init random

.gitea/workflows/ubuntu.yaml

@@ -7,15 +7,26 @@ 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
+      - name: Prepare Xmake
         uses: xmake-io/github-action-setup-xmake@v1
         with:
           xmake-version: latest
           actions-cache-folder: '.xmake-cache'
-          actions-cache-key: 'ubuntu'
+          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

.gitignore

@@ -7,3 +7,6 @@ build/
 
 # VsCode
 .vscode
+
+#ImGui
+imgui.ini

.vscode/c_cpp_properties.json

@@ -2,8 +2,9 @@
     "configurations": [
         {
             "name": "Pivot",
-            "cppStandard": "c++17",
-            "includePath": ["include"]
+            "cppStandard": "c++20",
+            "includePath": ["include"],
+            "compileCommands": "${workspaceFolder}/.vscode/compile_commands.json"
         }
     ],
     "version": 4

include/Gauss.h

@@ -10,10 +10,10 @@ class Matrix;
 namespace Gauss {
 
 /**
- * \brief Echelonne une matrice en utilisant l'algorithme de Gauss-Jordan
- * \param mat La matrice à échelonner
- * \param reduite Mets des 0 au dessus des pivots
- * \param normalise Mets les pivots à 1
+ * \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);
 

include/Matrix.h

@@ -10,13 +10,16 @@
 #include <string>
 #include <vector>
 
+#include "NR.h"
+
 /**
  * \class Matrix
  * \brief Représente une matrice d'éléments
  */
 class Matrix {
   public:
-	typedef long double Element;
+	typedef NR Element;
+	typedef std::vector<Element>::iterator iterator;
 
   private:
 	std::size_t m_Raws;
@@ -30,7 +33,7 @@ class Matrix {
 	Matrix() : m_Raws(0), m_Columns(0) {}
 
 	/**
-	 * \brief Construit une matrice de taille donnée remplit de données aléatoires (et peut-être invalides !)
+	 * \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
 	 */
@@ -51,12 +54,12 @@ class Matrix {
 	~Matrix() {}
 
 	/**
-	 * \brief Retourne le nombre de ligne de la matrice
+	 * \brief Retourne le nombre de lignes de la matrice
 	 */
 	std::size_t GetRawCount() const;
 
 	/**
-	 * \brief Retourne le nombre de colonne de la matrice
+	 * \brief Retourne le nombre de colonnes de la matrice
 	 */
 	std::size_t GetColumnCount() const;
 
@@ -66,12 +69,25 @@ class Matrix {
 	void Transpose();
 
 	/**
-	 * \brief Augmente la matrice actuelle avec une autre
+	 * \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
@@ -132,9 +148,29 @@ class Matrix {
 	 * 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(T var) {
+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

@@ -3,17 +3,20 @@
 #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
+	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
+	NR(Int entier);
+	NR(Int numerator, Int denominator);	 // check if denominator != 0
 
-	int GetNumerator() const;
-	int GetDenominator() const;
+	Int GetNumerator() const;
+	Int GetDenominator() const;
 
 	bool operator==(const NR& opNR) const;
 	bool operator<(const NR& opNR) const;
@@ -43,5 +46,3 @@ class NR {
   private:
 	void Reduce();
 };
-
-int PGCD(int x, int y);

include/Solver.h

@@ -18,14 +18,14 @@ class Solver {
 	 * \param a_Matrix La matrice à traiter
 	 * \return L'espace vectoriel correspondant
 	 */
-	Vect Image(const Matrix& a_Matrix) const;
+	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(const Matrix& a_Matrix) const;
+	Vect Kernel(Matrix&& a_Matrix) const;
 
