Lab 01, compilation errors

.idea/.name

@@ -0,0 +1 @@
+GTI320-labos

CMakeLists.txt

@@ -37,7 +37,7 @@ set( NANOGUI_USE_OPENGL ON CACHE BOOL "" FORCE)
 FetchContent_MakeAvailable(nanogui)
 
 set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
-include_directories(${CMAKE_SOURCE_DIR}/labo01/src ${COMMON_INCLUDES})
+include_directories(${CMAKE_SOURCE_DIR}/labo01 ${COMMON_INCLUDES})
 add_subdirectory(labo01)
 add_subdirectory(labo_ik)
 

labo01/CMakeLists.txt

@@ -3,18 +3,21 @@ cmake_minimum_required(VERSION 3.15)
 project(labo01)
 
 # Setup language requirements
-set(CMAKE_CXX_STANDARD 11)
+set(CMAKE_CXX_STANDARD 17)
 set(CMAKE_CXX_STANDARD_REQUIRED ON)
 
 # Add .cpp and .h files
-file(GLOB_RECURSE TESTS_SOURCES RELATIVE "${CMAKE_CURRENT_SOURCE_DIR}" CONFIGURE_DEPENDS "tests/*.cpp")
+file(GLOB_RECURSE MAIN_SOURCES RELATIVE "${CMAKE_CURRENT_SOURCE_DIR}" CONFIGURE_DEPENDS "*.h")
-file(GLOB_RECURSE MAIN_SOURCES RELATIVE "${CMAKE_CURRENT_SOURCE_DIR}" CONFIGURE_DEPENDS "src/*.h")
 add_executable(labo01 main.cpp ${MAIN_SOURCES} ${TESTS_SOURCES})
 
+# Add .cpp and .h files
+#set(HEADERS DenseStorage.h MatrixBase.h Matrix.h Math3D.h Vector.h Operators.h)
+#set(SOURCE main.cpp)
+#add_executable(labo01 ${SOURCE} ${HEADERS})
+
 # Add linking information for Google Test
 target_link_libraries(labo01 gtest)
 
-
 # Set labo01 as the startup project for Visual Studio
 if( MSVC )
 	set_property(TARGET labo01 PROPERTY VS_DEBUGGER_WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}/labo01)

labo01/DenseStorage.h

@@ -5,18 +5,19 @@
  *
  * @brief Stockage dense pour des données à taille fixe ou dynamique.
  *
- * Nom:
+ * Nom: William Nolin
- * Code permanent :
+ * Code permanent : NOLW76060101
- * Email :
+ * Email : william.nolin.1@ens.etsmtl.ca
  *
  */
 
 #include <cstring>
 #include <cassert>
 
-namespace gti320
+namespace gti320 {
-{
+    enum SizeType {
-    enum SizeType { Dynamic = -1 };
+        Dynamic = -1
+    };
 
     /**
      * Stockage à taille fixe.
@@ -27,43 +28,37 @@ namespace gti320
      * Un tampon (tableau) de taille `_Size_` est alloué sur la pile d'exécution.
      */
     template<typename _Scalar, int _Size>
-    class DenseStorage
+    class DenseStorage {
-    {
     private:
 
-        // TODO déclarer une variable m_data et allouer la mémoire pour y stocker _Size éléments
+        _Scalar m_data[_Size];
-        _Scalar* m_data;  // <-- Ceci n'est pas bon, à modifier
 
     public:
 
         /**
          * Constructeur par défaut
          */
-        DenseStorage() { }
+        DenseStorage() {}
 
         /**
          * Constructeur de copie
          */
-        DenseStorage(const DenseStorage& other)
+        DenseStorage(const DenseStorage &other) {
-        {
             memcpy(m_data, other.m_data, sizeof(m_data));
         }
 
         /**
-         * Constructeur avec taille spécifiée.
+         * Constructeur avec taille spécifiée
-         * Doit être la même que la taille spécifiée dans le patron
          *
+         * (doit être la même que la taille spécifiée dans le patron)
          */
-        explicit DenseStorage(int _size) 
+        explicit DenseStorage(int _size) {
-        {
-            assert(_size > 0 && _size == _Size);
         }
 
         /**
-         * Constructeur avec taille (_size) et données initiales (_data).
+         * Constructor avec taille (_size) et données initiales (_data).
          */
-        explicit DenseStorage(const _Scalar* _data, int _size)
+        explicit DenseStorage(const _Scalar *_data, int _size) {
-        {
             assert(_size >= 0 && _size == _Size);
             memcpy(m_data, _data, sizeof(_Scalar) * _size);
         }
@@ -71,10 +66,8 @@ namespace gti320
         /**
          * Opérateur de copie
          */
-        DenseStorage& operator=(const DenseStorage& other)
+        DenseStorage &operator=(const DenseStorage &other) {
-        {
+            if (this != &other) {
-            if (this != &other)
-            {
                 assert(other.size() == _Size);
                 memcpy(m_data, other.m_data, sizeof(m_data));
             }
@@ -86,38 +79,33 @@ namespace gti320
         /**
          * Redimensionne le stockage pour qu'il contienne `size` élément.
          */
-        void resize(int size)
+        void resize(int size) {
-        {
             // Ne rien faire. Invalide pour les matrices à taille fixe.
         }
 
         /**
          * Mets tous les éléments à zéro.
          */
-        void setZero()
+        void setZero() {
-        {
             memset(m_data, 0, sizeof(_Scalar) * _Size);
         }
 
         /**
          * Accès au tampon de données (en lecteur seulement)
          */
-        const _Scalar* data() const
+        const _Scalar *data() const {
-        {
+            return &m_data[0];
-            return m_data;
         }
 
         /**
          * Accès au tampon de données (pour lecture et écriture)
          */
-        _Scalar* data()
+        _Scalar *data() {
-        {
+            return &m_data[0];
-            return m_data;
         }
     };
 
 
-
     /**
      * Stockage à taille dynamique.
      *
@@ -126,10 +114,9 @@ namespace gti320
      * l'opérateur `new []` et la mémoire doit être libérée avec `delete[]`
      */
     template<typename _Scalar>
-    class DenseStorage<_Scalar, Dynamic>
+    class DenseStorage<_Scalar, Dynamic> {
-    {
     private:
-        _Scalar* m_data;
+        _Scalar *m_data;
         int m_size;
 
     public:
@@ -142,42 +129,36 @@ namespace gti320
         /**
          * Constructeur avec taille spécifiée
          */
-        explicit DenseStorage(int _size) : m_data(nullptr), m_size(_size)
+        explicit DenseStorage(int _size) : m_data(new _Scalar[_size]), m_size(_size) {
-        {
+            setZero();
-            // TODO allouer un tampon pour stocker _size éléments de type _Scalar.
-
-            // TODO initialiser ce tampon à zéro.
         }
 
         /**
          * Constructeur de copie
          */
-        DenseStorage(const DenseStorage& other)
+        DenseStorage(const DenseStorage &other)
-            : m_data(nullptr)
+                : m_data(new _Scalar[other.m_size]), m_size(other.m_size) {
-            , m_size(other.m_size)
+            memcpy(m_data, other.m_data, m_size * sizeof(_Scalar));
-        {
-            // TODO allouer un tampon pour stocker _size éléments de type _Scalar.
-
-            // TODO copier other.m_data dans m_data.
-
         }
 
         /**
          * Opérateur de copie
          */
-        DenseStorage& operator=(const DenseStorage& other)
+        DenseStorage &operator=(const DenseStorage &other) {
-        {
+            if (m_size != other.size()) {
-            // TODO implémenter !
+                resize(other.size());
+            }
+
+            m_size = other.m_size;
+            memcpy(m_data, other.m_data, m_size * sizeof(_Scalar));
             return *this;
         }
 
         /**
          * Destructeur
          */
-        ~DenseStorage()
+        ~DenseStorage() {
-        {
+            delete[] m_data;
-            // TODO libérer la mémoire allouée
-
         }
 
         /**
@@ -188,33 +169,36 @@ namespace gti320
         /**
          * Redimensionne le tampon alloué pour le stockage.
          * La mémoire qui n'est plus utilisée doit être libérée.
-         * 
+         *
          * Note :​ Toutes opérations de redimensionnement entraînent une réallocation de mémoire.
          * Il n’est pas pertinent de copier les données car le résultat serait de toute façon incohérent.
          */
-        void resize(int _size)
+        void resize(int _size) {
-        {
+            auto *data = new _Scalar[_size];
-            // TODO redimensionner la mémoire allouée
 
+            delete[] m_data;
+            m_data = data;
+            m_size = _size;
+
+            setZero();
         }
 
         /**
          * Met tous les éléments à zéro.
          */
-        void setZero()
+        void setZero() {
-        {
+            memset(m_data, 0, m_size * sizeof(_Scalar));
-            // TODO implémenter !
         }
 
         /**
          * Accès au tampon de données (en lecteur seulement)
          */
-        const _Scalar* data() const { return m_data; }
+        const _Scalar *data() const { return m_data; }
 
         /**
          * Accès au tampon de données (pour lecture et écriture)
          */
-        _Scalar* data() { return m_data; }
+        _Scalar *data() { return m_data; }
     };
 
 }

labo01/Math3D.h

@@ -0,0 +1,139 @@
+#pragma once
+
+/**
+ * @file Math3D.h
+ *
+ * @brief Fonctions pour l'intinialisation et la manipulation de matrices de
+ * rotation, des matrices de transformations en coordonnées homogènes et les
+ * vecteurs 3D.
+ *
+ * Nom: William Nolin
+ * Code permanent : NOLW76060101
+ * Email : william.nolin.1@ens.etsmtl.ca
+ *
+ */
+
+#include "Matrix.h"
+#include "Vector.h"
+#include "Operators.h"
+
+#ifndef _USE_MATH_DEFINES
+#define _USE_MATH_DEFINES
+#endif
+
+#include <math.h>
+
+
+namespace gti320 {
+
+    // Deux types de vecteurs 3D considérés ici
+    typedef Vector<double, 3> Vector3d;
+    typedef Vector<float, 3> Vector3f;
+
+    // Dans le cadre de ce projet, nous considérons seulement deux
+    // cas :
+    //
+    //  - les rotations
+    //  - les translations
+    //
+    // Deux types de matrices en coordonnées homogèes :
+    typedef Matrix<double, 4, 4, ColumnStorage> Matrix4d;
+    typedef Matrix<float, 4, 4, ColumnStorage> Matrix4f;
+    //
+    // Deux types de matrices pour les rotations
+    typedef Matrix<double, 3, 3, ColumnStorage> Matrix3d;
+    typedef Matrix<float, 3, 3, ColumnStorage> Matrix3f;
+
+    /**
+     * Initialise et retourne la matrice identité
+     */
+    template<>
+    inline void Matrix4d::setIdentity() {
+        this->setZero();
+
+        for (int i = 0; i < 4; i++) {
+            (*this)(i, i) = 1;
+        }
+    }
+
+    /**
+     * Calcul de la matrice inverse, SPÉCIALISÉ pour le cas d'une matrice de
+     * transformation en coordonnées homogènes.
+     */
+    template<>
+    inline Matrix4d Matrix4d::inverse() const {
+        auto transposed_rotation = this->block(0, 0, 3, 3).transpose<double, 3, 3, ColumnStorage>();
+        auto translation = Vector<double, 3>();
+        for (int i = 0; i < 3; i++) {
+            translation(i) = (*this)(i, 3);
+        }
+
+        auto result = Matrix4d();
+        result(3, 3) = 1;
+
+        // Applique la matrice de rotation
+        result.block(0, 0, 3, 3) = transposed_rotation;
+
+        // Applique le vecteur de translation
+        auto inverted_translation = (-1.0 * transposed_rotation) * translation;
+        auto trans_block = result.block(0, 3, 3, 1);
+        trans_block(0, 0) = inverted_translation(0);
+        trans_block(1, 0) = inverted_translation(1);
+        trans_block(2, 0) = inverted_translation(2);
+
+        return result;
+    }
+
+    /**
+     * Calcul de la matrice inverse, SPÉCIALISÉ pour le cas d'une matrice de rotation.
+     *
+     * (vous pouvez supposer qu'il s'agit d'une matrice de rotation)
+     */
+    template<>
+    inline Matrix3d Matrix3d::inverse() const {
+        return this->transpose<double, 3, 3, ColumnStorage>();
+    }
+
+    /**
+     * Multiplication d'une matrice 4x4 avec un vecteur 3D où la matrice
+     * représente une transformation en coordonnées homogène.
+     */
+    template<typename _Scalar>
+    Vector<_Scalar, 3> operator*(const Matrix<_Scalar, 4, 4, ColumnStorage> &A, const Vector<_Scalar, 3> &v) {
+        auto homogeneous = Vector<_Scalar, 4>(v);
+        homogeneous(3) = 1;
+        Vector<_Scalar, 4> transformed = A * homogeneous;
+        return Vector<_Scalar, 3>(transformed);
+    }
+
+
+    /**
+     * Initialise et retourne la matrice de rotation définie par les angles
+     * d'Euler XYZ exprimés en radians.
+     *
+     * La matrice doit correspondre au produit : Rz*Ry*Rx.
+     */
+    template<typename _Scalar>
+    static Matrix<_Scalar, 3, 3> makeRotation(_Scalar x, _Scalar y, _Scalar z) {
+        double sin_theta = std::sin(x);
+        double cos_theta = std::cos(x);
+        double sin_phi = std::sin(y);
+        double cos_phi = std::cos(y);
+        double sin_psi = std::sin(z);
+        double cos_psi = std::cos(z);
+
+        auto m = Matrix<_Scalar, 3, 3>();
+        m(0, 0) = cos_phi * cos_psi;
+        m(1, 0) = cos_phi * sin_psi;
+        m(2, 0) = -sin_phi;
+        m(0, 1) = sin_theta * sin_phi * cos_psi - cos_theta * sin_psi;
+        m(1, 1) = sin_theta * sin_phi * sin_psi + cos_theta * cos_psi;
+        m(2, 1) = sin_theta * cos_phi;
+        m(0, 2) = cos_theta * sin_phi * cos_psi + sin_theta * sin_psi;
+        m(1, 2) = cos_theta * sin_phi * sin_psi - sin_theta * cos_psi;
+        m(2, 2) = cos_theta * cos_phi;
+
+        return m;
+    }
+
+}

labo01/Matrix.h

@@ -0,0 +1,401 @@
+#pragma once
+
+/**
+ * @file Matrix.h
+ *
+ * @brief Implémentation de matrices simples.
+ *
+ * Nom: William Nolin
+ * Code permanent : NOLW76060101
+ * Email : william.nolin.1@ens.etsmtl.ca
+ *
+ */
+
+#include <complex>
+#include <iostream>
+#include "MatrixBase.h"
+
+namespace gti320 {
+    enum StorageType {
+        ColumnStorage = 0,
+        RowStorage = 1
+    };
+
+    // Déclaration avancée
+    template<typename _Scalar, int _RowsAtCompile, int _ColsAtCompile, int _StorageType>
+    class SubMatrix;
+
+    /**
+     * Classe Matrix spécialisé pour le cas générique. (defaut par colonne)
+     *
+     * (le cas d'un stockage par ligne fait l'objet d'une spécialisation de patron, voir plus bas)
+     */
+    template<typename _Scalar = double, int _RowsAtCompile = Dynamic, int _ColsAtCompile = Dynamic, int _StorageType = ColumnStorage>
+    class Matrix : public MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile> {
+    public:
+
+        /**
+         * Constructeur par défaut
+         */
+        Matrix() : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>() {}
+
+        /**
+         * Constructeur de copie
+         */
+        Matrix(const Matrix &other) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(other) {}
+
+        /**
+         * Constructeur avec spécification du nombre de ligne et de colonnes
+         */
+        explicit Matrix(int _rows, int _cols) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(_rows, _cols) {}
+
+        /**
+         * Destructeur
+         */
+        ~Matrix() {}
+
+        /**
+         * Opérateur de copie à partir d'une sous-matrice.
+         *
+         * Exemple : Matrix B = A.block(i,j,m,n);
+         */
+        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
+        Matrix &operator=(const SubMatrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage> &submatrix) {
+            if (this->rows() != submatrix->rows() || this->cols() != submatrix->cols()) {
+                this->resize(submatrix->rows(), submatrix->cols());
+            }
+
+            for (int col = 0; col < this->cols(); col++) {
+                for (int row = 0; row < this->rows(); row++) {
+                    this(row, col) = submatrix(row, col);
+                }
+            }
+            return *this;
+        }
+
+        /**
+         * Accesseur à une entrée de la matrice (lecture seule)
+         */
+        _Scalar operator()(int i, int j) const {
+            int index = i + j * this->rows();
+            return this->m_storage.data()[index];
+        }
+
+        /**
+         * Accesseur à une entrée de la matrice (lecture ou écriture)
+         */
+        _Scalar &operator()(int i, int j) {
+            int index = i + j * this->rows();
+            return this->m_storage.data()[index];
+        }
+
+        /**
+         * Crée une sous-matrice pour un block de taille (rows, cols) à partir de l'index (i,j).
+         */
+        SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType> block(int i, int j, int rows, int cols) const {
+            return SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType>(*this, i, j, rows, cols);
+        }
+
+        /**
+         * Calcule l'inverse de la matrice
+         */
+        Matrix inverse() const {
+            // Do nothing.
+            return *this;
+        }
+
+        /**
+         * Retourne la transposée de la matrice
+         */
+        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
+        Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage> transpose() const {
+            auto transposed = Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage>(this->cols(), this->rows());
+            for (int col = 0; col < this->cols(); col++) {
+                for (int row = 0; row < this->rows(); row++) {
+                    transposed(col, row) = (*this)(row, col);
+                }
+            }
+            return transposed;
+        }
+
+        /**
+         * Affecte l'identité à la matrice
+         */
+        inline void setIdentity() {
+            this->m_storage.setZero();
+            int smallest = std::min(this->rows(), this->cols());
+
+            for (int i = 0; i < smallest; i++) {
+                (*this)(i, i) = 1;
+            }
+        }
+
+    };
+
+    /**
+     * Classe Matrix spécialisée pour un stockage par lignes
+     */
+    template<typename _Scalar, int _RowsAtCompile, int _ColsAtCompile>
+    class Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, RowStorage>
+            : public MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile> {
+
+    public:
+        /**
+         * Constructeur par défaut
+         */
+        Matrix() : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>() {}
+
+        /**
+         * Constructeur de copie
+         */
+        Matrix(const Matrix &other) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(other) {}
+
+        /**
+         * Constructeur avec spécification du nombre de ligne et de colonnes
+         */
+        explicit Matrix(int rows, int cols) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(rows, cols) {}
+
+        /**
+         * Destructeur
+         */
+        ~Matrix() {}
+
+        /**
+         * Opérateur de copie à partir d'une sous-matrice.
+         *
+         * Exemple : Matrix B = A.block(i,j,m,n);
+         */
+        template<typename _OtherScalar, int OtherRows, int _OtherCols, int _OtherStorage>
+        Matrix &operator=(const SubMatrix<_OtherScalar, OtherRows, _OtherCols, _OtherStorage> &submatrix) {
+            if (this->rows() != submatrix->rows() || this->cols() != submatrix->cols()) {
+                this->resize(submatrix->rows(), submatrix->cols());
+            }
+
+            for (int row = 0; row < this->rows(); row++) {
+                for (int col = 0; col < this->cols(); col++) {
+                    this(row, col) = submatrix(row, col);
+                }
+            }
+            return *this;
+        }
+
+        /**
+         * Accesseur à une entrée de la matrice (lecture seule)
+         */
+        _Scalar operator()(int i, int j) const {
+            int index = i * this->cols() + j;
+            return this->m_storage.data()[index];
+        }
+
+        /**
+         * Accesseur à une entrée de la matrice (lecture ou écriture)
+         */
+        _Scalar &operator()(int i, int j) {
+            int index = i * this->cols() + j;
+            return this->m_storage.data()[index];
+        }
+
+        /**
+         * Crée une sous-matrice pour un block de taille (rows, cols) à partir de l'index (i,j).
+         */
+        SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, RowStorage> block(int i, int j, int rows, int cols) const {
+            return SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, RowStorage>(*this, i, j, rows, cols);
+        }
+
+        /**
+         * Calcule l'inverse de la matrice
+         */
+        Matrix inverse() const {
+            // Do nothing.
+            return *this;
+        }
+
+        /**
+         * Retourne la transposée de la matrice
+         */
+        Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, ColumnStorage> transpose() const {
+            auto t = Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, ColumnStorage>(this->cols(), this->rows());
+
+            for (int row = 0; row < this->rows(); row++) {
+                for (int col = 0; col < this->cols(); col++) {
+                    t(col, row) = (*this)(row, col);
+                }
+            }
+
+            return t;
+        }
+
+        /**
+         * Affecte l'identité à la matrice
+         */
+        inline void setIdentity() {
+            this->m_storage.setZero();
+
+            int small_size = std::min(this->rows(), this->cols());
+            for (int i = 0; i < small_size; i++) {
+                (*this)(i, i) = 1;
+            }
+        }
+
+    };
+
+    /**
+     * Classe pour accéder à une sous-matrice.
+     *
+     * Un sous-matrice ne copie pas les données. Au lieu de cela, elle conserve une
+     * référence à la matrice originale.
+     */
+    template<typename _Scalar, int _RowsAtCompile, int _ColsAtCompile, int _StorageType>
+    class SubMatrix {
+    private:
+        // Référence à la matrice originale
+        Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType> &m_matrix;
+
+        // Constructeur par défaut (privé)
+        SubMatrix() {}
+
+        // (i,j) est le coin supérieur gauche de la sous-matrice
+        int m_i;        // Décalage en ligne
+        int m_j;        // Décalage en colonne
+
+        // la sous-matrice est de dimension : m_rows x m_cols
+        int m_rows;     // Hauteur de la sous-matrice (nombre de lignes)
+        int m_cols;     // Largeur de la sous-matrice (nombre de colonnes)
+
+    public:
+
+        /**
+         * Constructeur à partir d'une référence en lecture seule à une matrice.
+         */
+        SubMatrix(const Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType> &_matrix, int _i, int _j,
+                  int _rows, int _cols) :
+                m_matrix(const_cast<Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType> &>(_matrix)),
+                m_i(_i), m_j(_j), m_rows(_rows), m_cols(_cols) {
+        }
+
+        /**
+         * Constructeur à partir d'une référence en lecture et écriture à une matrice.
+         */
+        explicit SubMatrix(Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType> &_matrix, int _i, int _j,
+                           int _rows, int _cols) :
+                m_matrix(_matrix),
+                m_i(_i), m_j(_j), m_rows(_rows), m_cols(_cols) {
+
+        }
+
+        /**
+         * Constructeur de copie
+         */
+        SubMatrix(const SubMatrix &other) :
+                m_matrix(other.m_matrix),
+                m_i(other.m_i), m_j(other.m_j), m_rows(other.m_rows), m_cols(other.m_cols) {
+        }
+
+        /**
+         * Destructeur
+         */
+        ~SubMatrix() {}
+
+        /**
+         * Opérateur de copie (à partir d'une matrice)
+         *
+         * Copies toutes les entrées de la matrice dans la sous-matrice.
+         *
+         * Note : la taille de la matrice doit correspondre à la taille de la
+         * sous-matrice.
+         */
+        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
+        SubMatrix &operator=(const Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage> &matrix) {
+            assert(this->rows() == matrix.rows());
+            assert(this->cols() == matrix.cols());
+
+            for (int col = 0; col < this->cols(); col++) {
+                for (int row = 0; row < this->rows(); row++) {
+                    (*this)(row, col) = matrix(row, col);
+                }
+            }
+
+            return *this;
+        }
+
+        /**
+         * Opérateur de d'addition d'une autre matrice
+         *
+         * Ajoute toutes les entrées de la matrice dans la sous-matrice.
+         *
+         * Note : la taille de la matrice doit correspondre à la taille de la
+         * sous-matrice.
+         */
+        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
+        SubMatrix &operator+=(const Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage> &matrix) {
+            assert(this->rows() == matrix.rows());
+            assert(this->cols() == matrix.cols());
+
+            for (int col = 0; col < this->cols(); col++) {
+                for (int row = 0; row < this->rows(); row++) {
+                    (*this)(row, col) = (*this)(row, col) + matrix(row, col);
+                }
+            }
+
+            return *this;
+        }
+
+        /**
+         * Accesseur aux entrées de la sous-matrice (lecture seule)
+         *
+         * Note : il faut s'assurer que les indices respectent la taille de la
+         * sous-matrice
+         */
+        _Scalar operator()(int i, int j) const {
+            assert(i >= 0);
+            assert(i <= this->rows());
+            assert(j >= 0);
+            assert(j <= this->cols());
+
+            int full_i = this->m_i + i;
+            int full_j = this->m_j + j;
+
+            return this->m_matrix(full_i, full_j);
+        }
+
+        /**
+         * Accesseur aux entrées de la sous-matrice (lecture et écriture)
+         *
+         * Note : il faut s'assurer que les indices respectent la taille de la
+         * sous-matrice
+         */
+        _Scalar &operator()(int i, int j) {
+            assert(i >= 0);
+            assert(i <= this->rows());
+            assert(j >= 0);
+            assert(j <= this->cols());
+
+            int full_i = this->m_i + i;
+            int full_j = this->m_j + j;
+
+            return this->m_matrix(full_i, full_j);
+        }
+
+        /**
+         * Retourne la transposée de la sous-matrice sous la forme d'une matrice.
+         */
+        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
+        Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage> transpose() const {
+            auto t = Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage>(this->rows(), this->cols());
+
+            for (int col = 0; col < this->cols(); col++) {
+                for (int row = 0; row < this->rows(); row++) {
+                    t(col, row) = (*this)(row, col);
+                }
+            }
+
+            return t;
+        }
+
+        inline int rows() const { return m_rows; }
+
+        inline int cols() const { return m_cols; }
+
+    };
+
+}

labo01/MatrixBase.h

@@ -5,9 +5,9 @@
  *
  * @brief Classe contenant les éléments de base des matrices et des vecteurs.
  *
- * Nom:
+ * Nom: William Nolin
- * Code permanent :
+ * Code permanent : NOLW76060101
- * Email :
+ * Email : william.nolin.1@ens.etsmtl.ca
  *
  */
 
@@ -23,7 +23,7 @@ namespace gti320
 	class MatrixBase
 	{
 	protected:
-		DenseStorage<_Scalar, _Rows* _Cols> m_storage;
+		DenseStorage<_Scalar, _Rows * _Cols> m_storage;
 
 	public:
 
@@ -37,14 +37,18 @@ namespace gti320
 		/**
 		 * Constructeur de copie
 		 */
-		MatrixBase(const MatrixBase& other) : m_storage(other.m_storage) { }
+		MatrixBase(const MatrixBase& other) : m_storage(other.m_storage) {
+        }
 
-		explicit MatrixBase(int _rows, int _cols) : m_storage() { }
+		explicit MatrixBase(int _rows, int _cols) : m_storage() {
+            setZero();
+        }
 
 		/**
 		 * Destructeur
 		 */
-		~MatrixBase() { }
+		~MatrixBase() {
+        }
 
 
 		/**
@@ -118,7 +122,9 @@ namespace gti320
 		 */
 		MatrixBase() : m_storage(), m_rows(0) { }
 
-		explicit MatrixBase(int _rows, int _cols) : m_storage(_rows* _Cols), m_rows(_rows) { }
+		explicit MatrixBase(int _rows, int _cols) : m_storage(_rows* _Cols), m_rows(_rows) {
+            setZero();
+        }
 
 		/**
 		 * Constructeur de copie
@@ -204,7 +210,9 @@ namespace gti320
 		 */
 		MatrixBase() : m_storage() { }
 
-		explicit MatrixBase(int _rows, int _cols) : m_storage(_rows* _cols), m_cols(_cols) { }
+		explicit MatrixBase(int _rows, int _cols) : m_storage(_rows* _cols), m_cols(_cols) {
+            setZero();
+        }
 
 		/**
 		 * Constructeur de copie
@@ -290,7 +298,9 @@ namespace gti320
 		 */
 		MatrixBase() : m_storage(), m_rows(0), m_cols(0) { }
 
-		explicit MatrixBase(int _rows, int _cols) : m_storage(_rows* _cols), m_rows(_rows), m_cols(_cols) { }
+		explicit MatrixBase(int _rows, int _cols) : m_storage(_rows* _cols), m_rows(_rows), m_cols(_cols) {
+            setZero();
+        }
 
