");
+
+	// Convert the "result" string back to a matrix
+	Matrix resultMatrix = LoadMatrixFromStdVect(guiMatrix.matrixValues);
+
+	// Apply the Gauss-Jordan elimination to the matrix
+	Gauss::GaussJordan(resultMatrix, true, true);  // Assuming you want to reduce and normalize the matrix
+
+	// Display the matrix
+	for (std::size_t i = 0; i < resultMatrix.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < resultMatrix.GetColumnCount(); j++) {
+			ImGui::PushID(i * resultMatrix.GetColumnCount() + j);
+			if (ImGui::Button(ElementToString(resultMatrix.at(i, j)).c_str(), ImVec2(70, 70))) {  // Adjust the size as needed
+																								  // Handle button click here if needed
+			}
+			ImGui::PopID();
+			if (j < resultMatrix.GetColumnCount() - 1)
+				ImGui::SameLine();
+		}
+	}
+
+	ImGui::EndChild();
+}
+
+static void RenderRightGaussChild(bool& refresh, GuiMatrix& guiMatrix) {
+	static Solver solver;
+	// Begin fenetre top right
+	// ImGui::SetNextWindowSize(topRightWindowSize);
+	// ImGui::SetNextWindowPos(ImVec2(windowPos.x + topLeftWindowSize.x, 0));	// Position at the top-right corner
+	ImGui::BeginChild("Right Top Window", {0, 0}, ImGuiChildFlags_Border);
+	// ImGui::Begin("Right Top Window", nullptr,
+	//	ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
+
+	// rajouter le code pour la partie top right
+
+	static std::string result = "";
+
+	if (refresh) {
+
+		// Calculate the kernel and image
+		Vect image = solver.Image(LoadMatrixFromStdVect(guiMatrix.matrixValues));
+		Matrix linearSystem = image.GetLinearSystem();
+
+		// Store the equationsResult strings in the global variable
+		equationsResultImage = "Equations cartesiennes de l'espace vectoriel (Image):\n";
+		for (size_t i = 0; i < linearSystem.GetRawCount(); ++i) {
+			for (size_t j = 0; j < linearSystem.GetColumnCount(); ++j) {
+				equationsResultImage +=
+					ElementToString(linearSystem.at(i, j)) + "*" + std::string {static_cast<char>('a' + j)} + " + ";
+			}
+			equationsResultImage = equationsResultImage.substr(0, equationsResultImage.size() - 3) + " = 0\n";
+		}
+
+		result = "\nNoyau: \n" + PrintVect(solver.Kernel(LoadMatrixFromStdVect(guiMatrix.matrixValues))) + "\n" +
+				 "\n" + "Rang: " + "\n" + std::to_string(solver.Rank(LoadMatrixFromStdVect(guiMatrix.matrixValues))) + "\n" + "\n" +
+				 "Image: " + "\n" + PrintVect(image);
+	}
+
+	refresh = false;
+
+	// Display the equationsResult strings in the GUI if they are not empty
+	if (!equationsResultImage.empty()) {
+		ImGui::TextWrapped("%s", equationsResultImage.c_str());
+	}
+
+	ImGui::TextWrapped("%s", result.c_str());
+
+	ImGui::EndChild();	// End fenetre top right
+}
+
+static void RenderGaussTab() {
+	static GuiMatrix guiMatrix;
+	static bool refresh = true;
+
+	RenderLeftGaussChild(refresh, guiMatrix);
+	ImGui::SameLine();
+	RenderRightGaussChild(refresh, guiMatrix);
+}
+
+static void RenderMainWindow() {
+	ImGuiIO& io = ImGui::GetIO();
+
+	ImGui::SetNextWindowSize(io.DisplaySize);
+	ImGui::SetNextWindowPos({0, 0});
+	ImGui::Begin("MainWindow", nullptr,
+		ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
+	ImGui::BeginTabBar("MainBar");
+	if (ImGui::BeginTabItem("Noyau et Image")) {
+		RenderGaussTab();
+		ImGui::EndTabItem();
+	}
+	if (ImGui::BeginTabItem("Systèmes")) {
+		RenderSystemTab();
+		ImGui::EndTabItem();
+	}
+	ImGui::EndTabBar();
+	ImGui::End();
+}
+
+void PivotGui::Render() {
+
+	RenderMainWindow();
+
+#ifndef NDEBUG
+	ImGui::ShowDemoWindow(nullptr);
+#endif
+}
+
+void PivotGui::Destroy() {}

