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Solveurs, problèmes de perf

This commit is contained in:
william 2024-03-09 16:19:14 -05:00
parent 65b6524520
commit 847964fd1e
6 changed files with 252 additions and 198 deletions
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2
labo01/DenseStorage.h
View File

@ -137,7 +137,7 @@ namespace gti320 {
* Constructeur de copie
*/
DenseStorage(const DenseStorage &other)
: m_data(new _Scalar[m_size]), m_size(other.m_size) {
: m_data(new _Scalar[other.m_size]), m_size(other.m_size) {
memcpy(m_data, other.m_data, m_size * sizeof(_Scalar));
}

2
labo01/Operators.h
View File

@ -27,7 +27,7 @@ namespace gti320 {
operator*(const Matrix<_Scalar, RowsA, ColsA, StorageA> &A, const Matrix<_Scalar, RowsB, ColsB, StorageB> &B) {
assert(A.cols() == B.rows());
auto result = Matrix<_Scalar, Dynamic, Dynamic>(A.rows(), B.cols());
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++) {

323
labo_physique/ParticleSimApplication.cpp
View File

@ -27,16 +27,14 @@
using namespace gti320;
namespace
{
namespace {
static const float deltaT = 0.01667f;
/**
* Crée un système masse-ressort qui simule un tissu suspendu
*/
static inline void createHangingCloth(ParticleSystem& particleSystem, float k)
{
static inline void createHangingCloth(ParticleSystem &particleSystem, float k) {
particleSystem.clear();
const int N = 16;
@ -46,10 +44,8 @@ namespace
const int dy = 32;
int index = 0;
for (int i = 0; i < N; ++i)
{
for (int j = 0; j < N; ++j)
{
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
const int x = x_start + j * dx;
const int y = y_start + i * dy;
@ -58,20 +54,17 @@ namespace
if (j == (N - 1) && i == (N - 1)) particle.fixed = true;
particleSystem.addParticle(particle);
if (i > 0)
{
Spring s(index - N, index, k, (float)dy);
if (i > 0) {
Spring s(index - N, index, k, (float) dy);
particleSystem.addSpring(s);
}
if (j > 0)
{
Spring s(index - 1, index, k, (float)dx);
if (j > 0) {
Spring s(index - 1, index, k, (float) dx);
particleSystem.addSpring(s);
}
if (i > 0 && j > 0)
{
Spring s(index - N - 1, index, k, std::sqrt((float)dx * dx + (float)dy * dy));
if (i > 0 && j > 0) {
Spring s(index - N - 1, index, k, std::sqrt((float) dx * dx + (float) dy * dy));
particleSystem.addSpring(s);
}
++index;
@ -84,8 +77,7 @@ namespace
/**
* Crée un système masse-ressort qui simule un grand tissu suspendu
*/
static inline void createLargeHangingCloth(ParticleSystem& particleSystem, float k)
{
static inline void createLargeHangingCloth(ParticleSystem &particleSystem, float k) {
particleSystem.clear();
const int N = 32;
@ -95,10 +87,8 @@ namespace
const int dy = 16;
int index = 0;
for (int i = 0; i < N; ++i)
{
for (int j = 0; j < N; ++j)
{
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
const int x = x_start + j * dx;
const int y = y_start + i * dy;
@ -106,20 +96,17 @@ namespace
if (j == 0 && i == (N - 1)) particle.fixed = true;
if (j == (N - 1) && i == (N - 1)) particle.fixed = true;
particleSystem.addParticle(particle);
if (i > 0)
{
Spring s(index - N, index, k, (float)dy);
if (i > 0) {
Spring s(index - N, index, k, (float) dy);
particleSystem.addSpring(s);
}
if (j > 0)
{
Spring s(index - 1, index, k, (float)dx);
if (j > 0) {
Spring s(index - 1, index, k, (float) dx);
particleSystem.addSpring(s);
}
if (i > 0 && j > 0)
{
Spring s(index - N - 1, index, k, std::sqrt((float)dx * dx + (float)dy * dy));
if (i > 0 && j > 0) {
Spring s(index - N - 1, index, k, std::sqrt((float) dx * dx + (float) dy * dy));
particleSystem.addSpring(s);
}
++index;
@ -132,8 +119,7 @@ namespace
* Crée un système masse-ressort qui simule une corde suspendu par ses
* extrémités.