 		/**
 		 * Constructeur de copie

labo01/Operators.h

@@ -0,0 +1,364 @@
+#pragma once
+
+/**
+ * @file Operators.h
+ *
+ * @brief Opérateurs arithmétiques pour les matrices et les vecteurs.
+ *
+ * Nom: William Nolin
+ * Code permanent : NOLW76060101
+ * Email : william.nolin.1@ens.etsmtl.ca
+ *
+ */
+
+#include "Matrix.h"
+#include "Vector.h"
+
+/**
+ * Implémentation de divers opérateurs arithmétiques pour les matrices et les vecteurs.
+ */
+namespace gti320 {
+
+    /**
+     * Multiplication : Matrice * Matrice (générique)
+     */
+    template<typename _Scalar, int RowsA, int ColsA, int StorageA, int RowsB, int ColsB, int StorageB>
+    Matrix<_Scalar, RowsA, ColsB>
+    operator*(const Matrix<_Scalar, RowsA, ColsA, StorageA> &A, const Matrix<_Scalar, RowsB, ColsB, StorageB> &B) {
+        assert(A.cols() == B.rows());
+
+        auto result = Matrix<_Scalar, RowsA, ColsB>(A.rows(), B.cols());
+
+        for (int col = 0; col < B.cols(); col++) {
+            for (int row = 0; row < A.rows(); row++) {
+                for (int k = 0; k < A.cols(); k++) {
+                    result(row, col) += A(row, k) * B(k, col);
+                }
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Multiplication : Matrice (colonne) * Matrice (ligne)
+     *
+     * Spécialisation de l'opérateur de multiplication pour le cas où les matrices
+     * ont un stockage à taille dynamique et où la matrice de gauche utilise un
+     * stockage par colonnes et celle de droite un stockage par lignes.
+     */
+    template<typename _Scalar>
+    Matrix<_Scalar, Dynamic, Dynamic> operator*(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> &A,
+                                                const Matrix<_Scalar, Dynamic, Dynamic, RowStorage> &B) {
+        assert(A.cols() == B.rows());
+
+        auto result = Matrix<_Scalar, Dynamic, Dynamic>(A.rows(), B.cols());
+
+        for (int col = 0; col < A.cols(); col++) {
+            for (int row = 0; row < B.rows(); row++) {
+                for (int k = 0; k < B.cols(); k++) {
+                    result(row, k) += A(row, col) * B(col, k);
+                }
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Multiplication : Matrice (ligne) * Matrice (colonne)
+     *
+     * Spécialisation de l'opérateur de multiplication pour le cas où les matrices
+     * ont un stockage à taille dynamique et où la matrice de gauche utilise un
+     * stockage par lignes et celle de droite un stockage par colonnes.
+     */
+    template<typename _Scalar>
+    Matrix<_Scalar, Dynamic, Dynamic> operator*(const Matrix<_Scalar, Dynamic, Dynamic, RowStorage> &A,
+                                                const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> &B) {
+        assert(A.cols() == B.rows());
+
+        auto result = Matrix<_Scalar, Dynamic, Dynamic>(A.rows(), B.cols());
+
+        for (int col = 0; col < B.cols(); col++) {
+            for (int row = 0; row < A.rows(); row++) {
+                for (int k = 0; k < A.cols(); k++) {
+                    result(row, col) += A(row, k) * B(k, col);
+                }
+            }
+        }
+
+        return result;
+    }
+
+
+    /**
+     * Addition : Matrice + Matrice (générique)
+     */
+    template<typename _Scalar, int Rows, int Cols, int StorageA, int StorageB>
+    Matrix<_Scalar, Rows, Cols>
+    operator+(const Matrix<_Scalar, Rows, Cols, StorageA> &A, const Matrix<_Scalar, Rows, Cols, StorageB> &B) {
+        assert(A.rows() == B.rows());
+        assert(A.cols() == B.cols());
+
+        auto result = Matrix<_Scalar, Rows, Cols, StorageA>(A.rows(), A.cols());
+
+        for (int row = 0; row < A.rows(); row++) {
+            for (int col = 0; col < A.cols(); col++) {
+                result(row, col) = A(row, col) + B(row, col);
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Addition : Matrice (colonne) + Matrice (colonne)
+     *
+     * Spécialisation de l'opérateur d'addition pour le cas où les deux matrices
+     * sont stockées par colonnes.
+     */
+    template<typename _Scalar>
+    Matrix<_Scalar, Dynamic, Dynamic> operator+(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> &A,
+                                                const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> &B) {
+        assert(A.rows() == B.rows());
+        assert(A.cols() == B.cols());
+
+        auto result = Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>(A.rows(), A.cols());
+
+        for (int col = 0; col < A.cols(); col++) {
+            for (int row = 0; row < A.rows(); row++) {
+                result(row, col) = A(row, col) + B(row, col);
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Addition : Matrice (ligne) + Matrice (ligne)
+     *
+     * Spécialisation de l'opérateur d'addition pour le cas où les deux matrices
+     * sont stockées par lignes.
+     */
+    template<typename _Scalar>
+    Matrix<_Scalar, Dynamic, Dynamic, RowStorage> operator+(const Matrix<_Scalar, Dynamic, Dynamic, RowStorage> &A,
+                                                            const Matrix<_Scalar, Dynamic, Dynamic, RowStorage> &B) {
+        assert(A.rows() == B.rows());
+        assert(A.cols() == B.cols());
+
+        auto result = Matrix<_Scalar, Dynamic, Dynamic, RowStorage>(A.rows(), A.cols());
+
+        for (int row = 0; row < A.rows(); row++) {
+            for (int col = 0; col < A.cols(); col++) {
+                result(row, col) = A(row, col) + B(row, col);
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Multiplication  : Scalaire * Matrice (colonne)
+     *
+     * Spécialisation de l'opérateur de multiplication par un scalaire pour le
+     * cas d'une matrice stockée par colonnes.
+     */
+    template<typename _Scalar, int _Rows, int _Cols>
+    Matrix<_Scalar, _Rows, _Cols, ColumnStorage>
+    operator*(const _Scalar &a, const Matrix<_Scalar, _Rows, _Cols, ColumnStorage> &A) {
+        auto result = Matrix<_Scalar, _Rows, _Cols, ColumnStorage>(A.rows(), A.cols());
+
+        for (int col = 0; col < A.cols(); col++) {
+            for (int row = 0; row < A.rows(); row++) {
+                result(col, row) = a * A(col, row);
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Multiplication  : Scalaire * Matrice (ligne)
+     *
+     * Spécialisation de l'opérateur de multiplication par un scalaire pour le
+     * cas d'une matrice stockée par lignes.
+     */
+    template<typename _Scalar, int _Rows, int _Cols>
+    Matrix<_Scalar, _Rows, _Cols, RowStorage>
+    operator*(const _Scalar &a, const Matrix<_Scalar, _Rows, _Cols, RowStorage> &A) {
+        auto result = Matrix<_Scalar, _Rows, _Cols, RowStorage>(A.rows(), A.cols());
+
+        for (int row = 0; row < A.rows(); row++) {
+            for (int col = 0; col < A.cols(); col++) {
+                result(col, row) = a * A(col, row);
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Multiplication : Matrice (ligne) * Vecteur
+     *
+     * Spécialisation de l'opérateur de multiplication matrice*vecteur pour le
+     * cas où la matrice est représentée par lignes.
+     */
+    template<typename _Scalar, int _Rows, int _Cols>
+    Vector<_Scalar, _Rows>
+    operator*(const Matrix<_Scalar, _Rows, _Cols, RowStorage> &A, const Vector<_Scalar, _Cols> &v) {
+        assert(A.cols() == v.size());
+
+        auto result = Vector<_Scalar, _Rows>(A.rows());
+
+        for (int row = 0; row < A.rows(); row++) {
+            _Scalar dotP = 0;
+
+            for (int col = 0; col < A.cols(); col++) {
+                dotP += A(col, row) * v(col);
+            }
+
+            result(row) = dotP;
+        }
+
+        return result;
+    }
+
+    /**
+     * Multiplication : Matrice (colonne) * Vecteur
+     *
+     * Spécialisation de l'opérateur de multiplication matrice*vecteur pour le
+     * cas où la matrice est représentée par colonnes.
+     */
+    template<typename _Scalar, int _Rows, int _Cols>
+    Vector<_Scalar, _Rows>
+    operator*(const Matrix<_Scalar, _Rows, _Cols, ColumnStorage> &A, const Vector<_Scalar, _Cols> &v) {
+        assert(A.cols() == v.size());
+
+        auto result = Vector<_Scalar, _Rows>(A.rows());
+
+        for (int col = 0; col < A.cols(); col++) {
+            _Scalar v_col = v(col);
+
+            for (int row = 0; row < A.rows(); row++) {
+                result(row) += A(row, col) * v_col;
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Multiplication : Scalaire * Vecteur
+     */
+    template<typename _Scalar, int _Rows>
+    Vector<_Scalar, _Rows> operator*(const _Scalar &a, const Vector<_Scalar, _Rows> &v) {
+        auto result = Vector<_Scalar, _Rows>(v.rows());
+
+        for (int row = 0; row < v.rows(); row++) {
+            result(row) = a * v(row);
+        }
+
+        return result;
+    }
+
+
+    /**
+     * Addition : Vecteur + Vecteur
+     */
+    template<typename _Scalar, int _RowsA, int _RowsB>
+    Vector<_Scalar, _RowsA> operator+(const Vector<_Scalar, _RowsA> &a, const Vector<_Scalar, _RowsB> &b) {
+        assert(a.rows() == b.rows());
+
+        auto result = Vector<_Scalar, _RowsA>(a.rows());
+
+        for (int row = 0; row < a.rows(); row++) {
+            result(row) = a(row) + b(row);
+        }
+
+        return result;
+    }
+
+    /**
+     * Soustraction : Vecteur - Vecteur
+     */
+    template<typename _Scalar, int _RowsA, int _RowsB>
+    Vector<_Scalar, _RowsA> operator-(const Vector<_Scalar, _RowsA> &a, const Vector<_Scalar, _RowsB> &b) {
+        assert(a.rows() == b.rows());
+
+        auto result = Vector<_Scalar, _RowsA>(a.rows());
+
+        for (int row = 0; row < a.rows(); row++) {
+            result(row) = a(row) - b(row);
+        }
+
+        return result;
+    }
+
+    template<typename _Scalar, int _Rows, int _Cols>
+    void print_matrix(const Matrix<_Scalar, _Rows, _Cols> &m) {
+        std::cout << "+----" << '\n';
+        std::cout.precision(2);
+        for (int row = 0; row < m.rows(); row++) {
+            for (int col = 0; col < m.cols(); col++) {
+                std::cout << m(row, col) << "," << "\t";
+            }
+            std::cout << "\n";
+        }
+    }
+
+    template<typename _Scalar>
+    _Scalar det(const Matrix<_Scalar, 1, 1> &m) {
+        return m(0, 0);
+    }
+
+    template<typename _Scalar>
+    _Scalar det(const Matrix<_Scalar, 2, 2> &m) {
+        _Scalar a = m(0, 0);
+        _Scalar b = m(0, 1);
+        _Scalar c = m(1, 0);
+        _Scalar d = m(1, 1);
+
+        return (a * d) - (b * c);
+    }
+
+    template<typename _Scalar, int _Rows, int _Cols>
+    double det(const Matrix<_Scalar, _Rows, _Cols> &m) {
+        assert(m.rows() == m.cols());
+
+        auto l = Matrix<double, _Rows, _Cols>();
+        auto u = Matrix<double, _Rows, _Cols>();
+
+        for (int j = 0; j < m.cols(); j++) {
+            for (int i = 0; i < m.rows(); i++) {
+                u(i, j) = m(i, j);
+                l(i, j) = m(i, j);
+
+                for (int k = 0; k < i; k++) {
+                    u(i, j) -= l(i, k) * u(k, j);
+                }
+
+                for (int k = 0; k < j; k++) {
+                    l(i, j) -= l(i, k) * u(k, j);
+                }
+
+                l(i, j) = 1 / u(j, j);
+            }
+        }
+
+        print_matrix(l);
+        print_matrix(u);
+        return det_tri(l) * det_tri(u);
+    }
+
+    template<typename _Scalar, int _Rows, int _Cols>
+    _Scalar det_tri(const Matrix<_Scalar, _Rows, _Cols> &m) {
+        int n = std::min(m.rows(), m.cols());
+
+        int det = 1;
+        for (int i = 0; i < n; i++) {
+            det *= m(i, i);
+        }
+
+        return det;
+    }
+}

labo01/Vector.h

@@ -0,0 +1,123 @@
+#pragma once
+
+/**
+ * @file Vector.h
+ *
+ * @brief Implémentation de vecteurs simples
+ *
+ * Nom: William Nolin
+ * Code permanent : NOLW76060101
+ * Email : william.nolin.1@ens.etsmtl.ca
+ *
+ */
+
+#include <cmath>
+#include "MatrixBase.h"
+
+namespace gti320 {
+
+    /**
+     * Classe vecteur générique.
+     *
+     * Cette classe réutilise la classe `MatrixBase` et ses spécialisations de
+     * templates pour les manipulation bas niveau.
+     */
+    template<typename _Scalar = double, int _Rows = Dynamic>
+    class Vector : public MatrixBase<_Scalar, _Rows, 1> {
+    public:
+
+        /**
+         * Constructeur par défaut
+         */
+        Vector() : MatrixBase<_Scalar, _Rows, 1>() {}
+
+        /**
+         * Contructeur à partir d'un taille (rows).
+         */
+        explicit Vector(int rows) : MatrixBase<_Scalar, _Rows, 1>(rows, 1) {}
+
+        /**
+         * Constructeur de copie
+         */
+        Vector(const Vector &other) : MatrixBase<_Scalar, _Rows, 1>(other) {}
+
+        /**
+         * Constructeur de copie avec une grandeur différente
+         * @tparam _OtherRows
+         * @param other
+         */
+        template<int _OtherRows>
+        Vector(const Vector<_Scalar, _OtherRows> &other) : MatrixBase<_Scalar, _Rows, 1>() {
+            int n = std::min(other.size(), _Rows);
+            const _Scalar *src = other.data();
+            _Scalar *dest = this->m_storage.data();
+            memcpy(dest, src, n * sizeof(_Scalar));
+
+            if (n < _Rows) {
+                memset(&dest[n], 0, (_Rows - n) * sizeof(_Scalar));
+            }
+        }
+
+        /**
+         * Destructeur
+         */
+        ~Vector() {}
+
+        /**
+         * Opérateur de copie
+         */
+        Vector &operator=(const Vector &other) {
+            this->m_storage = other.m_storage;
+            this->m_rows = other.rows();
+            return *this;
+        }
+
+        /**
+         * Accesseur à une entrée du vecteur (lecture seule)
+         */
+        _Scalar operator()(int i) const {
+            return this->m_storage.data()[i];
+        }
+
+        /**
+         * Accesseur à une entrée du vecteur (lecture et écriture)
+         */
+        _Scalar &operator()(int i) {
+            return this->m_storage.data()[i];
+        }
+
+        /**
+         * Modifie le nombre de lignes du vecteur
+         */
+        void resize(int _rows) {
+            MatrixBase<_Scalar, _Rows, 1>::resize(_rows, 1);
+        }
+
+        /**
+         * Produit scalaire de *this et other.
+         */
+        inline _Scalar dot(const Vector &other) const {
+            assert(this->size() == other.size());
+
+            _Scalar product = 0;
+            for (int i = 0; i < this->size(); i++) {
+                product += (*this)(i) * other(i);
+            }
+
+            return product;
+        }
+
+        /**
+         * Retourne la norme euclidienne du vecteur
+         */
+        inline _Scalar norm() const {
+            _Scalar norm = 0;
+
+            for (int i = 0; i < this->size(); i++) {
+                norm += std::pow((*this)(i), 2);
+            }
+
+            return std::sqrt(norm);
+        }
+    };
+}

labo01/main.cpp

@@ -1,28 +1,704 @@
 /**
  * @file main.cpp
  *
- * @brief Execute unit tests for a simple linear algebra library.
+ * @brief Unit tests for a simple linear algebra library.
  *
- * Nom:
+ * Nom: William Nolin
- * Code permanent :
+ * Code permanent : NOLW76060101
- * Email :
+ * Email : william.nolin.1@ens.etsmtl.ca
  *
  */
 
+#include "Matrix.h"
+#include "Vector.h"
+#include "Math3D.h"
+#include "Operators.h"
+
 #include <gtest/gtest.h>
+#include <chrono>
 
-int main(int argc, char** argv)
+using namespace gti320;
-{
-	// Executer tous les tests unitaires.
-	// 
-	// Les tests sont écrites dans les fichiers:
-	//   tests/Tests1a.cpp
-	//   tests/Tests1b.cpp
-	//   tests/TestsSupplementaire1a.cpp
-	//   tests/TestsSupplementaire1b.cpp
-	//
-	::testing::InitGoogleTest(&argc, argv);
-	const int ret = RUN_ALL_TESTS();
 