src/gui/PivotGui.h

@@ -0,0 +1,9 @@
+#pragma once
+
+namespace PivotGui {
+
+void Init();
+void Render();
+void Destroy();
+
+}  // namespace PivotGui

src/gui/mainGui.cpp

@@ -0,0 +1,174 @@
+// Dear ImGui: standalone example application for SDL2 + OpenGL
+// (SDL is a cross-platform general purpose library for handling windows, inputs, OpenGL/Vulkan/Metal graphics context creation, etc.)
+
+// Learn about Dear ImGui:
+// - FAQ                  https://dearimgui.com/faq
+// - Getting Started      https://dearimgui.com/getting-started
+// - Documentation        https://dearimgui.com/docs (same as your local docs/ folder).
+// - Introduction, links and more at the top of imgui.cpp
+
+#include <SDL2/SDL.h>
+#include <imgui.h>
+#include <imgui_impl_opengl3.h>
+#include <imgui_impl_opengl3_loader.h>
+#include <imgui_impl_sdl2.h>
+#include <stdio.h>
+
+#include "PivotGui.h"
+
+// This example can also compile and run with Emscripten! See 'Makefile.emscripten' for details.
+#ifdef __EMSCRIPTEN__
+#include "../libs/emscripten/emscripten_mainloop_stub.h"
+#endif
+
+// Main code
+int main(int, char**) {
+	// Setup SDL
+	if (SDL_Init(SDL_INIT_VIDEO | SDL_INIT_TIMER | SDL_INIT_GAMECONTROLLER) != 0) {
+		printf("Error: %s\n", SDL_GetError());
+		return -1;
+	}
+
+	// Decide GL+GLSL versions
+#if defined(IMGUI_IMPL_OPENGL_ES2)
+	// GL ES 2.0 + GLSL 100
+	const char* glsl_version = "#version 100";
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_FLAGS, 0);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_PROFILE_MASK, SDL_GL_CONTEXT_PROFILE_ES);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_MAJOR_VERSION, 2);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_MINOR_VERSION, 0);
+#elif defined(__APPLE__)
+	// GL 3.2 Core + GLSL 150
+	const char* glsl_version = "#version 150";
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_FLAGS, SDL_GL_CONTEXT_FORWARD_COMPATIBLE_FLAG);	// Always required on Mac
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_PROFILE_MASK, SDL_GL_CONTEXT_PROFILE_CORE);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_MAJOR_VERSION, 3);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_MINOR_VERSION, 2);
+#else
+	// GL 3.0 + GLSL 130
+	const char* glsl_version = "#version 130";
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_FLAGS, 0);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_PROFILE_MASK, SDL_GL_CONTEXT_PROFILE_CORE);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_MAJOR_VERSION, 3);
+	SDL_GL_SetAttribute(SDL_GL_CONTEXT_MINOR_VERSION, 0);
+#endif
+
+	// From 2.0.18: Enable native IME.
+#ifdef SDL_HINT_IME_SHOW_UI
+	SDL_SetHint(SDL_HINT_IME_SHOW_UI, "1");
+#endif
+
+	// Create window with graphics context
+	SDL_GL_SetAttribute(SDL_GL_DOUBLEBUFFER, 1);
+	SDL_GL_SetAttribute(SDL_GL_DEPTH_SIZE, 24);
+	SDL_GL_SetAttribute(SDL_GL_STENCIL_SIZE, 8);
+	SDL_WindowFlags window_flags = (SDL_WindowFlags)(SDL_WINDOW_OPENGL | SDL_WINDOW_RESIZABLE | SDL_WINDOW_ALLOW_HIGHDPI);
+	SDL_Window* window = SDL_CreateWindow("Solver Gui", SDL_WINDOWPOS_CENTERED, SDL_WINDOWPOS_CENTERED, 1280, 720, window_flags);
+	if (window == nullptr) {
+		printf("Error: SDL_CreateWindow(): %s\n", SDL_GetError());
+		return -1;
+	}
+
+	SDL_GLContext gl_context = SDL_GL_CreateContext(window);
+	SDL_GL_MakeCurrent(window, gl_context);
+	SDL_GL_SetSwapInterval(1);	// Enable vsync
+
+	// Setup Dear ImGui context
+	IMGUI_CHECKVERSION();
+	ImGui::CreateContext();
+	ImGuiIO& io = ImGui::GetIO();
+	io.ConfigFlags |= ImGuiConfigFlags_NavEnableKeyboard;  // Enable Keyboard Controls
+	io.ConfigFlags |= ImGuiConfigFlags_NavEnableGamepad;   // Enable Gamepad Controls
+
+	// Setup Dear ImGui style
+	ImGui::StyleColorsDark();
+	// ImGui::StyleColorsLight();
+
+	// Setup Platform/Renderer backends
