A complete re-write of the cubic interpolation code.
The key change is that there is a new layer of abstract,
a Array object that the interpolator depends on.
The Array provides a one dimension or two dimensional
array like interface independent of the underlying representation
of the data.
Also included here is support for vector valued functions.
Change-Id: Ica68f03778cf0d84192db00cd55653f8b4124d51
diff --git a/internal/ceres/cubic_interpolation_test.cc b/internal/ceres/cubic_interpolation_test.cc
index 0b4bb12..04a7b33 100644
--- a/internal/ceres/cubic_interpolation_test.cc
+++ b/internal/ceres/cubic_interpolation_test.cc
@@ -31,31 +31,147 @@
#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 {
-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;
+
+TEST(Array1D, OneDataDimension) {
+ int x[] = {1, 2, 3};
+ Array1D<int, 1> array(x, 3);
+ for (int i = 0; i < 3; ++i) {
+ double value;
+ array.GetValue(i, &value);
+ EXPECT_EQ(value, static_cast<double>(i + 1));
+ }
}
-static const double kTolerance = 1e-12;
+TEST(Array1D, TwoDataDimensionIntegerDataInterleaved) {
+ int x[] = {1, 5,
+ 2, 6,
+ 3, 7};
+
+ Array1D<int, 2, true> array(x, 3);
+ for (int i = 0; i < 3; ++i) {
+ double value[2];
+ array.GetValue(i, value);
+ EXPECT_EQ(value[0], static_cast<double>(i + 1));
+ EXPECT_EQ(value[1], static_cast<double>(i + 5));
+ }
+}
+
+TEST(Array1D, TwoDataDimensionIntegerDataStacked) {
+ int x[] = {1, 2, 3,
+ 5, 6, 7};
+
+ Array1D<int, 2, false> array(x, 3);
+ for (int i = 0; i < 3; ++i) {
+ double value[2];
+ array.GetValue(i, value);
+ EXPECT_EQ(value[0], static_cast<double>(i + 1));
+ EXPECT_EQ(value[1], static_cast<double>(i + 5));
+ }
+}
+
+TEST(Array2D, OneDataDimensionRowMajor) {
+ int x[] = {1, 2, 3,
+ 2, 3, 4};
+ Array2D<int, 1, true, true> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value;
+ array.GetValue(r, c, &value);
+ EXPECT_EQ(value, static_cast<double>(r + c + 1));
+ }
+ }
+}
+
+TEST(Array2D, TwoDataDimensionRowMajorInterleaved) {
+ int x[] = {1, 4, 2, 8, 3, 12,
+ 2, 8, 3, 12, 4, 16};
+ Array2D<int, 2, true, true> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.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(Array2D, TwoDataDimensionRowMajorStacked) {
+ int x[] = {1, 2, 3,
+ 2, 3, 4,
+ 4, 8, 12,
+ 8, 12, 16};
+ Array2D<int, 2, true, false> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.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(Array2D, TwoDataDimensionColMajorInterleaved) {
+ int x[] = { 1, 4, 2, 8,
+ 2, 8, 3, 12,
+ 3, 12, 4, 16};
+ Array2D<int, 2, false, true> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.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(Array2D, TwoDataDimensionColMajorStacked) {
+ int x[] = {1, 2,
+ 2, 3,
+ 3, 4,
+ 4, 8,
+ 8, 12,
+ 12, 16};
+ Array2D<int, 2, false, false> array(x, 2, 3);
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 3; ++c) {
+ double value[2];
+ array.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) {
- values_[x] = a * x * x * x + b * x * x + c * x + d;
+ for (int dim = 0; dim < kDataDimension; ++dim) {
+ values_[x * kDataDimension + dim] =
+ (dim * dim + 1) * (a * x * x * x + b * x * x + c * x + d);
+ }
}
- CubicInterpolator interpolator(values_, kNumSamples);
+ Array1D<double, kDataDimension> array(values_.get(), kNumSamples);
+ CubicInterpolator<Array1D<double, kDataDimension> > interpolator(array);
// Check values in the all the cells but the first and the last
// ones. In these cells, the interpolated function values should
@@ -66,46 +182,63 @@
// 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;
+ double expected_f[kDataDimension], expected_dfdx[kDataDimension];
+ double f[kDataDimension], dfdx[kDataDimension];
- 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;
+ 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);
+ }
+
+ EXPECT_TRUE(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;
- double values_[kNumSamples];
+ scoped_array<double> values_;
};
TEST_F(CubicInterpolatorTest, ConstantFunction) {
- RunPolynomialInterpolationTest(0.0, 0.0, 0.0, 0.5);
+ 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(0.0, 0.0, 1.0, 0.5);
+ 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(0.0, 0.4, 1.0, 0.5);
+ 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, 3.0};
- CubicInterpolator interpolator(values, 4);
- double f, dfdx;
+ const double values[] = {1.0, 2.0, 2.0, 5.0, 3.0, 9.0, 2.0, 7.0};
+
+ Array1D<double, 2, true> array(values, 4);
+ CubicInterpolator<Array1D<double, 2, true> > interpolator(array);
+
+ double f[2], dfdx[2];
const double x = 2.5;
- EXPECT_TRUE(interpolator.Evaluate(x, &f, &dfdx));
+ EXPECT_TRUE(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.