*/
static inline void createHangingRope(ParticleSystem& particleSystem, float k)
{
static inline void createHangingRope(ParticleSystem &particleSystem, float k) {
particleSystem.clear();
const int N = 20;
@ -141,17 +127,15 @@ namespace
const int dx = 32;
int index = 0;
for (int j = 0; j < N; ++j)
{
for (int j = 0; j < N; ++j) {
const int x = x_start + j * dx;
const int y = 480;
Particle particle(Vector2f(x, y), Vector2f(0, 0), Vector2f(0, 0), 1.0);
particle.fixed = (index == 0) || (index == N - 1);
particleSystem.addParticle(particle);
if (j > 0)
{
Spring s(index - 1, index, k, (float)dx);
if (j > 0) {
Spring s(index - 1, index, k, (float) dx);
particleSystem.addSpring(s);
}
++index;
@ -162,8 +146,7 @@ namespace
/**
* Crée un système masse-ressort qui simule une poutre flexible
*/
static inline void createBeam(ParticleSystem& particleSystem, float k)
{
static inline void createBeam(ParticleSystem &particleSystem, float k) {
particleSystem.clear();
const int N = 20;
@ -173,8 +156,7 @@ namespace
const int dy = 32;
int index = 0;
for (int j = 0; j < N; ++j)
{
for (int j = 0; j < N; ++j) {
const int x = x_start + j * dx;
// Bottom particle
@ -182,11 +164,10 @@ namespace
Particle particle(Vector2f(x, y_start), Vector2f(0, 0), Vector2f(0, 0), 1.0);
particle.fixed = (j == 0);
particleSystem.addParticle(particle);
if (j > 0)
{
Spring s(index - 1, index, k, (float)sqrt((float)dx * dx + (float)dy * dy));
if (j > 0) {
Spring s(index - 1, index, k, (float) sqrt((float) dx * dx + (float) dy * dy));
particleSystem.addSpring(s);
Spring s2(index - 2, index, k, (float)dx);
Spring s2(index - 2, index, k, (float) dx);
particleSystem.addSpring(s2);
}
@ -199,13 +180,12 @@ namespace
Particle particle(Vector2f(x, y_start + dy), Vector2f(0, 0), Vector2f(0, 0), 1.0);
particle.fixed = (j == 0);
particleSystem.addParticle(particle);
Spring s(index - 1, index, k, (float)dy);
Spring s(index - 1, index, k, (float) dy);
particleSystem.addSpring(s);
if (j > 0)
{
Spring s2(index - 2, index, k, (float)dx);
if (j > 0) {
Spring s2(index - 2, index, k, (float) dx);
particleSystem.addSpring(s2);
Spring s3(index - 3, index, k, (float)sqrt((float)dx * dx + (float)dy * dy));
Spring s3(index - 3, index, k, (float) sqrt((float) dx * dx + (float) dy * dy));
particleSystem.addSpring(s3);
}
++index;
@ -218,8 +198,7 @@ namespace
/**
* TODO Créez votre propre exemple
*/
static inline void createVotreExemple(ParticleSystem& particleSystem, float k)
{
static inline void createVotreExemple(ParticleSystem &particleSystem, float k) {
particleSystem.clear();
// TODO Amusez-vous. Rendu ici, vous le méritez.