+	ImGui_ImplSDL2_InitForOpenGL(window, gl_context);
+	ImGui_ImplOpenGL3_Init(glsl_version);
+
+	// Load Fonts
+	// - If no fonts are loaded, dear imgui will use the default font. You can also load multiple fonts and use
+	// ImGui::PushFont()/PopFont() to select them.
+	// - AddFontFromFileTTF() will return the ImFont* so you can store it if you need to select the font among multiple.
+	// - If the file cannot be loaded, the function will return a nullptr. Please handle those errors in your application (e.g. use an
+	// assertion, or display an error and quit).
+	// - The fonts will be rasterized at a given size (w/ oversampling) and stored into a texture when calling
+	// ImFontAtlas::Build()/GetTexDataAsXXXX(), which ImGui_ImplXXXX_NewFrame below will call.
+	// - Use '#define IMGUI_ENABLE_FREETYPE' in your imconfig file to use Freetype for higher quality font rendering.
+	// - Read 'docs/FONTS.md' for more instructions and details.
+	// - Remember that in C/C++ if you want to include a backslash \ in a string literal you need to write a double backslash \\ !
+	// - Our Emscripten build process allows embedding fonts to be accessible at runtime from the "fonts/" folder. See
+	// Makefile.emscripten for details.
+	// io.Fonts->AddFontDefault();
+	// io.Fonts->AddFontFromFileTTF("c:\\Windows\\Fonts\\segoeui.ttf", 18.0f);
+	// io.Fonts->AddFontFromFileTTF("../../misc/fonts/DroidSans.ttf", 16.0f);
+	// io.Fonts->AddFontFromFileTTF("../../misc/fonts/Roboto-Medium.ttf", 16.0f);
+	// io.Fonts->AddFontFromFileTTF("../../misc/fonts/Cousine-Regular.ttf", 15.0f);
+	// ImFont* font = io.Fonts->AddFontFromFileTTF("c:\\Windows\\Fonts\\ArialUni.ttf", 18.0f, nullptr,
+	// io.Fonts->GetGlyphRangesJapanese()); IM_ASSERT(font != nullptr);
+
+	ImFontConfig cfg;
+	cfg.SizePixels = 30.0f;
+	io.Fonts->AddFontDefault(&cfg);
+
+	PivotGui::Init();
+
+	// Main loop
+	bool done = false;
+#ifdef __EMSCRIPTEN__
+	// For an Emscripten build we are disabling file-system access, so let's not attempt to do a fopen() of the imgui.ini file.
+	// You may manually call LoadIniSettingsFromMemory() to load settings from your own storage.
+	io.IniFilename = nullptr;
+	EMSCRIPTEN_MAINLOOP_BEGIN
+#else
+	while (!done)
+#endif
+	{
+		// Poll and handle events (inputs, window resize, etc.)
+		// You can read the io.WantCaptureMouse, io.WantCaptureKeyboard flags to tell if dear imgui wants to use your inputs.
+		// - When io.WantCaptureMouse is true, do not dispatch mouse input data to your main application, or clear/overwrite your copy
+		// of the mouse data.
+		// - When io.WantCaptureKeyboard is true, do not dispatch keyboard input data to your main application, or clear/overwrite your
+		// copy of the keyboard data. Generally you may always pass all inputs to dear imgui, and hide them from your application based
+		// on those two flags.
+		SDL_Event event;
+		while (SDL_PollEvent(&event)) {
+			ImGui_ImplSDL2_ProcessEvent(&event);
+			if (event.type == SDL_QUIT)
+				done = true;
+			if (event.type == SDL_WINDOWEVENT && event.window.event == SDL_WINDOWEVENT_CLOSE &&
+				event.window.windowID == SDL_GetWindowID(window))
+				done = true;
+		}
+
+		// Start the Dear ImGui frame
+		ImGui_ImplOpenGL3_NewFrame();
+		ImGui_ImplSDL2_NewFrame();
+		ImGui::NewFrame();
+
+		PivotGui::Render();
+
+		// Rendering
+		ImGui::Render();
+		glViewport(0, 0, (int)io.DisplaySize.x, (int)io.DisplaySize.y);
+		glClear(GL_COLOR_BUFFER_BIT);
+		ImGui_ImplOpenGL3_RenderDrawData(ImGui::GetDrawData());
+		SDL_GL_SwapWindow(window);
+	}
+#ifdef __EMSCRIPTEN__
+	EMSCRIPTEN_MAINLOOP_END;
+#endif
+
+	// Cleanup
+	ImGui_ImplOpenGL3_Shutdown();
+	ImGui_ImplSDL2_Shutdown();
+	ImGui::DestroyContext();
+
+	SDL_GL_DeleteContext(gl_context);
+	SDL_DestroyWindow(window);
+	SDL_Quit();
+
+	return 0;
+}