 	/**
 	 * \brief Résout le système rectangulaire de la forme AX=B, avec X et B, des vecteurs colonne.
@@ -33,12 +33,12 @@ class Solver {
 	 * \param a_VectorB La matrice colonne jouant le rôle de B
 	 * \return L'espace affine associé
 	 */
-	VectAffine RectangularSystem(const Matrix& a_MatrixA, const Matrix& a_VectorB) const;
+	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(const Matrix& a_Matrix) const;
+	std::size_t Rank(Matrix&& a_Matrix) const;
 };

include/Vect.h

@@ -21,7 +21,7 @@ class Vect {
 	 * Les colonnes de 0 sont ignorées
 	 * \param a_Matrix Une matrice échelonnée.
 	 */
-	Vect(const Matrix& a_Matrix);
+	Vect(Matrix&& a_Matrix);
 
 	/**
 	 * \brief Permet d'obtenir le ieme vecteur de la base
@@ -105,12 +105,6 @@ class VectAffine {
 	 */
 	bool IsElementOf(const Matrix& a_Vector) 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;
-
 	bool operator==(const VectAffine& a_VectAffine) const {
 		return m_Origin == a_VectAffine.GetOrigin() && m_Base == a_VectAffine.GetBase();
 	};

src/Gauss.cpp

@@ -2,18 +2,20 @@
 
 #include "Matrix.h"
 
+#include <algorithm>
+#include <execution>
+#include <ranges>
+
 namespace Gauss {
 
 static void SwapLines(Matrix& mat, std::size_t line1, std::size_t line2) {
-	for (std::size_t k = 0; k < mat.GetColumnCount(); k++) {
-		std::swap(mat.at(line1, k), mat.at(line2, k));
-	}
+	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) {
-	for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
-		mat.at(line, j) /= 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) {
@@ -29,12 +31,14 @@ static void SimplifyLine(Matrix& mat, std::size_t line, std::size_t pivot_line,
 	const Matrix::Element pivot = mat.at(pivot_line, pivot_column);
 	const Matrix::Element anul = mat.at(line, pivot_column);
 
-	for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
+	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;
-	}
+	});
 }
 
-void GaussJordan(Matrix& a_Matrix, bool a_Reduite, bool a_Normalise) {
+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++) {
@@ -56,14 +60,54 @@ void GaussJordan(Matrix& a_Matrix, bool a_Reduite, bool 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
-		for (std::size_t i = (a_Reduite ? 0 : j); i < a_Matrix.GetRawCount(); i++) {
-			// Pour les lignes autre que la ligne pivot
+		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/Matrix.cpp

@@ -18,10 +18,7 @@ Matrix::Matrix(std::size_t a_Raws, std::size_t a_Columns, std::initializer_list<
 }
 
 Matrix Matrix::operator*(const Matrix& a_Other) const {
-	if (m_Columns != a_Other.m_Raws) {
-		std::cerr << "Mutiplication impossible car la dimensions des matrices est incompatible" << std::endl;
-		return {};
-	}
+	assert(m_Columns == a_Other.m_Raws);
 
 	Matrix result(m_Raws, a_Other.m_Columns);
 
@@ -73,6 +70,10 @@ Matrix Matrix::RawVector(std::initializer_list<Element>&& 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};
@@ -92,6 +93,25 @@ void Matrix::Augment(const Matrix& a_Right) {
 	*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());
 
@@ -121,8 +141,7 @@ Matrix Matrix::operator-(const Matrix& a_Other) const {
 }
 
 bool Matrix::operator==(const Matrix& a_Other) const {
-	if (m_Raws != a_Other.m_Raws || m_Columns != a_Other.m_Columns)
-		return false;
+	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++) {
@@ -135,10 +154,12 @@ bool Matrix::operator==(const Matrix& a_Other) const {
 }
 
 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];
 }
 
@@ -164,3 +185,15 @@ Matrix Matrix::SubMatrix(
 
 	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/NR.cpp

@@ -3,7 +3,7 @@
 #include <cassert>
 #include <iostream>
 
-int PGCD(int x, int y) {
+NR::Int PGCD(NR::Int x, NR::Int y) {
 	if (x == 0 || y == 0)
 		return 1;
 	else if (x % y == 0)
@@ -14,18 +14,18 @@ int PGCD(int x, int y) {
 
