caca

.vscode/launch.json

@@ -7,8 +7,8 @@
         {
             "type": "xmake",
             "request": "launch",
-            "name": "Debug XMake target",
-            "target": "Pivot",
+            "name": "Debug random kernel",
+            "target": "test_random_kernel",
             "cwd": "${workspaceFolder}/matricies",
         }
     ]

.vscode/settings.json

@@ -44,6 +44,23 @@
         "stdexcept": "cpp",
         "streambuf": "cpp",
         "cinttypes": "cpp",
-        "typeinfo": "cpp"
+        "typeinfo": "cpp",
+        "codecvt": "cpp",
+        "condition_variable": "cpp",
+        "cstring": "cpp",
+        "ctime": "cpp",
+        "ratio": "cpp",
+        "fstream": "cpp",
+        "future": "cpp",
+        "iomanip": "cpp",
+        "mutex": "cpp",
+        "semaphore": "cpp",
+        "sstream": "cpp",
+        "stop_token": "cpp",
+        "thread": "cpp",
+        "chrono": "cpp",
+        "optional": "cpp",
+        "ranges": "cpp",
+        "span": "cpp"
     }
 }

imgui.ini

@@ -0,0 +1,16 @@
+[Window][Debug##Default]
+Pos=60,60
+Size=400,400
+
+[Window][Right Top Window]
+Pos=640,0
+Size=640,576
+
+[Window][Bottom Part]
+Pos=0,576
+Size=1280,144
+
+[Window][Left Top Window]
+Pos=0,0
+Size=640,576
+

include/Matrix.h

@@ -18,7 +18,7 @@
  */
 class Matrix {
   public:
-	typedef NR Element;
+	typedef long double Element;
 	typedef std::vector<Element>::iterator iterator;
 
   private:

include/Vect.h

@@ -105,6 +105,12 @@ 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();
 	};

matricies/plot.tex

@@ -0,0 +1,135 @@
+% GNUPLOT: LaTeX picture with Postscript
+\begingroup
+  \makeatletter
+  \providecommand\color[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package color not loaded in conjunction with
+      terminal option `colourtext'%
+    }{See the gnuplot documentation for explanation.%
+    }{Either use 'blacktext' in gnuplot or load the package
+      color.sty in LaTeX.}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\includegraphics[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package graphicx or graphics not loaded%
+    }{See the gnuplot documentation for explanation.%
+    }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
+    \renewcommand\includegraphics[2][]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \@ifundefined{ifGPcolor}{%
+    \newif\ifGPcolor
+    \GPcolortrue
+  }{}%
+  \@ifundefined{ifGPblacktext}{%
+    \newif\ifGPblacktext
+    \GPblacktexttrue
+  }{}%
+  % define a \g@addto@macro without @ in the name:
+  \let\gplgaddtomacro\g@addto@macro
+  % define empty templates for all commands taking text:
+  \gdef\gplbacktext{}%
+  \gdef\gplfronttext{}%
+  \makeatother
+  \ifGPblacktext
+    % no textcolor at all
+    \def\colorrgb#1{}%
+    \def\colorgray#1{}%
+  \else
+    % gray or color?
+    \ifGPcolor
+      \def\colorrgb#1{\color[rgb]{#1}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
+      \expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
+      \expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
+      \expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
+      \expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
+      \expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
+      \expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
+      \expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
+      \expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
+    \else
+      % gray
+      \def\colorrgb#1{\color{black}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color{black}}%
+      \expandafter\def\csname LT1\endcsname{\color{black}}%
+      \expandafter\def\csname LT2\endcsname{\color{black}}%
+      \expandafter\def\csname LT3\endcsname{\color{black}}%
+      \expandafter\def\csname LT4\endcsname{\color{black}}%
+      \expandafter\def\csname LT5\endcsname{\color{black}}%
+      \expandafter\def\csname LT6\endcsname{\color{black}}%
+      \expandafter\def\csname LT7\endcsname{\color{black}}%
+      \expandafter\def\csname LT8\endcsname{\color{black}}%
+    \fi
+  \fi
+    \setlength{\unitlength}{0.0500bp}%
+    \ifx\gptboxheight\undefined%
+      \newlength{\gptboxheight}%
+      \newlength{\gptboxwidth}%
+      \newsavebox{\gptboxtext}%
+    \fi%
+    \setlength{\fboxrule}{0.5pt}%
+    \setlength{\fboxsep}{1pt}%
+    \definecolor{tbcol}{rgb}{1,1,1}%
+\begin{picture}(7200.00,5040.00)%
+    \gplgaddtomacro\gplbacktext{%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,554){\makebox(0,0)[r]{\strut{}0}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,1141){\makebox(0,0)[r]{\strut{}0.05}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,1727){\makebox(0,0)[r]{\strut{}0.1}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,2314){\makebox(0,0)[r]{\strut{}0.15}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,2901){\makebox(0,0)[r]{\strut{}0.2}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,3488){\makebox(0,0)[r]{\strut{}0.25}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,4074){\makebox(0,0)[r]{\strut{}0.3}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(803,4661){\makebox(0,0)[r]{\strut{}0.35}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(935,334){\makebox(0,0){\strut{}0}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(1865,334){\makebox(0,0){\strut{}50}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(2795,334){\makebox(0,0){\strut{}100}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(3725,334){\makebox(0,0){\strut{}150}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(4655,334){\makebox(0,0){\strut{}200}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(5585,334){\makebox(0,0){\strut{}250}}%
+      \colorrgb{0.15,0.15,0.15}%%
+      \put(6515,334){\makebox(0,0){\strut{}300}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
+      \csname LTb\endcsname%%
+      \put(66,2607){\rotatebox{-270}{\makebox(0,0){\strut{}Temps d'exécution (s)}}}%
+      \put(3725,4){\makebox(0,0){\strut{}Taille des matrices}}%
+      \csname LTb\endcsname%%
+      \put(1922,4488){\makebox(0,0)[l]{\strut{}Echelonnage non réduit}}%
+      \csname LTb\endcsname%%
+      \put(1922,4268){\makebox(0,0)[l]{\strut{}Echelonnage réduit}}%
+      \csname LTb\endcsname%%
+      \put(1922,4048){\makebox(0,0)[l]{\strut{}Echelonnage non réduit normalisé}}%
+      \csname LTb\endcsname%%
+      \put(1922,3828){\makebox(0,0)[l]{\strut{}Echelonnage réduit normalisé}}%
+      \csname LTb\endcsname%%
+      \put(3725,4991){\makebox(0,0){/:Bold Echelonnage de matrices}}%
+    }%
+    \gplbacktext
+    \put(0,0){\includegraphics[width={360.00bp},height={252.00bp}]{plot}}%
+    \gplfronttext
+  \end{picture}%
+\endgroup

