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// Ceres Solver - A fast non-linear least squares minimizer
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// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)
// mierle@gmail.com (Keir Mierle)
#include "ceres/dynamic_numeric_diff_cost_function.h"
#include <cstddef>
#include <memory>
#include "gtest/gtest.h"
namespace ceres::internal {
using std::vector;
const double kTolerance = 1e-6;
// Takes 2 parameter blocks:
// parameters[0] is size 10.
// parameters[1] is size 5.
// Emits 21 residuals:
// A: i - parameters[0][i], for i in [0,10) -- this is 10 residuals
// B: parameters[0][i] - i, for i in [0,10) -- this is another 10.
// C: sum(parameters[0][i]^2 - 8*parameters[0][i]) + sum(parameters[1][i])
class MyCostFunctor {
public:
bool operator()(double const* const* parameters, double* residuals) const {
const double* params0 = parameters[0];
int r = 0;
for (int i = 0; i < 10; ++i) {
residuals[r++] = i - params0[i];
residuals[r++] = params0[i] - i;
}
double c_residual = 0.0;
for (int i = 0; i < 10; ++i) {
c_residual += pow(params0[i], 2) - 8.0 * params0[i];
}
const double* params1 = parameters[1];
for (int i = 0; i < 5; ++i) {
c_residual += params1[i];
}
residuals[r++] = c_residual;
return true;
}
};
TEST(DynamicNumericdiffCostFunctionTest, TestResiduals) {
vector<double> param_block_0(10, 0.0);
vector<double> param_block_1(5, 0.0);
DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
new MyCostFunctor());
cost_function.AddParameterBlock(param_block_0.size());
cost_function.AddParameterBlock(param_block_1.size());
cost_function.SetNumResiduals(21);
// Test residual computation.
vector<double> residuals(21, -100000);
vector<double*> parameter_blocks(2);
parameter_blocks[0] = &param_block_0[0];
parameter_blocks[1] = &param_block_1[0];
EXPECT_TRUE(
cost_function.Evaluate(&parameter_blocks[0], residuals.data(), nullptr));
for (int r = 0; r < 10; ++r) {
EXPECT_EQ(1.0 * r, residuals.at(r * 2));
EXPECT_EQ(-1.0 * r, residuals.at(r * 2 + 1));
}
EXPECT_EQ(0, residuals.at(20));
}
TEST(DynamicNumericdiffCostFunctionTest, TestJacobian) {
// Test the residual counting.
vector<double> param_block_0(10, 0.0);
for (int i = 0; i < 10; ++i) {
param_block_0[i] = 2 * i;
}
vector<double> param_block_1(5, 0.0);
DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
new MyCostFunctor());
cost_function.AddParameterBlock(param_block_0.size());
cost_function.AddParameterBlock(param_block_1.size());
cost_function.SetNumResiduals(21);
// Prepare the residuals.
vector<double> residuals(21, -100000);
// Prepare the parameters.
vector<double*> parameter_blocks(2);
parameter_blocks[0] = &param_block_0[0];
parameter_blocks[1] = &param_block_1[0];
// Prepare the jacobian.
vector<vector<double>> jacobian_vect(2);
jacobian_vect[0].resize(21 * 10, -100000);
jacobian_vect[1].resize(21 * 5, -100000);
vector<double*> jacobian;
jacobian.push_back(jacobian_vect[0].data());
jacobian.push_back(jacobian_vect[1].data());
// Test jacobian computation.
EXPECT_TRUE(cost_function.Evaluate(
parameter_blocks.data(), residuals.data(), jacobian.data()));
for (int r = 0; r < 10; ++r) {
EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
}
EXPECT_EQ(420, residuals.at(20));
for (int p = 0; p < 10; ++p) {
// Check "A" Jacobian.
EXPECT_NEAR(-1.0, jacobian_vect[0][2 * p * 10 + p], kTolerance);
// Check "B" Jacobian.
