// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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 "ceres/internal/scoped_ptr.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
static const double kTolerance = 1e-12;
TEST(Grid1D, OneDataDimension) {
int x[] = {1, 2, 3};
Grid1D<int, 1> grid(x, 0, 3);
for (int i = 0; i < 3; ++i) {
double value;
grid.GetValue(i, &value);
EXPECT_EQ(value, static_cast<double>(i + 1));
}
}
TEST(Grid1D, OneDataDimensionOutOfBounds) {
int x[] = {1, 2, 3};
Grid1D<int, 1> grid(x, 0, 3);
double value;
grid.GetValue(-1, &value);
EXPECT_EQ(value, x[0]);
grid.GetValue(-2, &value);
EXPECT_EQ(value, x[0]);
grid.GetValue(3, &value);
EXPECT_EQ(value, x[2]);
grid.GetValue(4, &value);
EXPECT_EQ(value, x[2]);
}
TEST(Grid1D, TwoDataDimensionIntegerDataInterleaved) {
int x[] = {1, 5,
2, 6,
3, 7};
Grid1D<int, 2, true> grid(x, 0, 3);
for (int i = 0; i < 3; ++i) {
double value[2];
grid.GetValue(i, value);
EXPECT_EQ(value[0], static_cast<double>(i + 1));
EXPECT_EQ(value[1], static_cast<double>(i + 5));
}
}
TEST(Grid1D, TwoDataDimensionIntegerDataStacked) {
int x[] = {1, 2, 3,
5, 6, 7};
Grid1D<int, 2, false> grid(x, 0, 3);
for (int i = 0; i < 3; ++i) {
double value[2];
grid.GetValue(i, value);
EXPECT_EQ(value[0], static_cast<double>(i + 1));
EXPECT_EQ(value[1], static_cast<double>(i + 5));
}
}
TEST(Grid2D, OneDataDimensionRowMajor) {
int x[] = {1, 2, 3,
2, 3, 4};
Grid2D<int, 1, true, true> grid(x, 0, 2, 0, 3);
for (int r = 0; r < 2; ++r) {
for (int c = 0; c < 3; ++c) {
double value;
grid.GetValue(r, c, &value);
EXPECT_EQ(value, static_cast<double>(r + c + 1));
}
}
}
TEST(Grid2D, OneDataDimensionRowMajorOutOfBounds) {
int x[] = {1, 2, 3,
2, 3, 4};
Grid2D<int, 1, true, true> grid(x, 0, 2, 0, 3);
double value;
grid.GetValue(-1, -1, &value);
EXPECT_EQ(value, x[0]);
grid.GetValue(-1, 0, &value);
EXPECT_EQ(value, x[0]);
grid.GetValue(-1, 1, &value);
EXPECT_EQ(value, x[1]);
grid.GetValue(-1, 2, &value);
EXPECT_EQ(value, x[2]);
grid.GetValue(-1, 3, &value);
EXPECT_EQ(value, x[2]);
grid.GetValue(0, 3, &value);
EXPECT_EQ(value, x[2]);
grid.GetValue(1, 3, &value);
EXPECT_EQ(value, x[5]);
grid.GetValue(2, 3, &value);
EXPECT_EQ(value, x[5]);
grid.GetValue(2, 2, &value);
EXPECT_EQ(value, x[5]);
grid.GetValue(2, 1, &value);
EXPECT_EQ(value, x[4]);
grid.GetValue(2, 0, &value);
EXPECT_EQ(value, x[3]);
grid.GetValue(2, -1, &value);
EXPECT_EQ(value, x[3]);
grid.GetValue(1, -1, &value);
EXPECT_EQ(value, x[3]);
grid.GetValue(0, -1, &value);
EXPECT_EQ(value, x[0]);
}
TEST(Grid2D, TwoDataDimensionRowMajorInterleaved) {
int x[] = {1, 4, 2, 8, 3, 12,
2, 8, 3, 12, 4, 16};
Grid2D<int, 2, true, true> grid(x, 0, 2, 0, 3);
for (int r = 0; r < 2; ++r) {
for (int c = 0; c < 3; ++c) {
double value[2];
grid.GetValue(r, c, value);
EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
}
}
}
TEST(Grid2D, TwoDataDimensionRowMajorStacked) {
int x[] = {1, 2, 3,
2, 3, 4,
4, 8, 12,
8, 12, 16};
Grid2D<int, 2, true, false> grid(x, 0, 2, 0, 3);
for (int r = 0; r < 2; ++r) {
for (int c = 0; c < 3; ++c) {
double value[2];
grid.GetValue(r, c, value);
EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
}
}
}
TEST(Grid2D, TwoDataDimensionColMajorInterleaved) {
int x[] = { 1, 4, 2, 8,
2, 8, 3, 12,
3, 12, 4, 16};