-	return ret;
+/**
+ * Multiplication  matrice * vecteur,  utilisant une implémentation naive
+ */
+template<typename _Scalar>
+static inline Vector<_Scalar, Dynamic>
+naiveMatrixMult(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> &A, const Vector<_Scalar, Dynamic> &v) {
+    assert(A.cols() == v.rows());
+
+    Vector<_Scalar, Dynamic> b(A.rows());
+    assert(b.rows() == A.rows());
+
+    for (int i = 0; i < A.rows(); ++i) {
+        b(i) = 0.0;
+        for (int j = 0; j < A.cols(); ++j) {
+            b(i) += A(i, j) * v(j);
+        }
+    }
+
+    return b;
+}
+
+/**
+ * Addition  matrice + matrice,  utilisant une implémentation naive
+ */
+template<typename _Scalar>
+static inline Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>
+naiveMatrixAddition(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> &A,
+                    const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> &B) {
+    assert(A.cols() == B.cols() && A.rows() == B.rows());
+
+    Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> C(A.rows(), A.cols());
+    assert(C.rows() == A.rows() && C.cols() == A.cols());
+    for (int i = 0; i < C.rows(); ++i) {
+        for (int j = 0; j < C.cols(); ++j) {
+            C(i, j) = A(i, j) + B(i, j);
+        }
+    }
+    return C;
+}
+
+/**
+ * Multiplication  matrice * matrice,  utilisant une implémentation naive.
+ */
+template<typename _Scalar, int _Storage>
+static inline Matrix<_Scalar, Dynamic, Dynamic, _Storage>
+naiveMatrixMult(const Matrix<_Scalar, Dynamic, Dynamic, _Storage> &A,
+                const Matrix<_Scalar, Dynamic, Dynamic, _Storage> &B) {
+    assert(A.cols() == B.rows());
+    Matrix<_Scalar, Dynamic, Dynamic> product(A.rows(), B.cols());
+    for (int i = 0; i < A.rows(); ++i) {
+        for (int j = 0; j < B.cols(); ++j) {
+            for (int k = 0; k < A.cols(); ++k) {
+                product(i, j) += A(i, k) * B(k, j);
+            }
+        }
+    }
+    return product;
+}
+
+// Test les matrice avec redimensionnement dynamique
+TEST(TestLabo1, DynamicMatrixTests) {
+    // Crée une matrice à taille dynamique
+    // (note : les valeurs par défaut du patron de la classe `Matrix` mettent le
+    // le nombre de ligne et de colonnes à `Dynamic`)
+    Matrix<double> M(3, 5);
+    EXPECT_EQ(M.cols(), 5);
+    EXPECT_EQ(M.rows(), 3);
+
+    // Redimensionne la matrice
+    M.resize(100, 1000);
+    EXPECT_EQ(M.cols(), 1000);
+    EXPECT_EQ(M.rows(), 100);
+
+    // Test - stockage par colonnes
+    Matrix<double, Dynamic, Dynamic, ColumnStorage> ColM(100, 100);
+    ColM.setZero();
+    ColM(0, 0) = 1.0;
+    ColM(99, 99) = 99.0;
+    ColM(10, 33) = 5.0;
+    EXPECT_EQ(ColM(0, 0), 1.0);
+    EXPECT_EQ(ColM(10, 33), 5.0);
+    EXPECT_EQ(ColM(99, 99), 99.0);
+
+    // Test - stockage par lignes
+    Matrix<double, Dynamic, Dynamic, RowStorage> RowM(5, 4);
+    RowM.setZero();
+    RowM(0, 0) = 2.1;
+    RowM(3, 3) = -0.2;
+    RowM(4, 3) = 1.2;
+    EXPECT_EQ(RowM.rows(), 5);
+    EXPECT_EQ(RowM.cols(), 4);
+    EXPECT_DOUBLE_EQ(RowM(0, 0), 2.1);
+    EXPECT_DOUBLE_EQ(RowM(3, 3), -0.2);
+    EXPECT_DOUBLE_EQ(RowM(4, 3), 1.2);
+    EXPECT_DOUBLE_EQ(RowM(3, 2), 0.0);
+
+    // Transposée
+    const auto RowMT = RowM.transpose();
+    EXPECT_EQ(RowMT.rows(), 4);
+    EXPECT_EQ(RowMT.cols(), 5);
+    EXPECT_DOUBLE_EQ(RowMT(0, 0), 2.1);
+    EXPECT_DOUBLE_EQ(RowMT(3, 3), -0.2);
+    EXPECT_DOUBLE_EQ(RowMT(3, 4), 1.2);
+    EXPECT_DOUBLE_EQ(RowMT(2, 3), 0.0);
+}
+
+
+
+/**
+ * Test pour les vecteurs à taille dynamique
+ */
+TEST(TestLabo1, DynamicVectorSizeTest) {
+    Vector<double> v(5);
+    v.setZero();
+
+    EXPECT_EQ(v.rows(), 5);
+
+    v.resize(3);
+    EXPECT_EQ(v.rows(), 3);
+
+    v(0) = 1.0;
+    v(1) = 2.0;
+    v(2) = 3.0;
+
+    EXPECT_DOUBLE_EQ(v.norm(), 3.7416573867739413855837487323165);
+
+    Vector<double, Dynamic> v2(3);
+    v2.setZero();
+    v2(1) = 2.0;
+
+    EXPECT_DOUBLE_EQ(v2.dot(v), 4.0);
+    EXPECT_DOUBLE_EQ(v2(0), 0.0);
+    EXPECT_DOUBLE_EQ(v2(1), 2.0);
+    EXPECT_DOUBLE_EQ(v2(2), 0.0);
+}
+
+/**
+ * Test pour les matrice à taille fixe
+ */
+TEST(TestLabo1, Matrix4x4SizeTest) {
+    Matrix4d M;
+    M.setZero();
+
+    EXPECT_EQ(M.cols(), 4);
+    EXPECT_EQ(M.rows(), 4);
+}
+
+/**
+ * Test pour les opérateurs d'arithmétique matricielle.
+ */
+TEST(TestLabo1, MatrixMatrixOperators) {
+    // Opérations arithmétiques avec matrices à taille dynamique
+    {
+        // Test : matrice identité
+        Matrix<double> A(6, 6);
+        A.setIdentity();
+        EXPECT_DOUBLE_EQ(A(0, 0), 1.0);
+        EXPECT_DOUBLE_EQ(A(1, 1), 1.0);
+        EXPECT_DOUBLE_EQ(A(2, 2), 1.0);
+        EXPECT_DOUBLE_EQ(A(3, 3), 1.0);
+        EXPECT_DOUBLE_EQ(A(4, 4), 1.0);
+        EXPECT_DOUBLE_EQ(A(5, 5), 1.0);
+        EXPECT_DOUBLE_EQ(A(0, 1), 0.0);
+        EXPECT_DOUBLE_EQ(A(1, 0), 0.0);
+
+        // Test : produit  scalaire * matrice
+        const double alpha = 2.5;
+        Matrix<double> B = alpha * A;
+        EXPECT_DOUBLE_EQ(B(0, 0), alpha);
+        EXPECT_DOUBLE_EQ(B(1, 1), alpha);
+        EXPECT_DOUBLE_EQ(B(2, 2), alpha);
+        EXPECT_DOUBLE_EQ(B(3, 3), alpha);
+        EXPECT_DOUBLE_EQ(B(4, 4), alpha);
+        EXPECT_DOUBLE_EQ(B(5, 5), alpha);
+        EXPECT_DOUBLE_EQ(B(0, 1), 0.0);
+        EXPECT_DOUBLE_EQ(B(1, 0), 0.0);
+
+        // Test : produit  matrice * matrice
+        Matrix<double> C = A * B;
+        EXPECT_DOUBLE_EQ(C(0, 0), A(0, 0) * B(0, 0));
+        EXPECT_DOUBLE_EQ(C(1, 1), A(1, 1) * B(1, 1));
+        EXPECT_DOUBLE_EQ(C(2, 2), A(2, 2) * B(2, 2));
+        EXPECT_DOUBLE_EQ(C(3, 3), A(3, 3) * B(3, 3));
+        EXPECT_DOUBLE_EQ(C(4, 4), A(4, 4) * B(4, 4));
+        EXPECT_DOUBLE_EQ(C(5, 5), A(5, 5) * B(5, 5));
+        EXPECT_DOUBLE_EQ(C(0, 1), 0.0);
+        EXPECT_DOUBLE_EQ(C(2, 3), 0.0);
+
+        // Test : addition  matrice + matrice
+        Matrix<double> A_plus_B = A + B;
+        EXPECT_DOUBLE_EQ(A_plus_B(0, 0), A(0, 0) + B(0, 0));
+        EXPECT_DOUBLE_EQ(A_plus_B(1, 1), A(1, 1) + B(1, 1));
+        EXPECT_DOUBLE_EQ(A_plus_B(2, 2), A(2, 2) + B(2, 2));
+        EXPECT_DOUBLE_EQ(A_plus_B(3, 3), A(3, 3) + B(3, 3));
+        EXPECT_DOUBLE_EQ(A_plus_B(4, 4), A(4, 4) + B(4, 4));
+        EXPECT_DOUBLE_EQ(A_plus_B(5, 5), A(5, 5) + B(5, 5));
+        EXPECT_DOUBLE_EQ(A_plus_B(0, 1), 0.0);
+        EXPECT_DOUBLE_EQ(A_plus_B(2, 3), 0.0);
+    }
+
+    // Opérations arithmétique avec matrices à stockage par lignes et par
+    // colonnes.
+    {
+        // Création d'un matrice à stockage par lignes
+        Matrix<double, Dynamic, Dynamic, RowStorage> A(5, 5);
+        A(0, 0) = 0.8147;
+        A(0, 1) = 0.0975;
+        A(0, 2) = 0.1576;
+        A(0, 3) = 0.1419;
+        A(0, 4) = 0.6557;
+        A(1, 0) = 0.9058;
+        A(1, 1) = 0.2785;
+        A(1, 2) = 0.9706;
+        A(1, 3) = 0.4218;
+        A(1, 4) = 0.0357;
+        A(2, 0) = 0.1270;
+        A(2, 1) = 0.5469;
+        A(2, 2) = 0.9572;
+        A(2, 3) = 0.9157;
+        A(2, 4) = 0.8491;
+        A(3, 0) = 0.9134;
+        A(3, 1) = 0.9575;
+        A(3, 2) = 0.4854;
+        A(3, 3) = 0.7922;
+        A(3, 4) = 0.9340;
+        A(4, 0) = 0.6324;
+        A(4, 1) = 0.9649;
+        A(4, 2) = 0.8003;
+        A(4, 3) = 0.9595;
+        A(4, 4) = 0.6787;
+
+        // Test : transposée (le résultat est une matrice à stockage par
+        //        colonnes)
+        Matrix<double, Dynamic, Dynamic, ColumnStorage> B = A.transpose();
+
+        // Test : multiplication  matrix(ligne) * matrice(colonne)
+        // Note : teste seulement la première et la dernière colonne
+        const auto C = A * B;
+        EXPECT_NEAR(C(0, 0), 1.14815820000000, 1e-3);
+        EXPECT_NEAR(C(0, 4), 1.31659795000000, 1e-3);
+        EXPECT_NEAR(C(1, 0), 1.00133748000000, 1e-3);
+        EXPECT_NEAR(C(1, 4), 2.04727044000000, 1e-3);
+        EXPECT_NEAR(C(2, 0), 0.99433707000000, 1e-3);
+        EXPECT_NEAR(C(2, 4), 2.82896409000000, 1e-3);
+        EXPECT_NEAR(C(3, 0), 1.63883925000000, 1e-3);
+        EXPECT_NEAR(C(3, 4), 3.28401323000000, 1e-3);
+        EXPECT_NEAR(C(4, 0), 1.31659795000000, 1e-3);
+        EXPECT_NEAR(C(4, 4), 3.35271580000000, 1e-3);
+
+
+        // Test : multiplication  matrice(colonne) * matrice(ligne)
+        // Note : teste seulement la première et la dernière colonne
+        const auto C2 = B * A;
+        EXPECT_NEAR(C2(0, 0), 2.73456805000000, 1e-3);
+        EXPECT_NEAR(C2(0, 4), 1.95669703000000, 1e-3);
+        EXPECT_NEAR(C2(1, 0), 1.88593811000000, 1e-3);
+        EXPECT_NEAR(C2(1, 4), 2.08742862000000, 1e-3);
+        EXPECT_NEAR(C2(2, 0), 2.07860468000000, 1e-3);
+        EXPECT_NEAR(C2(2, 4), 1.94727447000000, 1e-3);
+        EXPECT_NEAR(C2(3, 0), 1.94434955000000, 1e-3);
+        EXPECT_NEAR(C2(3, 4), 2.27675041000000, 1e-3);
+        EXPECT_NEAR(C2(4, 0), 1.95669703000000, 1e-3);
+        EXPECT_NEAR(C2(4, 4), 2.48517748000000, 1e-3);
+
+        // Test : addition  matrice(ligne) + matrice(ligne)
+        // Note : teste seulement la première et la dernière colonne
+        const auto A_plus_A = A + A;
+        EXPECT_DOUBLE_EQ(A_plus_A(0, 0), A(0, 0) + A(0, 0));
+        EXPECT_DOUBLE_EQ(A_plus_A(0, 4), A(0, 4) + A(0, 4));
+        EXPECT_DOUBLE_EQ(A_plus_A(1, 0), A(1, 0) + A(1, 0));
+        EXPECT_DOUBLE_EQ(A_plus_A(1, 4), A(1, 4) + A(1, 4));
+        EXPECT_DOUBLE_EQ(A_plus_A(2, 0), A(2, 0) + A(2, 0));
+        EXPECT_DOUBLE_EQ(A_plus_A(2, 4), A(2, 4) + A(2, 4));
+        EXPECT_DOUBLE_EQ(A_plus_A(3, 0), A(3, 0) + A(3, 0));
+        EXPECT_DOUBLE_EQ(A_plus_A(3, 4), A(3, 4) + A(3, 4));
+        EXPECT_DOUBLE_EQ(A_plus_A(4, 0), A(4, 0) + A(4, 0));
+        EXPECT_DOUBLE_EQ(A_plus_A(4, 4), A(4, 4) + A(4, 4));
+
+        // Test : addition  matrice(colonne) + matrice(colonne)
+        // Note : teste seulement la première et la dernière colonne
+        const auto B_plus_B = B + B;
+        EXPECT_DOUBLE_EQ(B_plus_B(0, 0), B(0, 0) + B(0, 0));
+        EXPECT_DOUBLE_EQ(B_plus_B(0, 4), B(0, 4) + B(0, 4));
+        EXPECT_DOUBLE_EQ(B_plus_B(1, 0), B(1, 0) + B(1, 0));
+        EXPECT_DOUBLE_EQ(B_plus_B(1, 4), B(1, 4) + B(1, 4));
+        EXPECT_DOUBLE_EQ(B_plus_B(2, 0), B(2, 0) + B(2, 0));
+        EXPECT_DOUBLE_EQ(B_plus_B(2, 4), B(2, 4) + B(2, 4));
+        EXPECT_DOUBLE_EQ(B_plus_B(3, 0), B(3, 0) + B(3, 0));
+        EXPECT_DOUBLE_EQ(B_plus_B(3, 4), B(3, 4) + B(3, 4));
+        EXPECT_DOUBLE_EQ(B_plus_B(4, 0), B(4, 0) + B(4, 0));
+        EXPECT_DOUBLE_EQ(B_plus_B(4, 4), B(4, 4) + B(4, 4));
+
+    }
+}
+
+/**
+ * Test pour la multiplication  matrice * vecteur
+ */
+TEST(TestLabo1, MatrixVectorOperators) {
+    // Vecteur à taille dynamique
+    Vector<double> v(5);
+    v(0) = 1.0;
+    v(1) = 2.0;
+    v(2) = 4.0;
+    v(3) = 8.0;
+    v(4) = 16.0;
+
+    // Test : multiplication par la matrice identité
+    {
+        Matrix<double> M(5, 5);
+        M.setIdentity();
+
+        const auto b = M * v;
+        EXPECT_DOUBLE_EQ(b(0), 1.0);
+        EXPECT_DOUBLE_EQ(b(1), 2.0);
+        EXPECT_DOUBLE_EQ(b(2), 4.0);
+        EXPECT_DOUBLE_EQ(b(3), 8.0);
+        EXPECT_DOUBLE_EQ(b(4), 16.0);
+    }
+
+    // Test : multiplication par une matrice à taille dynamique avec stockage par ligne.
+    {
+        Matrix<double, Dynamic, Dynamic, RowStorage> M(5, 5);
+        M.setIdentity();
+        M = 2.0 * M;
+
+        Vector<double> b2 = M * v;
+        EXPECT_DOUBLE_EQ(b2(0), 2.0);
+        EXPECT_DOUBLE_EQ(b2(1), 4.0);
+        EXPECT_DOUBLE_EQ(b2(2), 8.0);
+        EXPECT_DOUBLE_EQ(b2(3), 16.0);
+        EXPECT_DOUBLE_EQ(b2(4), 32.0);
+    }
+}
+
+/**
+ * Opérateurs d'arithmétique vectorielle
+ */
+TEST(TestLabo1, VectorOperators) {
+    Vector<double> v(5);
+    v(0) = 0.1;
+    v(1) = 0.2;
+    v(2) = 0.4;
+    v(3) = 0.8;
+    v(4) = 1.6;
+
+    // Test : multiplication  scalaire * vecteur
+    const double alpha = 4.0;
+    const auto v2 = alpha * v;
+    EXPECT_DOUBLE_EQ(v2(0), alpha * v(0));
+    EXPECT_DOUBLE_EQ(v2(1), alpha * v(1));
+    EXPECT_DOUBLE_EQ(v2(2), alpha * v(2));
+    EXPECT_DOUBLE_EQ(v2(3), alpha * v(3));
+    EXPECT_DOUBLE_EQ(v2(4), alpha * v(4));
+
+    // Test : addition  vecteur + vecteur
+    const auto v3 = v + v2;
+    EXPECT_DOUBLE_EQ(v3(0), v(0) + v2(0));
+    EXPECT_DOUBLE_EQ(v3(1), v(1) + v2(1));
+    EXPECT_DOUBLE_EQ(v3(2), v(2) + v2(2));
+    EXPECT_DOUBLE_EQ(v3(3), v(3) + v2(3));
+    EXPECT_DOUBLE_EQ(v3(4), v(4) + v2(4));
+}
+
+
+/**
+ * Mathématiques 3D
+ */
+TEST(TestLabo1, Math3D) {
+    // Test : norme d'un vecteur de dimension 3
+    Vector3d v;
+    v.setZero();
+    v(1) = 2.0;
+    EXPECT_EQ(v.rows(), 3);
+    EXPECT_EQ(v.cols(), 1);
+    EXPECT_DOUBLE_EQ(v(0), 0.0);
+    EXPECT_DOUBLE_EQ(v(1), 2.0);
+    EXPECT_DOUBLE_EQ(v(2), 0.0);
+    EXPECT_DOUBLE_EQ(v.norm(), 2.0);
+
+    // Test : calcul de la norme d'un deuxième vecteur 3D
+    Vector3d v2;
+    v2(0) = 4.0;
+    v2(1) = 2.0;
+    v2(2) = 5.0;
+    EXPECT_EQ(v2.rows(), 3);
+    EXPECT_EQ(v2.cols(), 1);
+    EXPECT_DOUBLE_EQ(v2(0), 4.0);
+    EXPECT_DOUBLE_EQ(v2(1), 2.0);
+    EXPECT_DOUBLE_EQ(v2(2), 5.0);
+    EXPECT_DOUBLE_EQ(v2.norm(), 6.7082039324993690892275210061938);
+
+    // Test : produit scalaire
+    EXPECT_DOUBLE_EQ(v.dot(v2), 4.0);
+
+    // Test : matrice identité 4x4
+    Matrix4d M;
+    M.setIdentity();
+    EXPECT_DOUBLE_EQ(M(0, 0), 1.0);
+    EXPECT_DOUBLE_EQ(M(0, 1), 0.0);
+    EXPECT_DOUBLE_EQ(M(0, 2), 0.0);
+    EXPECT_DOUBLE_EQ(M(1, 1), 1.0);
+    EXPECT_DOUBLE_EQ(M(1, 0), 0.0);
+    EXPECT_DOUBLE_EQ(M(1, 2), 0.0);
+    EXPECT_DOUBLE_EQ(M(2, 0), 0.0);
+    EXPECT_DOUBLE_EQ(M(2, 1), 0.0);
+    EXPECT_DOUBLE_EQ(M(2, 2), 1.0);
+
+    // Test : création d'une matrice de rotation de 45 degrés autour de l'axe des x
+    const auto Rx = makeRotation<double>(M_PI / 4.0, 0, 0);
+    EXPECT_NEAR(Rx(0, 0), 1, 1e-3);
+    EXPECT_NEAR(Rx(0, 1), 0, 1e-3);
+    EXPECT_NEAR(Rx(0, 2), 0, 1e-3);
+    EXPECT_NEAR(Rx(1, 0), 0, 1e-3);
+    EXPECT_NEAR(Rx(1, 1), 0.7071, 1e-3);
+    EXPECT_NEAR(Rx(1, 2), -0.7071, 1e-3);
+    EXPECT_NEAR(Rx(2, 0), 0, 1e-3);
+    EXPECT_NEAR(Rx(2, 1), 0.7071, 1e-3);
+    EXPECT_NEAR(Rx(2, 2), 0.7071, 1e-3);
+
+    // Test : création d'une matrice de rotation de 45 degrés autour de l'axe des y
+    const auto Ry = makeRotation<double>(0, M_PI / 4.0, 0);
+    EXPECT_NEAR(Ry(0, 0), 0.7071, 1e-3);
+    EXPECT_NEAR(Ry(0, 1), 0, 1e-3);
+    EXPECT_NEAR(Ry(0, 2), 0.7071, 1e-3);
+    EXPECT_NEAR(Ry(1, 0), 0, 1e-3);
+    EXPECT_NEAR(Ry(1, 1), 1, 1e-3);
+    EXPECT_NEAR(Ry(1, 2), 0, 1e-3);
+    EXPECT_NEAR(Ry(2, 0), -0.7071, 1e-3);
+    EXPECT_NEAR(Ry(2, 1), 0, 1e-3);
+    EXPECT_NEAR(Ry(2, 2), 0.7071, 1e-3);
+
+    // Test : création d'une matrice de rotation de 45 degrés autour de l'axe des z
+    const auto Rz = makeRotation<double>(0, 0, M_PI / 4.0);
+    EXPECT_NEAR(Rz(0, 0), 0.7071, 1e-3);
+    EXPECT_NEAR(Rz(0, 1), -0.7071, 1e-3);
+    EXPECT_NEAR(Rz(0, 2), 0, 1e-3);
+    EXPECT_NEAR(Rz(1, 0), 0.7071, 1e-3);
+    EXPECT_NEAR(Rz(1, 1), 0.7071, 1e-3);
+    EXPECT_NEAR(Rz(1, 2), 0, 1e-3);
+    EXPECT_NEAR(Rz(2, 0), 0, 1e-3);
+    EXPECT_NEAR(Rz(2, 1), 0, 1e-3);
+    EXPECT_NEAR(Rz(2, 2), 1, 1e-3);
+
+    // Test : création d'une matrice de rotation quelconque.
+    const auto Rxyz = makeRotation<double>(M_PI / 3.0, -M_PI / 6.0, M_PI / 4.0);
+    EXPECT_NEAR(Rxyz(0, 0), 0.6124, 1e-3);
+    EXPECT_NEAR(Rxyz(0, 1), -0.6597, 1e-3);
+    EXPECT_NEAR(Rxyz(0, 2), 0.4356, 1e-3);
+    EXPECT_NEAR(Rxyz(1, 0), 0.6124, 1e-3);
+    EXPECT_NEAR(Rxyz(1, 1), 0.0474, 1e-3);
+    EXPECT_NEAR(Rxyz(1, 2), -0.7891, 1e-3);
+    EXPECT_NEAR(Rxyz(2, 0), 0.5, 1e-3);
+    EXPECT_NEAR(Rxyz(2, 1), 0.75, 1e-3);
+    EXPECT_NEAR(Rxyz(2, 2), 0.4330, 1e-3);
+
+    // Test : création d'une transformation homogène via la sous-matrice 3x3 en
+    // utilisant la fonction `block`
+    M.block(0, 0, 3, 3) = Rxyz;
+    M(0, 3) = -0.1;
+    M(1, 3) = 1.0;
+    M(2, 3) = 2.1;
+
+    // Test : calcule l'inverse de la matrice M et vérifie que M^(-1) * M * v = v
+    const Matrix4d Minv = M.inverse();
+    const Vector3d v3 = Minv * (M * v2);
+    EXPECT_DOUBLE_EQ(v3(0), v2(0));
+    EXPECT_DOUBLE_EQ(v3(1), v2(1));
+    EXPECT_DOUBLE_EQ(v3(2), v2(2));
+
+    // Test : translation d'un vecteur 3D effectuée avec une matrice 4x4 en coordonnées homogènes
+    Matrix4d T;
+    T.setIdentity();
+    T(0, 3) = 1.2;
+    T(1, 3) = 2.5;
+    T(2, 3) = -4.0;
+    const Vector3d t = T * v3;
+    EXPECT_DOUBLE_EQ(t(0), v3(0) + 1.2);
+    EXPECT_DOUBLE_EQ(t(1), v3(1) + 2.5);
+    EXPECT_DOUBLE_EQ(t(2), v3(2) - 4.0);
+
+    // Test : inverse d'un matrice de rotation
+    const Matrix3d Rinv = Rxyz.inverse();
+    const Matrix3d RT = Rxyz.transpose<double, 3, 3, ColumnStorage>();
+    EXPECT_DOUBLE_EQ(Rinv(0, 0), RT(0, 0));
+    EXPECT_DOUBLE_EQ(Rinv(1, 1), RT(1, 1));
+    EXPECT_DOUBLE_EQ(Rinv(0, 2), RT(0, 2));
+}
+
+/**
+ * Test des performance de la multiplication  matrice * vecteur
+ * pour de grandes dimensions.
+ */
+TEST(TestLabo1, PerformanceMatrixVector) {
+    Matrix<double> A(16384, 16384);     // grande matrice avec stockage colonne
+    Vector<double> v(16384);            // grand vecteur
+
+    using namespace std::chrono;
+    // Test : multiplication avec l'algorithme naif.
+    high_resolution_clock::time_point t = high_resolution_clock::now();
+    naiveMatrixMult(A, v);
+    const duration<double> naive_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
+
+    // Test : multiplication avec l'implémentation spécifique pour les matrices avec
+    // stockage par colonnes.
+    t = high_resolution_clock::now();
+    A * v;
+    const duration<double> optimal_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
+
+    EXPECT_TRUE(optimal_t < 0.4 * naive_t)
+                        << "Naive time: " << duration_cast<std::chrono::milliseconds>(naive_t).count() << " ms, "
+                        << "optimized time: " << duration_cast<std::chrono::milliseconds>(optimal_t).count() << " ms";
+}
+
+/**
+ * Test des performances de l'addition  matrice + matrice
+ * pour de grandes dimensions.
+ */
+TEST(TestLabo1, PerformanceLargeMatrixMatrix) {
+    // deux grandes matrices à stockage par colonnes
+    Matrix<double> A(16384, 16384);
+    Matrix<double> B(16384, 16384);
+
+    using namespace std::chrono;
+    high_resolution_clock::time_point t = high_resolution_clock::now();
+    // Test : addition avec l'algorithme naif
+    naiveMatrixAddition(A, B);
+    const duration<double> naive_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
+
+    // Test : addition avec l'implémentation spécifique pour les matrices à
+    // stockage par colonnes.
+    t = high_resolution_clock::now();
+    A + B;
+    const duration<double> optimal_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
+
+    EXPECT_TRUE(optimal_t < 0.4 * naive_t);
+}
+
+TEST(TestLabo1, Supplementaires) {
+    // === Stockage ===
+    // Test 1: Set zero
+    DenseStorage<int, Dynamic> S1(10);
+    S1.setZero();
+    for (int i = 0; i < S1.size(); i++) {
+        EXPECT_EQ(S1.data()[i], 0);
+    }
+
+    // Test 2: Resize dynamique
+    int size = 16;
+    S1.resize(size);
+    EXPECT_EQ(S1.size(), size);
+
+    // Test 3: Resize statique
+    DenseStorage<int, 10> S2;
+    S2.resize(size);
+    EXPECT_EQ(S2.size(), 10);
+
+    // Test 4: Copie
+    DenseStorage<int, Dynamic> S3(20);
+    S3.data()[5] = 123;
+    S3.data()[7] = 321;
+    S1 = S3;
+    EXPECT_EQ(S1.size(), S3.size());
+    EXPECT_EQ(S1.data()[5], S3.data()[5]);
+    EXPECT_EQ(S1.data()[7], S3.data()[7]);
+
+    // === Matrices ===
+    // Test 5: Identité
+    Matrix<int, -1, -1, ColumnStorage> MC(4, 6);
+    MC.setIdentity();
+    for (int col = 0; col < MC.cols(); col++) {
+        for (int row = 0; row < MC.rows(); row++) {
+            int expected = 0;
+            if (row == col) {
+                expected = 1;
+            }
+
+            EXPECT_EQ(MC(row, col), expected);
+        }
+    }
+
+    // Test 6: Création d'une sous-matrice
+    MC(1, 1) = 1;
+    MC(1, 2) = 2;
+    MC(1, 3) = 3;
+    MC(2, 1) = 4;
+    MC(2, 2) = 5;
+    MC(2, 3) = 6;
+    MC(3, 1) = 7;
+    MC(3, 2) = 8;
+    MC(3, 3) = 9;
+    SubMatrix<int, -1, -1, ColumnStorage> s = MC.block(1, 1, 3, 3);
+    for (int col = 0; col < s.cols(); col++) {
+        for (int row = 0; row < s.rows(); row++) {
+            EXPECT_EQ(s(col, row), MC(col + 1, row + 1));
+        }
+    }
+
+    // Test 7: Transposée d'une sous-matrice
+    const Matrix<int, -1, -1, ColumnStorage> t = s.transpose<int, -1, -1, ColumnStorage>();
+    for (int col = 0; col < t.cols(); col++) {
+        for (int row = 0; row < t.rows(); row++) {
+            EXPECT_EQ(t(col, row), s(row, col));
+        }
+    }
+
+    // Test 8: Stockage par colonne
+    MC(0, 0) = 4;
+    MC(1, 0) = 5;
+    MC(0, 1) = 6;
+    EXPECT_EQ(MC.data()[0], MC(0, 0));
+    EXPECT_EQ(MC.data()[1], MC(1, 0));
+
+    // Test 9: Stockage par rangée
+    Matrix<int, -1, -1, RowStorage> MS(4, 6);
+    MS(0, 0) = 4;
+    MS(1, 0) = 5;
+    MS(0, 1) = 6;
+    EXPECT_EQ(MS.data()[0], MS(0, 0));
+    EXPECT_EQ(MS.data()[1], MS(0, 1));
+
+    // === Vecteurs ===
+    // Test 10: Copie
+    Vector<int> V1(10);
+    Vector<int> V2(16);
+    V2(12) = 543;
+    V1 = V2;
+    EXPECT_EQ(V1.size(), V2.size());
+    EXPECT_EQ(V1(12), V2(12));
+
+    // === Copie de vecteurs de grandeur différente ===
+    // Test 11: Petit vers grand
+    Vector<int, 5> V3;
+    for (int i = 0; i < V3.size(); i++) {
+        V3(i) = i;
+    }
+    Vector<int, 7> V4(V3);
+
+    for (int i = 0; i < V3.size(); i++) {
+        EXPECT_EQ(V4(i), V3(i));
+    }
+    for (int i = V3.size(); i < V4.size(); i++) {
+        EXPECT_EQ(V4(i), 0);
+    }
+
+    // Test 12: Grand vers petit
+    Vector<int, 5> V5(V4);
+    for (int i = 0; i < V5.size(); i++) {
+        EXPECT_EQ(V5(i), V4(i));
+    }
+
+    // === Déterminants ===
+    Matrix<int, 1, 1> MD1x1;
+    MD1x1(0, 0) = 1;
+
+    Matrix<int, 2, 2> MD2x2;
+    MD2x2(0, 0) = 1;    MD2x2(0, 1) = 2;
+    MD2x2(1, 0) = 3;    MD2x2(1, 1) = 4;
+
+    Matrix<int, 3, 3> MD3x3;
+    MD3x3(0, 0) = 1;    MD3x3(0, 1) = 2;    MD3x3(0, 2) = 3;
+    MD3x3(1, 0) = 4;    MD3x3(1, 1) = 5;    MD3x3(1, 2) = 6;
+    MD3x3(2, 0) = 7;    MD3x3(2, 1) = 9;    MD3x3(2, 2) = 0;
+
+    // Test 13: 1x1
+    int det1 = det(MD1x1);
+    EXPECT_EQ(det1, MD1x1(0, 0));
+
+    // Test 14: 2x2
+    int det2 = det(MD2x2);
+    EXPECT_EQ(det2, -2);
+
+    // Test 15: 3x3
+    int det3 = det(MD3x3);
+    EXPECT_EQ(det3, 33);
+}
+
+int main(int argc, char **argv) {
+    ::testing::InitGoogleTest(&argc, argv);
+    const int ret = RUN_ALL_TESTS();
+
+    return ret;
 }

labo01/src/Math3D.h

@@ -1,110 +0,0 @@
-#pragma once
-
-/**
- * @file Math3D.h
- *
- * @brief Fonctions pour l'intinialisation et la manipulation de matrices de
- * rotation, des matrices de transformations en coordonnées homogènes et les
- * vecteurs 3D.
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include "Matrix.h"
-#include "Vector.h"
-#include "Operators.h"
-
-#ifndef _USE_MATH_DEFINES
-#define _USE_MATH_DEFINES
-#endif
-
-#include <math.h>
-
-
-namespace gti320 {
-
-    // Deux types de vecteurs 3D considérés ici
-    typedef Vector<double, 3> Vector3d;
-    typedef Vector<float, 3> Vector3f;
-
-    // Dans le cadre de ce projet, nous considérons seulement deux
-    // cas :
-    //
-    //  - les rotations
-    //  - les translations
-    //
-    // Deux types de matrices en coordonnées homogèes :
-    typedef Matrix<double, 4, 4, ColumnStorage> Matrix4d;
-    typedef Matrix<float, 4, 4, ColumnStorage> Matrix4f;
-    // 
-    // Deux types de matrices pour les rotations
-    typedef Matrix<double, 3, 3, ColumnStorage> Matrix3d;
-    typedef Matrix<float, 3, 3, ColumnStorage> Matrix3f;
-
-    /**
-     * Initialise et retourne la matrice identité
-     */
-    template<>
-    inline void Matrix4d::setIdentity()
-    {
-        // TODO affecter la valeur 0.0 partout, sauf sur la diagonale principale où c'est 1.0.
-        //      Note: ceci est une redéfinition d'une fonction membre!
-    }
-
-    /**
-     * Calcul de la matrice inverse, SPÉCIALISÉ pour le cas d'une matrice de
-     * transformation en coordonnées homogènes.
-     *
-     * TODO (vous pouvez supposer qu'il s'agit d'une matrice de transformation
-     * en coordonnées homogènes)
-     */
-    template<>
-    inline Matrix4d Matrix4d::inverse() const
-    {
-        // TODO : implémenter
-        return Matrix4d(); // Pas bon, à changer
-    }
-
-    /**
-     * Calcul de la matrice inverse, SPÉCIALISÉ pour le cas d'une matrice de rotation.
-     *
-     * (vous pouvez supposer qu'il s'agit d'une matrice de rotation)
-     */
-    template<>
-    inline Matrix3d Matrix3d::inverse() const
-    {
-        // TODO : implémenter
-        return Matrix3d();
-    }
-
-
-    /**
-     * Multiplication d'une matrice 4x4 avec un vecteur 3D où la matrice
-     * représente une transformation en coordonnées homogène.
-     */
-    template <typename _Scalar>
-    Vector<_Scalar, 3> operator*(const Matrix<_Scalar, 4, 4, ColumnStorage>& A, const Vector<_Scalar, 3>& v)
-    {
-        // TODO : implémenter
-        return Vector<_Scalar, 3>(); // pas bon, à changer
-    }
-
-
-    /**
-     * Initialise et retourne la matrice de rotation définie par les angles
-     * d'Euler XYZ exprimés en radians.
-     *
-     * La matrice doit correspondre au produit : Rz*Ry*Rx.
-     */
-    template<typename _Scalar>
-    static Matrix<_Scalar, 3, 3> makeRotation(_Scalar x, _Scalar y, _Scalar z)
-    {
-        // TODO : implémenter
-
-        return Matrix<_Scalar, 3, 3>(); //	 pas bon, à changer
-    }
-
-}

labo01/src/Matrix.h

@@ -1,350 +0,0 @@
-#pragma once
-
-/**
- * @file Matrix.h
- *
- * @brief Implémentation de matrices simples.
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include "MatrixBase.h"
-
-namespace gti320
-{
-    enum StorageType
-    {
-        ColumnStorage = 0,
-        RowStorage = 1
-    };
-
-    // Déclaration avancée
-    template <typename _Scalar, int _RowsAtCompile, int _ColsAtCompile, int _StorageType> class SubMatrix;
-
-    /**
-     * Classe Matrix spécialisé pour le cas générique. (defaut par colonne)
-     *
-     * (le cas d'un stockage par ligne fait l'objet d'une spécialisation de patron, voir plus bas)
-     */
-    template <typename _Scalar = double, int _RowsAtCompile = Dynamic, int _ColsAtCompile = Dynamic, int _StorageType = ColumnStorage>
-    class Matrix : public MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile> {
-    public:
-
-        /**
-         * Constructeur par défaut
-         */
-        Matrix() : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>() { }
-
-        /**
-         * Constructeur de copie
-         */
-        Matrix(const Matrix& other) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(other) { }
-
-        /**
-         * Constructeur avec spécification du nombre de ligne et de colonnes
-         */
-        explicit Matrix(int _rows, int _cols) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(_rows, _cols) { }
-
-        /**
-         * Destructeur
-         */
-        ~Matrix() { }
-
-        /**
-         * Opérateur de copie à partir d'une sous-matrice.
-         *
-         * Exemple :
-         *    Matrix<...> A(...);
-         *    Matrix<...> B(...);
-         *    B = A.block(i,j,m,n);
-
-         */
-        template<typename _OtherScalar, int OtherRows, int _OtherCols, int _OtherStorage>
-        Matrix& operator= (const SubMatrix<_OtherScalar, OtherRows, _OtherCols, _OtherStorage>& submatrix)
-        {
-            // TODO copier les données de la sous-matrice.
-            //   Note : si les dimensions ne correspondent pas, la matrice doit être redimensionnée.
-            //   Vous pouvez présumer qu'il s'agit d'un stockage par colonnes.
-            return *this;
-        }
-
-        /**
-         * Accesseur à une entrée de la matrice (lecture seule)
-         */
-        _Scalar operator()(int i, int j) const
-        {
-            // TODO implementer
-            return (double)(i + j);
-        }
-
-        /**
-         * Accesseur à une entrée de la matrice (lecture ou écriture)
-         */
-        _Scalar& operator()(int i, int j)
-        {
-            // TODO implementer
-            //      Indice : l'implémentation est identique à celle de la fonction précédente.
-            _Scalar x = (double)(i + j);
-            return x;
-        }
-
-        /**
-         * Crée une sous-matrice pour un block de taille (rows, cols) à partir de l'index (i,j).
-         */
-        SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType> block(int i, int j, int rows, int cols) const
-        {
-            return SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType>(*this, i, j, rows, cols);
-        }
-
-        /**
-         * Calcule l'inverse de la matrice
-         */
-        Matrix inverse() const
-        {
-            // Do nothing.
-            return *this;
-        }
-
-        /**
-         * Retourne la transposée de la matrice
-         */
-        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
-        Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage> transpose() const
-        {
-            // TODO calcule et retourne la transposée de la matrice.
-
-            return  Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage>(); // pas bon, à changer
-        }
-
-        /**
-         * Affecte l'identité à la matrice
-         */
-        inline void setIdentity()
-        {
-            // TODO affecter la valeur 0.0 partour, sauf sur la diagonale principale où c'est 1.0..
-            //      Votre implémentation devrait aussi fonctionner pour des matrices qui ne sont pas carrées.
-        }
-
-    };
-
-    /**
-     * Classe Matrix spécialisée pour un stockage par lignes
-     */
-    template <typename _Scalar, int _RowsAtCompile, int _ColsAtCompile>
-    class Matrix< _Scalar, _RowsAtCompile, _ColsAtCompile, RowStorage> : public MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile> {
-
-    public:
-        /**
-         * Constructeur par défaut
-         */
-        Matrix() : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>() { }
-
-        /**
-         * Constructeur de copie
-         */
-        Matrix(const Matrix& other) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(other) { }
-
-        /**
-         * Constructeur avec spécification du nombre de ligne et de colonnes
-         */
-        explicit Matrix(int rows, int cols) : MatrixBase<_Scalar, _RowsAtCompile, _ColsAtCompile>(rows, cols) { }
-
-        /**
-         * Destructeur
-         */
-        ~Matrix() { }
-
-        /**
-         * Opérateur de copie à partir d'une sous-matrice.
-         *
-         * Exemple :
-         *    Matrix<...> A(...);
-         *    Matrix<...> B(...);
-         *    B = A.block(i,j,m,n);
-         */
-        template<typename _OtherScalar, int OtherRows, int _OtherCols, int _OtherStorage>
-        Matrix& operator= (const SubMatrix<_OtherScalar, OtherRows, _OtherCols, _OtherStorage>& submatrix)
-        {
-            // TODO copier les données de la sous-matrice.
-            //   Note : si les dimensions ne correspondent pas, la matrice doit être redimensionnée.
-            //   Vous pouvez présumer qu'il s'agit d'un stockage par lignes.
-            return *this;
-        }
-
-        /**
-         * Accesseur à une entrée de la matrice (lecture seule)
-         */
-        _Scalar operator()(int i, int j) const
-        {
-            // TODO implementer
-            return 0.0;
-        }
-
-        /**
-         * Accesseur à une entrée de la matrice (lecture ou écriture)
-         */
-        _Scalar& operator()(int i, int j)
-        {
-            // TODO implementer
-            _Scalar x = 0.0;
-            return x;
-        }
-
-        /**
-         * Crée une sous-matrice pour un block de taille (rows, cols) à partir de l'index (i,j).
-         */
-        SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, RowStorage> block(int i, int j, int rows, int cols) const {
-            return SubMatrix<_Scalar, _RowsAtCompile, _ColsAtCompile, RowStorage>(*this, i, j, rows, cols);
-        }
-
-        /**
-         * Calcule l'inverse de la matrice
-         */
-        Matrix inverse() const
-        {
-            // Do nothing.
-            return *this;
-        }
-
-        /**
-         * Retourne la transposée de la matrice
-         */
-        Matrix<_Scalar, _ColsAtCompile, _RowsAtCompile, ColumnStorage> transpose() const
-        {
-            // TODO calcule et retourne la transposée de la matrice.
-            //    Optimisez cette fonction en tenant compte du type de stockage utilisé.
-
-            return Matrix<_Scalar, _ColsAtCompile, _RowsAtCompile, ColumnStorage>();
-        }
-
-        /**
-         * Affecte l'identité à la matrice
-         */
-        inline void setIdentity()
-        {
-            // TODO affecter la valeur 0.0 partour, sauf sur la diagonale principale où c'est 1.0..
-            //      Votre implémentation devrait aussi fonctionner pour des matrices qui ne sont pas carrées.
-        }
-
-    };
-
-    /**
-     * Classe pour accéder à une sous-matrice.
-     *
-     * Un sous-matrice ne copie pas les données. Au lieu de cela, elle conserve une
-     * référence à la matrice originale.
-     */
-    template <typename _Scalar, int _RowsAtCompile, int _ColsAtCompile, int _StorageType>
-    class SubMatrix
-    {
-    private:
-        // Référence à la matrice originale
-        Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType>& m_matrix;
-
-        // Constructeur par défaut (privé)
-        SubMatrix() {}
-
-        // (i,j) est le coin supérieur gauche de la sous-matrice
-        int m_i;        // Décalage en ligne 
-        int m_j;        // Décalage en colonne
-
-        // la sous-matrice est de dimension : m_rows x m_cols
-        int m_rows;     // Hauteur de la sous-matrice (nombre de lignes)
-        int m_cols;     // Largeur de la sous-matrice (nombre de colonnes)
-
-    public:
-
-        /**
-         * Constructeur à partir d'une référence en lecture seule à une matrice.
-         */
-        SubMatrix(const Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType>& _matrix, int _i, int _j, int _rows, int _cols) :
-            m_matrix(const_cast<Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType>&>(_matrix)),
-            m_i(_i), m_j(_j), m_rows(_rows), m_cols(_cols)
-        {
-        }
-
-        /**
-         * Constructeur à partir d'une référence en lecture et écriture à une matrice.
-         */
-        explicit SubMatrix(Matrix<_Scalar, _RowsAtCompile, _ColsAtCompile, _StorageType>& _matrix, int _i, int _j, int _rows, int _cols) :
-            m_matrix(_matrix),
-            m_i(_i), m_j(_j), m_rows(_rows), m_cols(_cols)
-        {
-
-        }
-
-        /**
-         * Constructeur de copie
-         */
-        SubMatrix(const SubMatrix& other) :
-            m_matrix(other.m_matrix),
-            m_i(other.m_i), m_j(other.m_j), m_rows(other.m_rows), m_cols(other.m_cols)
-        {
-        }
-
-        /**
-         * Destructeur
-         */
-        ~SubMatrix() { }
-
-        /**
-         * Opérateur de copie (à partir d'une matrice)
-         *
-         * Copies toutes les entrées de la matrice dans la sous-matrice.
-         *
-         * Note : la taille de la matrice doit correspondre à la taille de la
-         * sous-matrice.
-         */
-        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
-        SubMatrix& operator= (const Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage>& matrix)
-        {
-            // TODO Cpopie les valeurs de la matrice dans la sous-matrice.
-            //      Note les dimensions de la matrice doivent correspondre à celle de
-            //      la sous-matrice.
-            return *this;
-        }
-
-        /**
-         * Accesseur aux entrées de la sous-matrice (lecture seule)
-         *
-         * Note : il faut s'assurer que les indices respectent la taille de la
-         * sous-matrice
-         */
-        _Scalar operator()(int i, int j) const
-        {
-            // TODO implémenter
-            return 0.0;
-        }
-
-        /**
-         * Accesseur aux entrées de la sous-matrice (lecture et écriture)
-         *
-         * Note : il faut s'assurer que les indices respectent la taille de la
-         * sous-matrice
-         */
-        _Scalar& operator()(int i, int j)
-        {
-            // TODO implémenter
-            _Scalar x = 0.0;
-            return x;
-        }
-
-        /**
-         * Retourne la transposée de la sous-matrice sous la forme d'une matrice.
-         */
-        template<typename _OtherScalar, int _OtherRows, int _OtherCols, int _OtherStorage>
-        Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage> transpose() const
-        {
-            // TODO implémenter
-            return Matrix<_OtherScalar, _OtherRows, _OtherCols, _OtherStorage>();
-        }
-
-        inline int rows() const { return m_rows; }
-        inline int cols() const { return m_cols; }
-
-    };
-
-}

