fix action apt

.gitea/workflows/ubuntu.yaml

@@ -7,15 +7,26 @@ jobs:
   Build:
     runs-on: ubuntu-latest
     steps:
+      - name: Install opengl
+        run: |
+          apt update
+          apt install -y libsdl2-dev
+
       - 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: 'xmake-ubuntu'
+
+      - 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

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.

include/Gauss.h

@@ -17,12 +17,4 @@ namespace Gauss {
  */
 void GaussJordan(Matrix& a_Matrix, bool a_Reduite, bool a_Normalise);
 
-/**
- * \brief Echelonne une matrice en colonne 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 GaussJordanColumn(Matrix& a_Matrix, bool a_Reduite, bool a_Normalise);
-
 }  // namespace Gauss

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;
@@ -145,9 +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/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

@@ -2,30 +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));
-	}
-}
-
-static void SwapColumns(Matrix& mat, std::size_t column1, std::size_t column2) {
-	for (std::size_t k = 0; k < mat.GetRawCount(); k++) {
-		std::swap(mat.at(k, column1), mat.at(k, column2));
-	}
+	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;
-	}
-}
-
-static void DivideColumn(Matrix& mat, std::size_t column, Matrix::Element number) {
-	for (std::size_t j = 0; j < mat.GetRawCount(); j++) {
-		mat.at(j, column) /= 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) {
@@ -37,34 +27,18 @@ static int FirstNotNullElementIndexOnColumn(Matrix& mat, std::size_t column, std
 	return -1;
 }
 
-static int FirstNotNullElementIndexOnLine(Matrix& mat, std::size_t line, std::size_t startColumn = 0) {
-	for (std::size_t i = startColumn; i < mat.GetColumnCount(); i++) {
-		if (!IsEqualZero(mat.at(line, i))) {
-			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);
 
-	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;
-	}
+	});
 }
 
-static void SimplifyColumn(Matrix& mat, std::size_t column, 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(pivot_line, column);
-
-	for (std::size_t j = 0; j < mat.GetRawCount(); j++) {
-		mat.at(j, column) = mat.at(j, column) * pivot - mat.at(j, pivot_column) * 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++) {
@@ -86,46 +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);
 			}
-		}
+		});
 	}
 }
 
-void GaussJordanColumn(Matrix& a_Matrix, bool a_Reduite, bool a_Normalise) {
-	int indice_colonne_pivot = -1;
+static void GaussJordanTriangular(Matrix& a_Matrix, bool a_Normalise) {
+	int indice_ligne_pivot = -1;
 
-	for (std::size_t j = 0; j < a_Matrix.GetRawCount(); j++) {
+	for (std::size_t j = 0; j < a_Matrix.GetColumnCount(); j++) {
 
-		int indice_colonne_pivot_trouve = FirstNotNullElementIndexOnLine(a_Matrix, j, indice_colonne_pivot + 1);
+		int indice_ligne_pivot_trouve = FirstNotNullElementIndexOnColumn(a_Matrix, j, indice_ligne_pivot + 1);
 
-		if (indice_colonne_pivot_trouve < 0)  // ligne de 0
-			continue;						  // on regarde la prochaine ligne
+		if (indice_ligne_pivot_trouve < 0)	// colonne de 0
+			continue;						// on regarde la prochaine colonne
 
-		indice_colonne_pivot++;
+		indice_ligne_pivot++;
 
-		if (indice_colonne_pivot_trouve != indice_colonne_pivot) {
-			SwapColumns(a_Matrix, indice_colonne_pivot_trouve, indice_colonne_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(j, indice_colonne_pivot);
+		Matrix::Element pivot = a_Matrix.at(indice_ligne_pivot, j);
 
 		if (a_Normalise) {
-			DivideColumn(a_Matrix, indice_colonne_pivot, pivot);
+			DivideLine(a_Matrix, indice_ligne_pivot, pivot);
 		}
 
-		// On simplifie les autres lignes
-		for (std::size_t i = (a_Reduite ? 0 : j); i < a_Matrix.GetColumnCount(); i++) {
-			// Pour les lignes autre que la ligne pivot
-			if (i != static_cast<std::size_t>(indice_colonne_pivot)) {
-				SimplifyColumn(a_Matrix, i, j, indice_colonne_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

@@ -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];
 }
 
@@ -187,3 +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

@@ -2,9 +2,20 @@
 
 #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 {
-	Gauss::GaussJordanColumn(a_Matrix, true, true);
-	return {a_Matrix};
+	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
@@ -12,8 +23,10 @@ Vect Solver::Kernel(Matrix&& a_Matrix) const {
 	std::size_t matrixRawCount = a_Matrix.GetRawCount();
 	std::size_t matrixColumnCount = a_Matrix.GetColumnCount();
 
-	a_Matrix.AugmentBottom(Matrix::Identity(a_Matrix.GetColumnCount()));
-	Gauss::GaussJordanColumn(a_Matrix, true, true);
+	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();
@@ -32,15 +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

@@ -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();
 }
@@ -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 +1,311 @@
+#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;
+}

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 = 5;
 
-	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() {
@@ -34,20 +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;
 
 		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 = 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,
@@ -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

@@ -1,9 +1,19 @@
+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")
 
-set_languages("c++17")
+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("static")
@@ -19,9 +29,19 @@ 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")