internal/ceres/dynamic_numeric_diff_cost_function_test.cc - ceres-solver - Git at Google

 // 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)
 //         mierle@gmail.com (Keir Mierle)

 #include <cstddef>

 #include <memory>
 #include "ceres/dynamic_numeric_diff_cost_function.h"
 #include "gtest/gtest.h"

 namespace ceres {
 namespace internal {

 using std::vector;

 const double kTolerance = 1e-6;

 // Takes 2 parameter blocks:
 //     parameters[0] is size 10.
 //     parameters[1] is size 5.
 // Emits 21 residuals:
 //     A: i - parameters[0][i], for i in [0,10)  -- this is 10 residuals
 //     B: parameters[0][i] - i, for i in [0,10)  -- this is another 10.
 //     C: sum(parameters[0][i]^2 - 8*parameters[0][i]) + sum(parameters[1][i])
 class MyCostFunctor {
  public:
   bool operator()(double const* const* parameters, double* residuals) const {
     const double* params0 = parameters[0];
     int r = 0;
     for (int i = 0; i < 10; ++i) {
       residuals[r++] = i - params0[i];
       residuals[r++] = params0[i] - i;
     }

     double c_residual = 0.0;
     for (int i = 0; i < 10; ++i) {
       c_residual += pow(params0[i], 2) - 8.0 * params0[i];
     }

     const double* params1 = parameters[1];
     for (int i = 0; i < 5; ++i) {
       c_residual += params1[i];
     }
     residuals[r++] = c_residual;
     return true;
   }
 };

 TEST(DynamicNumericdiffCostFunctionTest, TestResiduals) {
   vector<double> param_block_0(10, 0.0);
   vector<double> param_block_1(5, 0.0);
   DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
       new MyCostFunctor());
   cost_function.AddParameterBlock(param_block_0.size());
   cost_function.AddParameterBlock(param_block_1.size());
   cost_function.SetNumResiduals(21);

   // Test residual computation.
   vector<double> residuals(21, -100000);
   vector<double*> parameter_blocks(2);
   parameter_blocks[0] = &param_block_0[0];
   parameter_blocks[1] = &param_block_1[0];
   EXPECT_TRUE(cost_function.Evaluate(&parameter_blocks[0],
                                      residuals.data(),
                                      NULL));
   for (int r = 0; r < 10; ++r) {
     EXPECT_EQ(1.0 * r, residuals.at(r * 2));
     EXPECT_EQ(-1.0 * r, residuals.at(r * 2 + 1));
   }
   EXPECT_EQ(0, residuals.at(20));
 }


 TEST(DynamicNumericdiffCostFunctionTest, TestJacobian) {
   // Test the residual counting.
   vector<double> param_block_0(10, 0.0);
   for (int i = 0; i < 10; ++i) {
     param_block_0[i] = 2 * i;
   }
   vector<double> param_block_1(5, 0.0);
   DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
       new MyCostFunctor());
   cost_function.AddParameterBlock(param_block_0.size());
   cost_function.AddParameterBlock(param_block_1.size());
   cost_function.SetNumResiduals(21);

   // Prepare the residuals.
   vector<double> residuals(21, -100000);

   // Prepare the parameters.
   vector<double*> parameter_blocks(2);
   parameter_blocks[0] = &param_block_0[0];
   parameter_blocks[1] = &param_block_1[0];

   // Prepare the jacobian.
   vector<vector<double>> jacobian_vect(2);
   jacobian_vect[0].resize(21 * 10, -100000);
   jacobian_vect[1].resize(21 * 5, -100000);
   vector<double*> jacobian;
   jacobian.push_back(jacobian_vect[0].data());
   jacobian.push_back(jacobian_vect[1].data());

   // Test jacobian computation.
   EXPECT_TRUE(cost_function.Evaluate(parameter_blocks.data(),
                                      residuals.data(),
                                      jacobian.data()));

   for (int r = 0; r < 10; ++r) {
     EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
     EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
   }
   EXPECT_EQ(420, residuals.at(20));
   for (int p = 0; p < 10; ++p) {
     // Check "A" Jacobian.
     EXPECT_NEAR(-1.0, jacobian_vect[0][2*p * 10 + p], kTolerance);
     // Check "B" Jacobian.
     EXPECT_NEAR(+1.0, jacobian_vect[0][(2*p+1) * 10 + p], kTolerance);
     jacobian_vect[0][2*p * 10 + p] = 0.0;
     jacobian_vect[0][(2*p+1) * 10 + p] = 0.0;
   }

   // Check "C" Jacobian for first parameter block.
   for (int p = 0; p < 10; ++p) {
     EXPECT_NEAR(4 * p - 8, jacobian_vect[0][20 * 10 + p], kTolerance);
     jacobian_vect[0][20 * 10 + p] = 0.0;
   }
   for (int i = 0; i < jacobian_vect[0].size(); ++i) {
     EXPECT_NEAR(0.0, jacobian_vect[0][i], kTolerance);
   }