@ -229,9 +208,11 @@ namespace
}
ParticleSimApplication::ParticleSimApplication() : nanogui::Screen(nanogui::Vector2i(1280, 720), "GTI320 Labo Physique lineaire", true, false, true, true, false, 4, 1)
, m_particleSystem(), m_stepping(false), m_fpsCounter(0), m_fpsTime(0.0), m_maxIter(10), m_solverType(kGaussSeidel)
{
ParticleSimApplication::ParticleSimApplication() : nanogui::Screen(nanogui::Vector2i(1280, 720),
"GTI320 Labo Physique lineaire", true, false, true,
true, false, 4, 1), m_particleSystem(),
m_stepping(false), m_fpsCounter(0), m_fpsTime(0.0), m_maxIter(10),
m_solverType(kGaussSeidel) {
initGui();
createBeam(m_particleSystem, m_stiffness); // le modèle "poutre" est sélectionné à l'initialisation
@ -241,8 +222,7 @@ ParticleSimApplication::ParticleSimApplication() : nanogui::Screen(nanogui::Vect
reset();
}
void ParticleSimApplication::initGui()
{
void ParticleSimApplication::initGui() {
// Initialisation de la fenêtre
m_window = new nanogui::Window(this, "Particle sim");
m_window->set_position(nanogui::Vector2i(8, 8));
@ -250,16 +230,16 @@ void ParticleSimApplication::initGui()
// initialisation du canvas où est affiché le système de particules
m_canvas = new ParticleSimGLCanvas(this);
m_canvas->set_background_color({ 255, 255, 255, 255 });
m_canvas->set_size({ 1000, 600 });
m_canvas->set_background_color({255, 255, 255, 255});
m_canvas->set_size({1000, 600});
m_canvas->set_draw_border(false);
// Initialisation de la fenêtre de contrôle
nanogui::Window* controls = new nanogui::Window(this, "Controls");
nanogui::Window *controls = new nanogui::Window(this, "Controls");
controls->set_position(nanogui::Vector2i(960, 10));
controls->set_layout(new nanogui::GroupLayout());
Widget* tools = new Widget(controls);
Widget *tools = new Widget(controls);
tools->set_layout(new nanogui::BoxLayout(nanogui::Orientation::Vertical, nanogui::Alignment::Middle, 0, 20));
// Intervalles des curseur
@ -276,7 +256,8 @@ void ParticleSimApplication::initGui()
// Affichage du numéro de frame
m_panelFrames = new Widget(tools);
m_panelFrames->set_layout(new nanogui::BoxLayout(nanogui::Orientation::Horizontal, nanogui::Alignment::Middle, 0, 5));
m_panelFrames->set_layout(
new nanogui::BoxLayout(nanogui::Orientation::Horizontal, nanogui::Alignment::Middle, 0, 5));
m_labelFrames = new nanogui::Label(m_panelFrames, "Frame :");
m_textboxFrames = new nanogui::TextBox(m_panelFrames);
m_textboxFrames->set_fixed_width(60);
@ -286,7 +267,7 @@ void ParticleSimApplication::initGui()
m_panelSolver = new Widget(tools);
m_panelSolver->set_layout(new nanogui::BoxLayout(nanogui::Orientation::Vertical, nanogui::Alignment::Middle, 0, 5));
new nanogui::Label(m_panelSolver, "Solver : ");
nanogui::Button* b = new nanogui::Button(m_panelSolver, "Gauss-Seidel");
nanogui::Button *b = new nanogui::Button(m_panelSolver, "Gauss-Seidel");
b->set_flags(nanogui::Button::RadioButton);
b->set_pushed(true);
b->set_callback([this] { m_solverType = kGaussSeidel; });
@ -301,115 +282,106 @@ void ParticleSimApplication::initGui()
b->set_flags(nanogui::Button::RadioButton);
// Curseur de rigidité
Widget* panelSimControl = new Widget(tools);
panelSimControl->set_layout(new nanogui::BoxLayout(nanogui::Orientation::Vertical, nanogui::Alignment::Middle, 0, 5));
Widget *panelSimControl = new Widget(tools);
panelSimControl->set_layout(
new nanogui::BoxLayout(nanogui::Orientation::Vertical, nanogui::Alignment::Middle, 0, 5));
m_panelStiffness = new Widget(panelSimControl);
m_panelStiffness->set_layout(new nanogui::BoxLayout(nanogui::Orientation::Horizontal, nanogui::Alignment::Middle, 0, 5));
m_panelStiffness->set_layout(
new nanogui::BoxLayout(nanogui::Orientation::Horizontal, nanogui::Alignment::Middle, 0, 5));
