Squashed 'third_party/ceres/' content from commit e51e9b4

Change-Id: I763587619d57e594d3fa158dc3a7fe0b89a1743b
git-subtree-dir: third_party/ceres
git-subtree-split: e51e9b46f6ca88ab8b2266d0e362771db6d98067
diff --git a/internal/ceres/gradient_checker_test.cc b/internal/ceres/gradient_checker_test.cc
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+++ b/internal/ceres/gradient_checker_test.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2016 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: wjr@google.com (William Rucklidge)
+//
+// This file contains tests for the GradientChecker class.
+
+#include "ceres/gradient_checker.h"
+
+#include <cmath>
+#include <cstdlib>
+#include <vector>
+
+#include "ceres/cost_function.h"
+#include "ceres/problem.h"
+#include "ceres/random.h"
+#include "ceres/solver.h"
+#include "ceres/test_util.h"
+#include "glog/logging.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+using std::vector;
+
+// We pick a (non-quadratic) function whose derivative are easy:
+//
+//    f = exp(- a' x).
+//   df = - f a.
+//
+// where 'a' is a vector of the same size as 'x'. In the block
+// version, they are both block vectors, of course.
+class GoodTestTerm : public CostFunction {
+ public:
+  GoodTestTerm(int arity, int const* dim) : arity_(arity), return_value_(true) {
+    // Make 'arity' random vectors.
+    a_.resize(arity_);
+    for (int j = 0; j < arity_; ++j) {
+      a_[j].resize(dim[j]);
+      for (int u = 0; u < dim[j]; ++u) {
+        a_[j][u] = 2.0 * RandDouble() - 1.0;
+      }
+    }
+
+    for (int i = 0; i < arity_; i++) {
+      mutable_parameter_block_sizes()->push_back(dim[i]);
+    }
+    set_num_residuals(1);
+  }
+
+  bool Evaluate(double const* const* parameters,
+                double* residuals,
+                double** jacobians) const {
+    if (!return_value_) {
+      return false;
+    }
+    // Compute a . x.
+    double ax = 0;
+    for (int j = 0; j < arity_; ++j) {
+      for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
+        ax += a_[j][u] * parameters[j][u];
+      }
+    }
+
+    // This is the cost, but also appears as a factor
+    // in the derivatives.
+    double f = *residuals = exp(-ax);
+
+    // Accumulate 1st order derivatives.
+    if (jacobians) {
+      for (int j = 0; j < arity_; ++j) {
+        if (jacobians[j]) {
+          for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
+            // See comments before class.
+            jacobians[j][u] = -f * a_[j][u];
+          }
+        }
+      }
+    }
+
+    return true;
+  }
+
+  void SetReturnValue(bool return_value) { return_value_ = return_value; }
+
+ private:
+  int arity_;
+  bool return_value_;
+  vector<vector<double>> a_;  // our vectors.
+};
+
+class BadTestTerm : public CostFunction {
+ public:
+  BadTestTerm(int arity, int const* dim) : arity_(arity) {
+    // Make 'arity' random vectors.
+    a_.resize(arity_);
+    for (int j = 0; j < arity_; ++j) {
+      a_[j].resize(dim[j]);
+      for (int u = 0; u < dim[j]; ++u) {
+        a_[j][u] = 2.0 * RandDouble() - 1.0;
+      }
+    }
+
+    for (int i = 0; i < arity_; i++) {
+      mutable_parameter_block_sizes()->push_back(dim[i]);
+    }
+    set_num_residuals(1);
+  }
+
+  bool Evaluate(double const* const* parameters,
+                double* residuals,
+                double** jacobians) const {
+    // Compute a . x.
+    double ax = 0;
+    for (int j = 0; j < arity_; ++j) {
+      for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
+        ax += a_[j][u] * parameters[j][u];
+      }
+    }
+
+    // This is the cost, but also appears as a factor
+    // in the derivatives.
+    double f = *residuals = exp(-ax);
+
+    // Accumulate 1st order derivatives.
+    if (jacobians) {
+      for (int j = 0; j < arity_; ++j) {
+        if (jacobians[j]) {
+          for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
+            // See comments before class.
+            jacobians[j][u] = -f * a_[j][u] + 0.001;
+          }
+        }
+      }
+    }
+
+    return true;
+  }
+
+ private:
+  int arity_;
+  vector<vector<double>> a_;  // our vectors.