   // Check "C" Jacobian for second parameter block.
   for (int p = 0; p < 5; ++p) {
     EXPECT_NEAR(1.0, jacobian_vect[1][20 * 5 + p], kTolerance);
     jacobian_vect[1][20 * 5 + p] = 0.0;
   }
   for (int i = 0; i < jacobian_vect[1].size(); ++i) {
     EXPECT_NEAR(0.0, jacobian_vect[1][i], kTolerance);
   }
 }

 TEST(DynamicNumericdiffCostFunctionTest, JacobianWithFirstParameterBlockConstant) {  // NOLINT
   // Test the residual counting.
   vector<double> param_block_0(10, 0.0);
   for (int i = 0; i < 10; ++i) {
     param_block_0[i] = 2 * i;
   }
   vector<double> param_block_1(5, 0.0);
   DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
       new MyCostFunctor());
   cost_function.AddParameterBlock(param_block_0.size());
   cost_function.AddParameterBlock(param_block_1.size());
   cost_function.SetNumResiduals(21);

   // Prepare the residuals.
   vector<double> residuals(21, -100000);

   // Prepare the parameters.
   vector<double*> parameter_blocks(2);
   parameter_blocks[0] = &param_block_0[0];
   parameter_blocks[1] = &param_block_1[0];

   // Prepare the jacobian.
   vector<vector<double>> jacobian_vect(2);
   jacobian_vect[0].resize(21 * 10, -100000);
   jacobian_vect[1].resize(21 * 5, -100000);
   vector<double*> jacobian;
   jacobian.push_back(NULL);
   jacobian.push_back(jacobian_vect[1].data());

   // Test jacobian computation.
   EXPECT_TRUE(cost_function.Evaluate(parameter_blocks.data(),
                                      residuals.data(),
                                      jacobian.data()));

   for (int r = 0; r < 10; ++r) {
     EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
     EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
   }
   EXPECT_EQ(420, residuals.at(20));

   // Check "C" Jacobian for second parameter block.
   for (int p = 0; p < 5; ++p) {
     EXPECT_NEAR(1.0, jacobian_vect[1][20 * 5 + p], kTolerance);
     jacobian_vect[1][20 * 5 + p] = 0.0;
   }
   for (int i = 0; i < jacobian_vect[1].size(); ++i) {
     EXPECT_EQ(0.0, jacobian_vect[1][i]);
   }
 }

 TEST(DynamicNumericdiffCostFunctionTest, JacobianWithSecondParameterBlockConstant) {  // NOLINT
   // Test the residual counting.
   vector<double> param_block_0(10, 0.0);
   for (int i = 0; i < 10; ++i) {
     param_block_0[i] = 2 * i;
   }
   vector<double> param_block_1(5, 0.0);
   DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
       new MyCostFunctor());
   cost_function.AddParameterBlock(param_block_0.size());
   cost_function.AddParameterBlock(param_block_1.size());
   cost_function.SetNumResiduals(21);

   // Prepare the residuals.
   vector<double> residuals(21, -100000);

   // Prepare the parameters.
   vector<double*> parameter_blocks(2);
   parameter_blocks[0] = &param_block_0[0];
   parameter_blocks[1] = &param_block_1[0];

   // Prepare the jacobian.
   vector<vector<double>> jacobian_vect(2);
   jacobian_vect[0].resize(21 * 10, -100000);
   jacobian_vect[1].resize(21 * 5, -100000);
   vector<double*> jacobian;
   jacobian.push_back(jacobian_vect[0].data());
   jacobian.push_back(NULL);

   // Test jacobian computation.
   EXPECT_TRUE(cost_function.Evaluate(parameter_blocks.data(),
                                      residuals.data(),
                                      jacobian.data()));

   for (int r = 0; r < 10; ++r) {
     EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
     EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
   }
   EXPECT_EQ(420, residuals.at(20));
   for (int p = 0; p < 10; ++p) {
     // Check "A" Jacobian.
     EXPECT_NEAR(-1.0, jacobian_vect[0][2*p * 10 + p], kTolerance);
     // Check "B" Jacobian.
     EXPECT_NEAR(+1.0, jacobian_vect[0][(2*p+1) * 10 + p], kTolerance);
     jacobian_vect[0][2*p * 10 + p] = 0.0;
     jacobian_vect[0][(2*p+1) * 10 + p] = 0.0;
   }

   // Check "C" Jacobian for first parameter block.
   for (int p = 0; p < 10; ++p) {
     EXPECT_NEAR(4 * p - 8, jacobian_vect[0][20 * 10 + p], kTolerance);
     jacobian_vect[0][20 * 10 + p] = 0.0;
   }
   for (int i = 0; i < jacobian_vect[0].size(); ++i) {
     EXPECT_EQ(0.0, jacobian_vect[0][i]);
   }
 }

