| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2014 Google Inc. All rights reserved. |
| // http://code.google.com/p/ceres-solver/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| |
| #include "ceres/cubic_interpolation.h" |
| |
| #include "ceres/jet.h" |
| #include "glog/logging.h" |
| #include "gtest/gtest.h" |
| |
| namespace ceres { |
| namespace internal { |
| |
| TEST(CubicInterpolator, NeedsAtleastTwoValues) { |
| double x[] = {1}; |
| EXPECT_DEATH_IF_SUPPORTED(CubicInterpolator c(x, 0), "num_values > 1"); |
| EXPECT_DEATH_IF_SUPPORTED(CubicInterpolator c(x, 1), "num_values > 1"); |
| } |
| |
| static const double kTolerance = 1e-12; |
| |
| class CubicInterpolatorTest : public ::testing::Test { |
| public: |
| void RunPolynomialInterpolationTest(const double a, |
| const double b, |
| const double c, |
| const double d) { |
| for (int x = 0; x < kNumSamples; ++x) { |
| values_[x] = a * x * x * x + b * x * x + c * x + d; |
| } |
| |
| CubicInterpolator interpolator(values_, kNumSamples); |
| |
| // Check values in the all the cells but the first and the last |
| // ones. In these cells, the interpolated function values should |
| // match exactly the values of the function being interpolated. |
| // |
| // On the boundary, we extrapolate the values of the function on |
| // the basis of its first derivative, so we do not expect the |
| // function values and its derivatives not to match. |
| for (int j = 0; j < kNumTestSamples; ++j) { |
| const double x = 1.0 + 7.0 / (kNumTestSamples - 1) * j; |
| const double expected_f = a * x * x * x + b * x * x + c * x + d; |
| const double expected_dfdx = 3.0 * a * x * x + 2.0 * b * x + c; |
| double f, dfdx; |
| |
| EXPECT_TRUE(interpolator.Evaluate(x, &f, &dfdx)); |
| EXPECT_NEAR(f, expected_f, kTolerance) |
| << "x: " << x |
| << " actual f(x): " << expected_f |
| << " estimated f(x): " << f; |
| EXPECT_NEAR(dfdx, expected_dfdx, kTolerance) |
| << "x: " << x |
| << " actual df(x)/dx: " << expected_dfdx |
| << " estimated df(x)/dx: " << dfdx; |
| } |
| } |
| |
| private: |
| static const int kNumSamples = 10; |
| static const int kNumTestSamples = 100; |
| double values_[kNumSamples]; |
| }; |
| |
| TEST_F(CubicInterpolatorTest, ConstantFunction) { |
| RunPolynomialInterpolationTest(0.0, 0.0, 0.0, 0.5); |
| } |
| |
| TEST_F(CubicInterpolatorTest, LinearFunction) { |
| RunPolynomialInterpolationTest(0.0, 0.0, 1.0, 0.5); |
| } |
| |
| TEST_F(CubicInterpolatorTest, QuadraticFunction) { |
| RunPolynomialInterpolationTest(0.0, 0.4, 1.0, 0.5); |
| } |
| |
| TEST(CubicInterpolator, JetEvaluation) { |
| const double values[] = {1.0, 2.0, 2.0, 3.0}; |
| CubicInterpolator interpolator(values, 4); |
| double f, dfdx; |
| const double x = 2.5; |
| EXPECT_TRUE(interpolator.Evaluate(x, &f, &dfdx)); |
| |
| // Create a Jet with the same scalar part as x, so that the output |
| // Jet will be evaluate at x. |
| Jet<double, 4> x_jet; |
| x_jet.a = x; |
| x_jet.v(0) = 1.0; |
| x_jet.v(1) = 1.1; |
| x_jet.v(2) = 1.2; |
| x_jet.v(3) = 1.3; |
| |
| Jet<double, 4> f_jet; |
| EXPECT_TRUE(interpolator.Evaluate(x_jet, &f_jet)); |
| |
| // Check that the scalar part of the Jet is f(x). |
| EXPECT_EQ(f_jet.a, f); |
| |
| // Check that the derivative part of the Jet is dfdx * x_jet.v |
| // by the chain rule. |
| EXPECT_EQ((f_jet.v - dfdx * x_jet.v).norm(), 0.0); |
| } |
| |
| class BiCubicInterpolatorTest : public ::testing::Test { |
| public: |
| void RunPolynomialInterpolationTest(const Eigen::Matrix3d& coeff) { |
| coeff_ = coeff; |
| double* v = values_; |
| for (int r = 0; r < kNumRows; ++r) { |
| for (int c = 0; c < kNumCols; ++c) { |
| *v++ = EvaluateF(r, c); |
| } |
| } |
| BiCubicInterpolator interpolator(values_, kNumRows, kNumCols); |
| |
| for (int j = 0; j < kNumRowSamples; ++j) { |
| const double r = 1.0 + 7.0 / (kNumRowSamples - 1) * j; |
| for (int k = 0; k < kNumColSamples; ++k) { |
| const double c = 1.0 + 7.0 / (kNumColSamples - 1) * k; |
| const double expected_f = EvaluateF(r, c); |