src/main.cpp

@@ -1,44 +1,59 @@
+#include "Gauss.h"
+#include "IO.h"
 #include "Matrix.h"
+#include "NR.h"
+#include "Solver.h"
+#include <iostream>
 
 void test() {
-	Matrix<float> mat{"matrice5x5.mat"};
+	/* Matrix mat{"matrice4x4.mat"};
 	mat.Print();
 	// mat.Save("matrice3x3.mat");
 	std::cout << "sdfdjiofoseifheoiefhoig\n";
 	mat.Print();
-	mat = {"matrice5x5.mat"};
-	mat.GaussJordan(false, true);
+	//mat = {"matrice4x4.mat"};
+	mat.GaussJordan(false);
 	std::cout << "\nResultat :\n";
 	mat.Print();
 	mat.Transpose();
+	std::cout << "<<\nTransposée:\n";
 	mat.Print();
-	// mat.Save("matrice4x4echelonne.mat");
+	// mat.Save("matrice4x4echelonne.mat"); */
+
+	Matrix mat2 = LoadMatrix("matrice4x4.mat");
+	Print(mat2);
+
+	Solver solver;
+
+	Vect image = solver.Image(Matrix{mat2});
+	Vect noyau = solver.Kernel(Matrix{mat2});
+
+	std::cout << "\tImage :\n";
+	Print(image);
+	std::cout << "Système :\n";
+	Print(image.GetLinearSystem());
+	std::cout << "\tNoyau :\n";
+	Print(noyau);
+	std::cout << "Système :\n";
+	Print(noyau.GetLinearSystem());
+
+	std::cout << "\n\n";
+	// Print(solver.TriangularSystem(mat2));
 }
 
 void prompt() {
-	std::cout << "Quelle est le nombre de lignes de votre matrice ?" << std::endl;
-	std::size_t lignes;
-	std::cin >> lignes;
-	std::cout << "Quelle est le nombre de colonnes de votre matrice ?" << std::endl;
-	std::size_t colonnes;
-	std::cin >> colonnes;
-	std::size_t dimension = lignes * colonnes;
-	std::cout << "Rentrez les coefficients de la matrice" << std::endl;
-	Matrix<float> mat(lignes, colonnes);
 
-	mat.Insert();
+	Matrix mat = InsertMatrix();
 
-	mat.Print();
-	Matrix<float> aug = mat.GaussJordan(true, true);
-	std::cout << std::endl;
-	std::cout << "Matrice echelonnee reduite" << std::endl;
-	mat.Print();
-	std::cout << "Matrice augmentee" << std::endl;
-	aug.Print();
+	Print(mat);
+
+	Gauss::GaussJordan(mat, true, true);
+
+	Print(mat);
 }
 
 int main(int argc, char** argv) {
-	// test();
+	test();
 	prompt();
 	return 0;
 }