labo01/src/Operators.h

@@ -1,179 +0,0 @@
-#pragma once
-
-/**
- * @file Operators.h
- *
- * @brief Opérateurs arithmétiques pour les matrices et les vecteurs.
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include "Matrix.h"
-#include "Vector.h"
-
- /**
-  * Implémentation de divers opérateurs arithmétiques pour les matrices et les vecteurs.
-  */
-namespace gti320 {
-
-    /**
-     * Multiplication : Matrice * Matrice (générique)
-     */
-    template <typename _Scalar, int RowsA, int ColsA, int StorageA, int RowsB, int ColsB, int StorageB>
-    Matrix<_Scalar, RowsA, ColsB> operator*(const Matrix<_Scalar, RowsA, ColsA, StorageA>& A, const Matrix<_Scalar, RowsB, ColsB, StorageB>& B)
-    {
-        // TODO implémenter
-        return Matrix<_Scalar, RowsA, ColsB>();
-    }
-
-    /**
-     * Multiplication : Matrice (colonne) * Matrice (ligne)
-     *
-     * Spécialisation de l'opérateur de multiplication pour le cas où les matrices
-     * ont un stockage à taille dynamique et où la matrice de gauche utilise un
-     * stockage par colonnes et celle de droite un stockage par lignes.
-     */
-    template <typename _Scalar>
-    Matrix<_Scalar, Dynamic, Dynamic> operator*(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& A, const Matrix<_Scalar, Dynamic, Dynamic, RowStorage>& B)
-    {
-        // TODO : implémenter
-        return Matrix<_Scalar, Dynamic, Dynamic>();
-    }
-
-    /**
-     * Multiplication : Matrice (ligne) * Matrice (colonne)
-     *
-     * Spécialisation de l'opérateur de multiplication pour le cas où les matrices
-     * ont un stockage à taille dynamique et où la matrice de gauche utilise un
-     * stockage par lignes et celle de droite un stockage par colonnes.
-     */
-    template <typename _Scalar>
-    Matrix<_Scalar, Dynamic, Dynamic> operator*(const Matrix<_Scalar, Dynamic, Dynamic, RowStorage>& A, const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& B)
-    {
-        // TODO : implémenter
-        return Matrix<_Scalar, Dynamic, Dynamic>();
-    }
-
-
-    /**
-     * Addition : Matrice + Matrice (générique)
-     */
-    template <typename _Scalar, int Rows, int Cols, int StorageA, int StorageB>
-    Matrix<_Scalar, Rows, Cols> operator+(const Matrix<_Scalar, Rows, Cols, StorageA>& A, const Matrix<_Scalar, Rows, Cols, StorageB>& B)
-    {
-        // TODO : implémenter
-        return Matrix<_Scalar, Rows, Cols>();
-    }
-
-    /**
-     * Addition : Matrice (colonne) + Matrice (colonne)
-     *
-     * Spécialisation de l'opérateur d'addition pour le cas où les deux matrices
-     * sont stockées par colonnes.
-     */
-    template <typename _Scalar>
-    Matrix<_Scalar, Dynamic, Dynamic> operator+(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& A, const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& B)
-    {
-        // TODO : implémenter
-        return Matrix<_Scalar, Dynamic, Dynamic>();
-    }
-
-    /**
-     * Addition : Matrice (ligne) + Matrice (ligne)
-     *
-     * Spécialisation de l'opérateur d'addition pour le cas où les deux matrices
-     * sont stockées par lignes.
-     */
-    template <typename _Scalar>
-    Matrix<_Scalar, Dynamic, Dynamic, RowStorage> operator+(const Matrix<_Scalar, Dynamic, Dynamic, RowStorage>& A, const Matrix<_Scalar, Dynamic, Dynamic, RowStorage>& B)
-    {
-        // TODO : implémenter
-        return Matrix<_Scalar, Dynamic, Dynamic, RowStorage>();
-    }
-
-    /**
-     * Multiplication  : Scalaire * Matrice (colonne)
-     *
-     * Spécialisation de l'opérateur de multiplication par un scalaire pour le
-     * cas d'une matrice stockée par colonnes.
-     */
-    template <typename _Scalar, int _Rows, int _Cols>
-    Matrix<_Scalar, _Rows, _Cols, ColumnStorage> operator*(const _Scalar& a, const Matrix<_Scalar, _Rows, _Cols, ColumnStorage>& A)
-    {
-        // TODO : implémenter
-        return Matrix<_Scalar, Dynamic, Dynamic>();
-    }
-
-    /**
-     * Multiplication  : Scalaire * Matrice (ligne)
-     *
-     * Spécialisation de l'opérateur de multiplication par un scalaire pour le
-     * cas d'une matrice stockée par lignes.
-     */
-    template <typename _Scalar, int _Rows, int _Cols>
-    Matrix<_Scalar, _Rows, _Cols, RowStorage> operator*(const _Scalar& a, const Matrix<_Scalar, _Rows, _Cols, RowStorage>& A)
-    {
-        // TODO : implémenter
-        return Matrix<_Scalar, Dynamic, Dynamic, RowStorage>();
-    }
-
-    /**
-     * Multiplication : Matrice (ligne) * Vecteur
-     *
-     * Spécialisation de l'opérateur de multiplication matrice*vecteur pour le
-     * cas où la matrice est représentée par lignes.
-     */
-    template <typename _Scalar, int _Rows, int _Cols>
-    Vector<_Scalar, _Rows> operator*(const Matrix<_Scalar, _Rows, _Cols, RowStorage>& A, const Vector<_Scalar, _Cols>& v)
-    {
-        // TODO : implémenter
-        return Vector<_Scalar, _Rows>();
-    }
-
-    /**
-     * Multiplication : Matrice (colonne) * Vecteur
-     *
-     * Spécialisation de l'opérateur de multiplication matrice*vecteur pour le
-     * cas où la matrice est représentée par colonnes.
-     */
-    template <typename _Scalar, int _Rows, int _Cols>
-    Vector<_Scalar, _Rows> operator*(const Matrix<_Scalar, _Rows, _Cols, ColumnStorage>& A, const Vector<_Scalar, _Cols>& v)
-    {
-        // TODO : implémenter
-        return Vector<_Scalar, _Rows>();
-    }
-
-    /**
-     * Multiplication : Scalaire * Vecteur
-     */
-    template <typename _Scalar, int _Rows>
-    Vector<_Scalar, _Rows> operator*(const _Scalar& a, const Vector<_Scalar, _Rows>& v)
-    {
-        // TODO : implémenter
-        return Vector<_Scalar, _Rows>();
-    }
-
-
-    /**
-     * Addition : Vecteur + Vecteur
-     */
-    template <typename _Scalar, int _RowsA, int _RowsB>
-    Vector<_Scalar, _RowsA> operator+(const Vector<_Scalar, _RowsA>& a, const Vector<_Scalar, _RowsB>& b)
-    {
-        // TODO : implémenter
-        return Vector<_Scalar, _RowsA>();
-    }
-
-    /**
-     * Soustraction : Vecteur - Vecteur
-     */
-    template <typename _Scalar, int _RowsA, int _RowsB>
-    Vector<_Scalar, _RowsA> operator-(const Vector<_Scalar, _RowsA>& a, const Vector<_Scalar, _RowsB>& b)
-    {
-        // TODO : implémenter
-        return Vector<_Scalar, _RowsA>();
-    }
-}

labo01/src/Vector.h

@@ -1,104 +0,0 @@
-#pragma once
-
-/**
- * @file Vector.h
- *
- * @brief Implémentation de vecteurs simples
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include <cmath>
-#include "MatrixBase.h"
-
-namespace gti320 {
-
-    /**
-     * Classe vecteur générique.
-     *
-     * Cette classe réutilise la classe `MatrixBase` et ses spécialisations de
-     * templates pour les manipulation bas niveau.
-     */
-    template <typename _Scalar = double, int _Rows = Dynamic>
-    class Vector : public MatrixBase<_Scalar, _Rows, 1> {
-    public:
-
-        /**
-         * Constructeur par défaut
-         */
-        Vector() : MatrixBase<_Scalar, _Rows, 1>() { }
-
-        /**
-         * Contructeur à partir d'un taille (rows).
-         */
-        explicit Vector(int rows) : MatrixBase<_Scalar, _Rows, 1>(rows, 1) { }
-
-        /**
-         * Constructeur de copie
-         */
-        Vector(const Vector& other) : MatrixBase<_Scalar, _Rows, 1>(other) { }
-
-        /**
-         * Destructeur
-         */
-        ~Vector() { }
-
-        /**
-         * Opérateur de copie
-         */
-        Vector& operator=(const Vector& other)
-        {
-            // TODO implémenter
-            this->m_storage = other.m_storage;
-            return *this;
-        }
-
-        /**
-         * Accesseur à une entrée du vecteur (lecture seule)
-         */
-        _Scalar operator()(int i) const
-        {
-            // TODO implémenter
-            return (double)i;
-        }
-
-        /**
-         * Accesseur à une entrée du vecteur (lecture et écriture)
-         */
-        _Scalar& operator()(int i)
-        {
-            // TODO implémenter
-            _Scalar x = (double)i;
-            return x;
-        }
-
-        /**
-         * Modifie le nombre de lignes du vecteur
-         */
-        void resize(int _rows)
-        {
-            MatrixBase<_Scalar, _Rows, 1>::resize(_rows, 1);
-        }
-
-        /**
-         * Produit scalaire de *this et other.
-         */
-        inline _Scalar dot(const Vector& other) const
-        {
-            // TODO implémenter
-            return 0.0;
-        }
-
-        /**
-         * Retourne la norme euclidienne du vecteur
-         */
-        inline _Scalar norm() const
-        {
-            // TODO implémenter
-            return 0.0;
-        }
-    };
-}

