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// ----------------------------------------------------------------------------
// - Open3D: www.open3d.org -
// ----------------------------------------------------------------------------
// Copyright (c) 2018-2024 www.open3d.org
// SPDX-License-Identifier: MIT
// ----------------------------------------------------------------------------
#include "open3d/utility/Eigen.h"
#include "tests/Tests.h"
namespace open3d {
namespace tests {
TEST(Eigen, TransformVector6dToMatrix4d) {
Eigen::Matrix4d ref_matrix4d;
ref_matrix4d << 0.829278, -0.425147, 0.362696, 0.666667, 0.453036, 0.891445,
0.009104, 0.833333, -0.327195, 0.156765, 0.931863, 1.000000,
0.000000, 0.000000, 0.000000, 1.000000;
Eigen::Vector6d vector6d = Eigen::Vector6d::Zero();
ExpectEQ(Zero6d, vector6d);
for (int i = 0; i < 6; i++) vector6d(i, 0) = (i + 1) / 6.0;
Eigen::Matrix4d matrix4d = utility::TransformVector6dToMatrix4d(vector6d);
ExpectEQ(ref_matrix4d, matrix4d);
}
TEST(Eigen, TransformMatrix4dToVector6d) {
Eigen::Matrix4d ref_matrix4d;
ref_matrix4d << 0.829278, -0.425147, 0.362696, 0.666667, 0.453036, 0.891445,
0.009104, 0.833333, -0.327195, 0.156765, 0.931863, 1.000000,
0.000000, 0.000000, 0.000000, 1.000000;
Eigen::Vector6d vector6d =
utility::TransformMatrix4dToVector6d(ref_matrix4d);
for (int i = 0; i < 6; i++)
EXPECT_NEAR((i + 1) / 6.0, vector6d(i, 0), THRESHOLD_1E_6);
}
TEST(Eigen, SolveLinearSystemPSD) {
Eigen::Matrix3d A;
Eigen::Vector3d b;
Eigen::Vector3d x;
Eigen::Vector3d x_ref;
bool status = false;
// API: SolveLinearSystemPSD(A, b, prefer_sparse,
// check_symmetric, check_det, check_psd)
// Rank == 2, check_det == true, should return error
A << 3, 2, 1, 30, 20, 10, -1, 0.5, -1;
b << 1, -2, 0;
x_ref << 0, 0, 0;
std::tie(status, x) =
utility::SolveLinearSystemPSD(A, b, false, false, true, false);
EXPECT_EQ(status, false);
ExpectEQ(x, x_ref);
// Rank == 3, not PSD, check_psd == true, should return error
A << 3, 2, -1, 2, -2, 4, -1, 0.5, -1;
b << 1, -2, 0;
x_ref << 0, 0, 0;
std::tie(status, x) =
utility::SolveLinearSystemPSD(A, b, false, false, false, true);
EXPECT_EQ(status, false);
ExpectEQ(x, x_ref);
// Rank == 3, "fake PSD" (eigen values >= 0 and full rank but not symmetric)
// check_psd == true, should return error
A << 3, 2, 1, 2, 3, 1, 1, 2, 3;
b << 39, 34, 26;
x_ref << 0, 0, 0; // 9.25, 4.25, 2.75 if solved in general form
std::tie(status, x) =
utility::SolveLinearSystemPSD(A, b, false, false, false, true);
EXPECT_EQ(status, false);
ExpectEQ(x, x_ref);
// A regular PSD case
A << 3, 0, 1, 0, 3, 0, 1, 0, 3;
b << 18, 15, 22;
x_ref << 4, 5, 6;
std::tie(status, x) =
utility::SolveLinearSystemPSD(A, b, false, false, true, true);
EXPECT_EQ(status, true);
ExpectEQ(x, x_ref);
// The sparse solver shall work as well
std::tie(status, x) =
utility::SolveLinearSystemPSD(A, b, true, false, true, true);
EXPECT_EQ(status, true);
ExpectEQ(x, x_ref);
}
TEST(Eigen, SolveJacobianSystemAndObtainExtrinsicMatrix) {
Eigen::Matrix6d JTJ = Eigen::Matrix6d::Random();
// make sure JTJ is positive semi-definite
JTJ = JTJ.transpose() * JTJ;
// make sure det(JTJ) != 0
JTJ = JTJ + Eigen::Matrix6d::Identity();
bool status = false;
Eigen::Matrix4d result;
int loops = 10000;
srand((unsigned int)time(0));
for (int i = 0; i < loops; i++) {
Eigen::Vector6d x = Eigen::Vector6d::Random();
Eigen::Vector6d JTr = JTJ * x;
std::tie(status, result) =
utility::SolveJacobianSystemAndObtainExtrinsicMatrix(JTJ, -JTr);
Eigen::Vector6d r = utility::TransformMatrix4dToVector6d(result);
ExpectEQ(r, x);
}
}
TEST(Eigen, SolveJacobianSystemAndObtainExtrinsicMatrixArray) {
Eigen::Matrix6d JTJ = Eigen::Matrix6d::Random();
// make sure JTJ is positive semi-definite
