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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2022 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/corrector.h"
#include <algorithm>
#include <cmath>
#include <cstring>
#include <random>
#include "ceres/internal/eigen.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
// If rho[1] is zero, the Corrector constructor should crash.
TEST(Corrector, ZeroGradientDeathTest) {
const double kRho[] = {0.0, 0.0, 1.0};
EXPECT_DEATH_IF_SUPPORTED({ Corrector c(1.0, kRho); }, ".*");
}
// If rho[1] is negative, the Corrector constructor should crash.
TEST(Corrector, NegativeGradientDeathTest) {
const double kRho[] = {0.0, -0.1, 1.0};
EXPECT_DEATH_IF_SUPPORTED({ Corrector c(1.0, kRho); }, ".*");
}
TEST(Corrector, ScalarCorrection) {
double residuals = sqrt(3.0);
double jacobian = 10.0;
double sq_norm = residuals * residuals;
const double kRho[] = {sq_norm, 0.1, -0.01};
// In light of the rho'' < 0 clamping now implemented in
// corrector.cc, alpha = 0 whenever rho'' < 0.
const double kAlpha = 0.0;
// Thus the expected value of the residual is
// residual[i] * sqrt(kRho[1]) / (1.0 - kAlpha).
const double kExpectedResidual = residuals * sqrt(kRho[1]) / (1 - kAlpha);
// The jacobian in this case will be
// sqrt(kRho[1]) * (1 - kAlpha) * jacobian.
const double kExpectedJacobian = sqrt(kRho[1]) * (1 - kAlpha) * jacobian;
Corrector c(sq_norm, kRho);
c.CorrectJacobian(1.0, 1.0, &residuals, &jacobian);
c.CorrectResiduals(1.0, &residuals);
ASSERT_NEAR(residuals, kExpectedResidual, 1e-6);
ASSERT_NEAR(kExpectedJacobian, jacobian, 1e-6);
}
TEST(Corrector, ScalarCorrectionZeroResidual) {
double residuals = 0.0;
double jacobian = 10.0;
double sq_norm = residuals * residuals;
const double kRho[] = {0.0, 0.1, -0.01};
Corrector c(sq_norm, kRho);
// The alpha equation is
// 1/2 alpha^2 - alpha + 0.0 = 0.
// i.e. alpha = 1.0 - sqrt(1.0).
// alpha = 0.0.
// Thus the expected value of the residual is
// residual[i] * sqrt(kRho[1])
const double kExpectedResidual = residuals * sqrt(kRho[1]);
// The jacobian in this case will be
// sqrt(kRho[1]) * jacobian.
const double kExpectedJacobian = sqrt(kRho[1]) * jacobian;
c.CorrectJacobian(1, 1, &residuals, &jacobian);
c.CorrectResiduals(1, &residuals);
ASSERT_NEAR(residuals, kExpectedResidual, 1e-6);
ASSERT_NEAR(kExpectedJacobian, jacobian, 1e-6);
}
// Scaling behaviour for one dimensional functions.
TEST(Corrector, ScalarCorrectionAlphaClamped) {
double residuals = sqrt(3.0);
double jacobian = 10.0;
double sq_norm = residuals * residuals;
const double kRho[] = {3, 0.1, -0.1};
// rho[2] < 0 -> alpha = 0.0
const double kAlpha = 0.0;
// Thus the expected value of the residual is
// residual[i] * sqrt(kRho[1]) / (1.0 - kAlpha).
const double kExpectedResidual = residuals * sqrt(kRho[1]) / (1.0 - kAlpha);
// The jacobian in this case will be scaled by
// sqrt(rho[1]) * (1 - alpha) * J.
const double kExpectedJacobian = sqrt(kRho[1]) * (1.0 - kAlpha) * jacobian;
Corrector c(sq_norm, kRho);
c.CorrectJacobian(1, 1, &residuals, &jacobian);
c.CorrectResiduals(1, &residuals);
ASSERT_NEAR(residuals, kExpectedResidual, 1e-6);
ASSERT_NEAR(kExpectedJacobian, jacobian, 1e-6);
}
// Test that the corrected multidimensional residual and jacobians
// match the expected values and the resulting modified normal
// equations match the robustified gauss newton approximation.
TEST(Corrector, MultidimensionalGaussNewtonApproximation) {
double residuals[3];
double jacobian[2 * 3];
double rho[3];
// Eigen matrix references for linear algebra.