Grid2D<int, 2, false, true> grid(x, 0, 2, 0, 3);
for (int r = 0; r < 2; ++r) {
for (int c = 0; c < 3; ++c) {
double value[2];
grid.GetValue(r, c, value);
EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
}
}
}
TEST(Grid2D, TwoDataDimensionColMajorStacked) {
int x[] = {1, 2,
2, 3,
3, 4,
4, 8,
8, 12,
12, 16};
Grid2D<int, 2, false, false> grid(x, 0, 2, 0, 3);
for (int r = 0; r < 2; ++r) {
for (int c = 0; c < 3; ++c) {
double value[2];
grid.GetValue(r, c, value);
EXPECT_EQ(value[0], static_cast<double>(r + c + 1));
EXPECT_EQ(value[1], static_cast<double>(4 *(r + c + 1)));
}
}
}
class CubicInterpolatorTest : public ::testing::Test {
public:
template <int kDataDimension>
void RunPolynomialInterpolationTest(const double a,
const double b,
const double c,
const double d) {
values_.reset(new double[kDataDimension * kNumSamples]);
for (int x = 0; x < kNumSamples; ++x) {
for (int dim = 0; dim < kDataDimension; ++dim) {
values_[x * kDataDimension + dim] =
(dim * dim + 1) * (a * x * x * x + b * x * x + c * x + d);
}
}
Grid1D<double, kDataDimension> grid(values_.get(), 0, kNumSamples);
CubicInterpolator<Grid1D<double, kDataDimension> > interpolator(grid);
// 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;
double expected_f[kDataDimension], expected_dfdx[kDataDimension];
double f[kDataDimension], dfdx[kDataDimension];
for (int dim = 0; dim < kDataDimension; ++dim) {
expected_f[dim] =
(dim * dim + 1) * (a * x * x * x + b * x * x + c * x + d);
expected_dfdx[dim] = (dim * dim + 1) * (3.0 * a * x * x + 2.0 * b * x + c);
}
interpolator.Evaluate(x, f, dfdx);
for (int dim = 0; dim < kDataDimension; ++dim) {
EXPECT_NEAR(f[dim], expected_f[dim], kTolerance)
<< "x: " << x << " dim: " << dim
<< " actual f(x): " << expected_f[dim]
<< " estimated f(x): " << f[dim];
EXPECT_NEAR(dfdx[dim], expected_dfdx[dim], kTolerance)
<< "x: " << x << " dim: " << dim
<< " actual df(x)/dx: " << expected_dfdx[dim]
<< " estimated df(x)/dx: " << dfdx[dim];
}
}
}
private:
static const int kNumSamples = 10;
static const int kNumTestSamples = 100;
scoped_array<double> values_;
};
TEST_F(CubicInterpolatorTest, ConstantFunction) {
RunPolynomialInterpolationTest<1>(0.0, 0.0, 0.0, 0.5);
RunPolynomialInterpolationTest<2>(0.0, 0.0, 0.0, 0.5);
RunPolynomialInterpolationTest<3>(0.0, 0.0, 0.0, 0.5);
}
TEST_F(CubicInterpolatorTest, LinearFunction) {
RunPolynomialInterpolationTest<1>(0.0, 0.0, 1.0, 0.5);
RunPolynomialInterpolationTest<2>(0.0, 0.0, 1.0, 0.5);
RunPolynomialInterpolationTest<3>(0.0, 0.0, 1.0, 0.5);
}
TEST_F(CubicInterpolatorTest, QuadraticFunction) {
RunPolynomialInterpolationTest<1>(0.0, 0.4, 1.0, 0.5);
RunPolynomialInterpolationTest<2>(0.0, 0.4, 1.0, 0.5);
RunPolynomialInterpolationTest<3>(0.0, 0.4, 1.0, 0.5);
}
TEST(CubicInterpolator, JetEvaluation) {
const double values[] = {1.0, 2.0, 2.0, 5.0, 3.0, 9.0, 2.0, 7.0};
Grid1D<double, 2, true> grid(values, 0, 4);
CubicInterpolator<Grid1D<double, 2, true> > interpolator(grid);
double f[2], dfdx[2];
const double x = 2.5;
interpolator.Evaluate(x, f, dfdx);
// Create a Jet with the same scalar part as x, so that the output
// Jet will be evaluated 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_jets[2];
interpolator.Evaluate(x_jet, f_jets);
// Check that the scalar part of the Jet is f(x).
