init random

.vscode/c_cpp_properties.json

@@ -3,7 +3,8 @@
         {
             "name": "Pivot",
             "cppStandard": "c++20",
-            "includePath": ["include"]
+            "includePath": ["include"],
+            "compileCommands": "${workspaceFolder}/.vscode/compile_commands.json"
         }
     ],
     "version": 4

include/Matrix.h

@@ -10,13 +10,15 @@
 #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:
@@ -154,6 +156,21 @@ class Matrix {
 };
 
 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/Vect.h

@@ -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/Matrix.cpp

@@ -71,11 +71,7 @@ Matrix Matrix::RawVector(std::initializer_list<Element>&& a_Elements) {
 }
 
 void Matrix::Fill(Element a_Element) {
-	for (std::size_t i = 0; i < m_Raws; i++) {
-		for (std::size_t j = 0; j < m_Columns; j++) {
-			at(i, j) = a_Element;
-		}
-	}
+	std::fill(GetLineIterator(0), GetLineIterator(m_Raws), a_Element);
 }
 
 void Matrix::Augment(const Matrix& a_Right) {
@@ -158,10 +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];
 }
 

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

@@ -2,6 +2,15 @@
 
 #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);
@@ -36,15 +45,21 @@ VectAffine Solver::RectangularSystem(Matrix&& a_MatrixA, const Matrix& a_VectorB
 	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};

src/Vect.cpp

@@ -14,7 +14,7 @@ static bool IsColumnNull(Matrix& mat, std::size_t column) {
 
 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();
 }
@@ -88,11 +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

@@ -1,8 +1,10 @@
 #include "PivotGui.h"
 
+#include "Gauss.h"
 #include "Matrix.h"
 #include "Solver.h"
 #include <imgui.h>
+#include <sstream>
 
 static std::string equationsResultImage;
 
@@ -16,8 +18,14 @@ static Matrix LoadMatrixFromStdVect(const std::vector<std::vector<int>>& data) {
 	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)
+	if (vect.GetCardinal() == 0)
 		return "{0}";
 
 	std::string result = "Vect( ";
@@ -25,11 +33,13 @@ static std::string PrintVect(const Vect& vect) {
 		Matrix vector = vect.GetVector(i);
 		result += " (";
 		for (std::size_t j = 0; j < vect.GetDimension(); j++) {
-			result += std::to_string(static_cast<int>((vector.at(j, 0)))) + ", ";
+			result += ElementToString(vector.at(j, 0)) + ", ";
 		}
+		result = result.substr(0, result.size() - 2);
 		result += " ), ";
 	}
-	result += " )";
+	result = result.substr(0, result.size() - 2);
+	result += "  )";
 	return result;
 }
 
@@ -43,10 +53,11 @@ void PivotGui::Render() {
 	static int matrixSizeY = 4;
 	static Solver solver;
 
+	static bool refresh = true;
+
 	// divisions des fenetres
-	ImVec2 topLeftWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y * 0.8f);
-	ImVec2 topRightWindowSize(io.DisplaySize.x * 0.5f, io.DisplaySize.y * 0.8f);
-	ImVec2 bottomWindowSize(io.DisplaySize.x, io.DisplaySize.y * 0.2f);
+	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);
@@ -59,22 +70,30 @@ void PivotGui::Render() {
 
 	ImGui::Text("Matrice initiale:");
 
-	ImGui::InputInt("##RowsMatriceInitiale", &matrixSizeY);
+	if (ImGui::InputInt("##RowsMatriceInitiale", &matrixSizeY))
+		refresh = true;
+	matrixSizeY = std::max(1, matrixSizeY);
 	ImGui::SameLine();
 	ImGui::Text("Lignes");
 
 
-	ImGui::InputInt("##ColumnsMatriceInitiale", &matrixSizeX);
+	if (ImGui::InputInt("##ColumnsMatriceInitiale", &matrixSizeX))
+		refresh = true;
+	matrixSizeX = std::max(1, matrixSizeX);
 	ImGui::SameLine();
 	ImGui::Text("Colonnes");
 
-	ImGui::BeginChild("MatriceInitiale", ImVec2(topLeftWindowSize.x, io.DisplaySize.y * 0.7f), false);
+	ImGui::NewLine();
+
+	// ImGui::BeginChild("MatriceInitiale", ImVec2(topLeftWindowSize.x, io.DisplaySize.y * 0.7f), false);
 
 	// Resize matrixValues and initialize new elements to 0
 
-	matrixValues.resize(matrixSizeY);
-	for (auto& row : matrixValues) {
-		row.resize(matrixSizeX, 0);
+	if (refresh) {
+		matrixValues.resize(matrixSizeY);
+		for (auto& row : matrixValues) {
+			row.resize(matrixSizeX, 0);
+		}
 	}
 
 	for (int y = 0; y < matrixSizeY; y++) {
@@ -82,19 +101,38 @@ void PivotGui::Render() {
 			if (x > 0)
 				ImGui::SameLine();
 			ImGui::PushID(y * matrixSizeX + x);
-			ImGui::PushItemWidth(30);  // Adjust this value to change the cell size
-			ImGui::InputInt("", &matrixValues[y][x], 0, 0, ImGuiInputTextFlags_CharsDecimal);
+			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();
 		}
 	}
 