EXPECT_NEAR(+1.0, jacobian_vect[0][(2 * p + 1) * 10 + p], kTolerance);
jacobian_vect[0][2 * p * 10 + p] = 0.0;
jacobian_vect[0][(2 * p + 1) * 10 + p] = 0.0;
}
// Check "C" Jacobian for first parameter block.
for (int p = 0; p < 10; ++p) {
EXPECT_NEAR(4 * p - 8, jacobian_vect[0][20 * 10 + p], kTolerance);
jacobian_vect[0][20 * 10 + p] = 0.0;
}
for (double entry : jacobian_vect[0]) {
EXPECT_NEAR(0.0, entry, kTolerance);
}
// Check "C" Jacobian for second parameter block.
for (int p = 0; p < 5; ++p) {
EXPECT_NEAR(1.0, jacobian_vect[1][20 * 5 + p], kTolerance);
jacobian_vect[1][20 * 5 + p] = 0.0;
}
for (double entry : jacobian_vect[1]) {
EXPECT_NEAR(0.0, entry, kTolerance);
}
}
TEST(DynamicNumericdiffCostFunctionTest,
JacobianWithFirstParameterBlockConstant) { // NOLINT
// Test the residual counting.
vector<double> param_block_0(10, 0.0);
for (int i = 0; i < 10; ++i) {
param_block_0[i] = 2 * i;
}
vector<double> param_block_1(5, 0.0);
DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
new MyCostFunctor());
cost_function.AddParameterBlock(param_block_0.size());
cost_function.AddParameterBlock(param_block_1.size());
cost_function.SetNumResiduals(21);
// Prepare the residuals.
vector<double> residuals(21, -100000);
// Prepare the parameters.
vector<double*> parameter_blocks(2);
parameter_blocks[0] = &param_block_0[0];
parameter_blocks[1] = &param_block_1[0];
// Prepare the jacobian.
vector<vector<double>> jacobian_vect(2);
jacobian_vect[0].resize(21 * 10, -100000);
jacobian_vect[1].resize(21 * 5, -100000);
vector<double*> jacobian;
jacobian.push_back(nullptr);
jacobian.push_back(jacobian_vect[1].data());
// Test jacobian computation.
EXPECT_TRUE(cost_function.Evaluate(
parameter_blocks.data(), residuals.data(), jacobian.data()));
for (int r = 0; r < 10; ++r) {
EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
}
EXPECT_EQ(420, residuals.at(20));
// Check "C" Jacobian for second parameter block.
for (int p = 0; p < 5; ++p) {
EXPECT_NEAR(1.0, jacobian_vect[1][20 * 5 + p], kTolerance);
jacobian_vect[1][20 * 5 + p] = 0.0;
}
for (double& i : jacobian_vect[1]) {
EXPECT_EQ(0.0, i);
}
}
TEST(DynamicNumericdiffCostFunctionTest,
JacobianWithSecondParameterBlockConstant) { // NOLINT
// Test the residual counting.
vector<double> param_block_0(10, 0.0);
for (int i = 0; i < 10; ++i) {
param_block_0[i] = 2 * i;
}
vector<double> param_block_1(5, 0.0);
DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
new MyCostFunctor());
cost_function.AddParameterBlock(param_block_0.size());
cost_function.AddParameterBlock(param_block_1.size());
cost_function.SetNumResiduals(21);
// Prepare the residuals.
vector<double> residuals(21, -100000);
// Prepare the parameters.
vector<double*> parameter_blocks(2);
parameter_blocks[0] = &param_block_0[0];
parameter_blocks[1] = &param_block_1[0];
// Prepare the jacobian.
vector<vector<double>> jacobian_vect(2);
jacobian_vect[0].resize(21 * 10, -100000);
jacobian_vect[1].resize(21 * 5, -100000);
vector<double*> jacobian;
jacobian.push_back(jacobian_vect[0].data());
jacobian.push_back(nullptr);
// Test jacobian computation.
EXPECT_TRUE(cost_function.Evaluate(
parameter_blocks.data(), residuals.data(), jacobian.data()));
for (int r = 0; r < 10; ++r) {
EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
}
EXPECT_EQ(420, residuals.at(20));
for (int p = 0; p < 10; ++p) {
// Check "A" Jacobian.
EXPECT_NEAR(-1.0, jacobian_vect[0][2 * p * 10 + p], kTolerance);
// Check "B" Jacobian.
EXPECT_NEAR(+1.0, jacobian_vect[0][(2 * p + 1) * 10 + p], kTolerance);
jacobian_vect[0][2 * p * 10 + p] = 0.0;
jacobian_vect[0][(2 * p + 1) * 10 + p] = 0.0;
}
// Check "C" Jacobian for first parameter block.
for (int p = 0; p < 10; ++p) {
EXPECT_NEAR(4 * p - 8, jacobian_vect[0][20 * 10 + p], kTolerance);
jacobian_vect[0][20 * 10 + p] = 0.0;
}
for (double& i : jacobian_vect[0]) {
EXPECT_EQ(0.0, i);
}
}
// Takes 3 parameter blocks:
// parameters[0] (x) is size 1.
// parameters[1] (y) is size 2.