JTJ = JTJ.transpose() * JTJ;
// make sure det(JTJ) != 0
JTJ = JTJ + Eigen::Matrix6d::Identity();
bool status = false;
std::vector<Eigen::Matrix4d, utility::Matrix4d_allocator> result;
int loops = 10000;
srand((unsigned int)time(0));
for (int i = 0; i < loops; i++) {
Eigen::Vector6d x = Eigen::Vector6d::Random();
Eigen::Vector6d JTr = JTJ * x;
std::tie(status, result) =
utility::SolveJacobianSystemAndObtainExtrinsicMatrixArray(JTJ,
-JTr);
Eigen::Vector6d r = utility::TransformMatrix4dToVector6d(result[0]);
ExpectEQ(r, x);
}
}
TEST(Eigen, ComputeJTJandJTr) {
Eigen::Matrix6d ref_JTJ;
ref_JTJ << 2.819131, 0.023929, -0.403568, 1.276125, 0.437555, -1.123875,
0.023929, 2.817778, 0.086121, 1.133195, -0.124291, -0.695210,
-0.403568, 0.086121, 3.435509, -0.094671, 0.466959, -0.215179,
1.276125, 1.133195, -0.094671, 3.826990, -0.235632, -0.917586,
0.437555, -0.124291, 0.466959, -0.235632, 2.802768, -0.496025,
-1.123875, -0.695210, -0.215179, -0.917586, -0.496025, 2.951511;
Eigen::Vector6d ref_JTr;
ref_JTr << 0.477778, -0.262092, -0.162745, -0.545752, -0.643791, -0.883007;
auto testFunction = [&](int i, Eigen::Vector6d &J_r, double &r, double &w) {
{
std::vector<double> v(6);
Rand(v, -1.0, 1.0, i);
for (int k = 0; k < 6; k++) J_r(k) = v[k];
r = (double)(i % 6) / 6;
w = 1.0;
}
};
int iteration_num = 10;
Eigen::Matrix6d JTJ = Eigen::Matrix6d::Zero();
Eigen::Vector6d JTr = Eigen::Vector6d::Zero();
double r = 0.0;
std::tie(JTJ, JTr, r) =
utility::ComputeJTJandJTr<Eigen::Matrix6d, Eigen::Vector6d>(
testFunction, iteration_num);
ExpectEQ(ref_JTr, JTr);
ExpectEQ(ref_JTJ, JTJ);
}
TEST(Eigen, ComputeJTJandJTr_vector) {
Eigen::Matrix6d ref_JTJ;
ref_JTJ << 28.191311, 0.239293, -4.035679, 12.761246, 4.375548, -11.238754,
0.239293, 28.177778, 0.861207, 11.331949, -1.242907, -6.952095,
-4.035679, 0.861207, 34.355094, -0.946713, 4.669589, -2.151788,
12.761246, 11.331949, -0.946713, 38.269896, -2.356324, -9.175855,
4.375548, -1.242907, 4.669589, -2.356324, 28.027682, -4.960246,
-11.238754, -6.952095, -2.151788, -9.175855, -4.960246, 29.515110;
Eigen::Vector6d ref_JTr;
ref_JTr << 2.896078, 4.166667, -1.629412, 1.386275, -4.468627, -7.115686;
auto testFunction =
[&](int i,
std::vector<Eigen::Vector6d, utility::Vector6d_allocator> &J_r,
std::vector<double> &r, std::vector<double> &w) {
{
size_t size = 10;
J_r.resize(size);
r.resize(size);
w.resize(size);
std::vector<double> v(6);
for (size_t s = 0; s < size; s++) {
Rand(v, -1.0, 1.0, i);
for (int k = 0; k < 6; k++) J_r[s](k) = v[k];
r[s] = (double)((i * s) % 6) / 6;
w[s] = 1.0;
}
}
};
int iteration_num = 10;
Eigen::Matrix6d JTJ = Eigen::Matrix6d::Zero();
Eigen::Vector6d JTr = Eigen::Vector6d::Zero();
double r = 0.0;
std::tie(JTJ, JTr, r) =
utility::ComputeJTJandJTr<Eigen::Matrix6d, Eigen::Vector6d>(
testFunction, iteration_num);
ExpectEQ(ref_JTr, JTr);
ExpectEQ(ref_JTJ, JTJ);
}
TEST(Eigen, ColorToUint8Round) {
auto rgb = utility::ColorToUint8({.001, .999, .501});
EXPECT_EQ(rgb(0), 0);
EXPECT_EQ(rgb(1), 255);
EXPECT_EQ(rgb(2), 128);
}
TEST(Eigen, ColorToUint8Clip) {
{
auto rgb = utility::ColorToUint8({-.001, -.5, -1000});
EXPECT_EQ(rgb(0), 0);
EXPECT_EQ(rgb(1), 0);
EXPECT_EQ(rgb(2), 0);
}
{
auto rgb = utility::ColorToUint8({1.001, 1.5, 1000});
EXPECT_EQ(rgb(0), 255);
EXPECT_EQ(rgb(1), 255);
EXPECT_EQ(rgb(2), 255);
}
}
TEST(Eigen, ColorToUint8ToDouble) {
for (int i = 0; i < 10000; ++i) {
Eigen::Vector3d d({i / 10000., i / 10000., i / 10000.});
auto rgb = utility::ColorToUint8(d);
Eigen::Vector3d conv = utility::ColorToDouble(rgb(0), rgb(1), rgb(2));
for (int j = 0; j < 3; j++) {
EXPECT_LT(std::abs(d(j) - conv(j)) * 255., 0.5);
}
}
}
} // namespace tests
} // namespace open3d
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