 // Takes 3 parameter blocks:
 //     parameters[0] (x) is size 1.
 //     parameters[1] (y) is size 2.
 //     parameters[2] (z) is size 3.
 // Emits 7 residuals:
 //     A: x[0] (= sum_x)
 //     B: y[0] + 2.0 * y[1] (= sum_y)
 //     C: z[0] + 3.0 * z[1] + 6.0 * z[2] (= sum_z)
 //     D: sum_x * sum_y
 //     E: sum_y * sum_z
 //     F: sum_x * sum_z
 //     G: sum_x * sum_y * sum_z
 class MyThreeParameterCostFunctor {
  public:
   template <typename T>
   bool operator()(T const* const* parameters, T* residuals) const {
     const T* x = parameters[0];
     const T* y = parameters[1];
     const T* z = parameters[2];

     T sum_x = x[0];
     T sum_y = y[0] + 2.0 * y[1];
     T sum_z = z[0] + 3.0 * z[1] + 6.0 * z[2];

     residuals[0] = sum_x;
     residuals[1] = sum_y;
     residuals[2] = sum_z;
     residuals[3] = sum_x * sum_y;
     residuals[4] = sum_y * sum_z;
     residuals[5] = sum_x * sum_z;
     residuals[6] = sum_x * sum_y * sum_z;
     return true;
   }
 };

 class ThreeParameterCostFunctorTest : public ::testing::Test {
  protected:
   void SetUp() final {
     // Prepare the parameters.
     x_.resize(1);
     x_[0] = 0.0;

     y_.resize(2);
     y_[0] = 1.0;
     y_[1] = 3.0;

     z_.resize(3);
     z_[0] = 2.0;
     z_[1] = 4.0;
     z_[2] = 6.0;

     parameter_blocks_.resize(3);
     parameter_blocks_[0] = &x_[0];
     parameter_blocks_[1] = &y_[0];
     parameter_blocks_[2] = &z_[0];

     // Prepare the cost function.
     typedef DynamicNumericDiffCostFunction<MyThreeParameterCostFunctor>
       DynamicMyThreeParameterCostFunction;
     DynamicMyThreeParameterCostFunction * cost_function =
       new DynamicMyThreeParameterCostFunction(
         new MyThreeParameterCostFunctor());
     cost_function->AddParameterBlock(1);
     cost_function->AddParameterBlock(2);
     cost_function->AddParameterBlock(3);
     cost_function->SetNumResiduals(7);

     cost_function_.reset(cost_function);

     // Setup jacobian data.
     jacobian_vect_.resize(3);
     jacobian_vect_[0].resize(7 * x_.size(), -100000);
     jacobian_vect_[1].resize(7 * y_.size(), -100000);
     jacobian_vect_[2].resize(7 * z_.size(), -100000);

     // Prepare the expected residuals.
     const double sum_x = x_[0];
     const double sum_y = y_[0] + 2.0 * y_[1];
     const double sum_z = z_[0] + 3.0 * z_[1] + 6.0 * z_[2];

     expected_residuals_.resize(7);
     expected_residuals_[0] = sum_x;
     expected_residuals_[1] = sum_y;
     expected_residuals_[2] = sum_z;
     expected_residuals_[3] = sum_x * sum_y;
     expected_residuals_[4] = sum_y * sum_z;
     expected_residuals_[5] = sum_x * sum_z;
     expected_residuals_[6] = sum_x * sum_y * sum_z;

     // Prepare the expected jacobian entries.
     expected_jacobian_x_.resize(7);
     expected_jacobian_x_[0] = 1.0;
     expected_jacobian_x_[1] = 0.0;
     expected_jacobian_x_[2] = 0.0;
     expected_jacobian_x_[3] = sum_y;
     expected_jacobian_x_[4] = 0.0;
     expected_jacobian_x_[5] = sum_z;
     expected_jacobian_x_[6] = sum_y * sum_z;

     expected_jacobian_y_.resize(14);
     expected_jacobian_y_[0] = 0.0;
     expected_jacobian_y_[1] = 0.0;
     expected_jacobian_y_[2] = 1.0;
     expected_jacobian_y_[3] = 2.0;
     expected_jacobian_y_[4] = 0.0;
     expected_jacobian_y_[5] = 0.0;
     expected_jacobian_y_[6] = sum_x;
     expected_jacobian_y_[7] = 2.0 * sum_x;
     expected_jacobian_y_[8] = sum_z;
     expected_jacobian_y_[9] = 2.0 * sum_z;
     expected_jacobian_y_[10] = 0.0;
     expected_jacobian_y_[11] = 0.0;
     expected_jacobian_y_[12] = sum_x * sum_z;
     expected_jacobian_y_[13] = 2.0 * sum_x * sum_z;