labo01/tests/Tests1a.cpp

@@ -1,398 +0,0 @@
-/**
- * @file Tests1a.cpp
- *
- * @brief Tests unitaires de la partie 1b
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include "Matrix.h"
-#include "Vector.h"
-
-#include <gtest/gtest.h>
-#include <chrono>
-
-using namespace gti320;
-
-TEST(TestLabo1a, DotAndNorm) {
-    {
-        Vector<double,3> u; u(0) = 81.74804972455644; u(1) = -74.09304417781078; u(2) = -91.38202093790602;
-        Vector<double,3> v; v(0) = 81.1462118959985; v(1) = 29.763442976156085; v(2) = 39.00787276684184;
-        EXPECT_NEAR(u.dot(v), 863.662223794679, 1e-4) << "(u=(81.74804972455644, -74.09304417781078, -91.38202093790602), v= (81.1462118959985, 29.763442976156085, 39.00787276684184))";
-        EXPECT_NEAR(u.norm(), 143.25919370148452, 1e-4) << "(u=(81.74804972455644, -74.09304417781078, -91.38202093790602))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 94.82712892764025, 1e-4) << "u=(81.74804972455644, -74.09304417781078, -91.38202093790602)";
-    }
-    {
-        Vector<double,3> u; u(0) = 13.087936541928485; u(1) = -26.541934227528046; u(2) = -48.13859302157102;
-        Vector<double,3> v; v(0) = -66.28108277028942; v(1) = 11.919000480625243; v(2) = -96.21367167640467;
-        EXPECT_NEAR(u.dot(v), 3447.7548518990116, 1e-4) << "(u=(13.087936541928485, -26.541934227528046, -48.13859302157102), v= (-66.28108277028942, 11.919000480625243, -96.21367167640467))";
-        EXPECT_NEAR(u.norm(), 56.50745520336602, 1e-4) << "(u=(13.087936541928485, -26.541934227528046, -48.13859302157102))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 117.44068768154457, 1e-4) << "u=(13.087936541928485, -26.541934227528046, -48.13859302157102)";
-    }
-    {
-        Vector<double,3> u; u(0) = -79.56972852806103; u(1) = -64.04761691711548; u(2) = 75.76398532227091;
-        Vector<double,3> v; v(0) = 68.1521534060019; v(1) = -38.02548546805114; v(2) = 44.66242384133133;
-        EXPECT_NEAR(u.dot(v), 396.3966055984092, 1e-4) << "(u=(-79.56972852806103, -64.04761691711548, 75.76398532227091), v= (68.1521534060019, -38.02548546805114, 44.66242384133133))";
-        EXPECT_NEAR(u.norm(), 127.17554954748255, 1e-4) << "(u=(-79.56972852806103, -64.04761691711548, 75.76398532227091))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 89.91877258025103, 1e-4) << "u=(-79.56972852806103, -64.04761691711548, 75.76398532227091)";
-    }
-    {
-        Vector<double,3> u; u(0) = -27.829925590795995; u(1) = 97.52374799957443; u(2) = -71.29949583706774;
-        Vector<double,3> v; v(0) = 15.413123773966177; v(1) = -25.9678191712148; v(2) = -70.46329734352945;
-        EXPECT_NEAR(u.dot(v), 2062.5724349077673, 1e-4) << "(u=(-27.829925590795995, 97.52374799957443, -71.29949583706774), v= (15.413123773966177, -25.9678191712148, -70.46329734352945))";
-        EXPECT_NEAR(u.norm(), 123.97178827819569, 1e-4) << "(u=(-27.829925590795995, 97.52374799957443, -71.29949583706774))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 76.66138721353245, 1e-4) << "u=(-27.829925590795995, 97.52374799957443, -71.29949583706774)";
-    }
-    {
-        Vector<double,3> u; u(0) = 46.94969707999718; u(1) = 92.7292896206543; u(2) = 61.3890905084975;
-        Vector<double,3> v; v(0) = 91.40236621394195; v(1) = -23.911909695536067; v(2) = -66.18706904017846;
-        EXPECT_NEAR(u.dot(v), -1989.1849652004407, 1e-4) << "(u=(46.94969707999718, 92.7292896206543, 61.3890905084975), v= (91.40236621394195, -23.911909695536067, -66.18706904017846))";
-        EXPECT_NEAR(u.norm(), 120.71294728783312, 1e-4) << "(u=(46.94969707999718, 92.7292896206543, 61.3890905084975))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 115.3555377211011, 1e-4) << "u=(46.94969707999718, 92.7292896206543, 61.3890905084975)";
-    }
-    {
-        Vector<double,3> u; u(0) = 9.836648455487577; u(1) = 27.373779624683323; u(2) = 33.47163213808042;
-        Vector<double,3> v; v(0) = -17.904556153169437; v(1) = -10.39159035574184; v(2) = 36.045191146582226;
-        EXPECT_NEAR(u.dot(v), 745.913449426867, 1e-4) << "(u=(9.836648455487577, 27.373779624683323, 33.47163213808042), v= (-17.904556153169437, -10.39159035574184, 36.045191146582226))";
-        EXPECT_NEAR(u.norm(), 44.344488065198725, 1e-4) << "(u=(9.836648455487577, 27.373779624683323, 33.47163213808042))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 41.566983123113395, 1e-4) << "u=(9.836648455487577, 27.373779624683323, 33.47163213808042)";
-    }
-    {
-        Vector<double,3> u; u(0) = 77.34524968701723; u(1) = -86.53838659054598; u(2) = 52.511893628372974;
-        Vector<double,3> v; v(0) = 39.390038592378005; v(1) = -53.13512176642368; v(2) = 60.23922457130902;
-        EXPECT_NEAR(u.dot(v), 10808.13583201148, 1e-4) << "(u=(77.34524968701723, -86.53838659054598, 52.511893628372974), v= (39.390038592378005, -53.13512176642368, 60.23922457130902))";
-        EXPECT_NEAR(u.norm(), 127.39183245121873, 1e-4) << "(u=(77.34524968701723, -86.53838659054598, 52.511893628372974))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 89.4632912562147, 1e-4) << "u=(77.34524968701723, -86.53838659054598, 52.511893628372974)";
-    }
-    {
-        Vector<double,3> u; u(0) = 72.58764125601218; u(1) = 13.004884623782146; u(2) = 6.688195585248067;
-        Vector<double,3> v; v(0) = -41.68110389567836; v(1) = 65.83906651972734; v(2) = 64.45916748876758;
-        EXPECT_NEAR(u.dot(v), -1738.1880334803595, 1e-4) << "(u=(72.58764125601218, 13.004884623782146, 6.688195585248067), v= (-41.68110389567836, 65.83906651972734, 64.45916748876758))";
-        EXPECT_NEAR(u.norm(), 74.04609812391155, 1e-4) << "(u=(72.58764125601218, 13.004884623782146, 6.688195585248067))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 101.12903329655835, 1e-4) << "u=(72.58764125601218, 13.004884623782146, 6.688195585248067)";
-    }
-    {
-        Vector<double,3> u; u(0) = 44.123038783178856; u(1) = 59.032307289173275; u(2) = -96.45920641599031;
-        Vector<double,3> v; v(0) = -23.433056105942327; v(1) = -95.82287577132844; v(2) = -87.71884659805113;
-        EXPECT_NEAR(u.dot(v), 1770.7072393377675, 1e-4) << "(u=(44.123038783178856, 59.032307289173275, -96.45920641599031), v= (-23.433056105942327, -95.82287577132844, -87.71884659805113))";
-        EXPECT_NEAR(u.norm(), 121.39206875965131, 1e-4) << "(u=(44.123038783178856, 59.032307289173275, -96.45920641599031))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 132.006544110677, 1e-4) << "u=(44.123038783178856, 59.032307289173275, -96.45920641599031)";
-    }
-    {
-        Vector<double,3> u; u(0) = -7.594864170286073; u(1) = -92.12702535387345; u(2) = 10.61833019724412;
-        Vector<double,3> v; v(0) = -57.88532008253067; v(1) = -61.95047768934079; v(2) = -50.9801175870505;
-        EXPECT_NEAR(u.dot(v), 5605.620650217189, 1e-4) << "(u=(-7.594864170286073, -92.12702535387345, 10.61833019724412), v= (-57.88532008253067, -61.95047768934079, -50.9801175870505))";
-        EXPECT_NEAR(u.norm(), 93.04740565161417, 1e-4) << "(u=(-7.594864170286073, -92.12702535387345, 10.61833019724412))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 98.9320188623685, 1e-4) << "u=(-7.594864170286073, -92.12702535387345, 10.61833019724412)";
-    }
-    {
-        Vector<double,3> u; u(0) = 28.01623276831728; u(1) = -35.47111447521442; u(2) = -80.09707278049716;
-        Vector<double,3> v; v(0) = 62.23810927998369; v(1) = -69.45561657190204; v(2) = -17.998932897185853;
-        EXPECT_NEAR(u.dot(v), 5649.007321253708, 1e-4) << "(u=(28.01623276831728, -35.47111447521442, -80.09707278049716), v= (62.23810927998369, -69.45561657190204, -17.998932897185853))";
-        EXPECT_NEAR(u.norm(), 91.97092110361056, 1e-4) << "(u=(28.01623276831728, -35.47111447521442, -80.09707278049716))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 94.98224310663369, 1e-4) << "u=(28.01623276831728, -35.47111447521442, -80.09707278049716)";
-    }
-    {
-        Vector<double,3> u; u(0) = 17.056114318144637; u(1) = -47.87236586884536; u(2) = -66.233990996889;
-        Vector<double,3> v; v(0) = -16.5274983107699; v(1) = -61.98159750757431; v(2) = -95.73085862430288;
-        EXPECT_NEAR(u.dot(v), 9025.947640683207, 1e-4) << "(u=(17.056114318144637, -47.87236586884536, -66.233990996889), v= (-16.5274983107699, -61.98159750757431, -95.73085862430288))";
-        EXPECT_NEAR(u.norm(), 83.48422613218729, 1e-4) << "(u=(17.056114318144637, -47.87236586884536, -66.233990996889))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 115.23573197124973, 1e-4) << "u=(17.056114318144637, -47.87236586884536, -66.233990996889)";
-    }
-    {
-        Vector<double,3> u; u(0) = 53.68514451573557; u(1) = 40.487633535881685; u(2) = -34.39102876903675;
-        Vector<double,3> v; v(0) = 5.723467714467617; v(1) = -11.984939376053532; v(2) = 71.57117734380691;
-        EXPECT_NEAR(u.dot(v), -2639.3830610897676, 1e-4) << "(u=(53.68514451573557, 40.487633535881685, -34.39102876903675), v= (5.723467714467617, -11.984939376053532, 71.57117734380691))";
-        EXPECT_NEAR(u.norm(), 75.52540016977055, 1e-4) << "(u=(53.68514451573557, 40.487633535881685, -34.39102876903675))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 72.79306478576713, 1e-4) << "u=(53.68514451573557, 40.487633535881685, -34.39102876903675)";
-    }
-    {
-        Vector<double,3> u; u(0) = -19.41880304735801; u(1) = 80.15388147841654; u(2) = 18.762371448279836;
-        Vector<double,3> v; v(0) = 56.544323419883455; v(1) = 37.75922627098413; v(2) = -45.767718603712495;
-        EXPECT_NEAR(u.dot(v), 1069.8145305211428, 1e-4) << "(u=(-19.41880304735801, 80.15388147841654, 18.762371448279836), v= (56.544323419883455, 37.75922627098413, -45.767718603712495))";
-        EXPECT_NEAR(u.norm(), 84.57991020455952, 1e-4) << "(u=(-19.41880304735801, 80.15388147841654, 18.762371448279836))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 81.96159921441485, 1e-4) << "u=(-19.41880304735801, 80.15388147841654, 18.762371448279836)";
-    }
-    {
-        Vector<double,3> u; u(0) = 14.53101118226931; u(1) = -87.12123268098249; u(2) = -12.733552633138217;
-        Vector<double,3> v; v(0) = -96.36370344463752; v(1) = -81.8797705320039; v(2) = -25.593956628649764;
-        EXPECT_NEAR(u.dot(v), 6059.106481886422, 1e-4) << "(u=(14.53101118226931, -87.12123268098249, -12.733552633138217), v= (-96.36370344463752, -81.8797705320039, -25.593956628649764))";
-        EXPECT_NEAR(u.norm(), 89.23790020217884, 1e-4) << "(u=(14.53101118226931, -87.12123268098249, -12.733552633138217))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 129.01670736710366, 1e-4) << "u=(14.53101118226931, -87.12123268098249, -12.733552633138217)";
-    }
-    {
-        Vector<double,3> u; u(0) = -68.15128360202914; u(1) = -35.22142681790423; u(2) = -80.20820520692742;
-        Vector<double,3> v; v(0) = -71.59083714955358; v(1) = -22.11220916087268; v(2) = -41.412146034892785;
-        EXPECT_NEAR(u.dot(v), 8979.424909853704, 1e-4) << "(u=(-68.15128360202914, -35.22142681790423, -80.20820520692742), v= (-71.59083714955358, -22.11220916087268, -41.412146034892785))";
-        EXPECT_NEAR(u.norm(), 110.98874963801407, 1e-4) << "(u=(-68.15128360202914, -35.22142681790423, -80.20820520692742))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 85.61053438078382, 1e-4) << "u=(-68.15128360202914, -35.22142681790423, -80.20820520692742)";
-    }
-    {
-        Vector<double,3> u; u(0) = 32.15880264107108; u(1) = -27.044272757999167; u(2) = -21.93384224298498;
-        Vector<double,3> v; v(0) = 94.98651607465004; v(1) = 96.25601423462368; v(2) = -4.364871517549744;
-        EXPECT_NEAR(u.dot(v), 547.2171237254174, 1e-4) << "(u=(32.15880264107108, -27.044272757999167, -21.93384224298498), v= (94.98651607465004, 96.25601423462368, -4.364871517549744))";
-        EXPECT_NEAR(u.norm(), 47.399100327501664, 1e-4) << "(u=(32.15880264107108, -27.044272757999167, -21.93384224298498))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 135.3022934606082, 1e-4) << "u=(32.15880264107108, -27.044272757999167, -21.93384224298498)";
-    }
-    {
-        Vector<double,3> u; u(0) = -38.55884639660741; u(1) = -32.44768663392304; u(2) = -86.51014461651837;
-        Vector<double,3> v; v(0) = -32.975270310868936; v(1) = -48.59524328395069; v(2) = -92.16520328196806;
-        EXPECT_NEAR(u.dot(v), 10821.51667331416, 1e-4) << "(u=(-38.55884639660741, -32.44768663392304, -86.51014461651837), v= (-32.975270310868936, -48.59524328395069, -92.16520328196806))";
-        EXPECT_NEAR(u.norm(), 100.1181408382185, 1e-4) << "(u=(-38.55884639660741, -32.44768663392304, -86.51014461651837))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 109.2853641523316, 1e-4) << "u=(-38.55884639660741, -32.44768663392304, -86.51014461651837)";
-    }
-    {
-        Vector<double,3> u; u(0) = -93.94403064987613; u(1) = -22.806019440495206; u(2) = -6.186803379242534;
-        Vector<double,3> v; v(0) = 99.58719003758503; v(1) = 11.426147026760503; v(2) = 89.17338366240898;
-        EXPECT_NEAR(u.dot(v), -10167.905155829267, 1e-4) << "(u=(-93.94403064987613, -22.806019440495206, -6.186803379242534), v= (99.58719003758503, 11.426147026760503, 89.17338366240898))";
-        EXPECT_NEAR(u.norm(), 96.87038739221866, 1e-4) << "(u=(-93.94403064987613, -22.806019440495206, -6.186803379242534))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 134.1642933468604, 1e-4) << "u=(-93.94403064987613, -22.806019440495206, -6.186803379242534)";
-    }
-    {
-        Vector<double,3> u; u(0) = 49.70172009239852; u(1) = 35.23095832735339; u(2) = -95.645812626239;
-        Vector<double,3> v; v(0) = -26.17330847186834; v(1) = -13.328976428902024; v(2) = 43.288466758804674;
-        EXPECT_NEAR(u.dot(v), -5910.811645163534, 1e-4) << "(u=(49.70172009239852, 35.23095832735339, -95.645812626239), v= (-26.17330847186834, -13.328976428902024, 43.288466758804674))";
-        EXPECT_NEAR(u.norm(), 113.40018905513546, 1e-4) << "(u=(49.70172009239852, 35.23095832735339, -95.645812626239))";
-        u = v;
-        EXPECT_NEAR(u.norm(), 52.31247502588592, 1e-4) << "u=(49.70172009239852, 35.23095832735339, -95.645812626239)";
-    }
-}
-
-// Test les matrice avec redimensionnement dynamique
-TEST(TestLabo1a, StaticMatrixTests)
-{
-    // Crée une matrice ŕ taille fixe
-    Matrix<double, 3, 5> M;
-    EXPECT_EQ(M.cols(), 5);
-    EXPECT_EQ(M.rows(), 3);
-
-    // Redimensionne la matrice (la taille ne doit pas changer). 
-    M.resize(100, 1000);
-    EXPECT_EQ(M.cols(), 5);
-    EXPECT_EQ(M.rows(), 3);
-
-    // Test - stockage par colonnes
-    Matrix<double, 100, 99, ColumnStorage> ColM;
-    ColM.setZero();
-    ColM(0, 0) = 1.0;
-    ColM(90, 17) = 99.0;
-    ColM(10, 33) = 7.2;
-    EXPECT_EQ(ColM(0, 0), 1.0);
-    EXPECT_EQ(ColM(90, 17), 99.0);
-    EXPECT_EQ(ColM(10, 33), 7.2);
-
-    // Test - stockage par lignes
-    Matrix<double, 5, 4, RowStorage> RowM;
-    RowM.setZero();
-    RowM(0, 0) = 2.1;
-    RowM(3, 3) = -0.2;
-    RowM(4, 3) = 1.2;
-    EXPECT_EQ(RowM.rows(), 5);
-    EXPECT_EQ(RowM.cols(), 4);
-    EXPECT_DOUBLE_EQ(RowM(0, 0), 2.1);
-    EXPECT_DOUBLE_EQ(RowM(3, 3), -0.2);
-    EXPECT_DOUBLE_EQ(RowM(4, 3), 1.2);
-    EXPECT_DOUBLE_EQ(RowM(3, 2), 0.0);
-
-    // Transposée
-    const auto RowMT = RowM.transpose();
-    EXPECT_EQ(RowMT.rows(), 4);
-    EXPECT_EQ(RowMT.cols(), 5);
-    EXPECT_DOUBLE_EQ(RowMT(0, 0), 2.1);
-    EXPECT_DOUBLE_EQ(RowMT(3, 3), -0.2);
-    EXPECT_DOUBLE_EQ(RowMT(3, 4), 1.2);
-    EXPECT_DOUBLE_EQ(RowMT(2, 3), 0.0);
-}
-
-
-// Test les matrice avec redimensionnement dynamique
-TEST(TestLabo1a, DynamicMatrixTests)
-{
-    // Crée une matrice ŕ taille dynamique
-    // (note : les valeurs par défaut du patron de la classe `Matrix` mettent le
-    // le nombre de ligne et de colonnes ŕ `Dynamic`)
-    Matrix<double> M(3, 5);
-    EXPECT_EQ(M.cols(), 5);
-    EXPECT_EQ(M.rows(), 3);
-
-    // Redimensionne la matrice
-    M.resize(100, 1000);
-    EXPECT_EQ(M.cols(), 1000);
-    EXPECT_EQ(M.rows(), 100);
-
-    // Test - stockage par colonnes
-    Matrix<double, Dynamic, Dynamic, ColumnStorage> ColM(100, 100);
-    ColM.setZero();
-    ColM(0, 0) = 1.0;
-    ColM(99, 99) = 99.0;
-    ColM(10, 33) = 5.0;
-    EXPECT_EQ(ColM(0, 0), 1.0);
-    EXPECT_EQ(ColM(10, 33), 5.0);
-    EXPECT_EQ(ColM(99, 99), 99.0);
-
-    // Test - stockage par lignes
-    Matrix<double, Dynamic, Dynamic, RowStorage> RowM(5, 4);
-    RowM.setZero();
-    RowM(0, 0) = 2.1;
-    RowM(3, 3) = -0.2;
-    RowM(4, 3) = 1.2;
-    EXPECT_EQ(RowM.rows(), 5);
-    EXPECT_EQ(RowM.cols(), 4);
-    EXPECT_DOUBLE_EQ(RowM(0, 0), 2.1);
-    EXPECT_DOUBLE_EQ(RowM(3, 3), -0.2);
-    EXPECT_DOUBLE_EQ(RowM(4, 3), 1.2);
-    EXPECT_DOUBLE_EQ(RowM(3, 2), 0.0);
-
-    // Transposée
-    const auto RowMT = RowM.transpose();
-    EXPECT_EQ(RowMT.rows(), 4);
-    EXPECT_EQ(RowMT.cols(), 5);
-    EXPECT_DOUBLE_EQ(RowMT(0, 0), 2.1);
-    EXPECT_DOUBLE_EQ(RowMT(3, 3), -0.2);
-    EXPECT_DOUBLE_EQ(RowMT(3, 4), 1.2);
-    EXPECT_DOUBLE_EQ(RowMT(2, 3), 0.0);
-}
-
-/**
- * Test pour les vecteurs ŕ taille dynamique
- */
-TEST(TestLabo1a, DynamicVectorSizeTest)
-{
-    Vector<double> v(5);
-    v.setZero();
-
-    EXPECT_EQ(v.rows(), 5);
-
-    v.resize(3);
-    EXPECT_EQ(v.rows(), 3);
-
-    v(0) = 1.0;
-    v(1) = 2.0;
-    v(2) = 3.0;
-
-    EXPECT_DOUBLE_EQ(v.norm(), 3.7416573867739413855837487323165);
-
-    Vector<double, Dynamic> v2(3);
-    v2.setZero();
-    v2(1) = 2.0;
-
-    EXPECT_DOUBLE_EQ(v2.dot(v), 4.0);
-    EXPECT_DOUBLE_EQ(v2(0), 0.0);
-    EXPECT_DOUBLE_EQ(v2(1), 2.0);
-    EXPECT_DOUBLE_EQ(v2(2), 0.0);
-}
-
-TEST(TestLabo1a, Transpose) {
-    {
-        Matrix<double, 3, -1, ColumnStorage> m; m.resize(3, 2);
-        m(0, 0) = 96.65562704596559; m(0, 1) = -5.374125981819006; m(1, 0) = 64.81364389648456; m(1, 1) = -69.97868420900502; m(2, 0) = -48.298014749653696; m(2, 1) = 81.5535983882881;
-        Matrix<double, -1, 3, RowStorage> mtr = m.transpose<double, -1, 3, RowStorage>();
-        EXPECT_DOUBLE_EQ(mtr(0, 0), 96.65562704596559); EXPECT_DOUBLE_EQ(mtr(0, 1), 64.81364389648456); EXPECT_DOUBLE_EQ(mtr(0, 2), -48.298014749653696); EXPECT_DOUBLE_EQ(mtr(1, 0), -5.374125981819006); EXPECT_DOUBLE_EQ(mtr(1, 1), -69.97868420900502); EXPECT_DOUBLE_EQ(mtr(1, 2), 81.5535983882881);
-        Matrix<double, -1, 3, ColumnStorage> mtc = m.transpose<double, -1, 3, ColumnStorage>();
-        EXPECT_DOUBLE_EQ(mtc(0, 0), 96.65562704596559); EXPECT_DOUBLE_EQ(mtc(0, 1), 64.81364389648456); EXPECT_DOUBLE_EQ(mtc(0, 2), -48.298014749653696); EXPECT_DOUBLE_EQ(mtc(1, 0), -5.374125981819006); EXPECT_DOUBLE_EQ(mtc(1, 1), -69.97868420900502); EXPECT_DOUBLE_EQ(mtc(1, 2), 81.5535983882881);
-    }
-    {
-        Matrix<double, 3, -1, ColumnStorage> m; m.resize(3, 11);
-        m(0, 0) = -93.11774348806081; m(0, 1) = -98.38480859022877; m(0, 2) = -70.06261616604155; m(0, 3) = 84.87535684986423; m(0, 4) = -99.9818642210925; m(0, 5) = -25.11185567441916; m(0, 6) = 8.85590979917103; m(0, 7) = 32.717509759851936; m(0, 8) = 12.677927494307738; m(0, 9) = -76.92757015087707; m(0, 10) = -80.99502606313347; m(1, 0) = -14.108330840223957; m(1, 1) = -94.81883611699344; m(1, 2) = -45.060719301725285; m(1, 3) = -41.383939879963094; m(1, 4) = 80.36741308691853; m(1, 5) = -87.50961508738959; m(1, 6) = -32.65290161505921; m(1, 7) = 18.529868291798238; m(1, 8) = -46.169755352790595; m(1, 9) = 83.67078184672366; m(1, 10) = -30.02053885691531; m(2, 0) = 5.8022044043901815; m(2, 1) = -39.507965223996266; m(2, 2) = 38.099939917456425; m(2, 3) = -11.891042873050296; m(2, 4) = 53.89070563872062; m(2, 5) = 23.280098882479578; m(2, 6) = -5.0318917624474295; m(2, 7) = 31.50255873280196; m(2, 8) = 22.629046207699318; m(2, 9) = 3.5102931218199416; m(2, 10) = -95.03021938861154;
-        Matrix<double, -1, 3, RowStorage> mtr = m.transpose<double, -1, 3, RowStorage>();
-        EXPECT_DOUBLE_EQ(mtr(0, 0), -93.11774348806081); EXPECT_DOUBLE_EQ(mtr(0, 1), -14.108330840223957); EXPECT_DOUBLE_EQ(mtr(0, 2), 5.8022044043901815); EXPECT_DOUBLE_EQ(mtr(1, 0), -98.38480859022877); EXPECT_DOUBLE_EQ(mtr(1, 1), -94.81883611699344); EXPECT_DOUBLE_EQ(mtr(1, 2), -39.507965223996266); EXPECT_DOUBLE_EQ(mtr(2, 0), -70.06261616604155); EXPECT_DOUBLE_EQ(mtr(2, 1), -45.060719301725285); EXPECT_DOUBLE_EQ(mtr(2, 2), 38.099939917456425); EXPECT_DOUBLE_EQ(mtr(3, 0), 84.87535684986423); EXPECT_DOUBLE_EQ(mtr(3, 1), -41.383939879963094); EXPECT_DOUBLE_EQ(mtr(3, 2), -11.891042873050296); EXPECT_DOUBLE_EQ(mtr(4, 0), -99.9818642210925); EXPECT_DOUBLE_EQ(mtr(4, 1), 80.36741308691853); EXPECT_DOUBLE_EQ(mtr(4, 2), 53.89070563872062); EXPECT_DOUBLE_EQ(mtr(5, 0), -25.11185567441916); EXPECT_DOUBLE_EQ(mtr(5, 1), -87.50961508738959); EXPECT_DOUBLE_EQ(mtr(5, 2), 23.280098882479578); EXPECT_DOUBLE_EQ(mtr(6, 0), 8.85590979917103); EXPECT_DOUBLE_EQ(mtr(6, 1), -32.65290161505921); EXPECT_DOUBLE_EQ(mtr(6, 2), -5.0318917624474295); EXPECT_DOUBLE_EQ(mtr(7, 0), 32.717509759851936); EXPECT_DOUBLE_EQ(mtr(7, 1), 18.529868291798238); EXPECT_DOUBLE_EQ(mtr(7, 2), 31.50255873280196); EXPECT_DOUBLE_EQ(mtr(8, 0), 12.677927494307738); EXPECT_DOUBLE_EQ(mtr(8, 1), -46.169755352790595); EXPECT_DOUBLE_EQ(mtr(8, 2), 22.629046207699318); EXPECT_DOUBLE_EQ(mtr(9, 0), -76.92757015087707); EXPECT_DOUBLE_EQ(mtr(9, 1), 83.67078184672366); EXPECT_DOUBLE_EQ(mtr(9, 2), 3.5102931218199416); EXPECT_DOUBLE_EQ(mtr(10, 0), -80.99502606313347); EXPECT_DOUBLE_EQ(mtr(10, 1), -30.02053885691531); EXPECT_DOUBLE_EQ(mtr(10, 2), -95.03021938861154);
-        Matrix<double, -1, 3, ColumnStorage> mtc = m.transpose<double, -1, 3, ColumnStorage>();
-        EXPECT_DOUBLE_EQ(mtc(0, 0), -93.11774348806081); EXPECT_DOUBLE_EQ(mtc(0, 1), -14.108330840223957); EXPECT_DOUBLE_EQ(mtc(0, 2), 5.8022044043901815); EXPECT_DOUBLE_EQ(mtc(1, 0), -98.38480859022877); EXPECT_DOUBLE_EQ(mtc(1, 1), -94.81883611699344); EXPECT_DOUBLE_EQ(mtc(1, 2), -39.507965223996266); EXPECT_DOUBLE_EQ(mtc(2, 0), -70.06261616604155); EXPECT_DOUBLE_EQ(mtc(2, 1), -45.060719301725285); EXPECT_DOUBLE_EQ(mtc(2, 2), 38.099939917456425); EXPECT_DOUBLE_EQ(mtc(3, 0), 84.87535684986423); EXPECT_DOUBLE_EQ(mtc(3, 1), -41.383939879963094); EXPECT_DOUBLE_EQ(mtc(3, 2), -11.891042873050296); EXPECT_DOUBLE_EQ(mtc(4, 0), -99.9818642210925); EXPECT_DOUBLE_EQ(mtc(4, 1), 80.36741308691853); EXPECT_DOUBLE_EQ(mtc(4, 2), 53.89070563872062); EXPECT_DOUBLE_EQ(mtc(5, 0), -25.11185567441916); EXPECT_DOUBLE_EQ(mtc(5, 1), -87.50961508738959); EXPECT_DOUBLE_EQ(mtc(5, 2), 23.280098882479578); EXPECT_DOUBLE_EQ(mtc(6, 0), 8.85590979917103); EXPECT_DOUBLE_EQ(mtc(6, 1), -32.65290161505921); EXPECT_DOUBLE_EQ(mtc(6, 2), -5.0318917624474295); EXPECT_DOUBLE_EQ(mtc(7, 0), 32.717509759851936); EXPECT_DOUBLE_EQ(mtc(7, 1), 18.529868291798238); EXPECT_DOUBLE_EQ(mtc(7, 2), 31.50255873280196); EXPECT_DOUBLE_EQ(mtc(8, 0), 12.677927494307738); EXPECT_DOUBLE_EQ(mtc(8, 1), -46.169755352790595); EXPECT_DOUBLE_EQ(mtc(8, 2), 22.629046207699318); EXPECT_DOUBLE_EQ(mtc(9, 0), -76.92757015087707); EXPECT_DOUBLE_EQ(mtc(9, 1), 83.67078184672366); EXPECT_DOUBLE_EQ(mtc(9, 2), 3.5102931218199416); EXPECT_DOUBLE_EQ(mtc(10, 0), -80.99502606313347); EXPECT_DOUBLE_EQ(mtc(10, 1), -30.02053885691531); EXPECT_DOUBLE_EQ(mtc(10, 2), -95.03021938861154);
-    }
-    {
-        Matrix<double, 3, -1, ColumnStorage> m; m.resize(3, 19);
-        m(0, 0) = 50.864090811708934; m(0, 1) = 86.72545584739655; m(0, 2) = -59.41096188367827; m(0, 3) = -81.01855448213378; m(0, 4) = -44.75527142333435; m(0, 5) = 6.881484559867502; m(0, 6) = 75.66386662485408; m(0, 7) = -56.002568995946575; m(0, 8) = -44.600865729883445; m(0, 9) = -18.413408652944696; m(0, 10) = -97.11569037525811; m(0, 11) = 53.19666636708692; m(0, 12) = -64.58909530248837; m(0, 13) = -13.336152508799714; m(0, 14) = -69.12350514623267; m(0, 15) = 56.52730125536351; m(0, 16) = 89.92552663330136; m(0, 17) = 94.33106257780301; m(0, 18) = 76.55814809986282; m(1, 0) = 14.747374583026797; m(1, 1) = -12.087041962746213; m(1, 2) = -63.3966872965287; m(1, 3) = -11.386504830855642; m(1, 4) = -76.29669292020178; m(1, 5) = -66.38097797841678; m(1, 6) = -20.191218640024687; m(1, 7) = -48.05245125934678; m(1, 8) = -83.87380388512868; m(1, 9) = -21.25569067138788; m(1, 10) = 4.889708648539596; m(1, 11) = -85.80217867074691; m(1, 12) = -85.26796006798745; m(1, 13) = 3.8169098134350605; m(1, 14) = 73.4920467291056; m(1, 15) = 98.24187210950205; m(1, 16) = -9.878913280704495; m(1, 17) = -63.027946780158196; m(1, 18) = 55.64310458734482; m(2, 0) = -75.20410363410058; m(2, 1) = 45.30781974344674; m(2, 2) = -43.85391331821933; m(2, 3) = 67.45134132003074; m(2, 4) = 55.35009554124747; m(2, 5) = -24.1599830304106; m(2, 6) = 89.85022708733555; m(2, 7) = 63.770995127367826; m(2, 8) = -7.388429976036122; m(2, 9) = 8.073425560498507; m(2, 10) = 76.76129649290999; m(2, 11) = -50.19697292034915; m(2, 12) = -25.310526646715076; m(2, 13) = 14.496228473119118; m(2, 14) = 46.35572803496012; m(2, 15) = -43.2905212948518; m(2, 16) = 72.28250601709692; m(2, 17) = 59.72857548888601; m(2, 18) = 39.776820197984875;
-        Matrix<double, -1, 3, RowStorage> mtr = m.transpose<double, -1, 3, RowStorage>();