test/test_assert.h

@@ -0,0 +1,42 @@
+#pragma once
+
+/**
+ * \file Test.h
+ * \brief Contient une assertion utilisable avec les optimisations
+ */
+
+#include <iostream>
+#include <stdexcept>
+
+/**
+ * \def TEST_SUCCESSFUL
+ * \brief Indique que le test a été passé
+ */
+#define TEST_SUCCESSFUL 0
+
+/**
+ * \def TEST_FAILED
+ * \brief Indique que le test a échoué
+ */
+#define TEST_FAILED 1
+
+#ifndef __FUNCTION_NAME__
+#ifdef _WIN32
+#define __FUNCTION_NAME__ __FUNCTION__
+#else
+#define __FUNCTION_NAME__ __PRETTY_FUNCTION__
+#endif
+#endif
+
+/**
+ * \def test_assert
+ * \param ... L'expression à évaluer
+ * \brief Evalue une expression et arrête le programme si elle n'est pas valide
+ * \note Cette macro équivaut à assert() mais fonctionne également avec les optimisations activées
+ */
+#define test_assert(...)                                                                                                              \
+	if (!static_cast<bool>(__VA_ARGS__)) {                                                                                            \
+		std::cout << __FILE__ << ":" << __LINE__ << ": " << __FUNCTION_NAME__ << ": Assertion failed !\n";                            \
+		std::cout << "    " << __LINE__ << "  |\t" << #__VA_ARGS__ << std::endl;                                                      \
+		throw std::runtime_error("Assertion failed !");                                                                               \
+	}

test/test_jordan.cpp

@@ -0,0 +1,43 @@
+#include "Gauss.h"
+#include "Matrix.h"
+#include "test_assert.h"
+
+struct Test {
+	Matrix mat;
+	Matrix res;
+};
+
+static const std::vector<Test> TEST_MATRICES = {
+    // test 1
+    {{3, 3, {
+        1, 2, 3,
+        4, 5, 6,
+        7, 8, 9,
+    }}, {3, 3, {
+        1, 0, -1,
+        0, 1, 2,
+        0, 0, 0,
+    }}},
+    // test 2
+    {{3, 3, {
+        4, 5, 6,
+        1, 2, 3,
+        7, 8, 9,
+    }}, {3, 3, {
+        1, 0, -1,
+        0, 1, 2,
+        0, 0, 0,
+    }}}
+};
+
+void test() {
+	for (Test test : TEST_MATRICES) {
+		Gauss::GaussJordan(test.mat, true, true);
+		test_assert(test.mat == test.res);
+	}
+}
+
+int main(int argc, char** argv) {
+	test();
+	return 0;
+}

test/test_random_kernel.cpp

@@ -0,0 +1,80 @@
+#include "Solver.h"
+
+#include "test_assert.h"
+#include <cstdlib>
+#include <future>
+#include <iostream>
+#include <vector>
+
+static constexpr int EXECUTION_COUNT = 1000;
+static constexpr int KERNEL_CHECKS = 100;
+static constexpr int MATRIX_MAX_SIZE = 9;
+
+static const Solver solver;
+
+static int GetRandomInt() {
+	return rand() % 11 - 5;
+}
+
+static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
+	Matrix matrix {a_Raw, a_Column};
+
+	for (std::size_t i = 0; i < matrix.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < matrix.GetColumnCount(); j++) {
+			matrix.at(i, j) = GetRandomInt();
+		}
+	}
+
+	return matrix;
+}
+
+static bool Test() {
+	Matrix matrix = GetRandomMatrix(rand() % MATRIX_MAX_SIZE + 1, rand() % MATRIX_MAX_SIZE + 1);
+
+	for (std::size_t i = 0; i < matrix.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < matrix.GetColumnCount(); j++) {
+			matrix.at(i, j) = GetRandomInt();
+		}
+	}
+
+	Matrix copy = matrix;
+
+	Vect kernel = solver.Kernel(std::move(copy));
+
+	Matrix nullVector {matrix.GetRawCount(), 1};
+	nullVector.Fill(0.0);
+
+	for (std::size_t i = 0; i < kernel.GetCardinal(); i++) {
+		test_assert(matrix * kernel.GetVector(i) == nullVector);
+	}
+
+	for (std::size_t i = 0; i < KERNEL_CHECKS; i++) {
+		Matrix vector = GetRandomMatrix(kernel.GetDimension(), 1);
+
+		test_assert(kernel.IsElementOf(vector) == (matrix * vector == nullVector));
+	}
+
+	Vect kernel2 = solver.Kernel(kernel.GetLinearSystem());
+
+	test_assert(kernel == kernel2);
+	return true;
+}
+
+int main() {
+	srand(time(0));
+
+	std::vector<std::future<bool>> results;
+
+	// appelle la fonction Test() en parallèle
+	for (int i = 0; i < EXECUTION_COUNT; i++) {
+		auto handle = std::async(std::launch::async, &Test);
+		results.push_back(std::move(handle));
+	}
+
+	for (auto& result : results) {
+		if (!result.get())
+			return EXIT_FAILURE;
+	}
+
+	return EXIT_SUCCESS;
+}

