From 5b9bcd3fdadd3d1694aae0ebf3cf498c32b89938 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Del=20Pino?= <stephane.delpino44@gmail.com>
Date: Wed, 5 Jul 2023 19:19:18 +0200
Subject: [PATCH] [ci-skip] Add jacobian and hessian (still buggy?)
---
src/mesh/MeshSmootherEscobar.cpp | 149 ++++++++++++++++++++++++++-----
1 file changed, 127 insertions(+), 22 deletions(-)
diff --git a/src/mesh/MeshSmootherEscobar.cpp b/src/mesh/MeshSmootherEscobar.cpp
index 793153c0a..bca86deec 100644
--- a/src/mesh/MeshSmootherEscobar.cpp
+++ b/src/mesh/MeshSmootherEscobar.cpp
@@ -2,7 +2,6 @@
#include <algebra/TinyMatrix.hpp>
#include <algebra/TinyVector.hpp>
-#include <geometry/TriangleTransformation.hpp>
#include <language/utils/InterpolateItemValue.hpp>
#include <mesh/Connectivity.hpp>
#include <mesh/ItemValueUtils.hpp>
@@ -220,53 +219,157 @@ class MeshSmootherEscobarHandler::MeshSmootherEscobar
constexpr double eps = 1E-15;
quality.fill(2);
- auto f_inner = [=](const NodeId node_id, const TinyVector<Dimension>& x) -> double {
+ auto f_inner = [=](const NodeId node_id, TinyVector<Dimension>& x) -> double {
auto cell_list = node_to_cell_matrix[node_id];
auto node_number_in_cell = node_number_in_their_cells[node_id];
const double alpha = 2 * std::acos(-1) / cell_list.size();
- const TinyMatrix<Dimension> W{1, std::cos(alpha), 0, std::sin(alpha)};
+ const TinyMatrix<Dimension> W{1, std::cos(alpha), //
+ 0, std::sin(alpha)};
const TinyMatrix<Dimension> inv_W = inverse(W);
- SmallArray<TinyMatrix<Dimension>> S(cell_list.size());
+ std::array<TinyMatrix<Dimension>, Dimension> S_gradient =
+ {TinyMatrix<Dimension>{-1, -1. / std::sin(alpha) + 1. / std::tan(alpha), //
+ +0, +0}, //
+ TinyMatrix<Dimension>{+0, +0, //
+ -1, -1. / std::sin(alpha) + 1. / std::tan(alpha)}};
+
+ SmallArray<TinyMatrix<Dimension>> S_list(cell_list.size());
for (size_t i_cell = 0; i_cell < cell_list.size(); ++i_cell) {
const size_t i_cell_node = node_number_in_cell[i_cell];
auto cell_node_list = cell_to_node_matrix[cell_list[i_cell]];
const size_t cell_nb_nodes = cell_node_list.size();
- TriangleTransformation<Dimension> T(x, //
- xr[cell_node_list[(i_cell_node + 1) % cell_nb_nodes]],
- xr[cell_node_list[(i_cell_node + cell_nb_nodes - 1) % cell_nb_nodes]]);
- S[i_cell] = T.jacobian() * inv_W;
+ const TinyVector a = xr[cell_node_list[(i_cell_node + 1) % cell_nb_nodes]];
+ const TinyVector b = xr[cell_node_list[(i_cell_node + cell_nb_nodes - 1) % cell_nb_nodes]];
+
+ const TinyMatrix<Dimension> A{a[0] - x[0], b[0] - x[0], //
+ a[1] - x[1], b[1] - x[1]};
+
+ S_list[i_cell] = A * inv_W;
}
- SmallArray<double> sigma(S.size());
- for (size_t j = 0; j < S.size(); ++j) {
- sigma[j] = det(S[j]);
+ SmallArray<double> sigma_list(S_list.size());
+ for (size_t i_cell = 0; i_cell < S_list.size(); ++i_cell) {
+ sigma_list[i_cell] = det(S_list[i_cell]);
}
- const double sigma_min = min(sigma);
+ const double sigma_min = min(sigma_list);
const double delta =
(sigma_min < eps) ? std::max(std::sqrt(eps * (eps - sigma_min)), std::sqrt(eps) * std::abs(sigma_min)) : 0;
- double f = 0;
- for (size_t j = 0; j < S.size(); ++j) {
- const TinyMatrix<Dimension> Sigma = sigma[j] * inverse(S[j]);
+ auto frobenius = [](const TinyMatrix<Dimension>& M) { return std::sqrt(trace(transpose(M) * M)); };
+
+ // TinyVector<Dimension> f_gradient = zero;
+ // TinyMatrix<Dimension> f_hessian = zero;
+
+ double final_f = 0;
+
+ for (size_t i_iter = 0; i_iter < 15; ++i_iter) {
+ SmallArray<TinyMatrix<Dimension>> S_list(cell_list.size());
+ for (size_t i_cell = 0; i_cell < cell_list.size(); ++i_cell) {
+ const size_t i_cell_node = node_number_in_cell[i_cell];
+ auto cell_node_list = cell_to_node_matrix[cell_list[i_cell]];
+ const size_t cell_nb_nodes = cell_node_list.size();
+
+ const TinyVector a = xr[cell_node_list[(i_cell_node + 1) % cell_nb_nodes]];
+ const TinyVector b = xr[cell_node_list[(i_cell_node + cell_nb_nodes - 1) % cell_nb_nodes]];
+
