609 lines
19 KiB
C++
609 lines
19 KiB
C++
/**
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* @file main.cpp
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*
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* @brief Unit tests for a simple linear algebra library.
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*
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* Nom: William Nolin
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* Code permanent : NOLW76060101
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* Email : william.nolin.1@ens.etsmtl.ca
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*
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*/
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#include "Matrix.h"
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#include "Vector.h"
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#include "Math3D.h"
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#include "Operators.h"
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#include <gtest/gtest.h>
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#include <chrono>
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using namespace gti320;
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/**
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* Multiplication matrice * vecteur, utilisant une implémentation naive
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*/
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template<typename _Scalar>
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static inline Vector<_Scalar, Dynamic> naiveMatrixMult(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& A, const Vector<_Scalar, Dynamic>& v)
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{
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assert(A.cols() == v.rows());
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Vector<_Scalar, Dynamic> b(A.rows());
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assert(b.rows() == A.rows());
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for (int i = 0; i < A.rows(); ++i) {
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b(i) = 0.0;
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for (int j = 0; j < A.cols(); ++j) {
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b(i) += A(i, j) * v(j);
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}
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}
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return b;
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}
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/**
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* Addition matrice + matrice, utilisant une implémentation naive
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*/
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template<typename _Scalar>
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static inline Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> naiveMatrixAddition(const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& A, const Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage>& B)
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{
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assert(A.cols() == B.cols() && A.rows() == B.rows());
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Matrix<_Scalar, Dynamic, Dynamic, ColumnStorage> C(A.rows(), A.cols());
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assert(C.rows() == A.rows() && C.cols() == A.cols());
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for (int i = 0; i < C.rows(); ++i) {
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for (int j = 0; j < C.cols(); ++j) {
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C(i, j) = A(i, j) + B(i, j);
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}
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}
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return C;
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}
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/**
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* Multiplication matrice * matrice, utilisant une implémentation naive.
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*/
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template<typename _Scalar, int _Storage>
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static inline Matrix<_Scalar, Dynamic, Dynamic, _Storage> naiveMatrixMult(const Matrix<_Scalar, Dynamic, Dynamic, _Storage>& A, const Matrix<_Scalar, Dynamic, Dynamic, _Storage>& B)
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{
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assert(A.cols() == B.rows());
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Matrix<_Scalar, Dynamic, Dynamic> product(A.rows(), B.cols());
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for (int i = 0; i < A.rows(); ++i)
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{
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for (int j = 0; j < B.cols(); ++j)
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{
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for (int k = 0; k < A.cols(); ++k)
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{
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product(i, j) += A(i, k) * B(k, j);
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}
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}
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}
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return product;
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}
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// Test les matrice avec redimensionnement dynamique
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TEST(TestLabo1, DynamicMatrixTests)
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{
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// Crée une matrice à taille dynamique
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// (note : les valeurs par défaut du patron de la classe `Matrix` mettent le
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// le nombre de ligne et de colonnes à `Dynamic`)
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Matrix<double> M(3, 5);
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EXPECT_EQ(M.cols(), 5);