m_labelStiffness = new nanogui::Label(m_panelStiffness, "Stiffness : ");
m_sliderStiffness = new nanogui::Slider(m_panelStiffness);
m_sliderStiffness->set_range(stiffnessMinMax);
m_textboxStiffness = new nanogui::TextBox(m_panelStiffness);
m_sliderStiffness->set_callback([this](float value)
{
m_stiffness = std::exp(value);
onStiffnessSliderChanged();
});
m_sliderStiffness->set_callback([this](float value) {
m_stiffness = std::exp(value);
onStiffnessSliderChanged();
});
m_sliderStiffness->set_value(std::log(300.f));
// Curseur du nombre maximum d'itération pour Jacobi et Gauss-Seidel
Widget* panelMaxIter = new Widget(panelSimControl);
panelMaxIter->set_layout(new nanogui::BoxLayout(nanogui::Orientation::Horizontal, nanogui::Alignment::Middle, 0, 5));
Widget *panelMaxIter = new Widget(panelSimControl);
panelMaxIter->set_layout(
new nanogui::BoxLayout(nanogui::Orientation::Horizontal, nanogui::Alignment::Middle, 0, 5));
new nanogui::Label(panelMaxIter, "Max iterations : ");
nanogui::Slider* sliderMaxIter = new nanogui::Slider(panelMaxIter);
nanogui::Slider *sliderMaxIter = new nanogui::Slider(panelMaxIter);
sliderMaxIter->set_range(iterMinMax);
nanogui::TextBox* textboxMaxIter = new nanogui::TextBox(panelMaxIter);
nanogui::TextBox *textboxMaxIter = new nanogui::TextBox(panelMaxIter);
textboxMaxIter->set_value(std::to_string(m_maxIter));
sliderMaxIter->set_value(m_maxIter);
sliderMaxIter->set_callback([this, textboxMaxIter](float value)
{
m_maxIter = (int)value;
textboxMaxIter->set_value(std::to_string(m_maxIter));
});
sliderMaxIter->set_callback([this, textboxMaxIter](float value) {
m_maxIter = (int) value;
textboxMaxIter->set_value(std::to_string(m_maxIter));
});
// Bouton «Simulate»
nanogui::Button* startStopButton = new nanogui::Button(panelSimControl, "Simulate");
nanogui::Button *startStopButton = new nanogui::Button(panelSimControl, "Simulate");
startStopButton->set_flags(nanogui::Button::ToggleButton);
startStopButton->set_change_callback([this](bool val)
{
m_stepping = val;
if (val)
{
m_prevTime = glfwGetTime();
draw_all();
}
});
startStopButton->set_change_callback([this](bool val) {
m_stepping = val;
if (val) {
m_prevTime = glfwGetTime();
draw_all();
}
});
// Bouton «Step»
nanogui::Button* stepButton = new nanogui::Button(panelSimControl, "Step");
stepButton->set_callback([this]
{
if (!m_stepping)
step(deltaT);
});
nanogui::Button *stepButton = new nanogui::Button(panelSimControl, "Step");
stepButton->set_callback([this] {
if (!m_stepping)
step(deltaT);
});
// Bouton «Reset»
nanogui::Button* resetButton = new nanogui::Button(panelSimControl, "Reset");
resetButton->set_callback([this]
{
reset();
});
nanogui::Button *resetButton = new nanogui::Button(panelSimControl, "Reset");
resetButton->set_callback([this] {
reset();
});
// Boutons pour le choix du modèle
Widget* panelExamples = new Widget(tools);
Widget *panelExamples = new Widget(tools);
panelExamples->set_layout(new nanogui::BoxLayout(nanogui::Orientation::Vertical, nanogui::Alignment::Middle, 0, 5));
new nanogui::Label(panelExamples, "Examples : ");
nanogui::Button* loadClothButton = new nanogui::Button(panelExamples, "Cloth");
loadClothButton->set_callback([this]
{
createHangingCloth(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button* loadLargeClothButton = new nanogui::Button(panelExamples, "Large cloth");
loadLargeClothButton->set_callback([this]
{
createLargeHangingCloth(m_particleSystem, m_sliderStiffness->value());
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button *loadClothButton = new nanogui::Button(panelExamples, "Cloth");
loadClothButton->set_callback([this] {
createHangingCloth(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button *loadLargeClothButton = new nanogui::Button(panelExamples, "Large cloth");