// parameters[2] (z) is size 3.
// Emits 7 residuals:
// A: x[0] (= sum_x)
// B: y[0] + 2.0 * y[1] (= sum_y)
// C: z[0] + 3.0 * z[1] + 6.0 * z[2] (= sum_z)
// D: sum_x * sum_y
// E: sum_y * sum_z
// F: sum_x * sum_z
// G: sum_x * sum_y * sum_z
class MyThreeParameterCostFunctor {
public:
template <typename T>
bool operator()(T const* const* parameters, T* residuals) const {
const T* x = parameters[0];
const T* y = parameters[1];
const T* z = parameters[2];
T sum_x = x[0];
T sum_y = y[0] + 2.0 * y[1];
T sum_z = z[0] + 3.0 * z[1] + 6.0 * z[2];
residuals[0] = sum_x;
residuals[1] = sum_y;
residuals[2] = sum_z;
residuals[3] = sum_x * sum_y;
residuals[4] = sum_y * sum_z;
residuals[5] = sum_x * sum_z;
residuals[6] = sum_x * sum_y * sum_z;
return true;
}
};
class ThreeParameterCostFunctorTest : public ::testing::Test {
protected:
void SetUp() final {
// Prepare the parameters.
x_.resize(1);
x_[0] = 0.0;
y_.resize(2);
y_[0] = 1.0;
y_[1] = 3.0;
z_.resize(3);
z_[0] = 2.0;
z_[1] = 4.0;
z_[2] = 6.0;
parameter_blocks_.resize(3);
parameter_blocks_[0] = &x_[0];
parameter_blocks_[1] = &y_[0];
parameter_blocks_[2] = &z_[0];
// Prepare the cost function.
using DynamicMyThreeParameterCostFunction =
DynamicNumericDiffCostFunction<MyThreeParameterCostFunctor>;
auto cost_function = std::make_unique<DynamicMyThreeParameterCostFunction>(
new MyThreeParameterCostFunctor());
cost_function->AddParameterBlock(1);
cost_function->AddParameterBlock(2);
cost_function->AddParameterBlock(3);
cost_function->SetNumResiduals(7);
cost_function_ = std::move(cost_function);
// Setup jacobian data.
jacobian_vect_.resize(3);
jacobian_vect_[0].resize(7 * x_.size(), -100000);
jacobian_vect_[1].resize(7 * y_.size(), -100000);
jacobian_vect_[2].resize(7 * z_.size(), -100000);
// Prepare the expected residuals.
const double sum_x = x_[0];
const double sum_y = y_[0] + 2.0 * y_[1];
const double sum_z = z_[0] + 3.0 * z_[1] + 6.0 * z_[2];
expected_residuals_.resize(7);
expected_residuals_[0] = sum_x;
expected_residuals_[1] = sum_y;
expected_residuals_[2] = sum_z;
expected_residuals_[3] = sum_x * sum_y;
expected_residuals_[4] = sum_y * sum_z;
expected_residuals_[5] = sum_x * sum_z;
expected_residuals_[6] = sum_x * sum_y * sum_z;
// Prepare the expected jacobian entries.
expected_jacobian_x_.resize(7);
expected_jacobian_x_[0] = 1.0;
expected_jacobian_x_[1] = 0.0;
expected_jacobian_x_[2] = 0.0;
expected_jacobian_x_[3] = sum_y;
expected_jacobian_x_[4] = 0.0;
expected_jacobian_x_[5] = sum_z;
expected_jacobian_x_[6] = sum_y * sum_z;
expected_jacobian_y_.resize(14);
expected_jacobian_y_[0] = 0.0;
expected_jacobian_y_[1] = 0.0;
expected_jacobian_y_[2] = 1.0;
expected_jacobian_y_[3] = 2.0;
expected_jacobian_y_[4] = 0.0;
expected_jacobian_y_[5] = 0.0;
expected_jacobian_y_[6] = sum_x;
expected_jacobian_y_[7] = 2.0 * sum_x;
expected_jacobian_y_[8] = sum_z;
expected_jacobian_y_[9] = 2.0 * sum_z;
expected_jacobian_y_[10] = 0.0;
expected_jacobian_y_[11] = 0.0;
expected_jacobian_y_[12] = sum_x * sum_z;
expected_jacobian_y_[13] = 2.0 * sum_x * sum_z;
expected_jacobian_z_.resize(21);
expected_jacobian_z_[0] = 0.0;
expected_jacobian_z_[1] = 0.0;
expected_jacobian_z_[2] = 0.0;
expected_jacobian_z_[3] = 0.0;
expected_jacobian_z_[4] = 0.0;