src/Gauss.cpp

@@ -16,6 +16,10 @@ static void SwapLines(Matrix& mat, std::size_t line1, std::size_t line2) {
 static void DivideLine(Matrix& mat, std::size_t line, Matrix::Element number) {
 	std::transform(std::execution::par_unseq, mat.GetLineIterator(line), mat.GetLineIterator(line + 1), mat.GetLineIterator(line),
 		[number](Matrix::Element e) { return e /= number; });
+
+	/*for (std::size_t i = 0; i < mat.GetColumnCount(); i++) {
+		mat.at(line, i) /= number;
+	}*/
 }
 
 static int FirstNotNullElementIndexOnColumn(Matrix& mat, std::size_t column, std::size_t startLine = 0) {
@@ -38,7 +42,7 @@ static void SimplifyLine(Matrix& mat, std::size_t line, std::size_t pivot_line,
 	});
 }
 
-static void GaussJordanReduced(Matrix& a_Matrix, bool a_Normalise) {
+static void GaussJordanReducedNorma(Matrix& a_Matrix) {
 	int indice_ligne_pivot = -1;
 
 	for (std::size_t j = 0; j < a_Matrix.GetColumnCount(); j++) {
@@ -56,9 +60,7 @@ static void GaussJordanReduced(Matrix& a_Matrix, bool a_Normalise) {
 
 		Matrix::Element pivot = a_Matrix.at(indice_ligne_pivot, j);
 
-		if (a_Normalise) {
 		DivideLine(a_Matrix, indice_ligne_pivot, pivot);
-		}
 
 		auto range = std::views::iota(static_cast<std::size_t>(0), a_Matrix.GetRawCount());
 
@@ -71,7 +73,7 @@ static void GaussJordanReduced(Matrix& a_Matrix, bool a_Normalise) {
 	}
 }
 
