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lib_math/labo01/main.cpp

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/**
* @file main.cpp
*
* @brief Unit tests for a simple linear algebra library.
*
* Nom: William Nolin
* Code permanent : NOLW76060101
* 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>
using namespace gti320;
/**
* Multiplication matrice * vecteur, utilisant une implémentation naive
*/
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) {
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);
}
}
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return b;
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}
/**
* Addition matrice + matrice, utilisant une implémentation naive
*/
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) {
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;
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}
/**
* Multiplication matrice * matrice, utilisant une implémentation naive.
*/
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) {
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;
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}
// Test les matrice avec redimensionnement dynamique
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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);
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}
/**
* Test pour les vecteurs à taille dynamique
*/
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TEST(TestLabo1, DynamicVectorSizeTest) {
Vector<double> v(5);
v.setZero();
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EXPECT_EQ(v.rows(), 5);
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v.resize(3);
EXPECT_EQ(v.rows(), 3);
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v(0) = 1.0;
v(1) = 2.0;
v(2) = 3.0;
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EXPECT_DOUBLE_EQ(v.norm(), 3.7416573867739413855837487323165);
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Vector<double, Dynamic> v2(3);
v2.setZero();
v2(1) = 2.0;
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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);
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}
/**
* Test pour les matrice à taille fixe
*/
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TEST(TestLabo1, Matrix4x4SizeTest) {
Matrix4d M;
M.setZero();
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EXPECT_EQ(M.cols(), 4);
EXPECT_EQ(M.rows(), 4);
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}
/**
* Test pour les opérateurs d'arithmétique matricielle.
*/
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TEST(TestLabo1, MatrixMatrixOperators) {
// Opérations arithmétiques avec matrices à taille dynamique
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{
// 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);
}
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// 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);
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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;
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;
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// 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));
}
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}
/**
* Test pour la multiplication matrice * vecteur
*/
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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);
}
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// 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);
}
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}
/**
* Opérateurs d'arithmétique vectorielle
*/
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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));
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}
/**
* Mathématiques 3D
*/
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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));
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}
/**
* Test des performance de la multiplication matrice * vecteur
* pour de grandes dimensions.
*/
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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";
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}
/**
* Test des performances de l'addition matrice + matrice
* pour de grandes dimensions.
*/
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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);
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}
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TEST(TestLabo1, Supplementaires) {
Partie 1 Finie
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// === 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]);
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// === Matrices ===
Partie 1 Finie
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// Test 5: Identité
Matrix<int, -1, -1, ColumnStorage> MC(4, 6);
MC.setIdentity();
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for (int col = 0; col < MC.cols(); col++) {
for (int row = 0; row < MC.rows(); row++) {
Partie 1 Finie
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int expected = 0;
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if (row == col) {
Partie 1 Finie
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expected = 1;
}
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EXPECT_EQ(MC(row, col), expected);
Partie 1 Finie
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}
}
// 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);
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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));
Partie 1 Finie
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}
}
// Test 7: Transposée d'une sous-matrice
const Matrix<int, -1, -1, ColumnStorage> t = s.transpose<int, -1, -1, ColumnStorage>();
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for (int col = 0; col < t.cols(); col++) {
for (int row = 0; row < t.rows(); row++) {
EXPECT_EQ(t(col, row), s(row, col));
Partie 1 Finie
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}
}
// 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));
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EXPECT_EQ(MC.data()[1], MC(1, 0));
Partie 1 Finie
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// 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));
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EXPECT_EQ(MS.data()[1], MS(0, 1));
Partie 1 Finie
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// === 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));
Dingu'yddie
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// === 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);
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}
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int main(int argc, char **argv) {
::testing::InitGoogleTest(&argc, argv);
const int ret = RUN_ALL_TESTS();
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return ret;
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}