-        EXPECT_DOUBLE_EQ(mtr(0, 0), 50.864090811708934); EXPECT_DOUBLE_EQ(mtr(0, 1), 14.747374583026797); EXPECT_DOUBLE_EQ(mtr(0, 2), -75.20410363410058); EXPECT_DOUBLE_EQ(mtr(1, 0), 86.72545584739655); EXPECT_DOUBLE_EQ(mtr(1, 1), -12.087041962746213); EXPECT_DOUBLE_EQ(mtr(1, 2), 45.30781974344674); EXPECT_DOUBLE_EQ(mtr(2, 0), -59.41096188367827); EXPECT_DOUBLE_EQ(mtr(2, 1), -63.3966872965287); EXPECT_DOUBLE_EQ(mtr(2, 2), -43.85391331821933); EXPECT_DOUBLE_EQ(mtr(3, 0), -81.01855448213378); EXPECT_DOUBLE_EQ(mtr(3, 1), -11.386504830855642); EXPECT_DOUBLE_EQ(mtr(3, 2), 67.45134132003074); EXPECT_DOUBLE_EQ(mtr(4, 0), -44.75527142333435); EXPECT_DOUBLE_EQ(mtr(4, 1), -76.29669292020178); EXPECT_DOUBLE_EQ(mtr(4, 2), 55.35009554124747); EXPECT_DOUBLE_EQ(mtr(5, 0), 6.881484559867502); EXPECT_DOUBLE_EQ(mtr(5, 1), -66.38097797841678); EXPECT_DOUBLE_EQ(mtr(5, 2), -24.1599830304106); EXPECT_DOUBLE_EQ(mtr(6, 0), 75.66386662485408); EXPECT_DOUBLE_EQ(mtr(6, 1), -20.191218640024687); EXPECT_DOUBLE_EQ(mtr(6, 2), 89.85022708733555); EXPECT_DOUBLE_EQ(mtr(7, 0), -56.002568995946575); EXPECT_DOUBLE_EQ(mtr(7, 1), -48.05245125934678); EXPECT_DOUBLE_EQ(mtr(7, 2), 63.770995127367826); EXPECT_DOUBLE_EQ(mtr(8, 0), -44.600865729883445); EXPECT_DOUBLE_EQ(mtr(8, 1), -83.87380388512868); EXPECT_DOUBLE_EQ(mtr(8, 2), -7.388429976036122); EXPECT_DOUBLE_EQ(mtr(9, 0), -18.413408652944696); EXPECT_DOUBLE_EQ(mtr(9, 1), -21.25569067138788); EXPECT_DOUBLE_EQ(mtr(9, 2), 8.073425560498507); EXPECT_DOUBLE_EQ(mtr(10, 0), -97.11569037525811); EXPECT_DOUBLE_EQ(mtr(10, 1), 4.889708648539596); EXPECT_DOUBLE_EQ(mtr(10, 2), 76.76129649290999); EXPECT_DOUBLE_EQ(mtr(11, 0), 53.19666636708692); EXPECT_DOUBLE_EQ(mtr(11, 1), -85.80217867074691); EXPECT_DOUBLE_EQ(mtr(11, 2), -50.19697292034915); EXPECT_DOUBLE_EQ(mtr(12, 0), -64.58909530248837); EXPECT_DOUBLE_EQ(mtr(12, 1), -85.26796006798745); EXPECT_DOUBLE_EQ(mtr(12, 2), -25.310526646715076); EXPECT_DOUBLE_EQ(mtr(13, 0), -13.336152508799714); EXPECT_DOUBLE_EQ(mtr(13, 1), 3.8169098134350605); EXPECT_DOUBLE_EQ(mtr(13, 2), 14.496228473119118); EXPECT_DOUBLE_EQ(mtr(14, 0), -69.12350514623267); EXPECT_DOUBLE_EQ(mtr(14, 1), 73.4920467291056); EXPECT_DOUBLE_EQ(mtr(14, 2), 46.35572803496012); EXPECT_DOUBLE_EQ(mtr(15, 0), 56.52730125536351); EXPECT_DOUBLE_EQ(mtr(15, 1), 98.24187210950205); EXPECT_DOUBLE_EQ(mtr(15, 2), -43.2905212948518); EXPECT_DOUBLE_EQ(mtr(16, 0), 89.92552663330136); EXPECT_DOUBLE_EQ(mtr(16, 1), -9.878913280704495); EXPECT_DOUBLE_EQ(mtr(16, 2), 72.28250601709692); EXPECT_DOUBLE_EQ(mtr(17, 0), 94.33106257780301); EXPECT_DOUBLE_EQ(mtr(17, 1), -63.027946780158196); EXPECT_DOUBLE_EQ(mtr(17, 2), 59.72857548888601); EXPECT_DOUBLE_EQ(mtr(18, 0), 76.55814809986282); EXPECT_DOUBLE_EQ(mtr(18, 1), 55.64310458734482); EXPECT_DOUBLE_EQ(mtr(18, 2), 39.776820197984875);
-        Matrix<double, -1, 3, ColumnStorage> mtc = m.transpose<double, -1, 3, ColumnStorage>();
-        EXPECT_DOUBLE_EQ(mtc(0, 0), 50.864090811708934); EXPECT_DOUBLE_EQ(mtc(0, 1), 14.747374583026797); EXPECT_DOUBLE_EQ(mtc(0, 2), -75.20410363410058); EXPECT_DOUBLE_EQ(mtc(1, 0), 86.72545584739655); EXPECT_DOUBLE_EQ(mtc(1, 1), -12.087041962746213); EXPECT_DOUBLE_EQ(mtc(1, 2), 45.30781974344674); EXPECT_DOUBLE_EQ(mtc(2, 0), -59.41096188367827); EXPECT_DOUBLE_EQ(mtc(2, 1), -63.3966872965287); EXPECT_DOUBLE_EQ(mtc(2, 2), -43.85391331821933); EXPECT_DOUBLE_EQ(mtc(3, 0), -81.01855448213378); EXPECT_DOUBLE_EQ(mtc(3, 1), -11.386504830855642); EXPECT_DOUBLE_EQ(mtc(3, 2), 67.45134132003074); EXPECT_DOUBLE_EQ(mtc(4, 0), -44.75527142333435); EXPECT_DOUBLE_EQ(mtc(4, 1), -76.29669292020178); EXPECT_DOUBLE_EQ(mtc(4, 2), 55.35009554124747); EXPECT_DOUBLE_EQ(mtc(5, 0), 6.881484559867502); EXPECT_DOUBLE_EQ(mtc(5, 1), -66.38097797841678); EXPECT_DOUBLE_EQ(mtc(5, 2), -24.1599830304106); EXPECT_DOUBLE_EQ(mtc(6, 0), 75.66386662485408); EXPECT_DOUBLE_EQ(mtc(6, 1), -20.191218640024687); EXPECT_DOUBLE_EQ(mtc(6, 2), 89.85022708733555); EXPECT_DOUBLE_EQ(mtc(7, 0), -56.002568995946575); EXPECT_DOUBLE_EQ(mtc(7, 1), -48.05245125934678); EXPECT_DOUBLE_EQ(mtc(7, 2), 63.770995127367826); EXPECT_DOUBLE_EQ(mtc(8, 0), -44.600865729883445); EXPECT_DOUBLE_EQ(mtc(8, 1), -83.87380388512868); EXPECT_DOUBLE_EQ(mtc(8, 2), -7.388429976036122); EXPECT_DOUBLE_EQ(mtc(9, 0), -18.413408652944696); EXPECT_DOUBLE_EQ(mtc(9, 1), -21.25569067138788); EXPECT_DOUBLE_EQ(mtc(9, 2), 8.073425560498507); EXPECT_DOUBLE_EQ(mtc(10, 0), -97.11569037525811); EXPECT_DOUBLE_EQ(mtc(10, 1), 4.889708648539596); EXPECT_DOUBLE_EQ(mtc(10, 2), 76.76129649290999); EXPECT_DOUBLE_EQ(mtc(11, 0), 53.19666636708692); EXPECT_DOUBLE_EQ(mtc(11, 1), -85.80217867074691); EXPECT_DOUBLE_EQ(mtc(11, 2), -50.19697292034915); EXPECT_DOUBLE_EQ(mtc(12, 0), -64.58909530248837); EXPECT_DOUBLE_EQ(mtc(12, 1), -85.26796006798745); EXPECT_DOUBLE_EQ(mtc(12, 2), -25.310526646715076); EXPECT_DOUBLE_EQ(mtc(13, 0), -13.336152508799714); EXPECT_DOUBLE_EQ(mtc(13, 1), 3.8169098134350605); EXPECT_DOUBLE_EQ(mtc(13, 2), 14.496228473119118); EXPECT_DOUBLE_EQ(mtc(14, 0), -69.12350514623267); EXPECT_DOUBLE_EQ(mtc(14, 1), 73.4920467291056); EXPECT_DOUBLE_EQ(mtc(14, 2), 46.35572803496012); EXPECT_DOUBLE_EQ(mtc(15, 0), 56.52730125536351); EXPECT_DOUBLE_EQ(mtc(15, 1), 98.24187210950205); EXPECT_DOUBLE_EQ(mtc(15, 2), -43.2905212948518); EXPECT_DOUBLE_EQ(mtc(16, 0), 89.92552663330136); EXPECT_DOUBLE_EQ(mtc(16, 1), -9.878913280704495); EXPECT_DOUBLE_EQ(mtc(16, 2), 72.28250601709692); EXPECT_DOUBLE_EQ(mtc(17, 0), 94.33106257780301); EXPECT_DOUBLE_EQ(mtc(17, 1), -63.027946780158196); EXPECT_DOUBLE_EQ(mtc(17, 2), 59.72857548888601); EXPECT_DOUBLE_EQ(mtc(18, 0), 76.55814809986282); EXPECT_DOUBLE_EQ(mtc(18, 1), 55.64310458734482); EXPECT_DOUBLE_EQ(mtc(18, 2), 39.776820197984875);
-    }
-    {
-        Matrix<double, 3, -1, ColumnStorage> m; m.resize(3, 12);
-        m(0, 0) = -32.75375661346618; m(0, 1) = -13.6098421772042; m(0, 2) = -46.86521220477553; m(0, 3) = 59.00702831249865; m(0, 4) = -4.564740481250126; m(0, 5) = 16.232920948792312; m(0, 6) = -65.0828541930055; m(0, 7) = -57.88248367433246; m(0, 8) = -81.72734394349992; m(0, 9) = 28.080964462881383; m(0, 10) = 36.6937632974539; m(0, 11) = 41.35837714070166; m(1, 0) = -47.68004182743719; m(1, 1) = -64.19046526329765; m(1, 2) = -75.66374889412242; m(1, 3) = -82.35155489863575; m(1, 4) = -75.40948179339736; m(1, 5) = -21.839837867220055; m(1, 6) = -7.047883213897393; m(1, 7) = -28.576424866142986; m(1, 8) = 36.45450614900494; m(1, 9) = -9.122226758045997; m(1, 10) = 39.94779111587877; m(1, 11) = 9.684112064820866; m(2, 0) = 34.000255287178476; m(2, 1) = 64.99966038549962; m(2, 2) = -11.973673265362649; m(2, 3) = 80.2812674443403; m(2, 4) = 95.91223898270886; m(2, 5) = -27.634369350449873; m(2, 6) = -75.21066302899243; m(2, 7) = -20.700089950120855; m(2, 8) = 86.68513293601455; m(2, 9) = 75.43854998281424; m(2, 10) = -88.06922362937304; m(2, 11) = -92.34886576586136;
-        Matrix<double, -1, 3, RowStorage> mtr = m.transpose<double, -1, 3, RowStorage>();
-        EXPECT_DOUBLE_EQ(mtr(0, 0), -32.75375661346618); EXPECT_DOUBLE_EQ(mtr(0, 1), -47.68004182743719); EXPECT_DOUBLE_EQ(mtr(0, 2), 34.000255287178476); EXPECT_DOUBLE_EQ(mtr(1, 0), -13.6098421772042); EXPECT_DOUBLE_EQ(mtr(1, 1), -64.19046526329765); EXPECT_DOUBLE_EQ(mtr(1, 2), 64.99966038549962); EXPECT_DOUBLE_EQ(mtr(2, 0), -46.86521220477553); EXPECT_DOUBLE_EQ(mtr(2, 1), -75.66374889412242); EXPECT_DOUBLE_EQ(mtr(2, 2), -11.973673265362649); EXPECT_DOUBLE_EQ(mtr(3, 0), 59.00702831249865); EXPECT_DOUBLE_EQ(mtr(3, 1), -82.35155489863575); EXPECT_DOUBLE_EQ(mtr(3, 2), 80.2812674443403); EXPECT_DOUBLE_EQ(mtr(4, 0), -4.564740481250126); EXPECT_DOUBLE_EQ(mtr(4, 1), -75.40948179339736); EXPECT_DOUBLE_EQ(mtr(4, 2), 95.91223898270886); EXPECT_DOUBLE_EQ(mtr(5, 0), 16.232920948792312); EXPECT_DOUBLE_EQ(mtr(5, 1), -21.839837867220055); EXPECT_DOUBLE_EQ(mtr(5, 2), -27.634369350449873); EXPECT_DOUBLE_EQ(mtr(6, 0), -65.0828541930055); EXPECT_DOUBLE_EQ(mtr(6, 1), -7.047883213897393); EXPECT_DOUBLE_EQ(mtr(6, 2), -75.21066302899243); EXPECT_DOUBLE_EQ(mtr(7, 0), -57.88248367433246); EXPECT_DOUBLE_EQ(mtr(7, 1), -28.576424866142986); EXPECT_DOUBLE_EQ(mtr(7, 2), -20.700089950120855); EXPECT_DOUBLE_EQ(mtr(8, 0), -81.72734394349992); EXPECT_DOUBLE_EQ(mtr(8, 1), 36.45450614900494); EXPECT_DOUBLE_EQ(mtr(8, 2), 86.68513293601455); EXPECT_DOUBLE_EQ(mtr(9, 0), 28.080964462881383); EXPECT_DOUBLE_EQ(mtr(9, 1), -9.122226758045997); EXPECT_DOUBLE_EQ(mtr(9, 2), 75.43854998281424); EXPECT_DOUBLE_EQ(mtr(10, 0), 36.6937632974539); EXPECT_DOUBLE_EQ(mtr(10, 1), 39.94779111587877); EXPECT_DOUBLE_EQ(mtr(10, 2), -88.06922362937304); EXPECT_DOUBLE_EQ(mtr(11, 0), 41.35837714070166); EXPECT_DOUBLE_EQ(mtr(11, 1), 9.684112064820866); EXPECT_DOUBLE_EQ(mtr(11, 2), -92.34886576586136);
-        Matrix<double, -1, 3, ColumnStorage> mtc = m.transpose<double, -1, 3, ColumnStorage>();
-        EXPECT_DOUBLE_EQ(mtc(0, 0), -32.75375661346618); EXPECT_DOUBLE_EQ(mtc(0, 1), -47.68004182743719); EXPECT_DOUBLE_EQ(mtc(0, 2), 34.000255287178476); EXPECT_DOUBLE_EQ(mtc(1, 0), -13.6098421772042); EXPECT_DOUBLE_EQ(mtc(1, 1), -64.19046526329765); EXPECT_DOUBLE_EQ(mtc(1, 2), 64.99966038549962); EXPECT_DOUBLE_EQ(mtc(2, 0), -46.86521220477553); EXPECT_DOUBLE_EQ(mtc(2, 1), -75.66374889412242); EXPECT_DOUBLE_EQ(mtc(2, 2), -11.973673265362649); EXPECT_DOUBLE_EQ(mtc(3, 0), 59.00702831249865); EXPECT_DOUBLE_EQ(mtc(3, 1), -82.35155489863575); EXPECT_DOUBLE_EQ(mtc(3, 2), 80.2812674443403); EXPECT_DOUBLE_EQ(mtc(4, 0), -4.564740481250126); EXPECT_DOUBLE_EQ(mtc(4, 1), -75.40948179339736); EXPECT_DOUBLE_EQ(mtc(4, 2), 95.91223898270886); EXPECT_DOUBLE_EQ(mtc(5, 0), 16.232920948792312); EXPECT_DOUBLE_EQ(mtc(5, 1), -21.839837867220055); EXPECT_DOUBLE_EQ(mtc(5, 2), -27.634369350449873); EXPECT_DOUBLE_EQ(mtc(6, 0), -65.0828541930055); EXPECT_DOUBLE_EQ(mtc(6, 1), -7.047883213897393); EXPECT_DOUBLE_EQ(mtc(6, 2), -75.21066302899243); EXPECT_DOUBLE_EQ(mtc(7, 0), -57.88248367433246); EXPECT_DOUBLE_EQ(mtc(7, 1), -28.576424866142986); EXPECT_DOUBLE_EQ(mtc(7, 2), -20.700089950120855); EXPECT_DOUBLE_EQ(mtc(8, 0), -81.72734394349992); EXPECT_DOUBLE_EQ(mtc(8, 1), 36.45450614900494); EXPECT_DOUBLE_EQ(mtc(8, 2), 86.68513293601455); EXPECT_DOUBLE_EQ(mtc(9, 0), 28.080964462881383); EXPECT_DOUBLE_EQ(mtc(9, 1), -9.122226758045997); EXPECT_DOUBLE_EQ(mtc(9, 2), 75.43854998281424); EXPECT_DOUBLE_EQ(mtc(10, 0), 36.6937632974539); EXPECT_DOUBLE_EQ(mtc(10, 1), 39.94779111587877); EXPECT_DOUBLE_EQ(mtc(10, 2), -88.06922362937304); EXPECT_DOUBLE_EQ(mtc(11, 0), 41.35837714070166); EXPECT_DOUBLE_EQ(mtc(11, 1), 9.684112064820866); EXPECT_DOUBLE_EQ(mtc(11, 2), -92.34886576586136);
-    }
-    {
-        Matrix<double, 3, -1, ColumnStorage> m; m.resize(3, 17);
-        m(0, 0) = 41.19222807334356; m(0, 1) = -9.647827035990119; m(0, 2) = 79.08578232010518; m(0, 3) = -81.30050511004372; m(0, 4) = 5.2008331502779725; m(0, 5) = -94.16930980955891; m(0, 6) = -13.738166181380976; m(0, 7) = 31.708028058804274; m(0, 8) = -98.07812519655093; m(0, 9) = -51.718134217817926; m(0, 10) = -81.49405897174573; m(0, 11) = 86.09136014594006; m(0, 12) = -23.14506976740256; m(0, 13) = 76.3616884219812; m(0, 14) = 60.28344358729666; m(0, 15) = -35.34123633864937; m(0, 16) = -87.33936780992902; m(1, 0) = 25.563530352835954; m(1, 1) = -43.62388501728416; m(1, 2) = 0.5379451108277209; m(1, 3) = 40.11963964000961; m(1, 4) = -63.945471933511236; m(1, 5) = 25.47334071885645; m(1, 6) = 20.998951793092573; m(1, 7) = 23.964236092014318; m(1, 8) = -53.69611952912465; m(1, 9) = -48.45849352784126; m(1, 10) = 0.03386109792266723; m(1, 11) = -43.90344163766924; m(1, 12) = -6.698621092523396; m(1, 13) = -99.37831178796779; m(1, 14) = -9.64088536276411; m(1, 15) = 3.118955974716698; m(1, 16) = -81.5481380106742; m(2, 0) = 62.07279507925867; m(2, 1) = 90.29145840318458; m(2, 2) = -25.71415288702252; m(2, 3) = 74.7395459171091; m(2, 4) = 24.394997421168824; m(2, 5) = -58.2301634354434; m(2, 6) = -4.768291835922895; m(2, 7) = 49.704487303266575; m(2, 8) = 18.65157355854312; m(2, 9) = 98.9073219636636; m(2, 10) = -45.19000115648366; m(2, 11) = -45.249286237965315; m(2, 12) = 97.09143831741096; m(2, 13) = -31.80834068260583; m(2, 14) = -78.03982967131924; m(2, 15) = -14.844621355572116; m(2, 16) = -66.64707457523824;
-        Matrix<double, -1, 3, RowStorage> mtr = m.transpose<double, -1, 3, RowStorage>();
-        EXPECT_DOUBLE_EQ(mtr(0, 0), 41.19222807334356); EXPECT_DOUBLE_EQ(mtr(0, 1), 25.563530352835954); EXPECT_DOUBLE_EQ(mtr(0, 2), 62.07279507925867); EXPECT_DOUBLE_EQ(mtr(1, 0), -9.647827035990119); EXPECT_DOUBLE_EQ(mtr(1, 1), -43.62388501728416); EXPECT_DOUBLE_EQ(mtr(1, 2), 90.29145840318458); EXPECT_DOUBLE_EQ(mtr(2, 0), 79.08578232010518); EXPECT_DOUBLE_EQ(mtr(2, 1), 0.5379451108277209); EXPECT_DOUBLE_EQ(mtr(2, 2), -25.71415288702252); EXPECT_DOUBLE_EQ(mtr(3, 0), -81.30050511004372); EXPECT_DOUBLE_EQ(mtr(3, 1), 40.11963964000961); EXPECT_DOUBLE_EQ(mtr(3, 2), 74.7395459171091); EXPECT_DOUBLE_EQ(mtr(4, 0), 5.2008331502779725); EXPECT_DOUBLE_EQ(mtr(4, 1), -63.945471933511236); EXPECT_DOUBLE_EQ(mtr(4, 2), 24.394997421168824); EXPECT_DOUBLE_EQ(mtr(5, 0), -94.16930980955891); EXPECT_DOUBLE_EQ(mtr(5, 1), 25.47334071885645); EXPECT_DOUBLE_EQ(mtr(5, 2), -58.2301634354434); EXPECT_DOUBLE_EQ(mtr(6, 0), -13.738166181380976); EXPECT_DOUBLE_EQ(mtr(6, 1), 20.998951793092573); EXPECT_DOUBLE_EQ(mtr(6, 2), -4.768291835922895); EXPECT_DOUBLE_EQ(mtr(7, 0), 31.708028058804274); EXPECT_DOUBLE_EQ(mtr(7, 1), 23.964236092014318); EXPECT_DOUBLE_EQ(mtr(7, 2), 49.704487303266575); EXPECT_DOUBLE_EQ(mtr(8, 0), -98.07812519655093); EXPECT_DOUBLE_EQ(mtr(8, 1), -53.69611952912465); EXPECT_DOUBLE_EQ(mtr(8, 2), 18.65157355854312); EXPECT_DOUBLE_EQ(mtr(9, 0), -51.718134217817926); EXPECT_DOUBLE_EQ(mtr(9, 1), -48.45849352784126); EXPECT_DOUBLE_EQ(mtr(9, 2), 98.9073219636636); EXPECT_DOUBLE_EQ(mtr(10, 0), -81.49405897174573); EXPECT_DOUBLE_EQ(mtr(10, 1), 0.03386109792266723); EXPECT_DOUBLE_EQ(mtr(10, 2), -45.19000115648366); EXPECT_DOUBLE_EQ(mtr(11, 0), 86.09136014594006); EXPECT_DOUBLE_EQ(mtr(11, 1), -43.90344163766924); EXPECT_DOUBLE_EQ(mtr(11, 2), -45.249286237965315); EXPECT_DOUBLE_EQ(mtr(12, 0), -23.14506976740256); EXPECT_DOUBLE_EQ(mtr(12, 1), -6.698621092523396); EXPECT_DOUBLE_EQ(mtr(12, 2), 97.09143831741096); EXPECT_DOUBLE_EQ(mtr(13, 0), 76.3616884219812); EXPECT_DOUBLE_EQ(mtr(13, 1), -99.37831178796779); EXPECT_DOUBLE_EQ(mtr(13, 2), -31.80834068260583); EXPECT_DOUBLE_EQ(mtr(14, 0), 60.28344358729666); EXPECT_DOUBLE_EQ(mtr(14, 1), -9.64088536276411); EXPECT_DOUBLE_EQ(mtr(14, 2), -78.03982967131924); EXPECT_DOUBLE_EQ(mtr(15, 0), -35.34123633864937); EXPECT_DOUBLE_EQ(mtr(15, 1), 3.118955974716698); EXPECT_DOUBLE_EQ(mtr(15, 2), -14.844621355572116); EXPECT_DOUBLE_EQ(mtr(16, 0), -87.33936780992902); EXPECT_DOUBLE_EQ(mtr(16, 1), -81.5481380106742); EXPECT_DOUBLE_EQ(mtr(16, 2), -66.64707457523824);
-        Matrix<double, -1, 3, ColumnStorage> mtc = m.transpose<double, -1, 3, ColumnStorage>();
-        EXPECT_DOUBLE_EQ(mtc(0, 0), 41.19222807334356); EXPECT_DOUBLE_EQ(mtc(0, 1), 25.563530352835954); EXPECT_DOUBLE_EQ(mtc(0, 2), 62.07279507925867); EXPECT_DOUBLE_EQ(mtc(1, 0), -9.647827035990119); EXPECT_DOUBLE_EQ(mtc(1, 1), -43.62388501728416); EXPECT_DOUBLE_EQ(mtc(1, 2), 90.29145840318458); EXPECT_DOUBLE_EQ(mtc(2, 0), 79.08578232010518); EXPECT_DOUBLE_EQ(mtc(2, 1), 0.5379451108277209); EXPECT_DOUBLE_EQ(mtc(2, 2), -25.71415288702252); EXPECT_DOUBLE_EQ(mtc(3, 0), -81.30050511004372); EXPECT_DOUBLE_EQ(mtc(3, 1), 40.11963964000961); EXPECT_DOUBLE_EQ(mtc(3, 2), 74.7395459171091); EXPECT_DOUBLE_EQ(mtc(4, 0), 5.2008331502779725); EXPECT_DOUBLE_EQ(mtc(4, 1), -63.945471933511236); EXPECT_DOUBLE_EQ(mtc(4, 2), 24.394997421168824); EXPECT_DOUBLE_EQ(mtc(5, 0), -94.16930980955891); EXPECT_DOUBLE_EQ(mtc(5, 1), 25.47334071885645); EXPECT_DOUBLE_EQ(mtc(5, 2), -58.2301634354434); EXPECT_DOUBLE_EQ(mtc(6, 0), -13.738166181380976); EXPECT_DOUBLE_EQ(mtc(6, 1), 20.998951793092573); EXPECT_DOUBLE_EQ(mtc(6, 2), -4.768291835922895); EXPECT_DOUBLE_EQ(mtc(7, 0), 31.708028058804274); EXPECT_DOUBLE_EQ(mtc(7, 1), 23.964236092014318); EXPECT_DOUBLE_EQ(mtc(7, 2), 49.704487303266575); EXPECT_DOUBLE_EQ(mtc(8, 0), -98.07812519655093); EXPECT_DOUBLE_EQ(mtc(8, 1), -53.69611952912465); EXPECT_DOUBLE_EQ(mtc(8, 2), 18.65157355854312); EXPECT_DOUBLE_EQ(mtc(9, 0), -51.718134217817926); EXPECT_DOUBLE_EQ(mtc(9, 1), -48.45849352784126); EXPECT_DOUBLE_EQ(mtc(9, 2), 98.9073219636636); EXPECT_DOUBLE_EQ(mtc(10, 0), -81.49405897174573); EXPECT_DOUBLE_EQ(mtc(10, 1), 0.03386109792266723); EXPECT_DOUBLE_EQ(mtc(10, 2), -45.19000115648366); EXPECT_DOUBLE_EQ(mtc(11, 0), 86.09136014594006); EXPECT_DOUBLE_EQ(mtc(11, 1), -43.90344163766924); EXPECT_DOUBLE_EQ(mtc(11, 2), -45.249286237965315); EXPECT_DOUBLE_EQ(mtc(12, 0), -23.14506976740256); EXPECT_DOUBLE_EQ(mtc(12, 1), -6.698621092523396); EXPECT_DOUBLE_EQ(mtc(12, 2), 97.09143831741096); EXPECT_DOUBLE_EQ(mtc(13, 0), 76.3616884219812); EXPECT_DOUBLE_EQ(mtc(13, 1), -99.37831178796779); EXPECT_DOUBLE_EQ(mtc(13, 2), -31.80834068260583); EXPECT_DOUBLE_EQ(mtc(14, 0), 60.28344358729666); EXPECT_DOUBLE_EQ(mtc(14, 1), -9.64088536276411); EXPECT_DOUBLE_EQ(mtc(14, 2), -78.03982967131924); EXPECT_DOUBLE_EQ(mtc(15, 0), -35.34123633864937); EXPECT_DOUBLE_EQ(mtc(15, 1), 3.118955974716698); EXPECT_DOUBLE_EQ(mtc(15, 2), -14.844621355572116); EXPECT_DOUBLE_EQ(mtc(16, 0), -87.33936780992902); EXPECT_DOUBLE_EQ(mtc(16, 1), -81.5481380106742); EXPECT_DOUBLE_EQ(mtc(16, 2), -66.64707457523824);
-    }
-    {
-        Matrix<double, 3, -1, ColumnStorage> m; m.resize(3, 11);
-        m(0, 0) = -44.385915446696366; m(0, 1) = 28.793505461441015; m(0, 2) = 71.2114986465838; m(0, 3) = 51.14773880111491; m(0, 4) = -7.958682467368476; m(0, 5) = -83.09905041318346; m(0, 6) = -22.191719125506793; m(0, 7) = -2.2844026553076873; m(0, 8) = -85.89049887253955; m(0, 9) = 7.359151344016439; m(0, 10) = -12.836173824817394; m(1, 0) = 60.864624834962456; m(1, 1) = 55.31797716120735; m(1, 2) = 54.86505134841502; m(1, 3) = 1.2088001265842365; m(1, 4) = 51.71783583087824; m(1, 5) = -97.7984372019131; m(1, 6) = -21.276052450577225; m(1, 7) = -38.9853136735308; m(1, 8) = -83.47696130822689; m(1, 9) = 3.197398523431062; m(1, 10) = -81.03476411018644; m(2, 0) = 78.17495315633076; m(2, 1) = -81.81693970564498; m(2, 2) = -30.34183030075195; m(2, 3) = -15.609525205781651; m(2, 4) = -27.0093291175411; m(2, 5) = 42.95413233280735; m(2, 6) = -72.61359152573652; m(2, 7) = 78.95917814822454; m(2, 8) = -83.12124753315223; m(2, 9) = 74.1286028999458; m(2, 10) = -87.09605709830836;
-        Matrix<double, -1, 3, RowStorage> mtr = m.transpose<double, -1, 3, RowStorage>();
-        EXPECT_DOUBLE_EQ(mtr(0, 0), -44.385915446696366); EXPECT_DOUBLE_EQ(mtr(0, 1), 60.864624834962456); EXPECT_DOUBLE_EQ(mtr(0, 2), 78.17495315633076); EXPECT_DOUBLE_EQ(mtr(1, 0), 28.793505461441015); EXPECT_DOUBLE_EQ(mtr(1, 1), 55.31797716120735); EXPECT_DOUBLE_EQ(mtr(1, 2), -81.81693970564498); EXPECT_DOUBLE_EQ(mtr(2, 0), 71.2114986465838); EXPECT_DOUBLE_EQ(mtr(2, 1), 54.86505134841502); EXPECT_DOUBLE_EQ(mtr(2, 2), -30.34183030075195); EXPECT_DOUBLE_EQ(mtr(3, 0), 51.14773880111491); EXPECT_DOUBLE_EQ(mtr(3, 1), 1.2088001265842365); EXPECT_DOUBLE_EQ(mtr(3, 2), -15.609525205781651); EXPECT_DOUBLE_EQ(mtr(4, 0), -7.958682467368476); EXPECT_DOUBLE_EQ(mtr(4, 1), 51.71783583087824); EXPECT_DOUBLE_EQ(mtr(4, 2), -27.0093291175411); EXPECT_DOUBLE_EQ(mtr(5, 0), -83.09905041318346); EXPECT_DOUBLE_EQ(mtr(5, 1), -97.7984372019131); EXPECT_DOUBLE_EQ(mtr(5, 2), 42.95413233280735); EXPECT_DOUBLE_EQ(mtr(6, 0), -22.191719125506793); EXPECT_DOUBLE_EQ(mtr(6, 1), -21.276052450577225); EXPECT_DOUBLE_EQ(mtr(6, 2), -72.61359152573652); EXPECT_DOUBLE_EQ(mtr(7, 0), -2.2844026553076873); EXPECT_DOUBLE_EQ(mtr(7, 1), -38.9853136735308); EXPECT_DOUBLE_EQ(mtr(7, 2), 78.95917814822454); EXPECT_DOUBLE_EQ(mtr(8, 0), -85.89049887253955); EXPECT_DOUBLE_EQ(mtr(8, 1), -83.47696130822689); EXPECT_DOUBLE_EQ(mtr(8, 2), -83.12124753315223); EXPECT_DOUBLE_EQ(mtr(9, 0), 7.359151344016439); EXPECT_DOUBLE_EQ(mtr(9, 1), 3.197398523431062); EXPECT_DOUBLE_EQ(mtr(9, 2), 74.1286028999458); EXPECT_DOUBLE_EQ(mtr(10, 0), -12.836173824817394); EXPECT_DOUBLE_EQ(mtr(10, 1), -81.03476411018644); EXPECT_DOUBLE_EQ(mtr(10, 2), -87.09605709830836);
-        Matrix<double, -1, 3, ColumnStorage> mtc = m.transpose<double, -1, 3, ColumnStorage>();
-        EXPECT_DOUBLE_EQ(mtc(0, 0), -44.385915446696366); EXPECT_DOUBLE_EQ(mtc(0, 1), 60.864624834962456); EXPECT_DOUBLE_EQ(mtc(0, 2), 78.17495315633076); EXPECT_DOUBLE_EQ(mtc(1, 0), 28.793505461441015); EXPECT_DOUBLE_EQ(mtc(1, 1), 55.31797716120735); EXPECT_DOUBLE_EQ(mtc(1, 2), -81.81693970564498); EXPECT_DOUBLE_EQ(mtc(2, 0), 71.2114986465838); EXPECT_DOUBLE_EQ(mtc(2, 1), 54.86505134841502); EXPECT_DOUBLE_EQ(mtc(2, 2), -30.34183030075195); EXPECT_DOUBLE_EQ(mtc(3, 0), 51.14773880111491); EXPECT_DOUBLE_EQ(mtc(3, 1), 1.2088001265842365); EXPECT_DOUBLE_EQ(mtc(3, 2), -15.609525205781651); EXPECT_DOUBLE_EQ(mtc(4, 0), -7.958682467368476); EXPECT_DOUBLE_EQ(mtc(4, 1), 51.71783583087824); EXPECT_DOUBLE_EQ(mtc(4, 2), -27.0093291175411); EXPECT_DOUBLE_EQ(mtc(5, 0), -83.09905041318346); EXPECT_DOUBLE_EQ(mtc(5, 1), -97.7984372019131); EXPECT_DOUBLE_EQ(mtc(5, 2), 42.95413233280735); EXPECT_DOUBLE_EQ(mtc(6, 0), -22.191719125506793); EXPECT_DOUBLE_EQ(mtc(6, 1), -21.276052450577225); EXPECT_DOUBLE_EQ(mtc(6, 2), -72.61359152573652); EXPECT_DOUBLE_EQ(mtc(7, 0), -2.2844026553076873); EXPECT_DOUBLE_EQ(mtc(7, 1), -38.9853136735308); EXPECT_DOUBLE_EQ(mtc(7, 2), 78.95917814822454); EXPECT_DOUBLE_EQ(mtc(8, 0), -85.89049887253955); EXPECT_DOUBLE_EQ(mtc(8, 1), -83.47696130822689); EXPECT_DOUBLE_EQ(mtc(8, 2), -83.12124753315223); EXPECT_DOUBLE_EQ(mtc(9, 0), 7.359151344016439); EXPECT_DOUBLE_EQ(mtc(9, 1), 3.197398523431062); EXPECT_DOUBLE_EQ(mtc(9, 2), 74.1286028999458); EXPECT_DOUBLE_EQ(mtc(10, 0), -12.836173824817394); EXPECT_DOUBLE_EQ(mtc(10, 1), -81.03476411018644); EXPECT_DOUBLE_EQ(mtc(10, 2), -87.09605709830836);
-    }
-}
-
-TEST(TestLabo1a, AffectationBySubMatrix)
-{
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m.setIdentity();
-        EXPECT_DOUBLE_EQ(m(0, 0), 1); EXPECT_DOUBLE_EQ(m(0, 1), 0); EXPECT_DOUBLE_EQ(m(0, 2), 0); EXPECT_DOUBLE_EQ(m(0, 3), 0); EXPECT_DOUBLE_EQ(m(1, 0), 0); EXPECT_DOUBLE_EQ(m(1, 1), 1); EXPECT_DOUBLE_EQ(m(1, 2), 0); EXPECT_DOUBLE_EQ(m(1, 3), 0); EXPECT_DOUBLE_EQ(m(2, 0), 0); EXPECT_DOUBLE_EQ(m(2, 1), 0); EXPECT_DOUBLE_EQ(m(2, 2), 1); EXPECT_DOUBLE_EQ(m(2, 3), 0); EXPECT_DOUBLE_EQ(m(3, 0), 0); EXPECT_DOUBLE_EQ(m(3, 1), 0); EXPECT_DOUBLE_EQ(m(3, 2), 0); EXPECT_DOUBLE_EQ(m(3, 3), 1);
-        Matrix<double, 4, 1, RowStorage> c;
-        c(0, 0) = 1.0; c(1, 0) = 2.0; c(2, 0) = 3.0; c(3, 0) = 4.0;
-        m.block(0, 0, 4, 1) = c;
-        m.block(0, 1, 4, 1) = c;
-        m.block(0, 2, 4, 1) = c;
-        m.block(0, 3, 4, 1) = c;
-        EXPECT_DOUBLE_EQ(m(0, 0), 1); EXPECT_DOUBLE_EQ(m(0, 1), 1); EXPECT_DOUBLE_EQ(m(0, 2), 1); EXPECT_DOUBLE_EQ(m(0, 3), 1); EXPECT_DOUBLE_EQ(m(1, 0), 2); EXPECT_DOUBLE_EQ(m(1, 1), 2); EXPECT_DOUBLE_EQ(m(1, 2), 2); EXPECT_DOUBLE_EQ(m(1, 3), 2); EXPECT_DOUBLE_EQ(m(2, 0), 3); EXPECT_DOUBLE_EQ(m(2, 1), 3); EXPECT_DOUBLE_EQ(m(2, 2), 3); EXPECT_DOUBLE_EQ(m(2, 3), 3); EXPECT_DOUBLE_EQ(m(3, 0), 4); EXPECT_DOUBLE_EQ(m(3, 1), 4); EXPECT_DOUBLE_EQ(m(3, 2), 4); EXPECT_DOUBLE_EQ(m(3, 3), 4);
-        Matrix<double, 2, 2, ColumnStorage> b;
-        b(0, 0) = 0.0; b(1, 0) = 1.0; b(0, 1) = 2.0; b(1, 1) = 3.0;
-        m.block(0, 0, 2, 2) = b;
-        m.block(2, 0, 2, 2) = b;
-        m.block(0, 2, 2, 2) = b;
-        m.block(2, 2, 2, 2) = b;
-        EXPECT_DOUBLE_EQ(m(0, 0), 0); EXPECT_DOUBLE_EQ(m(0, 1), 2); EXPECT_DOUBLE_EQ(m(0, 2), 0); EXPECT_DOUBLE_EQ(m(0, 3), 2); EXPECT_DOUBLE_EQ(m(1, 0), 1); EXPECT_DOUBLE_EQ(m(1, 1), 3); EXPECT_DOUBLE_EQ(m(1, 2), 1); EXPECT_DOUBLE_EQ(m(1, 3), 3); EXPECT_DOUBLE_EQ(m(2, 0), 0); EXPECT_DOUBLE_EQ(m(2, 1), 2); EXPECT_DOUBLE_EQ(m(2, 2), 0); EXPECT_DOUBLE_EQ(m(2, 3), 2); EXPECT_DOUBLE_EQ(m(3, 0), 1); EXPECT_DOUBLE_EQ(m(3, 1), 3); EXPECT_DOUBLE_EQ(m(3, 2), 1); EXPECT_DOUBLE_EQ(m(3, 3), 3);
-    }
-    {
-        Matrix<double, 4, 4, RowStorage> m;
-        m.setIdentity();
-        EXPECT_DOUBLE_EQ(m(0, 0), 1); EXPECT_DOUBLE_EQ(m(0, 1), 0); EXPECT_DOUBLE_EQ(m(0, 2), 0); EXPECT_DOUBLE_EQ(m(0, 3), 0); EXPECT_DOUBLE_EQ(m(1, 0), 0); EXPECT_DOUBLE_EQ(m(1, 1), 1); EXPECT_DOUBLE_EQ(m(1, 2), 0); EXPECT_DOUBLE_EQ(m(1, 3), 0); EXPECT_DOUBLE_EQ(m(2, 0), 0); EXPECT_DOUBLE_EQ(m(2, 1), 0); EXPECT_DOUBLE_EQ(m(2, 2), 1); EXPECT_DOUBLE_EQ(m(2, 3), 0); EXPECT_DOUBLE_EQ(m(3, 0), 0); EXPECT_DOUBLE_EQ(m(3, 1), 0); EXPECT_DOUBLE_EQ(m(3, 2), 0); EXPECT_DOUBLE_EQ(m(3, 3), 1);
-        Matrix<double, 4, 1, RowStorage> c;
-        c(0, 0) = 1.0; c(1, 0) = 2.0; c(2, 0) = 3.0; c(3, 0) = 4.0;
-        m.block(0, 0, 4, 1) = c;
-        m.block(0, 1, 4, 1) = c;
-        m.block(0, 2, 4, 1) = c;
-        m.block(0, 3, 4, 1) = c;
-        EXPECT_DOUBLE_EQ(m(0, 0), 1); EXPECT_DOUBLE_EQ(m(0, 1), 1); EXPECT_DOUBLE_EQ(m(0, 2), 1); EXPECT_DOUBLE_EQ(m(0, 3), 1); EXPECT_DOUBLE_EQ(m(1, 0), 2); EXPECT_DOUBLE_EQ(m(1, 1), 2); EXPECT_DOUBLE_EQ(m(1, 2), 2); EXPECT_DOUBLE_EQ(m(1, 3), 2); EXPECT_DOUBLE_EQ(m(2, 0), 3); EXPECT_DOUBLE_EQ(m(2, 1), 3); EXPECT_DOUBLE_EQ(m(2, 2), 3); EXPECT_DOUBLE_EQ(m(2, 3), 3); EXPECT_DOUBLE_EQ(m(3, 0), 4); EXPECT_DOUBLE_EQ(m(3, 1), 4); EXPECT_DOUBLE_EQ(m(3, 2), 4); EXPECT_DOUBLE_EQ(m(3, 3), 4);
-        Matrix<double, 2, 2, ColumnStorage> b;
-        b(0, 0) = 0.0; b(1, 0) = 1.0; b(0, 1) = 2.0; b(1, 1) = 3.0;
-        m.block(0, 0, 2, 2) = b;
-        m.block(2, 0, 2, 2) = b;
-        m.block(0, 2, 2, 2) = b;
-        m.block(2, 2, 2, 2) = b;
-        EXPECT_DOUBLE_EQ(m(0, 0), 0); EXPECT_DOUBLE_EQ(m(0, 1), 2); EXPECT_DOUBLE_EQ(m(0, 2), 0); EXPECT_DOUBLE_EQ(m(0, 3), 2); EXPECT_DOUBLE_EQ(m(1, 0), 1); EXPECT_DOUBLE_EQ(m(1, 1), 3); EXPECT_DOUBLE_EQ(m(1, 2), 1); EXPECT_DOUBLE_EQ(m(1, 3), 3); EXPECT_DOUBLE_EQ(m(2, 0), 0); EXPECT_DOUBLE_EQ(m(2, 1), 2); EXPECT_DOUBLE_EQ(m(2, 2), 0); EXPECT_DOUBLE_EQ(m(2, 3), 2); EXPECT_DOUBLE_EQ(m(3, 0), 1); EXPECT_DOUBLE_EQ(m(3, 1), 3); EXPECT_DOUBLE_EQ(m(3, 2), 1); EXPECT_DOUBLE_EQ(m(3, 3), 3);
-    }
-}