 NR::NR() : m_Numerator(0), m_Denominator(1) {}
 
-NR::NR(int entier) : m_Numerator(entier), m_Denominator(1) {}
+NR::NR(NR::Int entier) : m_Numerator(entier), m_Denominator(1) {}
 
-NR::NR(int numerator, int denominator) :
+NR::NR(NR::Int numerator, NR::Int denominator) :
 	m_Numerator((denominator > 0) ? numerator : -numerator), m_Denominator(std::abs(denominator)) {
-	assert(denominator != 0);
 	Reduce();
 }
 
 void NR::Reduce() {
-	int divisor = PGCD(m_Denominator, m_Numerator);
+	NR::Int divisor = PGCD(m_Denominator, m_Numerator);
 	m_Denominator /= divisor;
 	m_Numerator /= divisor;
+	assert(m_Denominator != 0);
 }
 
 NR NR::Inverse() const {
@@ -33,11 +33,11 @@ NR NR::Inverse() const {
 	return {m_Denominator, m_Numerator};
 }
 
-int NR::GetNumerator() const {
+NR::Int NR::GetNumerator() const {
 	return m_Numerator;
 }
 
-int NR::GetDenominator() const {
+NR::Int NR::GetDenominator() const {
 	return m_Denominator;
 }
 
@@ -66,48 +66,57 @@ bool NR::operator>=(const NR& opNR) const {
 }
 
 std::ostream& operator<<(std::ostream& os, const NR& opNR) {
-	os << opNR.GetNumerator() << "/" << opNR.GetDenominator();
+	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 >> opNR.m_Denominator;
+	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;
+	Int num, den;
 	num = m_Numerator * opNR.GetDenominator();
 	den = m_Denominator * opNR.GetDenominator();
 	num += (opNR.GetNumerator() * m_Denominator);
-	NR result(num, den);
+	NR result(num, num == 0 ? 1 : den);
 	return result;
 }
 
 NR NR::operator-(const NR& opNR) const {
-	int num, den;
+	Int num, den;
 	num = m_Numerator * opNR.GetDenominator();
 	den = m_Denominator * opNR.GetDenominator();
 	num -= (opNR.GetNumerator() * m_Denominator);
-	NR result(num, den);
+	NR result(num, num == 0 ? 1 : den);
 	return result;
 }
 
 NR NR::operator*(const NR& opNR) const {
-	int num, den;
+	Int num, den;
 	num = m_Numerator * opNR.GetNumerator();
 	den = m_Denominator * opNR.GetDenominator();
-	NR result(num, den);
+	NR result(num, num == 0 ? 1 : den);
 	return result;
 }
 
 NR NR::operator/(const NR& opNR) const {
-	int num, den;
+	Int num, den;
 	num = m_Numerator * opNR.GetDenominator();
 	den = m_Denominator * opNR.GetNumerator();
-	NR result(num, den);
+	NR result(num, num == 0 ? 1 : den);
 	return result;
 }
 

src/Solver.cpp

@@ -2,53 +2,69 @@
 
 #include "Gauss.h"
 
-Vect Solver::Image(const Matrix& a_Matrix) const {
-	Matrix result = a_Matrix;
-	result.Transpose();
-	Gauss::GaussJordan(result, true, true);
-	result.Transpose();
-	return {result};
+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(const Matrix& a_Matrix) const {
-	Matrix result = a_Matrix;
-	result.Transpose();
-	result.Augment(Matrix::Identity(result.GetRawCount()));
-	Gauss::GaussJordan(result, true, true);
-	result.Transpose();
+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(result.SubMatrix(0, 0, a_Matrix.GetRawCount(), a_Matrix.GetColumnCount())).GetCardinal();
+	std::size_t origine_colonne = Vect(a_Matrix.SubMatrix(0, 0, matrixRawCount, matrixColumnCount)).GetCardinal();
 
-	return {result.SubMatrix(a_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - a_Matrix.GetRawCount(),
-		result.GetColumnCount() - origine_colonne)};
+	return {a_Matrix.SubMatrix(
+		matrixRawCount, origine_colonne, a_Matrix.GetRawCount() - matrixRawCount, a_Matrix.GetColumnCount() - origine_colonne)};
 }
 