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EXPECT_EQ(M.rows(), 3);
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// Redimensionne la matrice
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M.resize(100, 1000);
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EXPECT_EQ(M.cols(), 1000);
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EXPECT_EQ(M.rows(), 100);
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// Test - stockage par colonnes
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Matrix<double, Dynamic, Dynamic, ColumnStorage> ColM(100, 100);
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ColM.setZero();
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ColM(0, 0) = 1.0;
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ColM(99, 99) = 99.0;
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ColM(10, 33) = 5.0;
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EXPECT_EQ(ColM(0, 0), 1.0);
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EXPECT_EQ(ColM(10, 33), 5.0);
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EXPECT_EQ(ColM(99, 99), 99.0);
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// Test - stockage par lignes
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Matrix<double, Dynamic, Dynamic, RowStorage> RowM(5, 4);
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RowM.setZero();
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RowM(0, 0) = 2.1;
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RowM(3, 3) = -0.2;
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RowM(4, 3) = 1.2;
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EXPECT_EQ(RowM.rows(), 5);
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EXPECT_EQ(RowM.cols(), 4);
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EXPECT_DOUBLE_EQ(RowM(0, 0), 2.1);
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EXPECT_DOUBLE_EQ(RowM(3, 3), -0.2);
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EXPECT_DOUBLE_EQ(RowM(4, 3), 1.2);
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EXPECT_DOUBLE_EQ(RowM(3, 2), 0.0);
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// Transposée
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const auto RowMT = RowM.transpose();
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EXPECT_EQ(RowMT.rows(), 4);
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EXPECT_EQ(RowMT.cols(), 5);
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EXPECT_DOUBLE_EQ(RowMT(0, 0), 2.1);
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EXPECT_DOUBLE_EQ(RowMT(3, 3), -0.2);
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EXPECT_DOUBLE_EQ(RowMT(3, 4), 1.2);
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EXPECT_DOUBLE_EQ(RowMT(2, 3), 0.0);
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}
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/**
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* Test pour les vecteurs à taille dynamique
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*/
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TEST(TestLabo1, DynamicVectorSizeTest)
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{
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Vector<double> v(5);
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v.setZero();
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EXPECT_EQ(v.rows(), 5);
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v.resize(3);
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EXPECT_EQ(v.rows(), 3);
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v(0) = 1.0;
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v(1) = 2.0;
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v(2) = 3.0;
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EXPECT_DOUBLE_EQ(v.norm(), 3.7416573867739413855837487323165);
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Vector<double, Dynamic> v2(3);
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v2.setZero();
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v2(1) = 2.0;
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EXPECT_DOUBLE_EQ(v2.dot(v), 4.0);
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EXPECT_DOUBLE_EQ(v2(0), 0.0);
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EXPECT_DOUBLE_EQ(v2(1), 2.0);
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EXPECT_DOUBLE_EQ(v2(2), 0.0);
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}
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/**
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* Test pour les matrice à taille fixe
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*/
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TEST(TestLabo1, Matrix4x4SizeTest)
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{
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Matrix4d M;
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M.setZero();
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EXPECT_EQ(M.cols(), 4);
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EXPECT_EQ(M.rows(), 4);
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}
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/**
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* Test pour les opérateurs d'arithmétique matricielle.
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*/
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TEST(TestLabo1, MatrixMatrixOperators)
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{
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// Opérations arithmétiques avec matrices à taille dynamique
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// {
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// // Test : matrice identité
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// Matrix<double> A(6, 6);
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// A.setIdentity();
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// EXPECT_DOUBLE_EQ(A(0, 0), 1.0);
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// EXPECT_DOUBLE_EQ(A(1, 1), 1.0);
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// EXPECT_DOUBLE_EQ(A(2, 2), 1.0);
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// EXPECT_DOUBLE_EQ(A(3, 3), 1.0);
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// EXPECT_DOUBLE_EQ(A(4, 4), 1.0);
