// 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:

//

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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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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR

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// 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