EXPECT_EQ(f_jets[0].a, f[0]);
EXPECT_EQ(f_jets[1].a, f[1]);
// Check that the derivative part of the Jet is dfdx * x_jet.v
// by the chain rule.
EXPECT_NEAR((f_jets[0].v - dfdx[0] * x_jet.v).norm(), 0.0, kTolerance);
EXPECT_NEAR((f_jets[1].v - dfdx[1] * x_jet.v).norm(), 0.0, kTolerance);
}
class BiCubicInterpolatorTest : public ::testing::Test {
public:
template <int kDataDimension>
void RunPolynomialInterpolationTest(const Eigen::Matrix3d& coeff) {
values_.reset(new double[kNumRows * kNumCols * kDataDimension]);
coeff_ = coeff;
double* v = values_.get();
for (int r = 0; r < kNumRows; ++r) {
for (int c = 0; c < kNumCols; ++c) {
for (int dim = 0; dim < kDataDimension; ++dim) {
*v++ = (dim * dim + 1) * EvaluateF(r, c);
}
}
}
Grid2D<double, kDataDimension> grid(values_.get(), 0, kNumRows, 0, kNumCols);
BiCubicInterpolator<Grid2D<double, kDataDimension> > interpolator(grid);
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;
double f[kDataDimension], dfdr[kDataDimension], dfdc[kDataDimension];
interpolator.Evaluate(r, c, f, dfdr, dfdc);
for (int dim = 0; dim < kDataDimension; ++dim) {
EXPECT_NEAR(f[dim], (dim * dim + 1) * EvaluateF(r, c), kTolerance);
EXPECT_NEAR(dfdr[dim], (dim * dim + 1) * EvaluatedFdr(r, c), kTolerance);
EXPECT_NEAR(dfdc[dim], (dim * dim + 1) * EvaluatedFdc(r, c), 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;
scoped_array<double> values_;
};
TEST_F(BiCubicInterpolatorTest, ZeroFunction) {
Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero();
RunPolynomialInterpolationTest<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree00Function) {
Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero();
coeff(2, 2) = 1.0;
RunPolynomialInterpolationTest<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(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<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(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<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(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<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(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<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(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<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(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<1>(coeff);
RunPolynomialInterpolationTest<2>(coeff);
RunPolynomialInterpolationTest<3>(coeff);
}
TEST(BiCubicInterpolator, JetEvaluation) {
const double values[] = {1.0, 5.0, 2.0, 10.0, 2.0, 6.0, 3.0, 5.0,
1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 3.0, 1.0};
Grid2D<double, 2> grid(values, 0, 2, 0, 4);
BiCubicInterpolator<Grid2D<double, 2> > interpolator(grid);
double f[2], dfdr[2], dfdc[2];
const double r = 0.5;
const double c = 2.5;
interpolator.Evaluate(r, c, f, dfdr, dfdc);
// Create a Jet with the same scalar part as x, so that the output
// Jet will be evaluated 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_jets[2];
interpolator.Evaluate(r_jet, c_jet, f_jets);
EXPECT_EQ(f_jets[0].a, f[0]);
EXPECT_EQ(f_jets[1].a, f[1]);
EXPECT_NEAR((f_jets[0].v - dfdr[0] * r_jet.v - dfdc[0] * c_jet.v).norm(),
0.0,
kTolerance);
EXPECT_NEAR((f_jets[1].v - dfdr[1] * r_jet.v - dfdc[1] * c_jet.v).norm(),
0.0,
kTolerance);
}
} // namespace internal
} // namespace ceres