From 4ffeea890028784a1d7685577afe9d855d801703 Mon Sep 17 00:00:00 2001
From: Persson-dev <sim16.prib@gmail.com>
Date: Wed, 14 Feb 2024 21:35:26 +0100
Subject: [PATCH] image et noyau

---
 src/Solver.cpp | 31 +++++++++++++++++++++++++++++++
 src/Solver.h   | 16 ++++++++++++++++
 src/main.cpp   | 26 ++++++++++----------------
 3 files changed, 57 insertions(+), 16 deletions(-)
 create mode 100644 src/Solver.cpp
 create mode 100644 src/Solver.h

diff --git a/src/Solver.cpp b/src/Solver.cpp
new file mode 100644
index 0000000..5e1634d
--- /dev/null
+++ b/src/Solver.cpp
@@ -0,0 +1,31 @@
+#include "Solver.h"
+
+Solver::Solver(const Matrix& mat) : m_Matrix(mat) {}
+
+Vect Solver::Image() const {
+	Matrix result = m_Matrix;
+	result.Transpose();
+	result.GaussJordan(true);
+	result.Transpose();
+	return {result};
+}
+
+// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
+Vect Solver::Noyau() const {
+	Matrix result = m_Matrix;
+	result.Transpose();
+	result.Augmenter(Matrix::Identity(result.GetRawCount()));
+	result.GaussJordan(true);
+	result.Transpose();
+
+	// nombre de colonnes non nulles
+	std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, m_Matrix.GetRawCount(), m_Matrix.GetColumnCount())).GetDimension();
+
+	return {result.SubMatrix(m_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - m_Matrix.GetRawCount(),
+		result.GetColumnCount() - origine_colonne)};
+}
+
+std::size_t Solver::Rang() const {
+	Vect image = Image();
+	return image.GetDimension();
+}
diff --git a/src/Solver.h b/src/Solver.h
new file mode 100644
index 0000000..aded7b5
--- /dev/null
+++ b/src/Solver.h
@@ -0,0 +1,16 @@
+#pragma once
+
+#include "Vect.h"
+
+class Solver {
+  private:
+	Matrix m_Matrix;
+  public:
+	Solver(const Matrix& mat);
+	~Solver() {}
+
+	Vect Image() const;
+	Vect Noyau() const;
+
+	std::size_t Rang() const;
+};
\ No newline at end of file
diff --git a/src/main.cpp b/src/main.cpp
index 8d66b28..30091d6 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,8 +1,8 @@
-#include "Vect.h"
+#include "Solver.h"
 #include <iostream>
 
 void test() {
-	Matrix mat{"matrice4x4.mat"};
+	/* Matrix mat{"matrice4x4.mat"};
 	mat.Print();
 	// mat.Save("matrice3x3.mat");
 	std::cout << "sdfdjiofoseifheoiefhoig\n";
@@ -14,23 +14,17 @@ void test() {
 	mat.Transpose();
 	std::cout << "<<\nTransposée:\n";
 	mat.Print();
-	// mat.Save("matrice4x4echelonne.mat");
+	// mat.Save("matrice4x4echelonne.mat"); */
 
-	Matrix mat2 {"matrice4x4.mat"};
-	mat2.Print();
-	
-	mat2.Transpose();
-	std::cout << "Transposée : \n";
-	mat2.Print();
-	
-	mat2.GaussJordan(true);
-	mat2.Transpose();
-
-	std::cout << "Echelonnée en colonne :\n";
+	Matrix mat2{"matrice4x4.mat"};
 	mat2.Print();
 
-	Vect sol {mat2};
-	sol.Print();
+	Solver solver{mat2};
+
+	std::cout << "\tImage :\n";
+	solver.Image().Print();
+	std::cout << "\tNoyau :\n";
+	solver.Noyau().Print();
 }
 
 void prompt() {