     expected_jacobian_z_.resize(21);
     expected_jacobian_z_[0] = 0.0;
     expected_jacobian_z_[1] = 0.0;
     expected_jacobian_z_[2] = 0.0;
     expected_jacobian_z_[3] = 0.0;
     expected_jacobian_z_[4] = 0.0;
     expected_jacobian_z_[5] = 0.0;
     expected_jacobian_z_[6] = 1.0;
     expected_jacobian_z_[7] = 3.0;
     expected_jacobian_z_[8] = 6.0;
     expected_jacobian_z_[9] = 0.0;
     expected_jacobian_z_[10] = 0.0;
     expected_jacobian_z_[11] = 0.0;
     expected_jacobian_z_[12] = sum_y;
     expected_jacobian_z_[13] = 3.0 * sum_y;
     expected_jacobian_z_[14] = 6.0 * sum_y;
     expected_jacobian_z_[15] = sum_x;
     expected_jacobian_z_[16] = 3.0 * sum_x;
     expected_jacobian_z_[17] = 6.0 * sum_x;
     expected_jacobian_z_[18] = sum_x * sum_y;
     expected_jacobian_z_[19] = 3.0 * sum_x * sum_y;
     expected_jacobian_z_[20] = 6.0 * sum_x * sum_y;
   }

  protected:
   vector<double> x_;
   vector<double> y_;
   vector<double> z_;

   vector<double*> parameter_blocks_;

   std::unique_ptr<CostFunction> cost_function_;

   vector<vector<double>> jacobian_vect_;

   vector<double> expected_residuals_;

   vector<double> expected_jacobian_x_;
   vector<double> expected_jacobian_y_;
   vector<double> expected_jacobian_z_;
 };

 TEST_F(ThreeParameterCostFunctorTest, TestThreeParameterResiduals) {
   vector<double> residuals(7, -100000);
   EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
                                        residuals.data(),
                                        NULL));
   for (int i = 0; i < 7; ++i) {
     EXPECT_EQ(expected_residuals_[i], residuals[i]);
   }
 }

 TEST_F(ThreeParameterCostFunctorTest, TestThreeParameterJacobian) {
   vector<double> residuals(7, -100000);

   vector<double*> jacobian;
   jacobian.push_back(jacobian_vect_[0].data());
   jacobian.push_back(jacobian_vect_[1].data());
   jacobian.push_back(jacobian_vect_[2].data());

   EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
                                        residuals.data(),
                                        jacobian.data()));

   for (int i = 0; i < 7; ++i) {
     EXPECT_EQ(expected_residuals_[i], residuals[i]);
   }

   for (int i = 0; i < 7; ++i) {
     EXPECT_NEAR(expected_jacobian_x_[i], jacobian[0][i], kTolerance);
   }

   for (int i = 0; i < 14; ++i) {
     EXPECT_NEAR(expected_jacobian_y_[i], jacobian[1][i], kTolerance);
   }

   for (int i = 0; i < 21; ++i) {
     EXPECT_NEAR(expected_jacobian_z_[i], jacobian[2][i], kTolerance);
   }
 }

 TEST_F(ThreeParameterCostFunctorTest,
        ThreeParameterJacobianWithFirstAndLastParameterBlockConstant) {
   vector<double> residuals(7, -100000);

   vector<double*> jacobian;
   jacobian.push_back(NULL);
   jacobian.push_back(jacobian_vect_[1].data());
   jacobian.push_back(NULL);

   EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
                                        residuals.data(),
                                        jacobian.data()));

   for (int i = 0; i < 7; ++i) {
     EXPECT_EQ(expected_residuals_[i], residuals[i]);
   }

   for (int i = 0; i < 14; ++i) {
     EXPECT_NEAR(expected_jacobian_y_[i], jacobian[1][i], kTolerance);
   }
 }

 TEST_F(ThreeParameterCostFunctorTest,
        ThreeParameterJacobianWithSecondParameterBlockConstant) {
   vector<double> residuals(7, -100000);

   vector<double*> jacobian;
   jacobian.push_back(jacobian_vect_[0].data());
   jacobian.push_back(NULL);
   jacobian.push_back(jacobian_vect_[2].data());

   EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
                                        residuals.data(),
                                        jacobian.data()));

   for (int i = 0; i < 7; ++i) {
     EXPECT_EQ(expected_residuals_[i], residuals[i]);
   }

   for (int i = 0; i < 7; ++i) {
     EXPECT_NEAR(expected_jacobian_x_[i], jacobian[0][i], kTolerance);
   }

   for (int i = 0; i < 21; ++i) {
     EXPECT_NEAR(expected_jacobian_z_[i], jacobian[2][i], kTolerance);
   }
 }