loadLargeClothButton->set_callback([this] {
createLargeHangingCloth(m_particleSystem, m_sliderStiffness->value());
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button* loadBeamButton = new nanogui::Button(panelExamples, "Beam");
loadBeamButton->set_callback([this]
{
createBeam(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button *loadBeamButton = new nanogui::Button(panelExamples, "Beam");
loadBeamButton->set_callback([this] {
createBeam(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button* loadRopeButton = new nanogui::Button(panelExamples, "Rope");
loadRopeButton->set_callback([this]
{
createHangingRope(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button *loadRopeButton = new nanogui::Button(panelExamples, "Rope");
loadRopeButton->set_callback([this] {
createHangingRope(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button* loadVotreExemple = new nanogui::Button(panelExamples, "Le vôtre");
loadVotreExemple->set_callback([this]
{
createVotreExemple(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
nanogui::Button *loadVotreExemple = new nanogui::Button(panelExamples, "Le vôtre");
loadVotreExemple->set_callback([this] {
createVotreExemple(m_particleSystem, m_stiffness);
m_particleSystem.pack(m_p0, m_v0, m_f0);
reset();
});
}
/**
* Réaction aux événements déclenchés par le clavier
*/
bool ParticleSimApplication::keyboard_event(int key, int scancode, int action, int modifiers)
{
bool ParticleSimApplication::keyboard_event(int key, int scancode, int action, int modifiers) {
if (Screen::keyboard_event(key, scancode, action, modifiers))
return true;
if (key == GLFW_KEY_ESCAPE && action == GLFW_PRESS) {
@ -427,12 +399,10 @@ bool ParticleSimApplication::keyboard_event(int key, int scancode, int action, i
* `step` est appelée pour faire avancer le système d'un intervalle de temps
* DELTA_T. Ensuite, l'affichage est mis à jour.
*/
void ParticleSimApplication::draw_contents()
{
void ParticleSimApplication::draw_contents() {
Screen::draw_contents();
if (m_stepping)
{
if (m_stepping) {
auto now = glfwGetTime();
float dt = now - m_prevTime;
@ -442,9 +412,8 @@ void ParticleSimApplication::draw_contents()
//
m_fpsTime += dt;
++m_fpsCounter;
if (m_fpsCounter > 30)
{
const float fps = (float)m_fpsCounter / m_fpsTime;
if (m_fpsCounter > 30) {
const float fps = (float) m_fpsCounter / m_fpsTime;
char buf[64];
snprintf(buf, sizeof(buf), "%3.1f", fps);
m_fpsCounter = 0;
@ -463,11 +432,9 @@ void ParticleSimApplication::draw_contents()
* Appelée lorsque le curseur de rigidité est modifié. La nouvelle rigidité est
* affectée à tous les ressorts
*/
void ParticleSimApplication::onStiffnessSliderChanged()
{
void ParticleSimApplication::onStiffnessSliderChanged() {
// Update all springs with the slider value
for (Spring& s : getParticleSystem().getSprings())
{
for (Spring &s: getParticleSystem().getSprings()) {
s.k = m_stiffness;
}
@ -479,8 +446,7 @@ void ParticleSimApplication::onStiffnessSliderChanged()
/**
* Effectue un pas de simulation de taille dt.
*/
void ParticleSimApplication::step(float dt)
{
void ParticleSimApplication::step(float dt) {
// Construction des matrices de masse et de rigidité
//
m_particleSystem.buildMassMatrix(m_M);
@ -520,33 +486,32 @@ void ParticleSimApplication::step(float dt)
// Version 2 utilise un seul constructeur et aucune copie
//////////////////////////////////////////////////////////////////////////////////
//
const Matrix<float, Dynamic, Dynamic> A;
const Vector<float, Dynamic> b;
const Matrix<float, Dynamic, Dynamic> A = m_M + -1.0f * std::pow(deltaT, 2.0f) * m_dfdx;
const Vector<float, Dynamic> b = deltaT * m_f + m_v;
// Résolution du système d'équations `A*v_plus = b`.
