ProjetMAM/Pivot
Archived
4
1
Fork 0
Code Issues Pull Requests Actions Releases 2 Activity

big internal rework

Browse Source
This commit is contained in:
Simon Pribylski
2024-02-29 14:48:36 +01:00
parent b9a5100cb0
commit d038ac5884
10 changed files with 224 additions and 193 deletions
Download Patch File Download Diff File Expand all files Collapse all files

104
src/Gauss.cpp
View File

@@ -4,72 +4,66 @@
namespace Gauss { namespace Gauss {
static void GaussNonJordan(Matrix& mat, bool reduite) { static void SwapLines(Matrix& mat, std::size_t line1, std::size_t line2) {
int r = -1;
for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
std::size_t indice_ligne_maximum = r + 1;
// Recherche maximum
for (std::size_t i = r + 1; i < mat.GetRawCount(); i++) {
if (std::abs(mat.at(i, j)) > std::abs(mat.at(indice_ligne_maximum, j)))
indice_ligne_maximum = i;
}
// Si A[k,j]≠0 alors (A[k,j] désigne la valeur de la ligne k et de la colonne j)
if (!IsEqualZero(mat.at(indice_ligne_maximum, j))) {
r++;
// Si k≠r alors
if (indice_ligne_maximum != r) {
// Échanger les lignes k et r (On place la ligne du pivot en position r)
for (std::size_t k = 0; k < mat.GetColumnCount(); k++) { for (std::size_t k = 0; k < mat.GetColumnCount(); k++) {
std::swap(mat.at(indice_ligne_maximum, k), mat.at(r, k)); std::swap(mat.at(line1, k), mat.at(line2, k));
}
}
// Pour i de 1 jusqu'à n (On simplifie les autres lignes)
for (std::size_t i = (reduite ? 0 : j); i < mat.GetRawCount(); i++) {
// Si i≠r alors
if (i != r) {
// Soustraire à la ligne i la ligne r multipliée par A[i,j] (de façon à
// annuler A[i,j])
for (int k = mat.GetColumnCount() - 1; k >= 0; k--) {
long double pivot = mat.at(r, j);
long double anul = mat.at(i, j);
mat.at(i, k) = mat.at(i, k) * pivot - mat.at(r, k) * anul;
}
}
}
}
} }
} }
static void GaussJordan(Matrix& mat, bool reduite) { static void DivideLine(Matrix& mat, std::size_t line, Matrix::Element number) {
GaussNonJordan(mat, reduite);
for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
int k = -1;
for (std::size_t j = 0; j < mat.GetColumnCount(); j++) { for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
if (!IsEqualZero(mat.at(i, j))) { mat.at(line, j) /= number;
k = j; }
break; }
static int FirstNotNullElementIndexOnColumn(Matrix& mat, std::size_t column, std::size_t startLine = 0) {
for (std::size_t i = startLine; i < mat.GetRawCount(); i++) {
if (!IsEqualZero(mat.at(i, column))) {
return i;
} }
} }
// ligne de 0 return -1;
if (k == -1) }
break;
// on divise la ligne par (i, k) static void SimplifyLine(Matrix& mat, std::size_t line, std::size_t pivot_line, std::size_t pivot_column) {
long double annul = mat.at(i, k); const Matrix::Element pivot = mat.at(pivot_line, pivot_column);
for (int j = 0; j < mat.GetColumnCount(); j++) { const Matrix::Element anul = mat.at(line, pivot_column);
mat.at(i, j) /= annul;
} for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
mat.at(line, j) = mat.at(line, j) * pivot - mat.at(pivot_line, j) * anul;
} }
} }
void GaussJordan(Matrix& mat, bool reduite, bool normalise) { void GaussJordan(Matrix& mat, bool reduite, bool normalise) {
if (normalise) int indice_ligne_pivot = -1;
GaussJordan(mat, reduite);
else for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
GaussNonJordan(mat, reduite);
int indice_ligne_pivot_trouve = FirstNotNullElementIndexOnColumn(mat, 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(mat, indice_ligne_pivot_trouve, indice_ligne_pivot);
}
Matrix::Element pivot = mat.at(indice_ligne_pivot, j);
if (normalise) {
DivideLine(mat, indice_ligne_pivot, pivot);
}
// On simplifie les autres lignes
for (std::size_t i = (reduite ? 0 : j); i < mat.GetRawCount(); i++) {
// Pour les lignes autre que la ligne pivot
if (i != static_cast<std::size_t>(indice_ligne_pivot)) {
SimplifyLine(mat, i, indice_ligne_pivot, j);
}
}
}
} }
} // namespace Gauss } // namespace Gauss