 }  // namespace internal
 }  // namespace ceres
	// 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)
	// mierle@gmail.com (Keir Mierle)

	#include <cstddef>

	#include <memory>
	#include "ceres/dynamic_numeric_diff_cost_function.h"
	#include "gtest/gtest.h"

	namespace ceres {
	namespace internal {

	using std::vector;

	const double kTolerance = 1e-6;

	// Takes 2 parameter blocks:
	// parameters[0] is size 10.
	// parameters[1] is size 5.
	// Emits 21 residuals:
	// A: i - parameters[0][i], for i in [0,10) -- this is 10 residuals
	// B: parameters[0][i] - i, for i in [0,10) -- this is another 10.
	// C: sum(parameters[0][i]^2 - 8*parameters[0][i]) + sum(parameters[1][i])
	class MyCostFunctor {
	public:
	bool operator()(double const* const* parameters, double* residuals) const {
	const double* params0 = parameters[0];
	int r = 0;
	for (int i = 0; i < 10; ++i) {
	residuals[r++] = i - params0[i];
	residuals[r++] = params0[i] - i;
	}

	double c_residual = 0.0;
	for (int i = 0; i < 10; ++i) {
	c_residual += pow(params0[i], 2) - 8.0 * params0[i];
	}

	const double* params1 = parameters[1];
	for (int i = 0; i < 5; ++i) {
	c_residual += params1[i];
	}
	residuals[r++] = c_residual;
	return true;
	}
	};

	TEST(DynamicNumericdiffCostFunctionTest, TestResiduals) {
	vector<double> param_block_0(10, 0.0);
	vector<double> param_block_1(5, 0.0);
	DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
	new MyCostFunctor());
	cost_function.AddParameterBlock(param_block_0.size());
	cost_function.AddParameterBlock(param_block_1.size());
	cost_function.SetNumResiduals(21);

	// Test residual computation.
	vector<double> residuals(21, -100000);
	vector<double*> parameter_blocks(2);
	parameter_blocks[0] = &param_block_0[0];
	parameter_blocks[1] = &param_block_1[0];
	EXPECT_TRUE(cost_function.Evaluate(&parameter_blocks[0],
	residuals.data(),
	NULL));
	for (int r = 0; r < 10; ++r) {
	EXPECT_EQ(1.0 * r, residuals.at(r * 2));
	EXPECT_EQ(-1.0 * r, residuals.at(r * 2 + 1));
	}
	EXPECT_EQ(0, residuals.at(20));
	}


	TEST(DynamicNumericdiffCostFunctionTest, TestJacobian) {
	// Test the residual counting.
	vector<double> param_block_0(10, 0.0);
	for (int i = 0; i < 10; ++i) {
	param_block_0[i] = 2 * i;
	}
	vector<double> param_block_1(5, 0.0);
	DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
	new MyCostFunctor());
	cost_function.AddParameterBlock(param_block_0.size());
	cost_function.AddParameterBlock(param_block_1.size());
	cost_function.SetNumResiduals(21);

	// Prepare the residuals.
	vector<double> residuals(21, -100000);

	// Prepare the parameters.
	vector<double*> parameter_blocks(2);
	parameter_blocks[0] = &param_block_0[0];
	parameter_blocks[1] = &param_block_1[0];

	// Prepare the jacobian.
	vector<vector<double>> jacobian_vect(2);
	jacobian_vect[0].resize(21 * 10, -100000);
	jacobian_vect[1].resize(21 * 5, -100000);
	vector<double*> jacobian;
	jacobian.push_back(jacobian_vect[0].data());
	jacobian.push_back(jacobian_vect[1].data());

	// Test jacobian computation.
	EXPECT_TRUE(cost_function.Evaluate(parameter_blocks.data(),
	residuals.data(),
	jacobian.data()));

	for (int r = 0; r < 10; ++r) {
	EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
	EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
	}
	EXPECT_EQ(420, residuals.at(20));
	for (int p = 0; p < 10; ++p) {
	// Check "A" Jacobian.
	EXPECT_NEAR(-1.0, jacobian_vect[0][2p 10 + p], kTolerance);
	// Check "B" Jacobian.
	EXPECT_NEAR(+1.0, jacobian_vect[0][(2p+1) 10 + p], kTolerance);
	jacobian_vect[0][2p 10 + p] = 0.0;
	jacobian_vect[0][(2p+1) 10 + p] = 0.0;
	}

	// Check "C" Jacobian for first parameter block.
	for (int p = 0; p < 10; ++p) {
	EXPECT_NEAR(4 * p - 8, jacobian_vect[0][20 * 10 + p], kTolerance);
	jacobian_vect[0][20 * 10 + p] = 0.0;
	}
	for (int i = 0; i < jacobian_vect[0].size(); ++i) {
	EXPECT_NEAR(0.0, jacobian_vect[0][i], kTolerance);
	}