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// EXPECT_DOUBLE_EQ(A(5, 5), 1.0);
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// EXPECT_DOUBLE_EQ(A(0, 1), 0.0);
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// EXPECT_DOUBLE_EQ(A(1, 0), 0.0);
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//
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// // Test : produit scalaire * matrice
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// const double alpha = 2.5;
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// Matrix<double> B = alpha * A;
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// EXPECT_DOUBLE_EQ(B(0, 0), alpha);
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// EXPECT_DOUBLE_EQ(B(1, 1), alpha);
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// EXPECT_DOUBLE_EQ(B(2, 2), alpha);
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// EXPECT_DOUBLE_EQ(B(3, 3), alpha);
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// EXPECT_DOUBLE_EQ(B(4, 4), alpha);
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// EXPECT_DOUBLE_EQ(B(5, 5), alpha);
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// EXPECT_DOUBLE_EQ(B(0, 1), 0.0);
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// EXPECT_DOUBLE_EQ(B(1, 0), 0.0);
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//
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// // Test : produit matrice * matrice
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// Matrix<double> C = A * B;
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// EXPECT_DOUBLE_EQ(C(0, 0), A(0, 0) * B(0, 0));
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// EXPECT_DOUBLE_EQ(C(1, 1), A(1, 1) * B(1, 1));
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// EXPECT_DOUBLE_EQ(C(2, 2), A(2, 2) * B(2, 2));
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// EXPECT_DOUBLE_EQ(C(3, 3), A(3, 3) * B(3, 3));
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// EXPECT_DOUBLE_EQ(C(4, 4), A(4, 4) * B(4, 4));
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// EXPECT_DOUBLE_EQ(C(5, 5), A(5, 5) * B(5, 5));
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// EXPECT_DOUBLE_EQ(C(0, 1), 0.0);
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// EXPECT_DOUBLE_EQ(C(2, 3), 0.0);
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//
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// // Test : addition matrice * matrice
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// Matrix<double> A_plus_B = A + B;
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// EXPECT_DOUBLE_EQ(A_plus_B(0, 0), A(0, 0) + B(0, 0));
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// EXPECT_DOUBLE_EQ(A_plus_B(1, 1), A(1, 1) + B(1, 1));
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// EXPECT_DOUBLE_EQ(A_plus_B(2, 2), A(2, 2) + B(2, 2));
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// EXPECT_DOUBLE_EQ(A_plus_B(3, 3), A(3, 3) + B(3, 3));
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// EXPECT_DOUBLE_EQ(A_plus_B(4, 4), A(4, 4) + B(4, 4));
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// EXPECT_DOUBLE_EQ(A_plus_B(5, 5), A(5, 5) + B(5, 5));
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// EXPECT_DOUBLE_EQ(A_plus_B(0, 1), 0.0);
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// EXPECT_DOUBLE_EQ(A_plus_B(2, 3), 0.0);
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// }
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// Opérations arithmétique avec matrices à stockage par lignes et par
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// colonnes.
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{
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// Création d'un matrice à stockage par lignes
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Matrix<double, Dynamic, Dynamic, RowStorage> A(5, 5);
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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;
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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;
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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;
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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;
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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;
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// Test : transposée (le résultat est une matrice à stockage par
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// colonnes)
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Matrix<double, Dynamic, Dynamic, ColumnStorage> B = A.transpose();
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// Test : multiplication matrix(ligne) * matrice(colonne)
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// Note : teste seulement la première et la dernière colonne
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const auto C = A * B;
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EXPECT_NEAR(C(0, 0), 1.14815820000000, 1e-3); EXPECT_NEAR(C(0, 4), 1.31659795000000, 1e-3);
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EXPECT_NEAR(C(1, 0), 1.00133748000000, 1e-3); EXPECT_NEAR(C(1, 4), 2.04727044000000, 1e-3);
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EXPECT_NEAR(C(2, 0), 0.99433707000000, 1e-3); EXPECT_NEAR(C(2, 4), 2.82896409000000, 1e-3);
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EXPECT_NEAR(C(3, 0), 1.63883925000000, 1e-3); EXPECT_NEAR(C(3, 4), 3.28401323000000, 1e-3);
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EXPECT_NEAR(C(4, 0), 1.31659795000000, 1e-3); EXPECT_NEAR(C(4, 4), 3.35271580000000, 1e-3);
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// Test : multiplication matrice(colonne) * matrice(ligne)
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// Note : teste seulement la première et la dernière colonne
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const auto C2 = B * A;
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EXPECT_NEAR(C2(0, 0), 2.73456805000000, 1e-3); EXPECT_NEAR(C2(0, 4), 1.95669703000000, 1e-3);
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EXPECT_NEAR(C2(1, 0), 1.88593811000000, 1e-3); EXPECT_NEAR(C2(1, 4), 2.08742862000000, 1e-3);