+ const TinyMatrix<Dimension> A{a[0] - x[0], b[0] - x[0], //
+ a[1] - x[1], b[1] - x[1]};
+
+ S_list[i_cell] = A * inv_W;
+ }
+
+ SmallArray<double> sigma_list(S_list.size());
+ for (size_t i_cell = 0; i_cell < S_list.size(); ++i_cell) {
+ sigma_list[i_cell] = det(S_list[i_cell]);
+ }
+
+ double f = 0;
+ TinyVector<Dimension> f_gradient = zero;
+ TinyMatrix<Dimension> f_hessian = zero;
+
+ for (size_t i_cell = 0; i_cell < S_list.size(); ++i_cell) {
+ const double sigma = sigma_list[i_cell];
+ const TinyMatrix<Dimension> S = S_list[i_cell];
+
+ const TinyMatrix<Dimension> Sigma = sigma * inverse(S);
+
+ const double S_norm = frobenius(S);
+ const double Sigma_norm = frobenius(Sigma);
+ const double S_norm2 = S_norm * S_norm;
+ const double Sigma_norm2 = Sigma_norm * Sigma_norm;
+
+ const double h = sigma + std::sqrt(sigma * sigma + 4 * delta * delta);
+
+ const double f_jr = S_norm * Sigma_norm / h;
+
+ TinyVector<Dimension> sigma_gradient{trace(Sigma * S_gradient[0]), //
+ trace(Sigma * S_gradient[1])};
+
+ const std::array<TinyMatrix<Dimension>, Dimension> //
+ Sigma_gradient{sigma_gradient[0] * inverse(S) - Sigma * S_gradient[0] * Sigma,
+ sigma_gradient[1] * inverse(S) - Sigma * S_gradient[1] * Sigma};
+
+ // TinyVector<Dimension> h_gradient = h / (h - sigma_list[i_cell]) * sigma_gradient;
+
+ TinyVector<Dimension> g{trace(transpose(S) * S_gradient[0]) / S_norm2 //
+ + trace(transpose(Sigma) * Sigma_gradient[0]) / Sigma_norm2 //
+ - trace(Sigma * S_gradient[0]) / (h - sigma),
+ //
+ trace(transpose(S) * S_gradient[1]) / S_norm2 //
+ + trace(transpose(Sigma) * Sigma_gradient[1]) / Sigma_norm2 //
+ - trace(Sigma * S_gradient[1]) / (h - sigma)};
+
+ const TinyVector<Dimension> f_jr_gradient = f_jr * g;
+ TinyMatrix<Dimension> f_jr_hessian = zero;
+ for (size_t i = 0; i < Dimension; ++i) {
+ for (size_t j = 0; j < Dimension; ++j) {
+ f_jr_hessian(i, j) = //
+ (trace(transpose(S_gradient[j]) * S_gradient[i]) / S_norm2 //
+ - 2 * trace(transpose(S) * S_gradient[j]) * trace(transpose(S) * S_gradient[i]) /
+ (S_norm2 * S_norm2) //
+ //
+ + trace(transpose(Sigma_gradient[j]) * Sigma_gradient[i]) / Sigma_norm2 // + 0
+ - 2 * trace(transpose(Sigma) * Sigma_gradient[j]) * trace(transpose(Sigma) * Sigma_gradient[i]) /
+ (Sigma_norm2 * Sigma_norm2) //
+ //
+ - 2 * trace(Sigma_gradient[j] * S_gradient[i]) / (h - sigma) //
+ + 2 * trace(Sigma * S_gradient[i]) * sigma / (std::pow(h - sigma, 3)) * sigma_gradient[j] //
+ + g[j] * g[i]) *
+ f_jr;
+ }
+ }
+
+ f += f_jr;
+ f_gradient += f_jr_gradient;
+ f_hessian += f_jr_hessian;
+ }
+
+ std::cout << "f = " << f << '\n';
+ std::cout << "grad(f) = " << f_gradient << '\n';
+ std::cout << "hess(f) = " << f_hessian << " | hess(f)^T -hess(f) = " << transpose(f_hessian) - f_hessian
+ << '\n';
+
+ std::cout << "inv(H) = " << inverse(f_hessian) << '\n';
+ std::cout << "inv(H)*grad(f) = " << inverse(f_hessian) * f_gradient << '\n';
- const double Sj_norm = std::sqrt(trace(transpose(S[j]) * S[j]));
- const double Sigma_norm = std::sqrt(trace(transpose(Sigma) * Sigma));
+ std::cout << "x = " << x << " -> " << x - inverse(f_hessian) * f_gradient << '\n';
- f += Sj_norm * Sigma_norm / (sigma[j] + std::sqrt(sigma[j] * sigma[j] + 4 * delta * delta));
+ x -= inverse(f_hessian) * f_gradient;
+
+ final_f = f;
}
- return f;
+ return final_f;
};
parallel_for(
connectivity.numberOfNodes(), PUGS_LAMBDA(NodeId node_id) {
- auto cell_list = node_to_cell_matrix[node_id];
- auto node_number_in_cell = node_number_in_their_cells[node_id];
+ // auto cell_list = node_to_cell_matrix[node_id];
+ // auto node_number_in_cell = node_number_in_their_cells[node_id];
if (is_boundary_node[node_id]) {
quality[node_id] = 1;
@@ -274,7 +377,9 @@ class MeshSmootherEscobarHandler::MeshSmootherEscobar
TinyVector x = xr[node_id];
quality[node_id] = f_inner(node_id, x);
- TinyMatrix<Dimension> B = identity;
+ std::exit(0);
+
+ // TinyMatrix<Dimension> B = identity;
}
});
--
GitLab