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ceres-solver/internal/ceres/cubic_interpolation_test.cc
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Sameer Agarwal 560940fa27 A refactor of the cubic interpolation code 
1. Push the boundary handling logic into the underlying array
object. This has two very significant impacts:

a. The interpolation code becomes extremely simple to write
and to test.

b. The user has more flexibility in implementing how out of bounds
values are handled. We provide one default implementation.

Change-Id: Ic2f6cf9257ce7110c62e492688e5a6c8be1e7df2
2015-08-06 14:49:55 -07:00

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// 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
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