//
Vector<float, Dynamic> v_plus;
Vector<float, Dynamic> acc; // vecteur d'accélérations
switch (m_solverType)
{
case kGaussSeidel:
gaussSeidel(A, b, v_plus, m_maxIter);
break;
case kColorGaussSeidel:
gaussSeidelColor(A, b, v_plus, m_graphColor.getPartitions(), m_maxIter);
break;
case kCholesky:
cholesky(A, b, v_plus);
break;
default:
case kNone:
// N'utilise pas de solveur, il s'agit de l'implémentation naive de
// l'intégration d'Euler.
acc.resize(m_M.rows()); // vecteur d'accélérations
for (int i = 0; i < m_M.rows(); ++i)
acc(i) = (1.0 / m_M(i, i)) * m_f(i);
v_plus = m_v + dt * acc;
break;
switch (m_solverType) {
case kGaussSeidel:
gaussSeidel(A, b, v_plus, m_maxIter);
break;
case kColorGaussSeidel:
gaussSeidelColor(A, b, v_plus, m_graphColor.getPartitions(), m_maxIter);
break;
case kCholesky:
cholesky(A, b, v_plus);
break;
default:
case kNone:
// N'utilise pas de solveur, il s'agit de l'implémentation naive de
// l'intégration d'Euler.
acc.resize(m_M.rows()); // vecteur d'accélérations
for (int i = 0; i < m_M.rows(); ++i)
acc(i) = (1.0 / m_M(i, i)) * m_f(i);
v_plus = m_v + dt * acc;
break;
}
// TODO Mise à jour du vecteur d'état de position via l'intégration d'Euler
@ -563,8 +528,7 @@ void ParticleSimApplication::step(float dt)
/**
* Réinitialisation du système de particules
*/
void ParticleSimApplication::reset()
{
void ParticleSimApplication::reset() {
m_frameCounter = 0;
m_particleSystem.unpack(m_p0, m_v0);
m_graphColor.color(m_particleSystem);
@ -575,8 +539,7 @@ void ParticleSimApplication::reset()
/**
* Mise à jour du compteur de frames
*/
void ParticleSimApplication::updateFrameCounter()
{
void ParticleSimApplication::updateFrameCounter() {
++m_frameCounter;
char buf[16];
snprintf(buf, sizeof(buf), "%d", m_frameCounter);

19
labo_physique/ParticleSystem.cpp
View File

@ -95,7 +95,7 @@ void ParticleSystem::unpack(const Vector<float, Dynamic> &_pos,
/**
* Construction de la matirce de masses.
* Construction de la matrice de masses.
*/
void ParticleSystem::buildMassMatrix(Matrix<float, Dynamic, Dynamic> &M) {
const int numParticles = m_particles.size();
@ -131,6 +131,9 @@ void ParticleSystem::buildDfDx(Matrix<float, Dynamic, Dynamic> &dfdx) {
dfdx.resize(dim, dim);
dfdx.setZero();
auto identity = Matrix<float, 2, 2>();
identity.setIdentity();
// Pour chaque ressort...
for (const Spring &spring: m_springs) {
// TODO
@ -141,6 +144,20 @@ void ParticleSystem::buildDfDx(Matrix<float, Dynamic, Dynamic> &dfdx) {
// Astuce: créer une matrice de taille fixe 2 par 2 puis utiliser la classe SubMatrix pour accumuler
// les modifications sur la diagonale (2 endroits) et pour mettre à jour les blocs non diagonale (2 endroits).
auto p0 = m_particles[spring.index0];
auto p1 = m_particles[spring.index1];
Vector<float, 2> distance = p1.x - p0.x;
Matrix<float, 2, 1> distance_m = distance.as_matrix();
Matrix<float, 1, 2> distance_t = distance_m.transpose<float, 1, 2, ColumnStorage>();
float l = distance.norm();
Matrix<float, 2, 2> l2_m = std::pow(l, 2.0f) * identity;
float l3 = std::pow(l, 3.0f);
Matrix<float, 2, 2> dd = -1.0f * (distance_m * distance_t);
Matrix<float, 2, 2> term1 = spring.k * identity;
Matrix<float, 2, 2> term2 = -1.0f * (1 / l3) * spring.k * spring.l0 * (l2_m + dd);
dfdx.block(spring.index0, spring.index1, 2, 2) = term1 + term2;
}
}

96
labo_physique/Solvers.h