-static void GaussJordanTriangular(Matrix& a_Matrix, bool a_Normalise) {
+static void GaussJordanReduced(Matrix& a_Matrix) {
 	int indice_ligne_pivot = -1;
 
 	for (std::size_t j = 0; j < a_Matrix.GetColumnCount(); j++) {
@@ -89,25 +91,85 @@ static void GaussJordanTriangular(Matrix& a_Matrix, bool a_Normalise) {
 
 		Matrix::Element pivot = a_Matrix.at(indice_ligne_pivot, j);
 
-		if (a_Normalise) {
-			DivideLine(a_Matrix, indice_ligne_pivot, pivot);
+		auto range = std::views::iota(static_cast<std::size_t>(0), a_Matrix.GetRawCount());
+
+		// On simplifie les autres lignes
+		std::for_each(std::execution::par_unseq, range.begin(), range.end(), [&a_Matrix, j, indice_ligne_pivot](std::size_t i) {
+			if (i != static_cast<std::size_t>(indice_ligne_pivot)) {
+				SimplifyLine(a_Matrix, i, indice_ligne_pivot, j);
 			}
+		});
+	}
+}
+
+static void GaussJordanTriangular(Matrix& a_Matrix) {
+	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);
 
 		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); 
-			});
+			[&a_Matrix, indice_ligne_pivot, j](std::size_t i) { SimplifyLine(a_Matrix, i, indice_ligne_pivot, j); });
+	}
+}
+
+static void GaussJordanTriangularNorma(Matrix& a_Matrix) {
+	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);
+
+		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);
+	if (a_Reduite) {
+		if (a_Normalise) {
+			GaussJordanReducedNorma(a_Matrix);
+		} else {
+			GaussJordanReduced(a_Matrix);
+		}
+	} else {
+		if (a_Normalise) {
+			GaussJordanTriangularNorma(a_Matrix);
+		} else {
+			GaussJordanTriangular(a_Matrix);
+		}
+	}
 }
 
 }  // namespace Gauss

src/Vect.cpp

@@ -88,3 +88,11 @@ 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

@@ -1,6 +1,5 @@
 #include "PivotGui.h"
 
-#include "Gauss.h"
 #include "Matrix.h"
 #include "Solver.h"
 #include <imgui.h>
@@ -56,8 +55,9 @@ void PivotGui::Render() {
 	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);
+	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);
 
 	// Begin fenetre top left
 	ImGui::SetNextWindowSize(topLeftWindowSize);
@@ -85,7 +85,7 @@ void PivotGui::Render() {
 
 	ImGui::NewLine();
 
-	// ImGui::BeginChild("MatriceInitiale", ImVec2(topLeftWindowSize.x, io.DisplaySize.y * 0.7f), false);
+	ImGui::BeginChild("MatriceInitiale", ImVec2(topLeftWindowSize.x, io.DisplaySize.y * 0.7f), false);
 
 	// Resize matrixValues and initialize new elements to 0
 
@@ -101,7 +101,7 @@ void PivotGui::Render() {
 			if (x > 0)
 				ImGui::SameLine();
 			ImGui::PushID(y * matrixSizeX + x);
-			ImGui::PushItemWidth(60);  // Adjust this value to change the cell size
+			ImGui::PushItemWidth(30);  // Adjust this value to change the cell size
 			if (ImGui::InputInt("", &matrixValues[y][x], 0, 0, ImGuiInputTextFlags_CharsDecimal))
 				refresh = true;
 			ImGui::PopItemWidth();
@@ -109,31 +109,13 @@ void PivotGui::Render() {
 		}
 	}
 
-	// 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();
-		}
+	// 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::End();  // End fenetre top left
 
 	// Begin fenetre top right
@@ -146,6 +128,16 @@ void PivotGui::Render() {
 
 	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 (refresh) {
 
 		// Calculate the kernel and image
@@ -168,15 +160,7 @@ void PivotGui::Render() {
 	}
 
 	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
+	ImGui::End();  // End fenetre bas
 }
 
 void PivotGui::Destroy() {}

test/test_jordan.cpp

@@ -2,6 +2,12 @@
 #include "Matrix.h"
 #include "test_assert.h"
 
+#include <chrono>
+#include <iostream>
+
+static constexpr int MATRIX_MAX_SIZE = 300;
+static constexpr int EXECUTION_COUNT = 1;
+
 struct Test {
 	Matrix mat;
 	Matrix res;
@@ -30,6 +36,22 @@ static const std::vector<Test> TEST_MATRICES = {
     }}}
 };
 