+};
+
+const double kTolerance = 1e-6;
+
+void CheckDimensions(const GradientChecker::ProbeResults& results,
+                     const std::vector<int>& parameter_sizes,
+                     const std::vector<int>& local_parameter_sizes,
+                     int residual_size) {
+  CHECK_EQ(parameter_sizes.size(), local_parameter_sizes.size());
+  int num_parameters = parameter_sizes.size();
+  ASSERT_EQ(residual_size, results.residuals.size());
+  ASSERT_EQ(num_parameters, results.local_jacobians.size());
+  ASSERT_EQ(num_parameters, results.local_numeric_jacobians.size());
+  ASSERT_EQ(num_parameters, results.jacobians.size());
+  ASSERT_EQ(num_parameters, results.numeric_jacobians.size());
+  for (int i = 0; i < num_parameters; ++i) {
+    EXPECT_EQ(residual_size, results.local_jacobians.at(i).rows());
+    EXPECT_EQ(local_parameter_sizes[i], results.local_jacobians.at(i).cols());
+    EXPECT_EQ(residual_size, results.local_numeric_jacobians.at(i).rows());
+    EXPECT_EQ(local_parameter_sizes[i],
+              results.local_numeric_jacobians.at(i).cols());
+    EXPECT_EQ(residual_size, results.jacobians.at(i).rows());
+    EXPECT_EQ(parameter_sizes[i], results.jacobians.at(i).cols());
+    EXPECT_EQ(residual_size, results.numeric_jacobians.at(i).rows());
+    EXPECT_EQ(parameter_sizes[i], results.numeric_jacobians.at(i).cols());
+  }
+}
+
+TEST(GradientChecker, SmokeTest) {
+  srand(5);
+
+  // Test with 3 blocks of size 2, 3 and 4.
+  int const num_parameters = 3;
+  std::vector<int> parameter_sizes(3);
+  parameter_sizes[0] = 2;
+  parameter_sizes[1] = 3;
+  parameter_sizes[2] = 4;
+
+  // Make a random set of blocks.
+  FixedArray<double*> parameters(num_parameters);
+  for (int j = 0; j < num_parameters; ++j) {
+    parameters[j] = new double[parameter_sizes[j]];
+    for (int u = 0; u < parameter_sizes[j]; ++u) {
+      parameters[j][u] = 2.0 * RandDouble() - 1.0;
+    }
+  }
+
+  NumericDiffOptions numeric_diff_options;
+  GradientChecker::ProbeResults results;
+
+  // Test that Probe returns true for correct Jacobians.
+  GoodTestTerm good_term(num_parameters, parameter_sizes.data());
+  GradientChecker good_gradient_checker(&good_term, NULL, numeric_diff_options);
+  EXPECT_TRUE(good_gradient_checker.Probe(parameters.get(), kTolerance, NULL));
+  EXPECT_TRUE(
+      good_gradient_checker.Probe(parameters.get(), kTolerance, &results))
+      << results.error_log;
+
+  // Check that results contain sensible data.
+  ASSERT_EQ(results.return_value, true);
+  ASSERT_EQ(results.residuals.size(), 1);
+  CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
+  EXPECT_GE(results.maximum_relative_error, 0.0);
+  EXPECT_TRUE(results.error_log.empty());
+
+  // Test that if the cost function return false, Probe should return false.
+  good_term.SetReturnValue(false);
+  EXPECT_FALSE(good_gradient_checker.Probe(parameters.get(), kTolerance, NULL));
+  EXPECT_FALSE(
+      good_gradient_checker.Probe(parameters.get(), kTolerance, &results))
+      << results.error_log;
+
+  // Check that results contain sensible data.
+  ASSERT_EQ(results.return_value, false);
+  ASSERT_EQ(results.residuals.size(), 1);
+  CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
+  for (int i = 0; i < num_parameters; ++i) {
+    EXPECT_EQ(results.local_jacobians.at(i).norm(), 0);
+    EXPECT_EQ(results.local_numeric_jacobians.at(i).norm(), 0);
+  }
+  EXPECT_EQ(results.maximum_relative_error, 0.0);
+  EXPECT_FALSE(results.error_log.empty());
+
+  // Test that Probe returns false for incorrect Jacobians.
+  BadTestTerm bad_term(num_parameters, parameter_sizes.data());
+  GradientChecker bad_gradient_checker(&bad_term, NULL, numeric_diff_options);
+  EXPECT_FALSE(bad_gradient_checker.Probe(parameters.get(), kTolerance, NULL));
+  EXPECT_FALSE(
+      bad_gradient_checker.Probe(parameters.get(), kTolerance, &results));
+
+  // Check that results contain sensible data.
+  ASSERT_EQ(results.return_value, true);
+  ASSERT_EQ(results.residuals.size(), 1);
+  CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
+  EXPECT_GT(results.maximum_relative_error, kTolerance);
+  EXPECT_FALSE(results.error_log.empty());
+
+  // Setting a high threshold should make the test pass.
+  EXPECT_TRUE(bad_gradient_checker.Probe(parameters.get(), 1.0, &results));
+
+  // Check that results contain sensible data.
+  ASSERT_EQ(results.return_value, true);
+  ASSERT_EQ(results.residuals.size(), 1);
+  CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
+  EXPECT_GT(results.maximum_relative_error, 0.0);
+  EXPECT_TRUE(results.error_log.empty());
+
+  for (int j = 0; j < num_parameters; j++) {
+    delete[] parameters[j];
+  }
+}
+
+/**
+ * Helper cost function that multiplies the parameters by the given jacobians
+ * and adds a constant offset.