View File

@ -14,10 +14,11 @@
#include "Math3D.h"
namespace gti320
{
namespace gti320 {
// Identification des solveurs
enum eSolverType { kNone, kGaussSeidel, kColorGaussSeidel, kCholesky };
enum eSolverType {
kNone, kGaussSeidel, kColorGaussSeidel, kCholesky
};
// Paramètres de convergences pour les algorithmes itératifs
static const float eps = 1e-4f;
@ -26,21 +27,54 @@ namespace gti320
/**
* Résout Ax = b avec la méthode Gauss-Seidel
*/
static void gaussSeidel(const Matrix<float, Dynamic, Dynamic>& A,
const Vector<float, Dynamic>& b,
Vector<float, Dynamic>& x, int k_max)
{
static void gaussSeidel(const Matrix<float, Dynamic, Dynamic> &A,
const Vector<float, Dynamic> &b,
Vector<float, Dynamic> &x, int k_max) {
// TODO
//
// Implémenter la méthode de Gauss-Seidel
int n = b.size();
x.resize(n);
x.setZero();
bool converged = false;
int k = 0;
do {
Vector<float, Dynamic> nx = x;
for (int i = 0; i < n; i++) {
nx(i) = b(i);
for (int j = 0; j < i; j++) {
nx(i) = nx(i) - A(i, j) * nx(j);
}
for (int j = i + 1; j < n; j++) {
nx(i) = nx(i) - A(i, j) * x(j);
}
nx(i) = nx(i) / A(i, i);
}
k++;
Vector<float, Dynamic> r = A * x - b;
converged = k >= k_max ||
(nx - x).norm() / nx.norm() < tau ||
r.norm() / b.norm() < eps;
x = nx;
} while (!converged);
}
/**
* Résout Ax = b avec la méthode Gauss-Seidel (coloration de graphe)
*/
static void gaussSeidelColor(const Matrix<float, Dynamic, Dynamic>& A, const Vector<float, Dynamic>& b, Vector<float, Dynamic>& x, const Partitions& P, const int maxIter)
{
static void gaussSeidelColor(const Matrix<float, Dynamic, Dynamic> &A, const Vector<float, Dynamic> &b,
Vector<float, Dynamic> &x, const Partitions &P, const int maxIter) {
// TODO
//
// Implémenter la méthode de Gauss-Seidel avec coloration de graphe.
@ -51,31 +85,63 @@ namespace gti320
/**
* Résout Ax = b avec la méthode de Cholesky
*/
static void cholesky(const Matrix<float, Dynamic, Dynamic>& A,
const Vector<float, Dynamic>& b,
Vector<float, Dynamic>& x)
{
static void cholesky(const Matrix<float, Dynamic, Dynamic> &A,
const Vector<float, Dynamic> &b,
Vector<float, Dynamic> &x) {
int n = A.rows();
x.resize(n);
x.setZero();
// TODO
//
// Calculer la matrice L de la factorisation de Cholesky
auto L = Matrix<float, Dynamic, Dynamic>(n, n);
for (int j = 0; j < n; j++) {
for (int i = j; i < n; i++) {
float s = 0;
for (int k = 0; k < j; k++) {
s += L(i, k) * L(j, k);
}
if (i == j) {
L(i, i) = std::sqrt(A(i, i) - s);
} else {
L(i, j) = (A(i, j) - s) / L(j, j);
}
}
}
// TODO
//
// Résoudre Ly = b
auto y = Vector<float, Dynamic>(n);
for (int i = 0; i < n; i++) {
y(i) = b(i);
for (int j = 0; j < i; j++) {
y(i) -= L(i, j) * y(j);
}
y(i) /= L(i, i);
}
// TODO
//
// Résoudre L^t x = y
//
// Remarque : ne pas caculer la transposer de L, c'est inutilement
// Remarque : ne pas calculer la transposée de L, c'est inutilement
// coûteux.
for (int i = n - 1; i >= 0; i--) {
x(i) = y(i);
for (int j = i + 1; j < n; j++) {
x(i) -= L(j, i) * x(j);
}
x(i) /= L(i, i);
}
}
}

8
labo_physique/Vector2d.h
View File

@ -11,6 +11,7 @@
*
*/
#include "Matrix.h"
#include "Math3D.h"
namespace gti320
@ -102,6 +103,13 @@ namespace gti320
{
return sqrt(dot(*this));
}
Matrix<_Scalar, 2, 1> as_matrix() const {
Matrix<_Scalar, 2, 1> mat;
mat(0, 0) = (*this)(0);
mat(1, 0) = (*this)(1);
return mat;
}
};
typedef Vector<float, 2> Vector2f;