| const double expected_dfdr = EvaluatedFdr(r, c); |
| const double expected_dfdc = EvaluatedFdc(r, c); |
| double f, dfdr, dfdc; |
| |
| EXPECT_TRUE(interpolator.Evaluate(r, c, &f, &dfdr, &dfdc)); |
| EXPECT_NEAR(f, expected_f, kTolerance); |
| EXPECT_NEAR(dfdr, expected_dfdr, kTolerance); |
| EXPECT_NEAR(dfdc, expected_dfdc, kTolerance); |
| } |
| } |
| } |
| |
| private: |
| double EvaluateF(double r, double c) { |
| Eigen::Vector3d x; |
| x(0) = r; |
| x(1) = c; |
| x(2) = 1; |
| return x.transpose() * coeff_ * x; |
| } |
| |
| double EvaluatedFdr(double r, double c) { |
| Eigen::Vector3d x; |
| x(0) = r; |
| x(1) = c; |
| x(2) = 1; |
| return (coeff_.row(0) + coeff_.col(0).transpose()) * x; |
| } |
| |
| double EvaluatedFdc(double r, double c) { |
| Eigen::Vector3d x; |
| x(0) = r; |
| x(1) = c; |
| x(2) = 1; |
| return (coeff_.row(1) + coeff_.col(1).transpose()) * x; |
| } |
| |
| |
| Eigen::Matrix3d coeff_; |
| static const int kNumRows = 10; |
| static const int kNumCols = 10; |
| static const int kNumRowSamples = 100; |
| static const int kNumColSamples = 100; |
| double values_[kNumRows * kNumCols]; |
| }; |
| |
| TEST_F(BiCubicInterpolatorTest, ZeroFunction) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST_F(BiCubicInterpolatorTest, Degree00Function) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| coeff(2, 2) = 1.0; |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST_F(BiCubicInterpolatorTest, Degree01Function) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| coeff(2, 2) = 1.0; |
| coeff(0, 2) = 0.1; |
| coeff(2, 0) = 0.1; |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST_F(BiCubicInterpolatorTest, Degree10Function) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| coeff(2, 2) = 1.0; |
| coeff(0, 1) = 0.1; |
| coeff(1, 0) = 0.1; |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST_F(BiCubicInterpolatorTest, Degree11Function) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| coeff(2, 2) = 1.0; |
| coeff(0, 1) = 0.1; |
| coeff(1, 0) = 0.1; |
| coeff(0, 2) = 0.2; |
| coeff(2, 0) = 0.2; |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST_F(BiCubicInterpolatorTest, Degree12Function) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| coeff(2, 2) = 1.0; |
| coeff(0, 1) = 0.1; |
| coeff(1, 0) = 0.1; |
| coeff(0, 2) = 0.2; |
| coeff(2, 0) = 0.2; |
| coeff(1, 1) = 0.3; |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST_F(BiCubicInterpolatorTest, Degree21Function) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| coeff(2, 2) = 1.0; |
| coeff(0, 1) = 0.1; |
| coeff(1, 0) = 0.1; |
| coeff(0, 2) = 0.2; |
| coeff(2, 0) = 0.2; |
| coeff(0, 0) = 0.3; |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST_F(BiCubicInterpolatorTest, Degree22Function) { |
| Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero(); |
| coeff(2, 2) = 1.0; |
| coeff(0, 1) = 0.1; |
| coeff(1, 0) = 0.1; |
| coeff(0, 2) = 0.2; |
| coeff(2, 0) = 0.2; |
| coeff(0, 0) = 0.3; |
| coeff(0, 1) = -0.4; |
| coeff(1, 0) = -0.4; |
| RunPolynomialInterpolationTest(coeff); |
| } |
| |
| TEST(BiCubicInterpolator, JetEvaluation) { |
| const double values[] = {1.0, 2.0, 2.0, 3.0, |
| 1.0, 2.0, 2.0, 3.0}; |
| BiCubicInterpolator interpolator(values, 2, 4); |
| double f, dfdr, dfdc; |
| const double r = 0.5; |
| const double c = 2.5; |
| EXPECT_TRUE(interpolator.Evaluate(r, c, &f, &dfdr, &dfdc)); |
| |
| // Create a Jet with the same scalar part as x, so that the output |
| // Jet will be evaluate at x. |
| Jet<double, 4> r_jet; |
| r_jet.a = r; |
| r_jet.v(0) = 1.0; |
| r_jet.v(1) = 1.1; |
| r_jet.v(2) = 1.2; |
| r_jet.v(3) = 1.3; |
| |
| Jet<double, 4> c_jet; |
| c_jet.a = c; |
| c_jet.v(0) = 2.0; |
| c_jet.v(1) = 3.1; |
| c_jet.v(2) = 4.2; |
| c_jet.v(3) = 5.3; |
| |
| Jet<double, 4> f_jet; |
| EXPECT_TRUE(interpolator.Evaluate(r_jet, c_jet, &f_jet)); |
| EXPECT_EQ(f_jet.a, f); |
| EXPECT_EQ((f_jet.v - dfdr * r_jet.v - dfdc * c_jet.v).norm(), 0.0); |
| } |
| |
| } // namespace internal |
| } // namespace ceres |