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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// 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 "ceres/dynamic_numeric_diff_cost_function.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+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:
+ virtual void SetUp() {
+ // 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_;
+
+ scoped_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
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