	// Check "C" Jacobian for second parameter block.
	for (int p = 0; p < 5; ++p) {
	EXPECT_NEAR(1.0, jacobian_vect[1][20 * 5 + p], kTolerance);
	jacobian_vect[1][20 * 5 + p] = 0.0;
	}
	for (int i = 0; i < jacobian_vect[1].size(); ++i) {
	EXPECT_NEAR(0.0, jacobian_vect[1][i], kTolerance);
	}
	}

	TEST(DynamicNumericdiffCostFunctionTest, JacobianWithFirstParameterBlockConstant) { // NOLINT
	// Test the residual counting.
	vector<double> param_block_0(10, 0.0);
	for (int i = 0; i < 10; ++i) {
	param_block_0[i] = 2 * i;
	}
	vector<double> param_block_1(5, 0.0);
	DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
	new MyCostFunctor());
	cost_function.AddParameterBlock(param_block_0.size());
	cost_function.AddParameterBlock(param_block_1.size());
	cost_function.SetNumResiduals(21);

	// Prepare the residuals.
	vector<double> residuals(21, -100000);

	// Prepare the parameters.
	vector<double*> parameter_blocks(2);
	parameter_blocks[0] = &param_block_0[0];
	parameter_blocks[1] = &param_block_1[0];

	// Prepare the jacobian.
	vector<vector<double>> jacobian_vect(2);
	jacobian_vect[0].resize(21 * 10, -100000);
	jacobian_vect[1].resize(21 * 5, -100000);
	vector<double*> jacobian;
	jacobian.push_back(NULL);
	jacobian.push_back(jacobian_vect[1].data());

	// Test jacobian computation.
	EXPECT_TRUE(cost_function.Evaluate(parameter_blocks.data(),
	residuals.data(),
	jacobian.data()));

	for (int r = 0; r < 10; ++r) {
	EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
	EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
	}
	EXPECT_EQ(420, residuals.at(20));

	// Check "C" Jacobian for second parameter block.
	for (int p = 0; p < 5; ++p) {
	EXPECT_NEAR(1.0, jacobian_vect[1][20 * 5 + p], kTolerance);
	jacobian_vect[1][20 * 5 + p] = 0.0;
	}
	for (int i = 0; i < jacobian_vect[1].size(); ++i) {
	EXPECT_EQ(0.0, jacobian_vect[1][i]);
	}
	}

	TEST(DynamicNumericdiffCostFunctionTest, JacobianWithSecondParameterBlockConstant) { // NOLINT
	// Test the residual counting.
	vector<double> param_block_0(10, 0.0);
	for (int i = 0; i < 10; ++i) {
	param_block_0[i] = 2 * i;
	}
	vector<double> param_block_1(5, 0.0);
	DynamicNumericDiffCostFunction<MyCostFunctor> cost_function(
	new MyCostFunctor());
	cost_function.AddParameterBlock(param_block_0.size());
	cost_function.AddParameterBlock(param_block_1.size());
	cost_function.SetNumResiduals(21);

	// Prepare the residuals.
	vector<double> residuals(21, -100000);

	// Prepare the parameters.
	vector<double*> parameter_blocks(2);
	parameter_blocks[0] = &param_block_0[0];
	parameter_blocks[1] = &param_block_1[0];

	// Prepare the jacobian.
	vector<vector<double>> jacobian_vect(2);
	jacobian_vect[0].resize(21 * 10, -100000);
	jacobian_vect[1].resize(21 * 5, -100000);
	vector<double*> jacobian;
	jacobian.push_back(jacobian_vect[0].data());
	jacobian.push_back(NULL);

	// Test jacobian computation.
	EXPECT_TRUE(cost_function.Evaluate(parameter_blocks.data(),
	residuals.data(),
	jacobian.data()));

	for (int r = 0; r < 10; ++r) {
	EXPECT_EQ(-1.0 * r, residuals.at(r * 2));
	EXPECT_EQ(+1.0 * r, residuals.at(r * 2 + 1));
	}
	EXPECT_EQ(420, residuals.at(20));
	for (int p = 0; p < 10; ++p) {
	// Check "A" Jacobian.
	EXPECT_NEAR(-1.0, jacobian_vect[0][2p 10 + p], kTolerance);
	// Check "B" Jacobian.
	EXPECT_NEAR(+1.0, jacobian_vect[0][(2p+1) 10 + p], kTolerance);
	jacobian_vect[0][2p 10 + p] = 0.0;
	jacobian_vect[0][(2p+1) 10 + p] = 0.0;
	}

	// Check "C" Jacobian for first parameter block.
	for (int p = 0; p < 10; ++p) {
	EXPECT_NEAR(4 * p - 8, jacobian_vect[0][20 * 10 + p], kTolerance);
	jacobian_vect[0][20 * 10 + p] = 0.0;
	}
	for (int i = 0; i < jacobian_vect[0].size(); ++i) {
	EXPECT_EQ(0.0, jacobian_vect[0][i]);
	}
	}