labo01/tests/Tests1b.cpp

@@ -1,801 +0,0 @@
-/**
- * @file Tests1b.cpp
- *
- * @brief Tests unitaires de la partie 1b
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include "Matrix.h"
-#include "Vector.h"
-#include "Math3D.h"
-#include "Operators.h"
-
-#include <gtest/gtest.h>
-#include <chrono>
-
-using namespace gti320; 
-
-namespace
-{
-    /**
-     * Multiplication  matrice * vecteur,  utilisant une implémentation naive
-     */
-    template<typename _Scalar>
-    static inline Vector<_Scalar, Dynamic> naiveMatrixMult(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& A, const Vector<_Scalar, Dynamic>& v)
-    {
-        assert(A.cols() == v.rows());
-
-        Vector<_Scalar, Dynamic> b(A.rows());
-        assert(b.rows() == A.rows());
-
-        for (int i = 0; i < A.rows(); ++i) {
-            b(i) = 0.0;
-            for (int j = 0; j < A.cols(); ++j) {
-                b(i) += A(i, j) * v(j);
-            }
-        }
-
-        return b;
-    }
-
-    /**
-     * Addition  matrice + matrice,  utilisant une implémentation naive
-     */
-    template<typename _Scalar>
-    static inline Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> naiveMatrixAddition(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& A, const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& B)
-    {
-        assert(A.cols() == B.cols() && A.rows() == B.rows());
-
-        Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> C(A.rows(), A.cols());
-        assert(C.rows() == A.rows() && C.cols() == A.cols());
-        for (int i = 0; i < C.rows(); ++i) {
-            for (int j = 0; j < C.cols(); ++j) {
-                C(i, j) = A(i, j) + B(i, j);
-            }
-        }
-        return C;
-    }
-
-    /**
-     * Multiplication  matrice * matrice,  utilisant une implémentation naive.
-     */
-    template<typename _Scalar, int _Storage>
-    static inline Matrix<_Scalar, Dynamic, Dynamic, _Storage> naiveMatrixMult(const Matrix<_Scalar, Dynamic, Dynamic, _Storage>& A, const Matrix<_Scalar, Dynamic, Dynamic, _Storage>& B)
-    {
-        assert(A.cols() == B.rows());
-        Matrix<_Scalar, Dynamic, Dynamic> product(A.rows(), B.cols());
-        for (int i = 0; i < A.rows(); ++i)
-        {
-            for (int j = 0; j < B.cols(); ++j)
-            {
-                for (int k = 0; k < A.cols(); ++k)
-                {
-                    product(i, j) += A(i, k) * B(k, j);
-                }
-            }
-        }
-        return product;
-    }
-}
-
-/**
- * Test pour les opérateurs d'arithmétique matricielle.
- */
-TEST(TestLabo1b, MatrixMatrixOperators)
-{
-    // Opérations arithmétiques avec matrices à taille dynamique
-    {
-        // Test : matrice identité
-        Matrix<double> A(6, 6);
-        A.setIdentity();
-        EXPECT_DOUBLE_EQ(A(0, 0), 1.0);
-        EXPECT_DOUBLE_EQ(A(1, 1), 1.0);
-        EXPECT_DOUBLE_EQ(A(2, 2), 1.0);
-        EXPECT_DOUBLE_EQ(A(3, 3), 1.0);
-        EXPECT_DOUBLE_EQ(A(4, 4), 1.0);
-        EXPECT_DOUBLE_EQ(A(5, 5), 1.0);
-        EXPECT_DOUBLE_EQ(A(0, 1), 0.0);
-        EXPECT_DOUBLE_EQ(A(1, 0), 0.0);
-
-        // Test : produit  scalaire * matrice
-        const double alpha = 2.5;
-        Matrix<double> B = alpha * A;
-        EXPECT_DOUBLE_EQ(B(0, 0), alpha);
-        EXPECT_DOUBLE_EQ(B(1, 1), alpha);
-        EXPECT_DOUBLE_EQ(B(2, 2), alpha);
-        EXPECT_DOUBLE_EQ(B(3, 3), alpha);
-        EXPECT_DOUBLE_EQ(B(4, 4), alpha);
-        EXPECT_DOUBLE_EQ(B(5, 5), alpha);
-        EXPECT_DOUBLE_EQ(B(0, 1), 0.0);
-        EXPECT_DOUBLE_EQ(B(1, 0), 0.0);
-
-        // Test : produit  matrice * matrice
-        Matrix<double> C = A * B;
-        EXPECT_DOUBLE_EQ(C(0, 0), A(0, 0) * B(0, 0));
-        EXPECT_DOUBLE_EQ(C(1, 1), A(1, 1) * B(1, 1));
-        EXPECT_DOUBLE_EQ(C(2, 2), A(2, 2) * B(2, 2));
-        EXPECT_DOUBLE_EQ(C(3, 3), A(3, 3) * B(3, 3));
-        EXPECT_DOUBLE_EQ(C(4, 4), A(4, 4) * B(4, 4));
-        EXPECT_DOUBLE_EQ(C(5, 5), A(5, 5) * B(5, 5));
-        EXPECT_DOUBLE_EQ(C(0, 1), 0.0);
-        EXPECT_DOUBLE_EQ(C(2, 3), 0.0);
-
-        // Test : addition  matrice * matrice
-        Matrix<double> A_plus_B = A + B;
-        EXPECT_DOUBLE_EQ(A_plus_B(0, 0), A(0, 0) + B(0, 0));
-        EXPECT_DOUBLE_EQ(A_plus_B(1, 1), A(1, 1) + B(1, 1));
-        EXPECT_DOUBLE_EQ(A_plus_B(2, 2), A(2, 2) + B(2, 2));
-        EXPECT_DOUBLE_EQ(A_plus_B(3, 3), A(3, 3) + B(3, 3));
-        EXPECT_DOUBLE_EQ(A_plus_B(4, 4), A(4, 4) + B(4, 4));
-        EXPECT_DOUBLE_EQ(A_plus_B(5, 5), A(5, 5) + B(5, 5));
-        EXPECT_DOUBLE_EQ(A_plus_B(0, 1), 0.0);
-        EXPECT_DOUBLE_EQ(A_plus_B(2, 3), 0.0);
-    }
-
-    // Opérations arithmétique avec matrices à stockage par lignes et par
-    // colonnes.
-    {
-        // Création d'un matrice à stockage par lignes
-        Matrix<double, Dynamic, Dynamic, RowStorage> A(5, 5);
-        A(0, 0) = 0.8147;    A(0, 1) = 0.0975;    A(0, 2) = 0.1576;    A(0, 3) = 0.1419;    A(0, 4) = 0.6557;
-        A(1, 0) = 0.9058;    A(1, 1) = 0.2785;    A(1, 2) = 0.9706;    A(1, 3) = 0.4218;    A(1, 4) = 0.0357;
-        A(2, 0) = 0.1270;    A(2, 1) = 0.5469;    A(2, 2) = 0.9572;    A(2, 3) = 0.9157;    A(2, 4) = 0.8491;
-        A(3, 0) = 0.9134;    A(3, 1) = 0.9575;    A(3, 2) = 0.4854;    A(3, 3) = 0.7922;    A(3, 4) = 0.9340;
-        A(4, 0) = 0.6324;    A(4, 1) = 0.9649;    A(4, 2) = 0.8003;    A(4, 3) = 0.9595;    A(4, 4) = 0.6787;
-
-        // Test : transposée (le résultat est une matrice à stockage par
-        //        colonnes)
-        Matrix<double, Dynamic, Dynamic, ColumnStorage> B = A.transpose();
-
-        // Test : multiplication  matrix(ligne) * matrice(colonne)
-        // Note : teste seulement la première et la dernière colonne
-        const auto C = A * B;
-        EXPECT_NEAR(C(0, 0), 1.14815820000000, 1e-3); EXPECT_NEAR(C(0, 4), 1.31659795000000, 1e-3);
-        EXPECT_NEAR(C(1, 0), 1.00133748000000, 1e-3); EXPECT_NEAR(C(1, 4), 2.04727044000000, 1e-3);
-        EXPECT_NEAR(C(2, 0), 0.99433707000000, 1e-3); EXPECT_NEAR(C(2, 4), 2.82896409000000, 1e-3);
-        EXPECT_NEAR(C(3, 0), 1.63883925000000, 1e-3); EXPECT_NEAR(C(3, 4), 3.28401323000000, 1e-3);
-        EXPECT_NEAR(C(4, 0), 1.31659795000000, 1e-3); EXPECT_NEAR(C(4, 4), 3.35271580000000, 1e-3);
-
-
-        // Test : multiplication  matrice(colonne) * matrice(ligne)
-        // Note : teste seulement la première et la dernière colonne
-        const auto C2 = B * A;
-        EXPECT_NEAR(C2(0, 0), 2.73456805000000, 1e-3); EXPECT_NEAR(C2(0, 4), 1.95669703000000, 1e-3);
-        EXPECT_NEAR(C2(1, 0), 1.88593811000000, 1e-3); EXPECT_NEAR(C2(1, 4), 2.08742862000000, 1e-3);
-        EXPECT_NEAR(C2(2, 0), 2.07860468000000, 1e-3); EXPECT_NEAR(C2(2, 4), 1.94727447000000, 1e-3);
-        EXPECT_NEAR(C2(3, 0), 1.94434955000000, 1e-3); EXPECT_NEAR(C2(3, 4), 2.27675041000000, 1e-3);
-        EXPECT_NEAR(C2(4, 0), 1.95669703000000, 1e-3); EXPECT_NEAR(C2(4, 4), 2.48517748000000, 1e-3);
-
-        // Test : addition  matrice(ligne) + matrice(ligne)
-        // Note : teste seulement la première et la dernière colonne
-        const auto A_plus_A = A + A;
-        EXPECT_DOUBLE_EQ(A_plus_A(0, 0), A(0, 0) + A(0, 0)); EXPECT_DOUBLE_EQ(A_plus_A(0, 4), A(0, 4) + A(0, 4));
-        EXPECT_DOUBLE_EQ(A_plus_A(1, 0), A(1, 0) + A(1, 0)); EXPECT_DOUBLE_EQ(A_plus_A(1, 4), A(1, 4) + A(1, 4));
-        EXPECT_DOUBLE_EQ(A_plus_A(2, 0), A(2, 0) + A(2, 0)); EXPECT_DOUBLE_EQ(A_plus_A(2, 4), A(2, 4) + A(2, 4));
-        EXPECT_DOUBLE_EQ(A_plus_A(3, 0), A(3, 0) + A(3, 0)); EXPECT_DOUBLE_EQ(A_plus_A(3, 4), A(3, 4) + A(3, 4));
-        EXPECT_DOUBLE_EQ(A_plus_A(4, 0), A(4, 0) + A(4, 0)); EXPECT_DOUBLE_EQ(A_plus_A(4, 4), A(4, 4) + A(4, 4));
-
-        // Test : addition  matrice(colonne) + matrice(colonne)
-        // Note : teste seulement la première et la dernière colonne
-        const auto B_plus_B = B + B;
-        EXPECT_DOUBLE_EQ(B_plus_B(0, 0), B(0, 0) + B(0, 0)); EXPECT_DOUBLE_EQ(B_plus_B(0, 4), B(0, 4) + B(0, 4));
-        EXPECT_DOUBLE_EQ(B_plus_B(1, 0), B(1, 0) + B(1, 0)); EXPECT_DOUBLE_EQ(B_plus_B(1, 4), B(1, 4) + B(1, 4));
-        EXPECT_DOUBLE_EQ(B_plus_B(2, 0), B(2, 0) + B(2, 0)); EXPECT_DOUBLE_EQ(B_plus_B(2, 4), B(2, 4) + B(2, 4));
-        EXPECT_DOUBLE_EQ(B_plus_B(3, 0), B(3, 0) + B(3, 0)); EXPECT_DOUBLE_EQ(B_plus_B(3, 4), B(3, 4) + B(3, 4));
-        EXPECT_DOUBLE_EQ(B_plus_B(4, 0), B(4, 0) + B(4, 0)); EXPECT_DOUBLE_EQ(B_plus_B(4, 4), B(4, 4) + B(4, 4));
-
-    }
-}
-
-/**
- * Test pour la multiplication  matrice * vecteur
- */
-TEST(TestLabo1b, MatrixVectorOperators)
-{
-    // Vecteur à taille dynamique
-    Vector<double> v(5);
-    v(0) = 1.0;
-    v(1) = 2.0;
-    v(2) = 4.0;
-    v(3) = 8.0;
-    v(4) = 16.0;
-
-    // Test : multiplication par la matrice identité
-    {
-        Matrix<double> M(5, 5);
-        M.setIdentity();
-
-        const auto b = M * v;
-        EXPECT_DOUBLE_EQ(b(0), 1.0);
-        EXPECT_DOUBLE_EQ(b(1), 2.0);
-        EXPECT_DOUBLE_EQ(b(2), 4.0);
-        EXPECT_DOUBLE_EQ(b(3), 8.0);
-        EXPECT_DOUBLE_EQ(b(4), 16.0);
-    }
-
-    // Test : multiplication par une matrice à taille dynamique avec stockage par ligne.
-    {
-        Matrix<double, Dynamic, Dynamic, RowStorage> M(5, 5);
-        M.setIdentity();
-        M = 2.0 * M;
-
-        Vector<double> b2 = M * v;
-        EXPECT_DOUBLE_EQ(b2(0), 2.0);
-        EXPECT_DOUBLE_EQ(b2(1), 4.0);
-        EXPECT_DOUBLE_EQ(b2(2), 8.0);
-        EXPECT_DOUBLE_EQ(b2(3), 16.0);
-        EXPECT_DOUBLE_EQ(b2(4), 32.0);
-    }
-    // Test : autres
-    {
-        Vector<double, 3> u; u(0) = 89.63885274026418; u(1) = 33.98267508829284; u(2) = 58.18085749457168;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = -37.761291293282206; m33(0, 1) = -58.77833883088219; m33(0, 2) = -80.31292383738193; m33(1, 0) = 82.42200051847567; m33(1, 1) = -21.616077216647483; m33(1, 2) = -81.41765352024458; m33(2, 0) = -1.826095889555674; m33(2, 1) = -72.65845670305742; m33(2, 2) = -68.43559055076148;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = -0.6810804556978075; m44(0, 1) = -0.3717461369121619; m44(0, 2) = -0.6308202775413543; m44(0, 3) = 65.25663257716863; m44(1, 0) = -0.7322085856273928; m44(1, 1) = 0.3457881173505905; m44(1, 2) = 0.5867718168356992; m44(1, 3) = -72.82746334890318; m44(2, 0) = 0.0; m44(2, 1) = 0.8615308396047228; m44(2, 2) = -0.5077052416609282; m44(2, 3) = -50.951590508183095; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), -10054.998796995307, 1e-3);
-        EXPECT_NEAR(v(1), 1916.692541293076, 1e-3);
-        EXPECT_NEAR(v(2), -6614.459208480986, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), -45.129230953732865, 1e-3);
-        EXPECT_NEAR(w(1), -92.57210823264782, 1e-3);
-        EXPECT_NEAR(w(2), -51.21319422167322, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = 21.26102327359945; u(1) = -63.632003812151375; u(2) = 21.749676556807557;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = -72.46587508929531; m33(0, 1) = 26.74413795088728; m33(0, 2) = 66.40155978725781; m33(1, 0) = 30.554539344667063; m33(1, 1) = 34.707428553000256; m33(1, 2) = -78.73225643210714; m33(2, 0) = 29.88002386285075; m33(2, 1) = 84.40743250651678; m33(2, 2) = 89.33116036637102;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = -0.8156253236747055; m44(0, 1) = 0.0; m44(0, 2) = 0.5785804450381398; m44(0, 3) = -36.44550865077372; m44(1, 0) = -0.4886547783002762; m44(1, 1) = 0.5354367269787551; m44(1, 2) = -0.6888570381774334; m44(1, 3) = 26.24571159164249; m44(2, 0) = -0.3097932197851331; m44(2, 1) = -0.8445753438280554; m44(2, 2) = -0.43671575374937205; m44(2, 3) = 58.09911341828064; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), -1798.269296618443, 1e-3);
-        EXPECT_NEAR(v(1), -3271.2835658593685, 1e-3);
-        EXPECT_NEAR(v(2), -2792.8103398519333, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), -41.2026000982854, 1e-3);
-        EXPECT_NEAR(w(1), -33.19691864907287, 1e-3);
-        EXPECT_NEAR(w(2), 95.75618766923024, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = 60.89920397428068; u(1) = 41.99263628824008; u(2) = 2.8397811977043403;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = 37.756340946034896; m33(0, 1) = 34.695096214807364; m33(0, 2) = 71.82563147437446; m33(1, 0) = 74.91874228380777; m33(1, 1) = 11.371524438829937; m33(1, 2) = 22.662878030996694; m33(2, 0) = -33.183135422386044; m33(2, 1) = -48.81237469926953; m33(2, 2) = 77.28631280104915;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = 0.09071108841607319; m44(0, 1) = 0.15875989354807826; m44(0, 2) = -0.9831412892555038; m44(0, 3) = -20.28034322391565; m44(1, 0) = 0.8682639927927074; m44(1, 1) = -0.49610244790735053; m44(1, 2) = 0.0; m44(1, 3) = -65.91591665493024; m44(2, 0) = -0.487738800238444; m44(2, 1) = -0.8536261812883538; m44(2, 2) = -0.18284749208295362; m44(2, 3) = -28.08938117342305; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), 3960.2387427031354, 1e-3);
-        EXPECT_NEAR(v(1), 5104.369672559086, 1e-3);
-        EXPECT_NEAR(v(2), -3851.1106117734685, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), -10.881269828726621, 1e-3);
-        EXPECT_NEAR(w(1), -33.87198031100272, 1e-3);
-        EXPECT_NEAR(w(2), -94.15754648234068, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = 5.188467455547638; u(1) = 18.80451508110363; u(2) = -21.656727889135595;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = 87.9457818703861; m33(0, 1) = 73.05874068692381; m33(0, 2) = 39.940251688233246; m33(1, 0) = 75.10237717805055; m33(1, 1) = 72.18489393198146; m33(1, 2) = 99.55423077694917; m33(2, 0) = -23.406607601688265; m33(2, 1) = 36.642344803461384; m33(2, 2) = 59.655570064408465;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = 0.17067228277067772; m44(0, 1) = -0.6737686724718157; m44(0, 2) = -0.7189622715340582; m44(0, 3) = -18.335201879756795; m44(1, 0) = -0.9693828421385298; m44(1, 1) = -0.24555428191629253; m44(1, 2) = 0.0; m44(1, 3) = 29.845708309352148; m44(2, 0) = -0.1765442643114522; m44(2, 1) = 0.6969496901700587; m44(2, 2) = -0.6950491005034012; m44(2, 3) = -31.894796135192152; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), 965.1628555052321, 1e-3);
-        EXPECT_NEAR(v(1), -408.9507197542059, 1e-3);
-        EXPECT_NEAR(v(2), -724.347344278602, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), -14.549197180540624, 1e-3);
-        EXPECT_NEAR(w(1), 20.198567783425617, 1e-3);
-        EXPECT_NEAR(w(2), -4.652500106271733, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = 37.47349664672282; u(1) = -60.74514266373965; u(2) = -40.46471876369226;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = -18.595918421354753; m33(0, 1) = -63.34971612297557; m33(0, 2) = 51.78315639657973; m33(1, 0) = 60.68830258069576; m33(1, 1) = -63.44130757420927; m33(1, 2) = 0.1227343978225548; m33(2, 0) = 69.14823593166864; m33(2, 1) = 49.45675635266332; m33(2, 2) = 81.76280170074256;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = -0.250151688477416; m44(0, 1) = -0.2581347286114716; m44(0, 2) = -0.9331616122819132; m44(0, 3) = 15.902624286413442; m44(1, 0) = -0.7181238873483027; m44(1, 1) = 0.6959152839389017; m44(1, 2) = 0.0; m44(1, 3) = -12.358184768214258; m44(2, 0) = 0.6494014283720508; m44(2, 1) = 0.6701256445360971; m44(2, 2) = -0.3594570980846258; m44(2, 3) = -95.12313555065694; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), 1055.9425967082998, 1e-3);
-        EXPECT_NEAR(v(1), 6122.987769732011, 1e-3);
-        EXPECT_NEAR(v(2), -3721.5403091682488, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), 59.969118945113756, 1e-3);
-        EXPECT_NEAR(w(1), -81.54227105743792, 1e-3);
-        EXPECT_NEAR(w(2), -96.94934080054827, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = -18.242981648343232; u(1) = 56.21809486615007; u(2) = 68.42388784251386;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = 72.32617531563085; m33(0, 1) = 16.921578626504015; m33(0, 2) = -27.34080821434577; m33(1, 0) = 75.31926937290174; m33(1, 1) = -81.4337114340538; m33(1, 2) = 49.516021610363254; m33(2, 0) = 40.651084247784695; m33(2, 1) = -19.615350275581747; m33(2, 2) = 96.61096468197644;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = 0.8628144975844739; m44(0, 1) = -0.39604187777629973; m44(0, 2) = 0.3141687027784186; m44(0, 3) = -15.592609294116613; m44(1, 0) = -0.5055206650158348; m44(1, 1) = -0.6759578736217757; m44(1, 2) = 0.5362180622943203; m44(1, 3) = 10.857285613068584; m44(2, 0) = 0.0; m44(2, 1) = -0.6214754895699024; m44(2, 2) = -0.7834336065448367; m44(2, 3) = -95.09026591014809; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), -2238.9105712501655, 1e-3);
-        EXPECT_NEAR(v(1), -2564.0174545638056, 1e-3);
-        EXPECT_NEAR(v(2), 4766.163205213616, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), -32.1009941127323, 1e-3);
-        EXPECT_NEAR(w(1), 18.768550516577342, 1e-3);
-        EXPECT_NEAR(w(2), -183.634007166056, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = -59.27939726364973; u(1) = 96.57872437189005; u(2) = -50.71931054476342;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = -53.51188145034156; m33(0, 1) = -39.773533094835024; m33(0, 2) = -81.91533947789623; m33(1, 0) = -48.98656664587613; m33(1, 1) = -30.35481126192778; m33(1, 2) = -24.41812181189411; m33(2, 0) = 50.987332445586844; m33(2, 1) = -15.614790715203753; m33(2, 2) = 1.953005394977339;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = -0.9781360701985449; m44(0, 1) = 0.0; m44(0, 2) = -0.20796593032645286; m44(0, 3) = 31.079492180635583; m44(1, 0) = 0.17988007252338098; m44(1, 1) = 0.5018585333987298; m44(1, 2) = -0.846038516832336; m44(1, 3) = 89.95140758767585; m44(2, 0) = 0.10436947679053606; m44(2, 1) = -0.8649497167205016; m44(2, 2) = -0.4908859336542387; m44(2, 3) = -66.61272043333199; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), 3485.5645301169448, 1e-3);
-        EXPECT_NEAR(v(1), 1210.7354976539962, 1e-3);
-        EXPECT_NEAR(v(2), -4629.6099911875845, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), 99.6106974667983, 1e-3);
-        EXPECT_NEAR(w(1), 170.66757254759543, 1e-3);
-        EXPECT_NEAR(w(2), -131.4380242858257, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = -33.64679408120854; u(1) = 57.74585710730173; u(2) = -38.78100535372986;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = -48.76215910463826; m33(0, 1) = -17.88064937607517; m33(0, 2) = -10.666843689761578; m33(1, 0) = 54.129177432133815; m33(1, 1) = -50.3409670888066; m33(1, 2) = 67.92880818886752; m33(2, 0) = -36.14536761608753; m33(2, 1) = 92.53432169416001; m33(2, 2) = 68.69365938680332;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = 0.4751126538005149; m44(0, 1) = 0.5241078534879362; m44(0, 2) = -0.7068089728568109; m44(0, 3) = 7.21266115268952; m44(1, 0) = -0.7408885299063788; m44(1, 1) = 0.671628011813954; m44(1, 2) = 0.0; m44(1, 3) = -99.71424185587028; m44(2, 0) = 0.4747127051720829; m44(2, 1) = 0.5236666608245202; m44(2, 2) = 0.7074044641427562; m44(2, 3) = -11.057694172067542; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), 1021.8278247323343, 1e-3);
-        EXPECT_NEAR(v(1), -7362.603053042772, 1e-3);
-        EXPECT_NEAR(v(2), 3895.640286793221, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), 48.90246330164035, 1e-3);
-        EXPECT_NEAR(w(1), -36.001982853511294, 1e-3);
-        EXPECT_NEAR(w(2), -24.22453095406812, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = 15.282052878141911; u(1) = -2.259998336973041; u(2) = 91.08586195638563;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = -88.39582865245377; m33(0, 1) = -64.58071224128338; m33(0, 2) = -4.675696828923634; m33(1, 0) = -86.1584474938788; m33(1, 1) = -34.543435043656444; m33(1, 2) = -62.495745585883625; m33(2, 0) = -59.183456388092395; m33(2, 1) = -57.14307430989349; m33(2, 2) = 44.41751022537625;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = 0.44386855289227883; m44(0, 1) = 0.5950916475208161; m44(0, 2) = 0.6699601770286612; m44(0, 3) = -72.72024311218823; m44(1, 0) = -0.8960919080949868; m44(1, 1) = 0.29477162558569525; m44(1, 2) = 0.33185686823727545; m44(1, 3) = 15.476209050615353; m44(2, 0) = 0.0; m44(2, 1) = -0.7476467212531113; m44(2, 2) = 0.6640966648007446; m44(2, 3) = 99.8824543736142; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), -1630.8073013173835, 1e-3);
-        EXPECT_NEAR(v(1), -6931.088700045262, 1e-3);
-        EXPECT_NEAR(v(2), 3270.5057477108207, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), -6.258026348579378, 1e-3);
-        EXPECT_NEAR(w(1), 31.343370633361097, 1e-3);
-        EXPECT_NEAR(w(2), 162.0619518560263, 1e-3);
-    }
-    {
-        Vector<double, 3> u; u(0) = -45.53190350588168; u(1) = 98.18869916536156; u(2) = 82.67567746788419;
-        Matrix<double, 3, 3, ColumnStorage> m33;
-        m33(0, 0) = -51.297389589304785; m33(0, 1) = -66.59459838930371; m33(0, 2) = 27.56805306675247; m33(1, 0) = 96.48690448918092; m33(1, 1) = 9.10079699500524; m33(1, 2) = 83.88487605323621; m33(2, 0) = 41.570057963368356; m33(2, 1) = 24.52264689542079; m33(2, 2) = -76.44940699537474;
-        Matrix<double, 4, 4, ColumnStorage> m44;
-        m44(0, 0) = 0.774965095070908; m44(0, 1) = 0.0; m44(0, 2) = 0.6320040359220331; m44(0, 3) = -94.78257020280037; m44(1, 0) = -0.5539089538751407; m44(1, 1) = 0.4815245168438749; m44(1, 2) = 0.6792046896887713; m44(1, 3) = 63.87247725975902; m44(2, 0) = -0.3043254380407359; m44(2, 1) = -0.8764326212997054; m44(2, 2) = 0.3731646929748866; m44(2, 3) = -95.85244653326883; m44(3, 0) = 0.0; m44(3, 1) = 0.0; m44(3, 2) = 0.0; m44(3, 3) = 1.0;