+static unsigned int GetRandomInt() {
+	return rand() % MATRIX_MAX_SIZE + 1;
+}
+
+static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
+	Matrix matrix {a_Raw, a_Column};
+
+	for (std::size_t i = 0; i < matrix.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < matrix.GetColumnCount(); j++) {
+			matrix.at(i, j) = GetRandomInt();
+		}
+	}
+
+	return matrix;
+}
+
 void test() {
 	for (Test test : TEST_MATRICES) {
 		Gauss::GaussJordan(test.mat, true, true);
@@ -37,7 +59,26 @@ void test() {
 	}
 }
 
+void gaussTest() {
+    auto start = std::chrono::system_clock::now();
+
+	for (int i = 0; i < EXECUTION_COUNT; i++) {
+		Matrix mat = GetRandomMatrix(500, 500);
+		Gauss::GaussJordan(mat, false, false);
+	}
+
+	auto end = std::chrono::system_clock::now();
+	std::chrono::duration<double> elapsed_seconds = end - start;
+	std::cout << "\tgauss jordan elapsed time : " << elapsed_seconds.count() << "s" << std::endl;
+}
+
+void speedTest() {
+    gaussTest();
+   // gaussColumnTest();
+}
+
 int main(int argc, char** argv) {
 	test();
+	speedTest();
 	return 0;
 }

test/test_plot.cpp

@@ -0,0 +1,109 @@
+#include <algorithm>
+#include <chrono>
+#include <cmath>
+#include <execution>
+#include <future>
+#include <matplot/matplot.h>
+
+#include "Gauss.h"
+#include "Matrix.h"
+#include "Solver.h"
+
+static constexpr int EXECUTION_COUNT = 100;
+static constexpr int MATRIX_MAX_SIZE = 300;
+
+static unsigned int GetRandomInt() {
+	return rand() % MATRIX_MAX_SIZE + 1;
+}
+
+static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
+	Matrix matrix {a_Raw, a_Column};
+
+	for (std::size_t i = 0; i < matrix.GetRawCount(); i++) {
+		for (std::size_t j = 0; j < matrix.GetColumnCount(); j++) {
+			matrix.at(i, j) = GetRandomInt();
+		}
+	}
+
+	return matrix;
+}
+
+std::vector<double> GaussJordan(const std::vector<double>& x) {
+	std::vector<double> y;
+
+	std::for_each(x.begin(), x.end(), [&y](double size) {
+		auto start = std::chrono::system_clock::now();
+
+		for (int j = 0; j < EXECUTION_COUNT; j++) {
+			Matrix mat = GetRandomMatrix(size, size);
+			Gauss::GaussJordan(mat, false, false);
+		}
+
+		auto end = std::chrono::system_clock::now();
+		std::chrono::duration<double> elapsed_seconds = end - start;
+		std::cout << "S " << size << "\n";
+		y.push_back(elapsed_seconds.count() / static_cast<double>(EXECUTION_COUNT));
+	});
+
+	return y;
+}
+
+
+std::vector<double> GaussJordanReduite(const std::vector<double>& x) {
+	std::vector<double> y;
+
+	std::for_each(x.begin(), x.end(), [&y](double size) {
+		auto start = std::chrono::system_clock::now();
+
+		for (int j = 0; j < EXECUTION_COUNT; j++) {
+			Matrix mat = GetRandomMatrix(size, size);
+			Gauss::GaussJordan(mat, true, false);
+		}
+
+		auto end = std::chrono::system_clock::now();
+		std::chrono::duration<double> elapsed_seconds = end - start;
+		std::cout << "R " << size << "\n";
+		y.push_back(elapsed_seconds.count() / static_cast<double>(EXECUTION_COUNT));
+	});
+
+	return y;
+}
+
+int main() {
+	srand(time(0));
+
+	int start = 1;
+
+	std::vector<double> x = matplot::linspace(start, MATRIX_MAX_SIZE, MATRIX_MAX_SIZE - start + 1);
+	//std::vector<double> x = {5000};
+	std::vector<double> y, y1, y2, y3;
+
+	// y2.resize(x.size());
+
+	{
+		auto result1 = std::async(std::launch::async, &GaussJordan, x);
+		auto result2 = std::async(std::launch::async, &GaussJordanReduite, x);
+		y = result1.get();
+		y1 = result2.get();
+	}
+
+
+	std::cout << "Fini !\n";
+
+
+	// std::transform(x.begin(), x.end(), y2.begin(), [](double x) { return 1.0 / (100.0 * 100.0) * 0.6 * x * x; });
+
+	matplot::title("Echelonnage de matrices");
+	matplot::xlabel("Taille des matrices");
+	matplot::ylabel("Temps d'exécution (s)");
+
+	matplot::hold(matplot::on);
+	matplot::plot(x, y);
+	matplot::plot(x, y1);
+
+	auto l = matplot::legend({"Echelonnage non réduit", "Echelonnage réduit", "Echelonnage non réduit normalisé", "Echelonnage réduit normalisé"});
+	l->location(matplot::legend::general_alignment::topleft);
+
+	matplot::show();
+	return 0;
+}