	// Takes 3 parameter blocks:
	// parameters[0] (x) is size 1.
	// parameters[1] (y) is size 2.
	// parameters[2] (z) is size 3.
	// Emits 7 residuals:
	// A: x[0] (= sum_x)
	// B: y[0] + 2.0 * y[1] (= sum_y)
	// C: z[0] + 3.0 * z[1] + 6.0 * z[2] (= sum_z)
	// D: sum_x * sum_y
	// E: sum_y * sum_z
	// F: sum_x * sum_z
	// G: sum_x * sum_y * sum_z
	class MyThreeParameterCostFunctor {
	public:
	template <typename T>
	bool operator()(T const* const* parameters, T* residuals) const {
	const T* x = parameters[0];
	const T* y = parameters[1];
	const T* z = parameters[2];

	T sum_x = x[0];
	T sum_y = y[0] + 2.0 * y[1];
	T sum_z = z[0] + 3.0 * z[1] + 6.0 * z[2];

	residuals[0] = sum_x;
	residuals[1] = sum_y;
	residuals[2] = sum_z;
	residuals[3] = sum_x * sum_y;
	residuals[4] = sum_y * sum_z;
	residuals[5] = sum_x * sum_z;
	residuals[6] = sum_x * sum_y * sum_z;
	return true;
	}
	};

	class ThreeParameterCostFunctorTest : public ::testing::Test {
	protected:
	void SetUp() final {
	// Prepare the parameters.
	x_.resize(1);
	x_[0] = 0.0;

	y_.resize(2);
	y_[0] = 1.0;
	y_[1] = 3.0;

	z_.resize(3);
	z_[0] = 2.0;
	z_[1] = 4.0;
	z_[2] = 6.0;

	parameter_blocks_.resize(3);
	parameter_blocks_[0] = &x_[0];
	parameter_blocks_[1] = &y_[0];
	parameter_blocks_[2] = &z_[0];

	// Prepare the cost function.
	typedef DynamicNumericDiffCostFunction<MyThreeParameterCostFunctor>
	DynamicMyThreeParameterCostFunction;
	DynamicMyThreeParameterCostFunction * cost_function =
	new DynamicMyThreeParameterCostFunction(
	new MyThreeParameterCostFunctor());
	cost_function->AddParameterBlock(1);
	cost_function->AddParameterBlock(2);
	cost_function->AddParameterBlock(3);
	cost_function->SetNumResiduals(7);

	cost_function_.reset(cost_function);

	// Setup jacobian data.
	jacobian_vect_.resize(3);
	jacobian_vect_[0].resize(7 * x_.size(), -100000);
	jacobian_vect_[1].resize(7 * y_.size(), -100000);
	jacobian_vect_[2].resize(7 * z_.size(), -100000);

	// Prepare the expected residuals.
	const double sum_x = x_[0];
	const double sum_y = y_[0] + 2.0 * y_[1];
	const double sum_z = z_[0] + 3.0 * z_[1] + 6.0 * z_[2];

	expected_residuals_.resize(7);
	expected_residuals_[0] = sum_x;
	expected_residuals_[1] = sum_y;
	expected_residuals_[2] = sum_z;
	expected_residuals_[3] = sum_x * sum_y;
	expected_residuals_[4] = sum_y * sum_z;
	expected_residuals_[5] = sum_x * sum_z;
	expected_residuals_[6] = sum_x * sum_y * sum_z;

	// Prepare the expected jacobian entries.
	expected_jacobian_x_.resize(7);
	expected_jacobian_x_[0] = 1.0;
	expected_jacobian_x_[1] = 0.0;
	expected_jacobian_x_[2] = 0.0;
	expected_jacobian_x_[3] = sum_y;
	expected_jacobian_x_[4] = 0.0;
	expected_jacobian_x_[5] = sum_z;
	expected_jacobian_x_[6] = sum_y * sum_z;

	expected_jacobian_y_.resize(14);
	expected_jacobian_y_[0] = 0.0;
	expected_jacobian_y_[1] = 0.0;
	expected_jacobian_y_[2] = 1.0;
	expected_jacobian_y_[3] = 2.0;
	expected_jacobian_y_[4] = 0.0;
	expected_jacobian_y_[5] = 0.0;
	expected_jacobian_y_[6] = sum_x;
	expected_jacobian_y_[7] = 2.0 * sum_x;
	expected_jacobian_y_[8] = sum_z;
	expected_jacobian_y_[9] = 2.0 * sum_z;
	expected_jacobian_y_[10] = 0.0;
	expected_jacobian_y_[11] = 0.0;
	expected_jacobian_y_[12] = sum_x * sum_z;
	expected_jacobian_y_[13] = 2.0 * sum_x * sum_z;