-        Vector<double, 3> v = m33 * u;
-        EXPECT_NEAR(v(0), -1923.9617306372265, 1e-3);
-        EXPECT_NEAR(v(1), 3435.6019505357876, 1e-3);
-        EXPECT_NEAR(v(2), -5805.423584529748, 1e-3);
-        Vector<double, 3> w = m44 * u;
-        EXPECT_NEAR(w(0), -77.81684429970429, 1e-3);
-        EXPECT_NEAR(w(1), 192.52698008315832, 1e-3);
-        EXPECT_NEAR(w(2), -137.20006524672516, 1e-3);
-    }
-}
-
-/**
- * Opérateurs d'arithmétique vectorielle
- */
-TEST(TestLabo1b, VectorOperators)
-{
-    Vector<double> v(5);
-    v(0) = 0.1;
-    v(1) = 0.2;
-    v(2) = 0.4;
-    v(3) = 0.8;
-    v(4) = 1.6;
-
-    // Test : multiplication  scalaire * vecteur
-    const double alpha = 4.0;
-    const auto v2 = alpha * v;
-    EXPECT_DOUBLE_EQ(v2(0), alpha * v(0));
-    EXPECT_DOUBLE_EQ(v2(1), alpha * v(1));
-    EXPECT_DOUBLE_EQ(v2(2), alpha * v(2));
-    EXPECT_DOUBLE_EQ(v2(3), alpha * v(3));
-    EXPECT_DOUBLE_EQ(v2(4), alpha * v(4));
-
-    // Test : addition  vecteur + vecteur
-    const auto v3 = v + v2;
-    EXPECT_DOUBLE_EQ(v3(0), v(0) + v2(0));
-    EXPECT_DOUBLE_EQ(v3(1), v(1) + v2(1));
-    EXPECT_DOUBLE_EQ(v3(2), v(2) + v2(2));
-    EXPECT_DOUBLE_EQ(v3(3), v(3) + v2(3));
-    EXPECT_DOUBLE_EQ(v3(4), v(4) + v2(4));
-}
-
-/**
- * Mathématiques 3D
- */
-TEST(TestLabo1b, Math3D)
-{
-    // Test : norme d'un vecteur de dimension 3
-    Vector3d v;
-    v.setZero();
-    v(1) = 2.0;
-    EXPECT_EQ(v.rows(), 3);
-    EXPECT_EQ(v.cols(), 1);
-    EXPECT_DOUBLE_EQ(v(0), 0.0);
-    EXPECT_DOUBLE_EQ(v(1), 2.0);
-    EXPECT_DOUBLE_EQ(v(2), 0.0);
-    EXPECT_DOUBLE_EQ(v.norm(), 2.0);
-
-    // Test : calcul de la norme d'un deuxième vecteur 3D
-    Vector3d v2;
-    v2(0) = 4.0;
-    v2(1) = 2.0;
-    v2(2) = 5.0;
-    EXPECT_EQ(v2.rows(), 3);
-    EXPECT_EQ(v2.cols(), 1);
-    EXPECT_DOUBLE_EQ(v2(0), 4.0);
-    EXPECT_DOUBLE_EQ(v2(1), 2.0);
-    EXPECT_DOUBLE_EQ(v2(2), 5.0);
-    EXPECT_DOUBLE_EQ(v2.norm(), 6.7082039324993690892275210061938);
-
-    // Test : produit scalaire 
-    EXPECT_DOUBLE_EQ(v.dot(v2), 4.0);
-
-    // Test : matrice identité 4x4
-    Matrix4d M;
-    M.setIdentity();
-    EXPECT_DOUBLE_EQ(M(0, 0), 1.0);
-    EXPECT_DOUBLE_EQ(M(0, 1), 0.0);
-    EXPECT_DOUBLE_EQ(M(0, 2), 0.0);
-    EXPECT_DOUBLE_EQ(M(1, 1), 1.0);
-    EXPECT_DOUBLE_EQ(M(1, 0), 0.0);
-    EXPECT_DOUBLE_EQ(M(1, 2), 0.0);
-    EXPECT_DOUBLE_EQ(M(2, 0), 0.0);
-    EXPECT_DOUBLE_EQ(M(2, 1), 0.0);
-    EXPECT_DOUBLE_EQ(M(2, 2), 1.0);
-
-    // Test : création d'une matrice de rotation de 45 degrés autour de l'axe des x
-    const auto Rx = makeRotation<double>(M_PI / 4.0, 0, 0);
-    EXPECT_NEAR(Rx(0, 0), 1, 1e-3); EXPECT_NEAR(Rx(0, 1), 0, 1e-3); EXPECT_NEAR(Rx(0, 2), 0, 1e-3);
-    EXPECT_NEAR(Rx(1, 0), 0, 1e-3); EXPECT_NEAR(Rx(1, 1), 0.7071, 1e-3); EXPECT_NEAR(Rx(1, 2), -0.7071, 1e-3);
-    EXPECT_NEAR(Rx(2, 0), 0, 1e-3); EXPECT_NEAR(Rx(2, 1), 0.7071, 1e-3); EXPECT_NEAR(Rx(2, 2), 0.7071, 1e-3);
-
-    // Test : création d'une matrice de rotation de 45 degrés autour de l'axe des y
-    const auto Ry = makeRotation<double>(0, M_PI / 4.0, 0);
-    EXPECT_NEAR(Ry(0, 0), 0.7071, 1e-3); EXPECT_NEAR(Ry(0, 1), 0, 1e-3); EXPECT_NEAR(Ry(0, 2), 0.7071, 1e-3);
-    EXPECT_NEAR(Ry(1, 0), 0, 1e-3); EXPECT_NEAR(Ry(1, 1), 1, 1e-3); EXPECT_NEAR(Ry(1, 2), 0, 1e-3);
-    EXPECT_NEAR(Ry(2, 0), -0.7071, 1e-3); EXPECT_NEAR(Ry(2, 1), 0, 1e-3); EXPECT_NEAR(Ry(2, 2), 0.7071, 1e-3);
-
-    // Test : création d'une matrice de rotation de 45 degrés autour de l'axe des z
-    const auto Rz = makeRotation<double>(0, 0, M_PI / 4.0);
-    EXPECT_NEAR(Rz(0, 0), 0.7071, 1e-3); EXPECT_NEAR(Rz(0, 1), -0.7071, 1e-3); EXPECT_NEAR(Rz(0, 2), 0, 1e-3);
-    EXPECT_NEAR(Rz(1, 0), 0.7071, 1e-3); EXPECT_NEAR(Rz(1, 1), 0.7071, 1e-3); EXPECT_NEAR(Rz(1, 2), 0, 1e-3);
-    EXPECT_NEAR(Rz(2, 0), 0, 1e-3); EXPECT_NEAR(Rz(2, 1), 0, 1e-3); EXPECT_NEAR(Rz(2, 2), 1, 1e-3);
-
-    // Test : création d'une matrice de rotation quelconque.
-    const auto Rxyz = makeRotation<double>(M_PI / 3.0, -M_PI / 6.0, M_PI / 4.0);
-    EXPECT_NEAR(Rxyz(0, 0), 0.6124, 1e-3); EXPECT_NEAR(Rxyz(0, 1), -0.6597, 1e-3); EXPECT_NEAR(Rxyz(0, 2), 0.4356, 1e-3);
-    EXPECT_NEAR(Rxyz(1, 0), 0.6124, 1e-3); EXPECT_NEAR(Rxyz(1, 1), 0.0474, 1e-3); EXPECT_NEAR(Rxyz(1, 2), -0.7891, 1e-3);
-    EXPECT_NEAR(Rxyz(2, 0), 0.5, 1e-3); EXPECT_NEAR(Rxyz(2, 1), 0.75, 1e-3); EXPECT_NEAR(Rxyz(2, 2), 0.4330, 1e-3);
-
-    // Test : création d'une transformation homogène via la sous-matrice 3x3 en
-    // utilisant la fonction `block`
-    M.block(0, 0, 3, 3) = Rxyz;
-    M(0, 3) = -0.1;
-    M(1, 3) = 1.0;
-    M(2, 3) = 2.1;
-
-    // Test : calcule l'inverse de la matrice M et vérifie que M^(-1) * M * v = v
-    const Matrix4d Minv = M.inverse();
-    const Vector3d v3 = Minv * (M * v2);
-    EXPECT_DOUBLE_EQ(v3(0), v2(0));
-    EXPECT_DOUBLE_EQ(v3(1), v2(1));
-    EXPECT_DOUBLE_EQ(v3(2), v2(2));
-
-    // Test : translation d'un vecteur 3D effectuée avec une matrice 4x4 en coordonnées homogènes
-    Matrix4d T;
-    T.setIdentity();
-    T(0, 3) = 1.2;
-    T(1, 3) = 2.5;
-    T(2, 3) = -4.0;
-    const Vector3d t = T * v3;
-    EXPECT_DOUBLE_EQ(t(0), v3(0) + 1.2);
-    EXPECT_DOUBLE_EQ(t(1), v3(1) + 2.5);
-    EXPECT_DOUBLE_EQ(t(2), v3(2) - 4.0);
-
-    // Test : inverse d'un matrice de rotation
-    const Matrix3d Rinv = Rxyz.inverse();
-    const Matrix3d RT = Rxyz.transpose<double, 3, 3, ColumnStorage>();
-    EXPECT_DOUBLE_EQ(Rinv(0, 0), RT(0, 0));
-    EXPECT_DOUBLE_EQ(Rinv(1, 1), RT(1, 1));
-    EXPECT_DOUBLE_EQ(Rinv(0, 2), RT(0, 2));
-}
-
-TEST(TestLabo1b, RigidTransformInverse) {
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = -0.7899179842354741; m(0, 1) = 0.5558875173441905; m(0, 2) = 0.2588795979645317; m(0, 3) = 63.53646575655944; m(1, 0) = -0.6132125065435026; m(1, 1) = -0.7160740240561843; m(1, 2) = -0.3334792555626483; m(1, 3) = 46.40415080808421; m(2, 0) = 0.0; m(2, 1) = -0.4221694684991984; m(2, 2) = 0.9065169275127214; m(2, 3) = 37.91755407005138; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), -0.7899179842354742, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.6132125065435026, 1e-3);
-        EXPECT_NEAR(mi(0, 2), 5.0321798256853854e-17, 1e-3);
-        EXPECT_NEAR(mi(0, 3), 78.64420258691568, 1e-3);
-        EXPECT_NEAR(mi(1, 0), 0.5558875173441905, 1e-3);
-        EXPECT_NEAR(mi(1, 1), -0.7160740240561843, 1e-3);
-        EXPECT_NEAR(mi(1, 2), -0.42216946849919834, 1e-3);
-        EXPECT_NEAR(mi(1, 3), 13.917312440360101, 1e-3);
-        EXPECT_NEAR(mi(2, 0), 0.25887959796453164, 1e-3);
-        EXPECT_NEAR(mi(2, 1), -0.33347925556264824, 1e-3);
-        EXPECT_NEAR(mi(2, 2), 0.9065169275127212, 1e-3);
-        EXPECT_NEAR(mi(2, 3), -35.34637765902901, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = 0.6589112893907124; m(0, 1) = -0.32720889915223983; m(0, 2) = 0.6773258071482646; m(0, 3) = -47.579657162583366; m(1, 0) = -0.7522206542720485; m(1, 1) = -0.2866202043457096; m(1, 2) = 0.5933067888937011; m(1, 3) = 30.029355381737275; m(2, 0) = 0.0; m(2, 1) = -0.9004350030826229; m(2, 2) = -0.4349905806147956; m(2, 3) = 80.66547089822612; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), 0.6589112893907124, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.7522206542720486, 1e-3);
-        EXPECT_NEAR(mi(0, 2), 5.551115123125783e-17, 1e-3);
-        EXPECT_NEAR(mi(0, 3), 53.939474602384124, 1e-3);
-        EXPECT_NEAR(mi(1, 0), -0.3272088991522398, 1e-3);
-        EXPECT_NEAR(mi(1, 1), -0.28662020434570956, 1e-3);
-        EXPECT_NEAR(mi(1, 2), -0.9004350030826228, 1e-3);
-        EXPECT_NEAR(mi(1, 3), 65.67254627057903, 1e-3);
-        EXPECT_NEAR(mi(2, 0), 0.6773258071482645, 1e-3);
-        EXPECT_NEAR(mi(2, 1), 0.5933067888937011, 1e-3);
-        EXPECT_NEAR(mi(2, 2), -0.43499058061479545, 1e-3);
-        EXPECT_NEAR(mi(2, 3), 49.49902929898342, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = -0.12921677297502387; m(0, 1) = 0.0; m(0, 2) = -0.9916163701663668; m(0, 3) = -85.67624239250289; m(1, 0) = 0.5536164401240612; m(1, 1) = -0.8296411663169171; m(1, 2) = -0.07214133611645579; m(1, 3) = -80.61895745285052; m(2, 0) = -0.8226857618837724; m(2, 1) = -0.5582969954713223; m(2, 2) = 0.1072035542387071; m(2, 3) = -59.16846832515195; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), -0.12921677297502387, 1e-3);
-        EXPECT_NEAR(mi(0, 1), 0.5536164401240611, 1e-3);
-        EXPECT_NEAR(mi(0, 2), -0.8226857618837723, 1e-3);
-        EXPECT_NEAR(mi(0, 3), -15.115883774598393, 1e-3);
-        EXPECT_NEAR(mi(1, 0), -0.0, 1e-3);
-        EXPECT_NEAR(mi(1, 1), -0.829641166316917, 1e-3);
-        EXPECT_NEAR(mi(1, 2), -0.5582969954713222, 1e-3);
-        EXPECT_NEAR(mi(1, 3), -99.91838398100924, 1e-3);
-        EXPECT_NEAR(mi(2, 0), -0.991616370166367, 1e-3);
-        EXPECT_NEAR(mi(2, 1), -0.07214133611645579, 1e-3);
-        EXPECT_NEAR(mi(2, 2), 0.10720355423870709, 1e-3);
-        EXPECT_NEAR(mi(2, 3), -84.43085369439521, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = 0.6178488588834932; m(0, 1) = 0.656563779114608; m(0, 2) = 0.4326508887441579; m(0, 3) = -3.573389719025613; m(1, 0) = -0.7862968825935693; m(1, 1) = 0.5159084191865928; m(1, 2) = 0.33996428553015007; m(1, 3) = 9.98340634305292; m(2, 0) = 0.0; m(2, 1) = -0.5502385909468138; m(2, 2) = 0.8350074808244923; m(2, 3) = 57.03623931292819; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), 0.6178488588834931, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.7862968825935694, 1e-3);
-        EXPECT_NEAR(mi(0, 2), -0.0, 1e-3);
-        EXPECT_NEAR(mi(0, 3), 10.057736045453359, 1e-3);
-        EXPECT_NEAR(mi(1, 0), 0.656563779114608, 1e-3);
-        EXPECT_NEAR(mi(1, 1), 0.5159084191865929, 1e-3);
-        EXPECT_NEAR(mi(1, 2), -0.5502385909468138, 1e-3);
-        EXPECT_NEAR(mi(1, 3), 28.57917482608178, 1e-3);
-        EXPECT_NEAR(mi(2, 0), 0.4326508887441579, 1e-3);
-        EXPECT_NEAR(mi(2, 1), 0.33996428553015007, 1e-3);
-        EXPECT_NEAR(mi(2, 2), 0.8350074808244924, 1e-3);
-        EXPECT_NEAR(mi(2, 3), -49.473657871198526, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = -0.30532791727234754; m(0, 1) = 0.42993321248800975; m(0, 2) = -0.8496659906892062; m(0, 3) = -4.900019523419871; m(1, 0) = -0.9522472698486095; m(1, 1) = -0.13785349298616878; m(1, 2) = 0.272436325656807; m(1, 3) = 61.254180348498465; m(2, 0) = 0.0; m(2, 1) = 0.8922745358191345; m(2, 2) = 0.45149324771113447; m(2, 3) = 41.98722428204593; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), -0.3053279172723474, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.9522472698486094, 1e-3);
-        EXPECT_NEAR(mi(0, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(0, 3), 56.83301324799237, 1e-3);
-        EXPECT_NEAR(mi(1, 0), 0.42993321248800975, 1e-3);
-        EXPECT_NEAR(mi(1, 1), -0.13785349298616878, 1e-3);
-        EXPECT_NEAR(mi(1, 2), 0.8922745358191346, 1e-3);
-        EXPECT_NEAR(mi(1, 3), -26.91334720059331, 1e-3);
-        EXPECT_NEAR(mi(2, 0), -0.8496659906892063, 1e-3);
-        EXPECT_NEAR(mi(2, 1), 0.27243632565680703, 1e-3);
-        EXPECT_NEAR(mi(2, 2), 0.4514932477111345, 1e-3);
-        EXPECT_NEAR(mi(2, 3), -39.80819202150404, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = -0.8426665329724763; m(0, 1) = -0.13329457405486883; m(0, 2) = 0.5216758291656588; m(0, 3) = 54.75958681320196; m(1, 0) = -0.5384358032376251; m(1, 1) = 0.20860959822407732; m(1, 2) = -0.81643672217793; m(1, 3) = 91.96965943681118; m(2, 0) = 0.0; m(2, 1) = -0.9688728461755547; m(2, 2) = -0.24755889792871488; m(2, 3) = 99.00199341303772; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), -0.8426665329724762, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.5384358032376252, 1e-3);
-        EXPECT_NEAR(mi(0, 2), -2.7755575615628914e-17, 1e-3);
-        EXPECT_NEAR(mi(0, 3), 95.66382861923651, 1e-3);
-        EXPECT_NEAR(mi(1, 0), -0.13329457405486886, 1e-3);
-        EXPECT_NEAR(mi(1, 1), 0.20860959822407737, 1e-3);
-        EXPECT_NEAR(mi(1, 2), -0.9688728461755547, 1e-3);
-        EXPECT_NEAR(mi(1, 3), 84.03374523091135, 1e-3);
-        EXPECT_NEAR(mi(2, 0), 0.5216758291656588, 1e-3);
-        EXPECT_NEAR(mi(2, 1), -0.8164367221779302, 1e-3);
-        EXPECT_NEAR(mi(2, 2), -0.2475588979287149, 1e-3);
-        EXPECT_NEAR(mi(2, 3), 71.02947881694217, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = -0.7135830808790772; m(0, 1) = 0.0; m(0, 2) = -0.7005706150582712; m(0, 3) = 46.98894352455778; m(1, 0) = 0.5815768734392242; m(1, 1) = 0.5575439866421585; m(1, 2) = -0.5923791380862643; m(1, 3) = -32.31315706340996; m(2, 0) = 0.39059893364393755; m(2, 1) = -0.8301473983330724; m(2, 2) = -0.39785395571371457; m(2, 3) = 7.702713412699751; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), -0.7135830808790772, 1e-3);
-        EXPECT_NEAR(mi(0, 1), 0.581576873439224, 1e-3);
-        EXPECT_NEAR(mi(0, 2), 0.39059893364393744, 1e-3);
-        EXPECT_NEAR(mi(0, 3), 49.314428298230084, 1e-3);
-        EXPECT_NEAR(mi(1, 0), -5.551115123125783e-17, 1e-3);
-        EXPECT_NEAR(mi(1, 1), 0.5575439866421584, 1e-3);
-        EXPECT_NEAR(mi(1, 2), -0.8301473983330723, 1e-3);
-        EXPECT_NEAR(mi(1, 3), 24.41039390978577, 1e-3);
-        EXPECT_NEAR(mi(2, 0), -0.7005706150582711, 1e-3);
-        EXPECT_NEAR(mi(2, 1), -0.5923791380862641, 1e-3);
-        EXPECT_NEAR(mi(2, 2), -0.3978539557137144, 1e-3);
-        EXPECT_NEAR(mi(2, 3), 16.841987936840617, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = 0.655199358191179; m(0, 1) = -0.7015590749923188; m(0, 2) = 0.2802296653136303; m(0, 3) = -24.378695814492147; m(1, 0) = -0.7554560219005917; m(1, 1) = -0.6084550818878111; m(1, 2) = 0.24304035117451178; m(1, 3) = 36.943036725120294; m(2, 0) = 0.0; m(2, 1) = -0.3709410702804682; m(2, 2) = -0.928656407063011; m(2, 3) = -32.64950630748629; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), 0.6551993581911789, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.7554560219005915, 1e-3);
-        EXPECT_NEAR(mi(0, 2), 5.1550786254351327e-17, 1e-3);
-        EXPECT_NEAR(mi(0, 3), 43.88174541248007, 1e-3);
-        EXPECT_NEAR(mi(1, 0), -0.7015590749923187, 1e-3);
-        EXPECT_NEAR(mi(1, 1), -0.6084550818878111, 1e-3);
-        EXPECT_NEAR(mi(1, 2), -0.37094107028046824, 1e-3);
-        EXPECT_NEAR(mi(1, 3), -6.735959663194609, 1e-3);
-        EXPECT_NEAR(mi(2, 0), 0.28022966531363025, 1e-3);
-        EXPECT_NEAR(mi(2, 1), 0.24304035117451175, 1e-3);
-        EXPECT_NEAR(mi(2, 2), -0.9286564070630109, 1e-3);
-        EXPECT_NEAR(mi(2, 3), -32.467188070139514, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = -0.12316316348384228; m(0, 1) = 0.47851608243384774; m(0, 2) = -0.8693981792095123; m(0, 3) = -97.68194268706864; m(1, 0) = -0.9684362001788849; m(1, 1) = -0.24926156178416892; m(1, 2) = 0.0; m(1, 3) = -93.30408292578261; m(2, 0) = -0.2167075479620758; m(2, 1) = 0.8419566691161013; m(2, 2) = 0.4941121390809829; m(2, 3) = -48.17348057895294; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), -0.12316316348384225, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.9684362001788847, 1e-3);
-        EXPECT_NEAR(mi(0, 2), -0.2167075479620758, 1e-3);
-        EXPECT_NEAR(mi(0, 3), -112.82942545947078, 1e-3);
-        EXPECT_NEAR(mi(1, 0), 0.47851608243384763, 1e-3);
-        EXPECT_NEAR(mi(1, 1), -0.2492615617841688, 1e-3);
-        EXPECT_NEAR(mi(1, 2), 0.8419566691161011, 1e-3);
-        EXPECT_NEAR(mi(1, 3), 64.04524235620795, 1e-3);
-        EXPECT_NEAR(mi(2, 0), -0.8693981792095123, 1e-3);
-        EXPECT_NEAR(mi(2, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(2, 2), 0.49411213908098284, 1e-3);
-        EXPECT_NEAR(mi(2, 3), -61.12140157794279, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-    {
-        Matrix<double, 4, 4, ColumnStorage> m;
-        m(0, 0) = -0.8820615884895145; m(0, 1) = -0.11346792289034995; m(0, 2) = -0.45726620757093356; m(0, 3) = -48.8253349197771; m(1, 0) = -0.12758811649101956; m(1, 1) = 0.9918272392560481; m(1, 2) = 0.0; m(1, 3) = 50.033634014775515; m(2, 0) = 0.4535290802601621; m(2, 1) = 0.058341734158967; m(2, 2) = -0.8893298687290875; m(2, 3) = 92.22065810812657; m(3, 0) = 0.0; m(3, 1) = 0.0; m(3, 2) = 0.0; m(3, 3) = 1.0;
-        Matrix<double, 4, 4, ColumnStorage> mi = m.inverse();
-        EXPECT_NEAR(mi(0, 0), -0.8820615884895142, 1e-3);
-        EXPECT_NEAR(mi(0, 1), -0.12758811649101953, 1e-3);
-        EXPECT_NEAR(mi(0, 2), 0.453529080260162, 1e-3);
-        EXPECT_NEAR(mi(0, 3), -78.50800560549041, 1e-3);
-        EXPECT_NEAR(mi(1, 0), -0.11346792289034992, 1e-3);
-        EXPECT_NEAR(mi(1, 1), 0.991827239256048, 1e-3);
-        EXPECT_NEAR(mi(1, 2), 0.05834173415896697, 1e-3);
-        EXPECT_NEAR(mi(1, 3), -60.545143551904374, 1e-3);
-        EXPECT_NEAR(mi(2, 0), -0.45726620757093345, 1e-3);
-        EXPECT_NEAR(mi(2, 1), 6.120531779240618e-18, 1e-3);
-        EXPECT_NEAR(mi(2, 2), -0.8893298687290875, 1e-3);
-        EXPECT_NEAR(mi(2, 3), 59.68841003726312, 1e-3);
-        EXPECT_NEAR(mi(3, 0), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 1), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 2), 0.0, 1e-3);
-        EXPECT_NEAR(mi(3, 3), 1.0, 1e-3);
-    }
-}
-
-/**
- * Test des performance de la multiplication  matrice * vecteur
- * pour de grandes dimensions.
- */
-TEST(TestLabo1b, PerformanceMatrixVector)
-{
-    Matrix<double> A(16384, 16384);     // grande matrice avec stockage colonne
-    Vector<double> v(16384);            // grand vecteur
-
-    using namespace std::chrono;
-    // Test : multiplication avec l'algorithme naif.
-    high_resolution_clock::time_point t = high_resolution_clock::now();
-    naiveMatrixMult(A, v);
-    const duration<double> naive_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
-
-    // Test : multiplication avec l'implémentation spécifique pour les matrices avec
-    // stockage par colonnes.
-    t = high_resolution_clock::now();
-    A* v;
-    const duration<double> optimal_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
-
-    EXPECT_TRUE(optimal_t < 0.4 * naive_t)
-        << "Naive time: " << duration_cast<std::chrono::milliseconds>(naive_t).count() << " ms, "
-        << "optimized time: " << duration_cast<std::chrono::milliseconds>(optimal_t).count() << " ms";
-}
-
-/**
- * Test des performances de l'addition  matrice + matrice
- * pour de grandes dimensions.
- */
-TEST(TestLabo1b, PerformanceLargeMatrixMatrix)
-{
-    // deux grandes matrices à stockage par colonnes
-    Matrix<double> A(16384, 16384);
-    Matrix<double> B(16384, 16384);
-
-    using namespace std::chrono;
-    high_resolution_clock::time_point t = high_resolution_clock::now();
-    // Test : addition avec l'algorithme naif 
-    naiveMatrixAddition(A, B);
-    const duration<double> naive_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
-
-    // Test : addition avec l'implémentation spécifique pour les matrices à
-    // stockage par colonnes.
-    t = high_resolution_clock::now();
-    A + B;
-    const duration<double> optimal_t = duration_cast<duration<double>>(high_resolution_clock::now() - t);
-
-    EXPECT_TRUE(optimal_t < 0.4 * naive_t);
-}
-
-/**
- * Test pour la matrice à taille fixe 4D
- */
-TEST(TestLabo1b, Matrix4x4SizeTest)
-{
-    Matrix4d M;
-
-    EXPECT_EQ(M.cols(), 4);
-    EXPECT_EQ(M.rows(), 4);
-}
-
-/**
- * Test pour la matrice à taille fixe 3D
- */
-TEST(TestLabo1b, Matrix3x3SizeTest)
-{
-    Matrix3d M;
-
-    EXPECT_EQ(M.cols(), 3);
-    EXPECT_EQ(M.rows(), 3);
-}

labo01/tests/TestsSupplementaire1a.cpp

@@ -1,54 +0,0 @@
-/**
- * @file TestsSupplementaire1a.cpp
- *
- * @brief Tests unitaires supplémentaires de la partie 1a
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include "Matrix.h"
-#include "Vector.h"
-
-#include <gtest/gtest.h>
-
-using namespace gti320;
-
-TEST(TestLabo1a, Supplementaires)
-{
-    // TODO vos propres tests ici
-
-    // TEST 1 
-    //
-
-    // TEST 2
-    //
-
-    // TEST 3 
-    //
-
-    // TEST 4 
-    //
-
-    // TEST 5 
-    //
-
-    // TEST 6 
-    //
-
-    // TEST 7
-    //
-
-    // TEST 8 
-    //
-
-    // TEST 9 
-    //
-
-    // TEST 10 
-    //
-    
-    EXPECT_TRUE(false);
-}

labo01/tests/TestsSupplementaire1b.cpp

@@ -1,56 +0,0 @@
-/**
- * @file TestsSupplementaire1b.cpp
- *
- * @brief Tests unitaires supplémentaires de la partie 1b
- *
- * Nom:
- * Code permanent :
- * Email :
- *
- */
-
-#include "Matrix.h"
-#include "Vector.h"
-#include "Math3D.h"
-#include "Operators.h"
-
-#include <gtest/gtest.h>
-
-using namespace gti320; 
-
-TEST(TestLabo1b, Supplementaires)
-{
-    // TODO vos propres tests ici
-
-    // TEST 1 
-    //
-
-    // TEST 2
-    //
-
-    // TEST 3 
-    //
-
-    // TEST 4 
-    //
-
-    // TEST 5 
-    //
-
-    // TEST 6 
-    //
-
-    // TEST 7
-    //
-
-    // TEST 8 
-    //
-
-    // TEST 9 
-    //
-
-    // TEST 10 
-    //
-
-    EXPECT_TRUE(false);
-}

labo_ik/IKApplication.cpp

@@ -20,6 +20,7 @@
 
 #define _USE_MATH_DEFINES
 #include <cmath>
+#include <random>
 
 #include "IKSolver.h"
 

labo_ik/IKApplication.h

@@ -18,6 +18,7 @@
 #include <nanogui/slider.h>
 #include <nanogui/screen.h>
 #include <nanogui/vscrollpanel.h>
+#include <memory>
 
 #include "Armature.h"
 #include "LinkUI.h"