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EXPECT_NEAR(C2(2, 0), 2.07860468000000, 1e-3); EXPECT_NEAR(C2(2, 4), 1.94727447000000, 1e-3);
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EXPECT_NEAR(C2(3, 0), 1.94434955000000, 1e-3); EXPECT_NEAR(C2(3, 4), 2.27675041000000, 1e-3);
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EXPECT_NEAR(C2(4, 0), 1.95669703000000, 1e-3); EXPECT_NEAR(C2(4, 4), 2.48517748000000, 1e-3);
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// Test : addition matrice(ligne) + matrice(ligne)
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// Note : teste seulement la première et la dernière colonne
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const auto A_plus_A = A + A;
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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));
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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));
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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));
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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));
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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));
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// Test : addition matrice(colonne) + matrice(colonne)
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// Note : teste seulement la première et la dernière colonne
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const auto B_plus_B = B + B;
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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));
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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));
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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));
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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));
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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));
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}
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}
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/**
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* Test pour la multiplication matrice * vecteur
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*/
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TEST(TestLabo1, MatrixVectorOperators)
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{
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// Vecteur à taille dynamique
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Vector<double> v(5);
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v(0) = 1.0;
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v(1) = 2.0;
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v(2) = 4.0;
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v(3) = 8.0;
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v(4) = 16.0;
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// Test : multiplication par la matrice identité
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{
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Matrix<double> M(5, 5);
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M.setIdentity();
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const auto b = M * v;
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EXPECT_DOUBLE_EQ(b(0), 1.0);
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EXPECT_DOUBLE_EQ(b(1), 2.0);
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EXPECT_DOUBLE_EQ(b(2), 4.0);
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EXPECT_DOUBLE_EQ(b(3), 8.0);
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EXPECT_DOUBLE_EQ(b(4), 16.0);
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}
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// Test : multiplication par une matrice à taille dynamique avec stockage par ligne.
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{
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Matrix<double, Dynamic, Dynamic, RowStorage> M(5, 5);
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M.setIdentity();
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M = 2.0 * M;
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Vector<double> b2 = M * v;
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EXPECT_DOUBLE_EQ(b2(0), 2.0);
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EXPECT_DOUBLE_EQ(b2(1), 4.0);
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EXPECT_DOUBLE_EQ(b2(2), 8.0);
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EXPECT_DOUBLE_EQ(b2(3), 16.0);
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EXPECT_DOUBLE_EQ(b2(4), 32.0);
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}
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}
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/**
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* Opérateurs d'arithmétique vectorielle
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*/
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TEST(TestLabo1, VectorOperators)
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{
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Vector<double> v(5);
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v(0) = 0.1;
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v(1) = 0.2;
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v(2) = 0.4;
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v(3) = 0.8;
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v(4) = 1.6;
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// Test : multiplication scalaire * vecteur
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const double alpha = 4.0;
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const auto v2 = alpha * v;
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EXPECT_DOUBLE_EQ(v2(0), alpha * v(0));
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EXPECT_DOUBLE_EQ(v2(1), alpha * v(1));
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EXPECT_DOUBLE_EQ(v2(2), alpha * v(2));
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EXPECT_DOUBLE_EQ(v2(3), alpha * v(3));