	expected_jacobian_z_.resize(21);
	expected_jacobian_z_[0] = 0.0;
	expected_jacobian_z_[1] = 0.0;
	expected_jacobian_z_[2] = 0.0;
	expected_jacobian_z_[3] = 0.0;
	expected_jacobian_z_[4] = 0.0;
	expected_jacobian_z_[5] = 0.0;
	expected_jacobian_z_[6] = 1.0;
	expected_jacobian_z_[7] = 3.0;
	expected_jacobian_z_[8] = 6.0;
	expected_jacobian_z_[9] = 0.0;
	expected_jacobian_z_[10] = 0.0;
	expected_jacobian_z_[11] = 0.0;
	expected_jacobian_z_[12] = sum_y;
	expected_jacobian_z_[13] = 3.0 * sum_y;
	expected_jacobian_z_[14] = 6.0 * sum_y;
	expected_jacobian_z_[15] = sum_x;
	expected_jacobian_z_[16] = 3.0 * sum_x;
	expected_jacobian_z_[17] = 6.0 * sum_x;
	expected_jacobian_z_[18] = sum_x * sum_y;
	expected_jacobian_z_[19] = 3.0 * sum_x * sum_y;
	expected_jacobian_z_[20] = 6.0 * sum_x * sum_y;
	}

	protected:
	vector<double> x_;
	vector<double> y_;
	vector<double> z_;

	vector<double*> parameter_blocks_;

	std::unique_ptr<CostFunction> cost_function_;

	vector<vector<double>> jacobian_vect_;

	vector<double> expected_residuals_;

	vector<double> expected_jacobian_x_;
	vector<double> expected_jacobian_y_;
	vector<double> expected_jacobian_z_;
	};

	TEST_F(ThreeParameterCostFunctorTest, TestThreeParameterResiduals) {
	vector<double> residuals(7, -100000);
	EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
	residuals.data(),
	NULL));
	for (int i = 0; i < 7; ++i) {
	EXPECT_EQ(expected_residuals_[i], residuals[i]);
	}
	}

	TEST_F(ThreeParameterCostFunctorTest, TestThreeParameterJacobian) {
	vector<double> residuals(7, -100000);

	vector<double*> jacobian;
	jacobian.push_back(jacobian_vect_[0].data());
	jacobian.push_back(jacobian_vect_[1].data());
	jacobian.push_back(jacobian_vect_[2].data());

	EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
	residuals.data(),
	jacobian.data()));

	for (int i = 0; i < 7; ++i) {
	EXPECT_EQ(expected_residuals_[i], residuals[i]);
	}

	for (int i = 0; i < 7; ++i) {
	EXPECT_NEAR(expected_jacobian_x_[i], jacobian[0][i], kTolerance);
	}

	for (int i = 0; i < 14; ++i) {
	EXPECT_NEAR(expected_jacobian_y_[i], jacobian[1][i], kTolerance);
	}

	for (int i = 0; i < 21; ++i) {
	EXPECT_NEAR(expected_jacobian_z_[i], jacobian[2][i], kTolerance);
	}
	}

	TEST_F(ThreeParameterCostFunctorTest,
	ThreeParameterJacobianWithFirstAndLastParameterBlockConstant) {
	vector<double> residuals(7, -100000);

	vector<double*> jacobian;
	jacobian.push_back(NULL);
	jacobian.push_back(jacobian_vect_[1].data());
	jacobian.push_back(NULL);

	EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
	residuals.data(),
	jacobian.data()));

	for (int i = 0; i < 7; ++i) {
	EXPECT_EQ(expected_residuals_[i], residuals[i]);
	}

	for (int i = 0; i < 14; ++i) {
	EXPECT_NEAR(expected_jacobian_y_[i], jacobian[1][i], kTolerance);
	}
	}

	TEST_F(ThreeParameterCostFunctorTest,
	ThreeParameterJacobianWithSecondParameterBlockConstant) {
	vector<double> residuals(7, -100000);

	vector<double*> jacobian;
	jacobian.push_back(jacobian_vect_[0].data());
	jacobian.push_back(NULL);
	jacobian.push_back(jacobian_vect_[2].data());

	EXPECT_TRUE(cost_function_->Evaluate(parameter_blocks_.data(),
	residuals.data(),
	jacobian.data()));

	for (int i = 0; i < 7; ++i) {
	EXPECT_EQ(expected_residuals_[i], residuals[i]);
	}

	for (int i = 0; i < 7; ++i) {
	EXPECT_NEAR(expected_jacobian_x_[i], jacobian[0][i], kTolerance);
	}

	for (int i = 0; i < 21; ++i) {
	EXPECT_NEAR(expected_jacobian_z_[i], jacobian[2][i], kTolerance);
	}
	}

	} // namespace internal
	} // namespace ceres