-VectAffine Solver::RectangularSystem(const Matrix& a_MatrixA, const Matrix& a_VectorB) const {
+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(a_MatrixA);
+	Vect noyau = solver.Kernel(std::move(a_MatrixA));
 	Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);
 
-	// on rajoute des 0 si il faut
-
+	// 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++) {
-		fullOrigin.at(i, 0) = origin.at(i, 0);
-	}
+		int pivot_index = FirstNotNullElementIndexOnLine(mat, i);
 		
-	for (std::size_t i = mat.GetRawCount(); i < mat.GetColumnCount() - 1; i++) {
-		fullOrigin.at(i, 0) = 0;
+		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(const Matrix& a_Matrix) const {
-	return Image(a_Matrix).GetCardinal();
+std::size_t Solver::Rank(Matrix&& a_Matrix) const {
+	return Image(std::move(a_Matrix)).GetCardinal();
 }

src/Vect.cpp

@@ -2,8 +2,6 @@
 
 #include "Gauss.h"
 #include "Solver.h"
-#include <cassert>
-#include <iostream>
 
 static bool IsColumnNull(Matrix& mat, std::size_t column) {
 	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
@@ -14,9 +12,9 @@ static bool IsColumnNull(Matrix& mat, std::size_t column) {
 	return true;
 }
 
-Vect::Vect(const Matrix& a_Matrix) : m_Data(a_Matrix) {
+Vect::Vect(Matrix&& a_Matrix) : m_Data(std::move(a_Matrix)) {
 	m_Data.Transpose();
-	Gauss::GaussJordan(m_Data, false, false);
+	Gauss::GaussJordan(m_Data, false, true);
 	m_Data.Transpose();
 	Simplify();
 }
@@ -75,9 +73,9 @@ Matrix Vect::GetLinearSystem() const {
 	vect.Transpose();
 
 	Solver solver;
-	vect = solver.Kernel(vect).m_Data;
-	vect.Transpose();
-	return vect;
+	Matrix result = solver.Kernel(std::move(vect)).m_Data;
+	result.Transpose();
+	return result;
 }
 
 std::size_t Vect::GetDimension() const {
@@ -90,11 +88,3 @@ VectAffine::VectAffine(const Vect& a_Base, const Matrix& a_Origin) :
 bool VectAffine::IsElementOf(const Matrix& a_Vector) const {
 	return m_Base.IsElementOf(a_Vector - m_Origin);
 }
-
-Matrix VectAffine::GetLinearSystem() const {
-	Matrix result = m_Base.GetLinearSystem();
-
-	result.Augment(m_Origin.SubMatrix(0, 0, result.GetRawCount(), 1));
-
-	return result;
-}