6
src/Gauss.h
View File

@@ -4,6 +4,12 @@ class Matrix;
namespace Gauss { namespace Gauss {
/**
* \brief Echelonne une matrice en utilisant l'algorithme de Gauss-Jordan
* \param mat La matrice à échelonner
* \param reduite Mets des 0 au dessus des pivots
* \param normalise Mets les pivots à 1
*/
void GaussJordan(Matrix& mat, bool reduite, bool normalise); void GaussJordan(Matrix& mat, bool reduite, bool normalise);
} // namespace Gauss } // namespace Gauss

101
src/IO.cpp Normal file
View File

@@ -0,0 +1,101 @@
#include "IO.h"
#include "Vect.h"
#include <fstream>
#include <iostream>
std::ostream& operator<<(std::ostream& stream, const Matrix& mat) {
stream << mat.GetRawCount() << " " << mat.GetColumnCount() << "\n";
for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
stream << mat.at(i, j) << " ";
}
stream << "\n";
}
return stream;
}
std::istream& operator>>(std::istream& stream, Matrix& mat) {
std::size_t raw, column;
stream >> raw >> column;
Matrix result {raw, column};
mat = result;
for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
stream >> mat.at(i, j);
}
}
return stream;
}
Matrix LoadMatrix(const std::string& fileName) {
std::ifstream in {fileName};
if (!in) {
std::cerr << "Impossible de charger la matrice !\n";
return {};
}
Matrix result;
in >> result;
return result;
}
void SaveMatrix(const Matrix& mat, const std::string& fileName) {
std::ofstream out {fileName};
if (!out) {
std::cerr << "Impossible de sauvegarder la matrice !\n";
return;
}
out << mat;
}
Matrix InsertMatrix() {
std::cout << "Quelle est le nombre de lignes de votre matrice ?" << std::endl;
std::size_t lignes;
std::cin >> lignes;
std::cout << "Quelle est le nombre de colonnes de votre matrice ?" << std::endl;
std::size_t colonnes;
std::cin >> colonnes;
std::cout << "Rentrez les coefficients de la matrice" << std::endl;
Matrix result(lignes, colonnes);
for (size_t i = 0; i < result.GetRawCount(); ++i) {
for (size_t j = 0; j < result.GetColumnCount(); ++j) {
std::cin >> result.at(i, j);
}
std::cout << std::endl;
}
return result;
}
void Print(const Matrix& mat) {
for (size_t i = 0; i < mat.GetRawCount(); ++i) {
std::cout << "[ ";
for (size_t j = 0; j < mat.GetColumnCount(); ++j) {
std::cout << mat.at(i, j) << " ";
}
std::cout << "]";
std::cout << std::endl;
}
}
void Print(const Vect& vect) {
std::cout << "Espace vectoriel de dimension " << vect.GetCardinal() << " de base :\n\n";
for (std::size_t i = 0; i < vect.GetDimension(); i++) {
for (std::size_t j = 0; j < vect.GetCardinal(); j++) {
Matrix vector = vect.GetVector(j);
std::cout << "[ " << vector.at(i, 0) << " ]\t";
}
std::cout << "\n";
}
}
void Print(const VectAffine& vect) {
std::cout << "\tEspace Affine :\n\n";
Print(vect.GetBase());
std::cout << "\nOrigine :\n\n";
Print(vect.GetOrigin());
}

19
src/IO.h Normal file
View File

@@ -0,0 +1,19 @@
#pragma once
#include <string>
class Matrix;
class Vect;
class VectAffine;
std::ostream& operator<<(std::ostream& stream, const Matrix& mat);
std::istream& operator>>(std::istream& stream, Matrix& mat);
Matrix LoadMatrix(const std::string& fileName);
void SaveMatrix(const Matrix& mat, const std::string& fileName);
Matrix InsertMatrix();
void Print(const Matrix& mat);
void Print(const Vect& vect);
void Print(const VectAffine& vect);

