// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// modification, are permitted provided that the following conditions are met:
//
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// this list of conditions and the following disclaimer.
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// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
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// used to endorse or promote products derived from this software without
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//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/corrector.h"
#include <algorithm>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include "gtest/gtest.h"
#include "ceres/random.h"
#include "ceres/internal/eigen.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);
srand(5);
for (int iter = 0; iter < 10000; ++iter) {
// Initialize the jacobian and residual.
for (int i = 0; i < 2 * 3; ++i)
jacobian[i] = RandDouble();
for (int i = 0; i < 3; ++i)
residuals[i] = RandDouble();
const double sq_norm = res.dot(res);
rho[0] = sq_norm;
rho[1] = RandDouble();
rho[2] = 2.0 * RandDouble() - 1.0;
// 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);
srand(5);
for (int iter = 0; iter < 10000; ++iter) {
// Initialize the jacobian.
for (int i = 0; i < 2 * 3; ++i)
jacobian[i] = RandDouble();
// Zero residuals
res.setZero();
const double sq_norm = res.dot(res);
rho[0] = sq_norm;
rho[1] = RandDouble();
rho[2] = 2 * RandDouble() - 1.0;
// 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