MatrixRef jac(jacobian, 3, 2);
VectorRef res(residuals, 3);
// Ground truth values of the modified jacobian and residuals.
Matrix g_jac(3, 2);
Vector g_res(3);
// Ground truth values of the robustified Gauss-Newton
// approximation.
Matrix g_hess(2, 2);
Vector g_grad(2);
// Corrected hessian and gradient implied by the modified jacobian
// and hessians.
Matrix c_hess(2, 2);
Vector c_grad(2);
std::mt19937 prng;
std::uniform_real_distribution<double> uniform01(0.0, 1.0);
for (int iter = 0; iter < 10000; ++iter) {
// Initialize the jacobian and residual.
for (double& jacobian_entry : jacobian) jacobian_entry = uniform01(prng);
for (double& residual : residuals) residual = uniform01(prng);
const double sq_norm = res.dot(res);
rho[0] = sq_norm;
rho[1] = uniform01(prng);
rho[2] = uniform01(
prng, std::uniform_real_distribution<double>::param_type(-1, 1));
// If rho[2] > 0, then the curvature correction to the correction
// and the gauss newton approximation will match. Otherwise, we
// will clamp alpha to 0.
const double kD = 1 + 2 * rho[2] / rho[1] * sq_norm;
const double kAlpha = (rho[2] > 0.0) ? 1 - sqrt(kD) : 0.0;
// Ground truth values.
g_res = sqrt(rho[1]) / (1.0 - kAlpha) * res;
g_jac =
sqrt(rho[1]) * (jac - kAlpha / sq_norm * res * res.transpose() * jac);
g_grad = rho[1] * jac.transpose() * res;
g_hess = rho[1] * jac.transpose() * jac +
2.0 * rho[2] * jac.transpose() * res * res.transpose() * jac;
Corrector c(sq_norm, rho);
c.CorrectJacobian(3, 2, residuals, jacobian);
c.CorrectResiduals(3, residuals);
// Corrected gradient and hessian.
c_grad = jac.transpose() * res;
c_hess = jac.transpose() * jac;
ASSERT_NEAR((g_res - res).norm(), 0.0, 1e-10);
ASSERT_NEAR((g_jac - jac).norm(), 0.0, 1e-10);
ASSERT_NEAR((g_grad - c_grad).norm(), 0.0, 1e-10);
}
}
TEST(Corrector, MultidimensionalGaussNewtonApproximationZeroResidual) {
double residuals[3];
double jacobian[2 * 3];
double rho[3];
// Eigen matrix references for linear algebra.
MatrixRef jac(jacobian, 3, 2);
VectorRef res(residuals, 3);
// Ground truth values of the modified jacobian and residuals.
Matrix g_jac(3, 2);
Vector g_res(3);
// Ground truth values of the robustified Gauss-Newton
// approximation.
Matrix g_hess(2, 2);
Vector g_grad(2);
// Corrected hessian and gradient implied by the modified jacobian
// and hessians.
Matrix c_hess(2, 2);
Vector c_grad(2);
std::mt19937 prng;
std::uniform_real_distribution<double> uniform01(0.0, 1.0);
for (int iter = 0; iter < 10000; ++iter) {
// Initialize the jacobian.
for (double& jacobian_entry : jacobian) jacobian_entry = uniform01(prng);
// Zero residuals
res.setZero();
const double sq_norm = res.dot(res);
rho[0] = sq_norm;
rho[1] = uniform01(prng);
rho[2] = uniform01(
prng, std::uniform_real_distribution<double>::param_type(-1, 1));
// Ground truth values.
g_res = sqrt(rho[1]) * res;
g_jac = sqrt(rho[1]) * jac;
g_grad = rho[1] * jac.transpose() * res;
g_hess = rho[1] * jac.transpose() * jac +
2.0 * rho[2] * jac.transpose() * res * res.transpose() * jac;
Corrector c(sq_norm, rho);
c.CorrectJacobian(3, 2, residuals, jacobian);
c.CorrectResiduals(3, residuals);
// Corrected gradient and hessian.
c_grad = jac.transpose() * res;
c_hess = jac.transpose() * jac;
ASSERT_NEAR((g_res - res).norm(), 0.0, 1e-10);
ASSERT_NEAR((g_jac - jac).norm(), 0.0, 1e-10);
ASSERT_NEAR((g_grad - c_grad).norm(), 0.0, 1e-10);
ASSERT_NEAR((g_hess - c_hess).norm(), 0.0, 1e-10);
}
}
} // namespace internal
} // namespace ceres