test/test_rational.cpp

@@ -0,0 +1,28 @@
+#include "NR.h"
+
+#include "test_assert.h"
+
+static void test() {
+	test_assert((NR {1, 5} == NR {5, 25}));
+	test_assert((NR {1, 5} != NR {4, 25}));
+
+	test_assert(NR {2} == NR {1} + 1);
+	test_assert(NR {1} == (NR {1, 4} + NR {3, 4}));
+	test_assert((NR {-3, -4} == NR {1, 2} + NR {1, 4}));
+
+	test_assert((NR {-1, 4} == NR {1, 4} - NR {1, 2}));
+	test_assert((NR {1, -4} == NR {1, 4} - NR {1, 2}));
+	test_assert((-NR {1, 4} == NR {1, 4} - NR {1, 2}));
+
+	test_assert((NR {2} == NR {4, 3} * NR {3, 2}));
+	test_assert((NR {3, 5} == NR {4, 5} * NR {3, 4}));
+
+	test_assert((NR {21, 16} == NR {7, 8} / NR {6, 9}));
+
+	test_assert((NR {4, 3} == NR {3, 4}.Inverse()));
+}
+
+int main(int argc, char** argv) {
+	test();
+	return 0;
+}

test/test_solver.cpp

@@ -0,0 +1,88 @@
+#include <algorithm>
+#include <filesystem>
+#include <fstream>
+#include <iostream>
+
+#include "IO.h"
+#include "Solver.h"
+#include "test_assert.h"
+
+namespace fs = std::filesystem;
+
+const static int EXECUTION_COUNT = 10000;
+static constexpr int MATRIX_MAX_SIZE = 5;
+
+static int GetRandomSize() {
+	return rand() % MATRIX_MAX_SIZE + 1;
+}
+
+static int GetRandomInt() {
+	return GetRandomSize();
+}
+
+static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
+	Matrix matrix {a_Raw, a_Column};
+
+	std::generate(matrix.GetLineIterator(0), matrix.GetLineIterator(a_Raw), []() { 
+		return GetRandomInt(); 
+	});
+
+	return matrix;
+}
+
+void TestRectangular(const Matrix& system, const Matrix& origin) {
+	Solver solver;
+
+	VectAffine solution = solver.RectangularSystem(std::move(Matrix(system)), origin);
+
+	for (std::size_t i = 0; i < solution.GetBase().GetCardinal(); i++) {
+		Matrix vector = solution.GetBase().GetVector(i) + solution.GetOrigin();
+		Matrix product = system * vector;
+		test_assert(product == origin);
+	}
+}
+
+void RandomRectangular() {
+	for (int i = 0; i < EXECUTION_COUNT; i++) {
+
+		Matrix system = GetRandomMatrix(GetRandomSize(), GetRandomSize());
+
+		Matrix origin = GetRandomMatrix(system.GetRawCount(), 1);
+
+		TestRectangular(system, origin);
+	}
+}
+
+void TestKernelImage() {
+	std::string path = "test";
+	for (const auto& entry : fs::directory_iterator(path)) {
+		std::string fileName = entry.path().string();
+
+		std::cout << "Opening " << fileName << " ...\n";
+
+		std::ifstream in {fileName};
+
+		Matrix mat, imageMat, noyauMat;
+		in >> mat >> imageMat >> noyauMat;
+
+		Vect image {std::move(imageMat)};
+		Vect noyau {std::move(noyauMat)};
+
+		Solver solver;
+
+		Matrix copy = mat;
+
+		Vect imageCalc = solver.Image(std::move(copy));
+		Vect kernelCalc = solver.Kernel(std::move(mat));
+
+		test_assert(imageCalc == image);
+		test_assert(kernelCalc == noyau);
+	}
+}
+
+int main() {
+	srand(time(0));
+	TestKernelImage();
+	RandomRectangular();
+	return 0;
+}