77
src/Matrix.cpp
View File

@@ -1,20 +1,17 @@
#include "Matrix.h" #include "Matrix.h"
#include "IO.h"
#include <algorithm> #include <algorithm>
#include <cassert> #include <cassert>
#include <cmath> #include <cmath>
#include <fstream> #include <fstream>
#include <iostream> #include <iostream>
Matrix::Matrix(const std::string& fileNameInput) {
Load(fileNameInput);
}
Matrix::Matrix(std::size_t lignes, std::size_t colonnes) : m_Raws(lignes), m_Columns(colonnes) { Matrix::Matrix(std::size_t lignes, std::size_t colonnes) : m_Raws(lignes), m_Columns(colonnes) {
m_Data.resize(m_Raws * m_Columns); m_Data.resize(m_Raws * m_Columns);
} }
Matrix::Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<long double>&& initList) : Matrix::Matrix(std::size_t lignes, std::size_t colonnes, std::initializer_list<Element>&& initList) :
m_Raws(lignes), m_Columns(colonnes) { m_Raws(lignes), m_Columns(colonnes) {
m_Data = initList; m_Data = initList;
m_Data.resize(m_Raws * m_Columns); m_Data.resize(m_Raws * m_Columns);
@@ -25,14 +22,14 @@ Matrix::~Matrix() {}
Matrix Matrix::operator*(const Matrix& other) const { Matrix Matrix::operator*(const Matrix& other) const {
if (m_Columns != other.m_Raws) { if (m_Columns != other.m_Raws) {
std::cerr << "Mutiplication impossible car la dimensions des matrices est incompatible" << std::endl; std::cerr << "Mutiplication impossible car la dimensions des matrices est incompatible" << std::endl;
return {1, 1, {0}}; return {};
} }
Matrix result(m_Raws, other.m_Columns); Matrix result(m_Raws, other.m_Columns);
for (std::size_t i = 0; i < m_Raws; ++i) { for (std::size_t i = 0; i < m_Raws; ++i) {
for (std::size_t j = 0; j < other.m_Columns; ++j) { for (std::size_t j = 0; j < other.m_Columns; ++j) {
long double sum = 0; Element sum = 0;
for (std::size_t k = 0; k < m_Columns; k++) { for (std::size_t k = 0; k < m_Columns; k++) {
sum += at(i, k) * other.at(k, j); sum += at(i, k) * other.at(k, j);
} }
@@ -42,44 +39,6 @@ Matrix Matrix::operator*(const Matrix& other) const {
return result; return result;
} }
void Matrix::Print() const {
for (size_t i = 0; i < m_Raws; ++i) {
std::cout << "[ ";
for (size_t j = 0; j < m_Columns; ++j) {
std::cout << at(i, j) << " ";
}
std::cout << "]";
std::cout << std::endl;
}
}
void Matrix::Insert() {
for (size_t i = 0; i < m_Raws; ++i) {
for (size_t j = 0; j < m_Columns; ++j) {
std::cin >> at(i, j);
}
std::cout << std::endl;
}
}
void Matrix::Save(const std::string& fileName) {
std::ofstream out {fileName};
if (!out) {
std::cerr << "Impossible de sauvegarder la matrice !\n";
return;
}
out << *this;
}
void Matrix::Load(const std::string& filename) {
std::ifstream in {filename};
if (!in) {
std::cerr << "Impossible de charger la matrice !\n";
return;
}
in >> *this;
}
void Matrix::Transpose() { void Matrix::Transpose() {
Matrix result {m_Columns, m_Raws}; Matrix result {m_Columns, m_Raws};
for (std::size_t i = 0; i < m_Raws; i++) { for (std::size_t i = 0; i < m_Raws; i++) {
@@ -133,15 +92,15 @@ bool Matrix::operator==(const Matrix& other) const {
return true; return true;
} }
long double& Matrix::operator[](std::size_t indice) { Matrix::Element& Matrix::operator[](std::size_t indice) {
return m_Data[indice]; return m_Data[indice];
} }
long double& Matrix::at(std::size_t ligne, std::size_t colonne) { Matrix::Element& Matrix::at(std::size_t ligne, std::size_t colonne) {
return m_Data[ligne * m_Columns + colonne]; return m_Data[ligne * m_Columns + colonne];
} }
long double Matrix::at(std::size_t ligne, std::size_t colonne) const { Matrix::Element Matrix::at(std::size_t ligne, std::size_t colonne) const {
return m_Data[ligne * m_Columns + colonne]; return m_Data[ligne * m_Columns + colonne];
} }
@@ -165,25 +124,3 @@ Matrix Matrix::SubMatrix(std::size_t origine_ligne, std::size_t origine_colonne,
return result; return result;
} }
std::ostream& operator<<(std::ostream& stream, const Matrix& mat) {
stream << mat.m_Raws << " " << mat.m_Columns << "\n";
for (std::size_t i = 0; i < mat.m_Raws; i++) {
for (std::size_t j = 0; j < mat.m_Columns; j++) {
stream << mat.at(i, j) << " ";
}
stream << "\n";
}
return stream;
}
std::istream& operator>>(std::istream& stream, Matrix& mat) {
stream >> mat.m_Raws >> mat.m_Columns;
mat.m_Data.resize(mat.m_Raws * mat.m_Columns);
for (std::size_t i = 0; i < mat.m_Raws; i++) {
for (std::size_t j = 0; j < mat.m_Columns; j++) {
stream >> mat.at(i, j);
}
}
return stream;
}