src/gui/PivotGui.cpp

@@ -0,0 +1,182 @@
+#include "PivotGui.h"
+
+#include "Gauss.h"
+#include "Matrix.h"
+#include "Solver.h"
+#include <imgui.h>
+#include <sstream>
+
+static std::string equationsResultImage;
+
+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 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 += " (";
+		for (std::size_t j = 0; j < vect.GetDimension(); j++) {
+			result += ElementToString(vector.at(j, 0)) + ", ";
+		}
+		result = result.substr(0, result.size() - 2);
+		result += " ), ";
+	}
+	result = result.substr(0, result.size() - 2);
+	result += "  )";
+	return result;
+}
+
+void PivotGui::Init() {}
+
+void PivotGui::Render() {
+	ImGuiIO& io = ImGui::GetIO();
+
+	static std::vector<std::vector<int>> matrixValues;
+	static int matrixSizeX = 4;
+	static int matrixSizeY = 4;
+	static Solver solver;
+
+	static bool refresh = true;
+
+	// divisions des fenetres
+	ImVec2 topLeftWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y);
+	ImVec2 topRightWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y);
+
+	// Begin fenetre top left
+	ImGui::SetNextWindowSize(topLeftWindowSize);
+	ImGui::SetNextWindowPos(ImVec2(0, 0));	// Position at the top-left corner
+	ImGui::Begin("Left Top Window", nullptr,
+		ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
+
+	// Get window position
+	ImVec2 windowPos = ImGui::GetWindowPos();
+
+	ImGui::Text("Matrice initiale:");
+
+	if (ImGui::InputInt("##RowsMatriceInitiale", &matrixSizeY))
+		refresh = true;
+	matrixSizeY = std::max(1, matrixSizeY);
+	ImGui::SameLine();
+	ImGui::Text("Lignes");
+
+
+	if (ImGui::InputInt("##ColumnsMatriceInitiale", &matrixSizeX))
+		refresh = true;
+	matrixSizeX = std::max(1, 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
+
+	if (refresh) {
+		matrixValues.resize(matrixSizeY);
+		for (auto& row : matrixValues) {
+			row.resize(matrixSizeX, 0);
+		}
+	}
+
+	for (int y = 0; y < matrixSizeY; y++) {
+		for (int x = 0; x < matrixSizeX; x++) {
+			if (x > 0)
+				ImGui::SameLine();
+			ImGui::PushID(y * matrixSizeX + x);
+			ImGui::PushItemWidth(60);  // Adjust this value to change the cell size
+			if (ImGui::InputInt("", &matrixValues[y][x], 0, 0, ImGuiInputTextFlags_CharsDecimal))
+				refresh = true;
+			ImGui::PopItemWidth();
+			ImGui::PopID();
+		}
+	}
+
+	// ImGui::EndChild();	// End Matrice initiale
+
+	ImGui::NewLine();
+
+	ImGui::Text("Matrice échelonnée:");
+
+	// Convert the "result" string back to a matrix
+	Matrix resultMatrix = LoadMatrixFromStdVect(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::End();  // End fenetre top left
+
+	// Begin fenetre top right
+	ImGui::SetNextWindowSize(topRightWindowSize);
+	ImGui::SetNextWindowPos(ImVec2(windowPos.x + topLeftWindowSize.x, 0));	// Position at the top-right corner
+	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(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 = std::string("Noyau: ") + "\n" + PrintVect(solver.Kernel(LoadMatrixFromStdVect(matrixValues))) + "\n" + "\n" +
+				 "Rang: " + "\n" + std::to_string(solver.Rank(LoadMatrixFromStdVect(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::End();  // End fenetre top right
+}
+
+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

@@ -25,8 +25,8 @@ void test() {
 
 	Solver solver;
 
-	Vect image = solver.Image(mat2);
-	Vect noyau = solver.Kernel(mat2);
+	Vect image = solver.Image(Matrix{mat2});
+	Vect noyau = solver.Kernel(Matrix{mat2});
 
 	std::cout << "\tImage :\n";
 	Print(image);

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

@@ -1,10 +1,6 @@
 #include "Gauss.h"
 #include "Matrix.h"
-#include <cassert>
-
-#ifdef NDEBUG
-#error "Il faut être en debug mode ! xmake f -m debug"
-#endif
+#include "test_assert.h"
 
 struct Test {
 	Matrix mat;
@@ -37,7 +33,7 @@ static const std::vector<Test> TEST_MATRICES = {
 void test() {
 	for (Test test : TEST_MATRICES) {
 		Gauss::GaussJordan(test.mat, true, true);
-		assert(test.mat == test.res);
+		test_assert(test.mat == test.res);
 	}
 }
 

test/test_random_kernel.cpp

@@ -1,21 +1,23 @@
 #include "Solver.h"
-#include <cassert>
+
+#include "test_assert.h"
 #include <cstdlib>
 #include <future>
 #include <iostream>
 #include <vector>
 
-static constexpr int EXECUTION_COUNT = 100;
-static constexpr int MATRIX_MAX_SIZE = 100;
+static constexpr int EXECUTION_COUNT = 1000;
+static constexpr int KERNEL_CHECKS = 100;
+static constexpr int MATRIX_MAX_SIZE = 9;
 
 static const Solver solver;
 