expected_jacobian_z_[5] = 0.0;
expected_jacobian_z_[6] = 1.0;
expected_jacobian_z_[7] = 3.0;
expected_jacobian_z_[8] = 6.0;
expected_jacobian_z_[9] = 0.0;
expected_jacobian_z_[10] = 0.0;
expected_jacobian_z_[11] = 0.0;
expected_jacobian_z_[12] = sum_y;
expected_jacobian_z_[13] = 3.0 * sum_y;
expected_jacobian_z_[14] = 6.0 * sum_y;
expected_jacobian_z_[15] = sum_x;
expected_jacobian_z_[16] = 3.0 * sum_x;
expected_jacobian_z_[17] = 6.0 * sum_x;
expected_jacobian_z_[18] = sum_x * sum_y;
expected_jacobian_z_[19] = 3.0 * sum_x * sum_y;
expected_jacobian_z_[20] = 6.0 * sum_x * sum_y;
}
protected:
vector<double> x_;
vector<double> y_;
vector<double> z_;
vector<double*> parameter_blocks_;
std::unique_ptr<CostFunction> cost_function_;
vector<vector<double>> jacobian_vect_;
vector<double> expected_residuals_;
vector<double> expected_jacobian_x_;
vector<double> expected_jacobian_y_;
vector<double> expected_jacobian_z_;
};
TEST_F(ThreeParameterCostFunctorTest, TestThreeParameterResiduals) {
vector<double> residuals(7, -100000);
EXPECT_TRUE(cost_function_->Evaluate(
parameter_blocks_.data(), residuals.data(), nullptr));
for (int i = 0; i < 7; ++i) {
EXPECT_EQ(expected_residuals_[i], residuals[i]);
}
}
TEST_F(ThreeParameterCostFunctorTest, TestThreeParameterJacobian) {
vector<double> residuals(7, -100000);
vector<double*> jacobian;
jacobian.push_back(jacobian_vect_[0].data());
jacobian.push_back(jacobian_vect_[1].data());
jacobian.push_back(jacobian_vect_[2].data());
EXPECT_TRUE(cost_function_->Evaluate(
parameter_blocks_.data(), residuals.data(), jacobian.data()));
for (int i = 0; i < 7; ++i) {
EXPECT_EQ(expected_residuals_[i], residuals[i]);
}
for (int i = 0; i < 7; ++i) {
EXPECT_NEAR(expected_jacobian_x_[i], jacobian[0][i], kTolerance);
}
for (int i = 0; i < 14; ++i) {
EXPECT_NEAR(expected_jacobian_y_[i], jacobian[1][i], kTolerance);
}
for (int i = 0; i < 21; ++i) {
EXPECT_NEAR(expected_jacobian_z_[i], jacobian[2][i], kTolerance);
}
}
TEST_F(ThreeParameterCostFunctorTest,
ThreeParameterJacobianWithFirstAndLastParameterBlockConstant) {
vector<double> residuals(7, -100000);
vector<double*> jacobian;
jacobian.push_back(nullptr);
jacobian.push_back(jacobian_vect_[1].data());
jacobian.push_back(nullptr);
EXPECT_TRUE(cost_function_->Evaluate(
parameter_blocks_.data(), residuals.data(), jacobian.data()));
for (int i = 0; i < 7; ++i) {
EXPECT_EQ(expected_residuals_[i], residuals[i]);
}
for (int i = 0; i < 14; ++i) {
EXPECT_NEAR(expected_jacobian_y_[i], jacobian[1][i], kTolerance);
}
}
TEST_F(ThreeParameterCostFunctorTest,
ThreeParameterJacobianWithSecondParameterBlockConstant) {
vector<double> residuals(7, -100000);
vector<double*> jacobian;
jacobian.push_back(jacobian_vect_[0].data());
jacobian.push_back(nullptr);
jacobian.push_back(jacobian_vect_[2].data());
EXPECT_TRUE(cost_function_->Evaluate(
parameter_blocks_.data(), residuals.data(), jacobian.data()));
for (int i = 0; i < 7; ++i) {
EXPECT_EQ(expected_residuals_[i], residuals[i]);
}
for (int i = 0; i < 7; ++i) {
EXPECT_NEAR(expected_jacobian_x_[i], jacobian[0][i], kTolerance);
}
for (int i = 0; i < 21; ++i) {
EXPECT_NEAR(expected_jacobian_z_[i], jacobian[2][i], kTolerance);
}
}
} // namespace ceres::internal