24
src/Matrix.h
View File

@@ -6,26 +6,23 @@
#include <vector> #include <vector>
class Matrix { class Matrix {
public:
typedef long double Element;
private: private:
std::size_t m_Raws; std::size_t m_Raws;
std::size_t m_Columns; std::size_t m_Columns;
std::vector<long double> m_Data; std::vector<Element> m_Data;
public: public:
Matrix(const std::string& fileNameInput); Matrix() : m_Raws(0), m_Columns(0) {}
Matrix(std::size_t raws, std::size_t columns); Matrix(std::size_t raws, std::size_t columns);
Matrix(std::size_t raws, std::size_t columns, std::initializer_list<long double>&& initList); Matrix(std::size_t raws, std::size_t columns, std::initializer_list<Element>&& initList);
~Matrix(); ~Matrix();
std::size_t GetRawCount() const; std::size_t GetRawCount() const;
std::size_t GetColumnCount() const; std::size_t GetColumnCount() const;
void Insert();
void Print() const;
void Save(const std::string& fileName);
void Load(const std::string& filename);
void Transpose(); void Transpose();
static Matrix Identity(std::size_t size); static Matrix Identity(std::size_t size);
@@ -36,13 +33,10 @@ class Matrix {
bool operator==(const Matrix& other) const; bool operator==(const Matrix& other) const;
Matrix operator*(const Matrix& other) const; Matrix operator*(const Matrix& other) const;
long double& operator[](std::size_t index); Element& operator[](std::size_t index);
long double& at(std::size_t raw, std::size_t column); Element& at(std::size_t raw, std::size_t column);
long double at(std::size_t raw, std::size_t column) const; Element at(std::size_t raw, std::size_t column) const;
friend std::ostream& operator<<(std::ostream& stream, const Matrix& mat);
friend std::istream& operator>>(std::istream& stream, Matrix& mat);
}; };
template <typename T> template <typename T>

37
src/Vect.cpp
View File

@@ -5,6 +5,15 @@
#include <cassert> #include <cassert>
#include <iostream> #include <iostream>
static bool IsColumnNull(Matrix& mat, std::size_t column) {
for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
if (!IsEqualZero(mat.at(i, column))) {
return false;
}
}
return true;
}
Vect::Vect(const Matrix& mat) : m_Data(mat) { Vect::Vect(const Matrix& mat) : m_Data(mat) {
Simplify(); Simplify();
} }
@@ -12,12 +21,7 @@ Vect::Vect(const Matrix& mat) : m_Data(mat) {
void Vect::Simplify() { void Vect::Simplify() {
Matrix mat = m_Data; Matrix mat = m_Data;
for (std::size_t j = 0; j < mat.GetColumnCount(); j++) { for (std::size_t j = 0; j < mat.GetColumnCount(); j++) {
std::size_t i; if (IsColumnNull(mat, j)) {
for (i = 0; i < mat.GetRawCount(); i++) {
if (!IsEqualZero(mat.at(i, j)))
break;
}
if (i == mat.GetRawCount()) {
m_Data = mat.SubMatrix(0, 0, mat.GetRawCount(), j); m_Data = mat.SubMatrix(0, 0, mat.GetRawCount(), j);
return; return;
} }
@@ -25,6 +29,10 @@ void Vect::Simplify() {
m_Data = mat; m_Data = mat;
} }
Matrix Vect::GetVector(std::size_t index) const {
return m_Data.SubMatrix(0, index, m_Data.GetRawCount(), 1);
}
std::size_t Vect::GetCardinal() const { std::size_t Vect::GetCardinal() const {
return m_Data.GetColumnCount(); return m_Data.GetColumnCount();
} }
@@ -65,26 +73,9 @@ Matrix Vect::GetLinearSystem() const {
return vect; return vect;
} }
void Vect::Print() const {
std::cout << "Espace vectoriel de dimension " << GetCardinal() << " de base :\n\n";
for (std::size_t i = 0; i < m_Data.GetRawCount(); i++) {
for (std::size_t j = 0; j < m_Data.GetColumnCount(); j++) {
std::cout << "[ " << m_Data.at(i, j) << " ]\t";
}
std::cout << "\n";
}
}
std::size_t Vect::GetDimension() const { std::size_t Vect::GetDimension() const {
return m_Data.GetRawCount(); return m_Data.GetRawCount();
} }
VectAffine::VectAffine(const Vect& base, const Matrix& origine) : VectAffine::VectAffine(const Vect& base, const Matrix& origine) :
m_Base(base), m_Origin(origine.SubMatrix(0, 0, m_Base.GetDimension(), 1)) {} m_Base(base), m_Origin(origine.SubMatrix(0, 0, m_Base.GetDimension(), 1)) {}
void VectAffine::Print() const {
std::cout << "\tEspace Affine :\n\n";
m_Base.Print();
std::cout << "\nOrigine :\n\n";
m_Origin.Print();
}