@@ -116,42 +249,48 @@
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));
+ Jet<double, 4> f_jets[2];
+ EXPECT_TRUE(interpolator.Evaluate(x_jet, f_jets));
// Check that the scalar part of the Jet is f(x).
- EXPECT_EQ(f_jet.a, f);
+ 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_EQ((f_jet.v - dfdx * x_jet.v).norm(), 0.0);
+ 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_;
+ double* v = values_.get();
for (int r = 0; r < kNumRows; ++r) {
for (int c = 0; c < kNumCols; ++c) {
- *v++ = EvaluateF(r, c);
+ for (int dim = 0; dim < kDataDimension; ++dim) {
+ *v++ = (dim * dim + 1) * EvaluateF(r, c);
+ }
}
}
- BiCubicInterpolator interpolator(values_, kNumRows, kNumCols);
+
+ Array2D<double, kDataDimension> array(values_.get(), kNumRows, kNumCols);
+ BiCubicInterpolator<Array2D<double, kDataDimension> > interpolator(array);
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);
+ double f[kDataDimension], dfdr[kDataDimension], dfdc[kDataDimension];
+ EXPECT_TRUE(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);
+ }
}
}
}
@@ -187,18 +326,22 @@
static const int kNumCols = 10;
static const int kNumRowSamples = 100;
static const int kNumColSamples = 100;
- double values_[kNumRows * kNumCols];
+ scoped_array<double> values_;
};
TEST_F(BiCubicInterpolatorTest, ZeroFunction) {
Eigen::Matrix3d coeff = Eigen::Matrix3d::Zero();
- RunPolynomialInterpolationTest(coeff);
+ 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(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree01Function) {
@@ -206,7 +349,9 @@
coeff(2, 2) = 1.0;
coeff(0, 2) = 0.1;
coeff(2, 0) = 0.1;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree10Function) {
@@ -214,7 +359,9 @@
coeff(2, 2) = 1.0;
coeff(0, 1) = 0.1;
coeff(1, 0) = 0.1;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree11Function) {
@@ -224,7 +371,9 @@
coeff(1, 0) = 0.1;
coeff(0, 2) = 0.2;
coeff(2, 0) = 0.2;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree12Function) {
@@ -235,7 +384,9 @@
coeff(0, 2) = 0.2;
coeff(2, 0) = 0.2;
coeff(1, 1) = 0.3;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree21Function) {
@@ -246,7 +397,9 @@
coeff(0, 2) = 0.2;
coeff(2, 0) = 0.2;
coeff(0, 0) = 0.3;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(coeff);
}
TEST_F(BiCubicInterpolatorTest, Degree22Function) {
@@ -259,17 +412,22 @@
coeff(0, 0) = 0.3;
coeff(0, 1) = -0.4;
coeff(1, 0) = -0.4;
- RunPolynomialInterpolationTest(coeff);
+ RunPolynomialInterpolationTest<1>(coeff);
+ RunPolynomialInterpolationTest<2>(coeff);
+ RunPolynomialInterpolationTest<3>(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 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};
+
+ Array2D<double, 2> array(values, 2, 4);
+ BiCubicInterpolator<Array2D<double, 2> > interpolator(array);
+
+ double f[2], dfdr[2], dfdc[2];
const double r = 0.5;
const double c = 2.5;
- EXPECT_TRUE(interpolator.Evaluate(r, c, &f, &dfdr, &dfdc));
+ 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 evaluated at x.
@@ -287,10 +445,16 @@
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);
+ Jet<double, 4> f_jets[2];
+ EXPECT_TRUE(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