test/test_vect.cpp

@@ -0,0 +1,84 @@
+#include "Vect.h"
+#include "test_assert.h"
+
+#include <algorithm>
+
+const static int EXECUTION_COUNT = 100000;
+static constexpr int MATRIX_MAX_SIZE = 5;
+
+static int GetRandomSize() {
+	return rand() % MATRIX_MAX_SIZE + 1;
+}
+
+static int GetRandomInt() {
+	return GetRandomSize();
+}
+
+static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
+	Matrix matrix {a_Raw, a_Column};
+
+	std::generate(matrix.GetLineIterator(0), matrix.GetLineIterator(a_Raw), []() { return GetRandomInt(); });
+
+	return matrix;
+}
+
+void TestVect() {
+	Vect vect1 {{3, 2, {
+		1, 2,
+		3, 4,
+		5, 6,
+	}}};
+	Vect vect2 {{3, 2, {
+		1, 0,
+		0, 0,
+		0, 1,
+	}}};
+	Vect vect3 {{3, 2, {
+		1, 3,
+		3, 7,
+		5, 11,
+	}}};
+	Vect vect4 {{3, 2, {
+		1, 0,
+		0, 0,
+		1, 11,
+	}}};
+
+	test_assert(vect1 == vect3);
+	test_assert(vect2 == vect4);
+	test_assert(vect1 != vect2);
+	test_assert(vect2 != vect3);
+	test_assert(vect3 != vect4);
+
+	test_assert(vect1.IsElementOf(Matrix::ColumnVector({3, 7, 11})));
+	test_assert(!vect1.IsElementOf(Matrix::ColumnVector({3, 7, 12})));
+}
+
+void TestVectAffine() {
+	VectAffine aff {Matrix::ColumnVector({-2, 3, 7}), Matrix::ColumnVector({5, 2, -8})};
+
+	test_assert(aff.IsElementOf(Matrix::ColumnVector({5, 2, -8})));
+	test_assert(aff.IsElementOf(Matrix::ColumnVector({3, 5, -1})));
+	test_assert(!aff.IsElementOf(Matrix::ColumnVector({1, 2, 3})));
+}
+
+void TestLinearSystem() {
+	for (std::size_t i = 0; i < EXECUTION_COUNT; i++) {
+		Vect vect = GetRandomMatrix(GetRandomSize(), GetRandomSize());
+
+		Matrix systeme = vect.GetLinearSystem();
+
+		for (std::size_t j = 0; j < vect.GetCardinal(); j++) {
+			Matrix nullMatrix {systeme.GetColumnCount(), 1};
+			test_assert(systeme * vect.GetVector(j) == nullMatrix);
+		}
+	}
+}
+
+int main() {
+	srand(time(0));
+	TestVect();
+	TestVectAffine();
+	TestLinearSystem();
+	return 0;
+}

xmake.lua

@@ -1,9 +1,64 @@
+set_project("Pivot")
+set_description("Solutionneur de matrice par le pivot de Gauss")
+set_license("MIT")
+
+set_xmakever("2.8.5")
+
+
 add_rules("mode.debug", "mode.release")
 
+add_requires("imgui", {configs = {sdl2_no_renderer = true, opengl3 = true}})
+
+set_languages("c++20")
+set_warnings("all")
+add_includedirs("include")
+
+
+-- Solver Library
 target("Pivot")
-    set_kind("binary")
+    set_kind("static")
     add_files("src/*.cpp")
+    remove_files("src/main.cpp")
+
+
+
+
+
+-- Solver Main
+target("PivotMain")
     set_rundir("$(projectdir)/matricies")
+    add_files("src/main.cpp")
+    add_deps("Pivot")
+    set_default(false)
+
+
+
+
+
+-- Gui interface
+target("PivotGui")
+    set_rundir("$(projectdir)")
+    add_files("src/gui/*.cpp")
+    add_deps("Pivot")
+    set_default(true)
+    add_packages("libsdl", "imgui")
+
+
+
+-- Solver tests
+for _, file in ipairs(os.files("test/test_*.cpp")) do
+    local name = path.basename(file)
+    target(name)
+        set_kind("binary")
+        add_files("test/" .. name .. ".cpp")
+        set_rundir("$(projectdir)/matricies")
+
+        set_default(false)
+
+        add_deps("Pivot")
+
+        add_tests("compile_and_run")
+end
 
 --
 -- If you want to known more usage about xmake, please see https://xmake.io