7
src/Vect.h
View File

@@ -15,10 +15,7 @@ class Vect {
*/ */
Vect(const Matrix& mat); Vect(const Matrix& mat);
/** Matrix GetVector(std::size_t index) const;
* \brief Affiche la base de l'espace vectoriel dans la console
*/
void Print() const;
std::size_t GetDimension() const; std::size_t GetDimension() const;
std::size_t GetCardinal() const; std::size_t GetCardinal() const;
@@ -46,8 +43,6 @@ class VectAffine {
public: public:
VectAffine(const Vect& base, const Matrix& origin); VectAffine(const Vect& base, const Matrix& origin);
void Print() const;
const Vect& GetBase() const { const Vect& GetBase() const {
return m_Base; return m_Base;
} }

31
src/main.cpp
View File

@@ -1,6 +1,7 @@
#include "Gauss.h"
#include "IO.h"
#include "Matrix.h" #include "Matrix.h"
#include "NR.h" #include "NR.h"
#include "Gauss.h"
#include "Solver.h" #include "Solver.h"
#include <iostream> #include <iostream>
@@ -19,8 +20,8 @@ void test() {
mat.Print(); mat.Print();
// mat.Save("matrice4x4echelonne.mat"); */ // mat.Save("matrice4x4echelonne.mat"); */
Matrix mat2 {"matrice4x4.mat"}; Matrix mat2 = LoadMatrix("matrice4x4.mat");
mat2.Print(); Print(mat2);
Solver solver {mat2}; Solver solver {mat2};
@@ -28,35 +29,27 @@ void test() {
Vect noyau = solver.Kernel(); Vect noyau = solver.Kernel();
std::cout << "\tImage :\n"; std::cout << "\tImage :\n";
image.Print(); Print(image);
std::cout << "Système :\n"; std::cout << "Système :\n";
image.GetLinearSystem().Print(); Print(image.GetLinearSystem());
std::cout << "\tNoyau :\n"; std::cout << "\tNoyau :\n";
noyau.Print(); Print(noyau);
std::cout << "Système :\n"; std::cout << "Système :\n";
noyau.GetLinearSystem().Print(); Print(noyau.GetLinearSystem());
std::cout << "\n\n"; std::cout << "\n\n";
solver.TriangularSystem().Print(); Print(solver.TriangularSystem());
} }
void prompt() { void prompt() {
std::cout << "Quelle est le nombre de lignes de votre matrice ?" << std::endl;
std::size_t lignes;
std::cin >> lignes;
std::cout << "Quelle est le nombre de colonnes de votre matrice ?" << std::endl;
std::size_t colonnes;
std::cin >> colonnes;
std::cout << "Rentrez les coefficients de la matrice" << std::endl;
Matrix mat(lignes, colonnes);
mat.Insert(); Matrix mat = InsertMatrix();
mat.Print(); Print(mat);
Gauss::GaussJordan(mat, true, true); Gauss::GaussJordan(mat, true, true);
mat.Print(); Print(mat);
} }
int main(int argc, char** argv) { int main(int argc, char** argv) {

3
test/test_solver.cpp
View File

@@ -3,6 +3,7 @@
#include <fstream> #include <fstream>
#include <iostream> #include <iostream>
#include "IO.h"
#include "Solver.h" #include "Solver.h"
namespace fs = std::filesystem; namespace fs = std::filesystem;
@@ -16,7 +17,7 @@ int main() {
std::ifstream in {fileName}; std::ifstream in {fileName};
Matrix mat {1, 1}, imageMat {1, 1}, noyauMat {1, 1}; Matrix mat, imageMat, noyauMat;
in >> mat >> imageMat >> noyauMat; in >> mat >> imageMat >> noyauMat;
Vect image {imageMat}; Vect image {imageMat};