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EXPECT_DOUBLE_EQ(v2(4), alpha * v(4));
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// Test : addition vecteur + vecteur
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const auto v3 = v + v2;
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EXPECT_DOUBLE_EQ(v3(0), v(0) + v2(0));
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EXPECT_DOUBLE_EQ(v3(1), v(1) + v2(1));
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EXPECT_DOUBLE_EQ(v3(2), v(2) + v2(2));
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EXPECT_DOUBLE_EQ(v3(3), v(3) + v2(3));
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EXPECT_DOUBLE_EQ(v3(4), v(4) + v2(4));
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}
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/**
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* Mathématiques 3D
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*/
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TEST(TestLabo1, Math3D)
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{
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// Test : norme d'un vecteur de dimension 3
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Vector3d v;
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v.setZero();
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v(1) = 2.0;
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EXPECT_EQ(v.rows(), 3);
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EXPECT_EQ(v.cols(), 1);
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EXPECT_DOUBLE_EQ(v(0), 0.0);
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EXPECT_DOUBLE_EQ(v(1), 2.0);
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EXPECT_DOUBLE_EQ(v(2), 0.0);
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EXPECT_DOUBLE_EQ(v.norm(), 2.0);
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// Test : calcul de la norme d'un deuxième vecteur 3D
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Vector3d v2;
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v2(0) = 4.0;
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v2(1) = 2.0;
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v2(2) = 5.0;
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EXPECT_EQ(v2.rows(), 3);
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EXPECT_EQ(v2.cols(), 1);
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EXPECT_DOUBLE_EQ(v2(0), 4.0);
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EXPECT_DOUBLE_EQ(v2(1), 2.0);
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EXPECT_DOUBLE_EQ(v2(2), 5.0);
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EXPECT_DOUBLE_EQ(v2.norm(), 6.7082039324993690892275210061938);
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// Test : produit scalaire
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EXPECT_DOUBLE_EQ(v.dot(v2), 4.0);
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// Test : matrice identité 4x4
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Matrix4d M;
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M.setIdentity();
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EXPECT_DOUBLE_EQ(M(0, 0), 1.0);
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EXPECT_DOUBLE_EQ(M(0, 1), 0.0);
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EXPECT_DOUBLE_EQ(M(0, 2), 0.0);
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EXPECT_DOUBLE_EQ(M(1, 1), 1.0);
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EXPECT_DOUBLE_EQ(M(1, 0), 0.0);
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EXPECT_DOUBLE_EQ(M(1, 2), 0.0);
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EXPECT_DOUBLE_EQ(M(2, 0), 0.0);
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EXPECT_DOUBLE_EQ(M(2, 1), 0.0);
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EXPECT_DOUBLE_EQ(M(2, 2), 1.0);
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|
|
|
// Test : création d'une matrice de rotation de 45 degrés autour de l'axe des x
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const auto Rx = makeRotation<double>(M_PI / 4.0, 0, 0);
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EXPECT_NEAR(Rx(0, 0), 1, 1e-3); EXPECT_NEAR(Rx(0, 1), 0, 1e-3); EXPECT_NEAR(Rx(0, 2), 0, 1e-3);
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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);
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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);
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|
|
|
// Test : création d'une matrice de rotation de 45 degrés autour de l'axe des y
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const auto Ry = makeRotation<double>(0, M_PI / 4.0, 0);
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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);
|
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EXPECT_NEAR(Ry(1, 0), 0, 1e-3); EXPECT_NEAR(Ry(1, 1), 1, 1e-3); EXPECT_NEAR(Ry(1, 2), 0, 1e-3);
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|
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);
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|
|
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// 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);
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|
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 i = 0; i < MC.rows(); i++) {
|
|
for (int j = 0; j < MC.cols(); j++) {
|
|
int expected = 0;
|
|
if (i == j) {
|
|
expected = 1;
|
|
}
|
|
|
|
EXPECT_EQ(MC(i, j), 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 i = 0; i < s.rows(); i++) {
|
|
for (int j = 0; j < s.cols(); j++) {
|
|
EXPECT_EQ(s(i, j), MC(i + 1, j + 1));
|
|
}
|
|
}
|
|
|
|
// Test 7: Transposée d'une sous-matrice
|
|
const Matrix<int, -1, -1, ColumnStorage> t = s.transpose<int, -1, -1, ColumnStorage>();
|
|
for (int i = 0; i < t.rows(); i++) {
|
|
for (int j = 0; j < t.cols(); j++) {
|
|
EXPECT_EQ(t(j, i), s(i, j));
|
|
}
|
|
}
|
|
|
|
// 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(0, 1));
|
|
|
|
// 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(1, 0));
|
|
|
|
// === 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));
|
|
}
|
|
|
|
int main(int argc, char** argv)
|
|
{
|
|
::testing::InitGoogleTest(&argc, argv);
|
|
const int ret = RUN_ALL_TESTS();
|
|
|
|
return ret;
|
|
}
|