-	// Display the equationsResult strings in the GUI if they are not empty
-	if (!equationsResultImage.empty()) {
-		ImGui::TextWrapped(equationsResultImage.c_str());
-	}
+	// ImGui::EndChild();	// End Matrice initiale
 
-	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
 
@@ -106,51 +144,39 @@ void PivotGui::Render() {
 
 	// rajouter le code pour la partie top right
 
-	static std::string result = "RIEN";
+	static std::string result = "";
 
-	ImGui::TextWrapped(result.c_str());
-
-	ImGui::End();  // End fenetre top right
-
-	// Begin fenetre bas
-	ImGui::SetNextWindowSize(bottomWindowSize);
-	ImGui::SetNextWindowPos(ImVec2(0, io.DisplaySize.y * 0.8f));  // Position at the bottom-left corner
-	ImGui::Begin("Bottom Part", nullptr,
-		ImGuiWindowFlags_NoResize | ImGuiWindowFlags_NoMove | ImGuiWindowFlags_NoTitleBar | ImGuiWindowFlags_NoScrollbar);
-
-	if (ImGui::Button("Calcul")) {
+	if (refresh) {
 
 		// Calculate the kernel and image
 		Vect image = solver.Image(LoadMatrixFromStdVect(matrixValues));
 		Matrix linearSystem = image.GetLinearSystem();
 
-		// Create a column matrix with as many elements as the number of columns in the linear system
-		std::vector<std::string> columnMatrix(linearSystem.GetColumnCount());
-		for (size_t i = 0; i < linearSystem.GetColumnCount(); ++i) {
-			columnMatrix[i] = std::string(1, 'a' + static_cast<char>(i));
-		}
-
-		// Multiply the linear system matrix by the column matrix
-		std::vector<std::string> resultMatrix(linearSystem.GetRawCount());
-		for (size_t i = 0; i < linearSystem.GetRawCount(); ++i) {
-			for (size_t j = 0; j < linearSystem.GetColumnCount(); ++j) {
-				resultMatrix[i] += std::to_string(static_cast<int>(linearSystem.at(i, j))) + "*" + columnMatrix[j] + " + ";
-			}
-			resultMatrix[i] = resultMatrix[i].substr(0, resultMatrix[i].length() - 3) + " = 0";
-		}
-
 		// Store the equationsResult strings in the global variable
 		equationsResultImage = "Equations cartesiennes de l'espace vectoriel (Image):\n";
-		for (const auto& equation : resultMatrix) {
-			equationsResultImage += equation + "\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);
+				 "Rang: " + "\n" + std::to_string(solver.Rank(LoadMatrixFromStdVect(matrixValues))) + "\n" + "\n" + "Image: " + "\n" +
+				 PrintVect(image);
 	}
 
-	ImGui::End();  // End fenetre bas
+	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

@@ -1,5 +1,4 @@
 #pragma once
-#include <vector>
 
 namespace PivotGui {
 

test/test_assert.h

@@ -6,6 +6,7 @@
  */
 
 #include <iostream>
+#include <stdexcept>
 
 /**
  * \def TEST_SUCCESSFUL
@@ -37,6 +38,5 @@
 	if (!static_cast<bool>(__VA_ARGS__)) {                                                                                            \
 		std::cout << __FILE__ << ":" << __LINE__ << ": " << __FUNCTION_NAME__ << ": Assertion failed !\n";                            \
 		std::cout << "    " << __LINE__ << "  |\t" << #__VA_ARGS__ << std::endl;                                                      \
-		std::exit(TEST_FAILED);                                                                                                       \
+		throw std::runtime_error("Assertion failed !");                                                                               \
 	}
-

test/test_random_kernel.cpp

@@ -6,14 +6,14 @@
 #include <iostream>
 #include <vector>
 
-static constexpr int EXECUTION_COUNT = 100;
+static constexpr int EXECUTION_COUNT = 1000;
 static constexpr int KERNEL_CHECKS = 100;
-static constexpr int MATRIX_MAX_SIZE = 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 Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
@@ -28,8 +28,8 @@ static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
 	return matrix;
 }
 
-static void Test() {
-	Matrix matrix = GetRandomMatrix(GetRandomInt(), GetRandomInt());
+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++) {
@@ -57,12 +57,13 @@ static void Test() {
 	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++) {
@@ -70,5 +71,10 @@ int main() {
 		results.push_back(std::move(handle));
 	}
 
+	for (auto& result : results) {
+		if (!result.get())
+			return EXIT_FAILURE;
+	}
+
 	return EXIT_SUCCESS;
 }

test/test_solver.cpp

@@ -1,3 +1,4 @@
+#include <algorithm>
 #include <filesystem>
 #include <fstream>
 #include <iostream>
@@ -8,18 +9,48 @@
 
 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(std::move(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() {
@@ -41,13 +72,17 @@ void TestKernelImage() {
 
 		Matrix copy = mat;
 
-		test_assert(solver.Image(std::move(copy)) == image);
-		test_assert(solver.Kernel(std::move(mat)) == noyau);
+		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

@@ -1,6 +1,27 @@
 #include "Vect.h"
 #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, {
 		1, 2,
@@ -41,8 +62,23 @@ void TestVectAffine() {
 	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 +1,5 @@
 add_rules("mode.debug", "mode.release")
 
-add_requires("libsdl 2.28.3", {configs = {sdlmain = false}})
 add_requires("imgui", {configs = {sdl2_no_renderer = true, opengl3 = true}})
 
 set_languages("c++20")