test/test_random_kernel.cpp

@@ -16,6 +16,16 @@ static int GetRandomInt() {
 	return rand() % 11 - 5;
 }
 
+#define print_time(i)                                                                                                                 \
+	end = std::chrono::system_clock::now();                                                                                           \
+	elapsed_seconds = end - start;                                                                                                    \
+	std::cout << "elapsed time " << i << " : " << elapsed_seconds.count() << "s" << std::endl;                                        \
+	start = std::chrono::system_clock::now()
+
+static unsigned int GetRandomSize() {
+	return rand() % MATRIX_MAX_SIZE + 1;
+}
+
 static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
 	Matrix matrix {a_Raw, a_Column};
 
@@ -29,24 +39,34 @@ static Matrix GetRandomMatrix(std::size_t a_Raw, std::size_t a_Column) {
 }
 
 static bool Test() {
-	Matrix matrix = GetRandomMatrix(rand() % MATRIX_MAX_SIZE + 1, rand() % MATRIX_MAX_SIZE + 1);
+	auto start = std::chrono::system_clock::now();
+	auto begin = start;
+	auto end = start;
+	std::chrono::duration<double> elapsed_seconds = end - start;
 
-	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();
-		}
-	}
+	std::cout << "Begin\n";
+
+	Matrix matrix = GetRandomMatrix(GetRandomSize(), GetRandomSize());
+
+	print_time(1);
 
 	Matrix copy = matrix;
 
 	Vect kernel = solver.Kernel(std::move(copy));
 
+	print_time(2);
+
 	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);
+		Matrix result = matrix * kernel.GetVector(i);
+		if(!(result == nullVector)) {
+			test_assert(false);
 		}
+	}
+
+	print_time(3);
 
 	for (std::size_t i = 0; i < KERNEL_CHECKS; i++) {
 		Matrix vector = GetRandomMatrix(kernel.GetDimension(), 1);
@@ -54,9 +74,22 @@ static bool Test() {
 		test_assert(kernel.IsElementOf(vector) == (matrix * vector == nullVector));
 	}
 
-	Vect kernel2 = solver.Kernel(kernel.GetLinearSystem());
+	print_time(4);
+
+	Matrix linearSystem = kernel.GetLinearSystem();
+
+	print_time(5);
+
+	Vect kernel2 = solver.Kernel(std::move(linearSystem));
 
 	test_assert(kernel == kernel2);
+
+	print_time(6);
+
+	elapsed_seconds = end - begin;
+	std::cout << "final elapsed time: " << elapsed_seconds.count() << "s" << std::endl;
+
+	std::cout << "End\n";
 	return true;
 }
 
@@ -69,6 +102,7 @@ int main() {
 	for (int i = 0; i < EXECUTION_COUNT; i++) {
 		auto handle = std::async(std::launch::async, &Test);
 		results.push_back(std::move(handle));
+		// Test();
 	}
 
 	for (auto& result : results) {

test/test_vect.cpp

@@ -1,27 +1,6 @@
 #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,
@@ -62,23 +41,8 @@ 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

@@ -1,15 +1,20 @@
 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")
 set_warnings("all")
 add_includedirs("include")
 
+add_requires("matplotplusplus")
+
 -- Solver Library
 target("Pivot")
     set_kind("static")
     add_files("src/*.cpp")
+    add_cxxflags("-ffast-math")
+    set_optimize("fastest")
     remove_files("src/main.cpp")
 
 
@@ -48,6 +53,7 @@ for _, file in ipairs(os.files("test/test_*.cpp")) do
         set_default(false)
 
         add_deps("Pivot")
+        add_packages("matplotplusplus")
 
         add_tests("compile_and_run")
 end