-static unsigned int GetRandomInt() {
-	return rand() % MATRIX_MAX_SIZE + 1;
+static int GetRandomInt() {
+	return rand() % 11 - 5;
 }
 
-static void Test() {
-	Matrix matrix {GetRandomInt(), GetRandomInt()};
+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++) {
@@ -23,21 +25,56 @@ static void Test() {
 		}
 	}
 
-	Vect vect1 = solver.Kernel(matrix);
-	Vect vect2 = solver.Kernel(vect1.GetLinearSystem());
+	return matrix;
+}
 
-	assert(vect1 == vect2);
+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<void>> results;
+	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

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

test/test_solver.cpp

@@ -1,25 +1,56 @@
-#include <cassert>
+#include <algorithm>
 #include <filesystem>
 #include <fstream>
 #include <iostream>
 
 #include "IO.h"
 #include "Solver.h"
+#include "test_assert.h"
 
 namespace fs = std::filesystem;
 
-void TestRectangular() {
-	Matrix mat2 = {2, 4, {
-		1, 1, 1, 1,
-		1, -1, -1, 2
-	}};
+const static int EXECUTION_COUNT = 10000;
+static constexpr int MATRIX_MAX_SIZE = 7;
 
-	VectAffine aff {Matrix::ColumnVector({0, -1, 1}), Matrix::ColumnVector({3.0 / 2.0, 0, -1.0 / 2.0})};
+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;
 
-	std::cout << solver.RectangularSystem(mat2, Matrix::ColumnVector({1, 2})).GetLinearSystem() << std::endl;
-	std::cout << aff.GetLinearSystem() << std::endl;
+	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() {
@@ -34,18 +65,24 @@ void TestKernelImage() {
 		Matrix mat, imageMat, noyauMat;
 		in >> mat >> imageMat >> noyauMat;
 
-		Vect image {imageMat};
-		Vect noyau {noyauMat};
+		Vect image {std::move(imageMat)};
+		Vect noyau {std::move(noyauMat)};
 
 		Solver solver;
 
-		assert(solver.Image(mat) == image);
-		assert(solver.Kernel(mat) == noyau);
+		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();
-	TestRectangular();
+	RandomRectangular();
 	return 0;
 }

test/test_vect.cpp

@@ -1,5 +1,26 @@
 #include "Vect.h"
-#include <cassert>
+#include "test_assert.h"
+
+#include <algorithm>
+
+const static int EXECUTION_COUNT = 100000;
+static constexpr int MATRIX_MAX_SIZE = 7;
+
+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, {
@@ -22,26 +43,42 @@ void TestVect() {
 		0, 0,
 		1, 11,
 	}}};
-	assert(vect1 == vect3);
-	assert(vect2 == vect4);
-	assert(vect1 != vect2);
-	assert(vect2 != vect3);
-	assert(vect3 != vect4);
 
-	assert(vect1.IsElementOf(Matrix::ColumnVector({3, 7, 11})));
-	assert(!vect1.IsElementOf(Matrix::ColumnVector({3, 7, 12})));
+	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 {3, 1, {-2, 3, 7}}, Matrix::ColumnVector({5, 2, -8})};
+	VectAffine aff {Matrix::ColumnVector({-2, 3, 7}), Matrix::ColumnVector({5, 2, -8})};
 
-	assert(aff.IsElementOf(Matrix::ColumnVector({5, 2, -8})));
-	assert(aff.IsElementOf(Matrix::ColumnVector({3, 5, -1})));
-	assert(!aff.IsElementOf(Matrix::ColumnVector({1, 2, 3})));
+	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

@@ -1,6 +1,8 @@
 add_rules("mode.debug", "mode.release")
 
-set_languages("c++17")
+add_requires("imgui", {configs = {sdl2_no_renderer = true, opengl3 = true}})
+
+set_languages("c++20")
 set_warnings("all")
 add_includedirs("include")
 
@@ -19,9 +21,19 @@ 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")