+ */
+class LinearCostFunction : public CostFunction {
+ public:
+  explicit LinearCostFunction(const Vector& residuals_offset)
+      : residuals_offset_(residuals_offset) {
+    set_num_residuals(residuals_offset_.size());
+  }
+
+  virtual bool Evaluate(double const* const* parameter_ptrs,
+                        double* residuals_ptr,
+                        double** residual_J_params) const {
+    CHECK_GE(residual_J_params_.size(), 0.0);
+    VectorRef residuals(residuals_ptr, residual_J_params_[0].rows());
+    residuals = residuals_offset_;
+
+    for (size_t i = 0; i < residual_J_params_.size(); ++i) {
+      const Matrix& residual_J_param = residual_J_params_[i];
+      int parameter_size = residual_J_param.cols();
+      ConstVectorRef param(parameter_ptrs[i], parameter_size);
+
+      // Compute residual.
+      residuals += residual_J_param * param;
+
+      // Return Jacobian.
+      if (residual_J_params != NULL && residual_J_params[i] != NULL) {
+        Eigen::Map<Matrix> residual_J_param_out(residual_J_params[i],
+                                                residual_J_param.rows(),
+                                                residual_J_param.cols());
+        if (jacobian_offsets_.count(i) != 0) {
+          residual_J_param_out = residual_J_param + jacobian_offsets_.at(i);
+        } else {
+          residual_J_param_out = residual_J_param;
+        }
+      }
+    }
+    return true;
+  }
+
+  void AddParameter(const Matrix& residual_J_param) {
+    CHECK_EQ(num_residuals(), residual_J_param.rows());
+    residual_J_params_.push_back(residual_J_param);
+    mutable_parameter_block_sizes()->push_back(residual_J_param.cols());
+  }
+
+  /// Add offset to the given Jacobian before returning it from Evaluate(),
+  /// thus introducing an error in the comutation.
+  void SetJacobianOffset(size_t index, Matrix offset) {
+    CHECK_LT(index, residual_J_params_.size());
+    CHECK_EQ(residual_J_params_[index].rows(), offset.rows());
+    CHECK_EQ(residual_J_params_[index].cols(), offset.cols());
+    jacobian_offsets_[index] = offset;
+  }
+
+ private:
+  std::vector<Matrix> residual_J_params_;
+  std::map<int, Matrix> jacobian_offsets_;
+  Vector residuals_offset_;
+};
+
+/**
+ * Helper local parameterization that multiplies the delta vector by the given
+ * jacobian and adds it to the parameter.
+ */
+class MatrixParameterization : public LocalParameterization {
+ public:
+  virtual bool Plus(const double* x,
+                    const double* delta,
+                    double* x_plus_delta) const {
+    VectorRef(x_plus_delta, GlobalSize()) =
+        ConstVectorRef(x, GlobalSize()) +
+        (global_J_local * ConstVectorRef(delta, LocalSize()));
+    return true;
+  }
+
+  virtual bool ComputeJacobian(const double* /*x*/, double* jacobian) const {
+    MatrixRef(jacobian, GlobalSize(), LocalSize()) = global_J_local;
+    return true;
+  }
+
+  virtual int GlobalSize() const { return global_J_local.rows(); }
+  virtual int LocalSize() const { return global_J_local.cols(); }
+
+  Matrix global_J_local;
+};
+
+// Helper function to compare two Eigen matrices (used in the test below).
+void ExpectMatricesClose(Matrix p, Matrix q, double tolerance) {
+  ASSERT_EQ(p.rows(), q.rows());
+  ASSERT_EQ(p.cols(), q.cols());
+  ExpectArraysClose(p.size(), p.data(), q.data(), tolerance);
+}
+
+TEST(GradientChecker, TestCorrectnessWithLocalParameterizations) {
+  // Create cost function.
+  Eigen::Vector3d residual_offset(100.0, 200.0, 300.0);
+  LinearCostFunction cost_function(residual_offset);
+  Eigen::Matrix<double, 3, 3, Eigen::RowMajor> j0;
+  j0.row(0) << 1.0, 2.0, 3.0;
+  j0.row(1) << 4.0, 5.0, 6.0;
+  j0.row(2) << 7.0, 8.0, 9.0;
+  Eigen::Matrix<double, 3, 2, Eigen::RowMajor> j1;
+  j1.row(0) << 10.0, 11.0;
+  j1.row(1) << 12.0, 13.0;
+  j1.row(2) << 14.0, 15.0;
+
+  Eigen::Vector3d param0(1.0, 2.0, 3.0);
+  Eigen::Vector2d param1(4.0, 5.0);
+
+  cost_function.AddParameter(j0);
+  cost_function.AddParameter(j1);
+
+  std::vector<int> parameter_sizes(2);
+  parameter_sizes[0] = 3;
+  parameter_sizes[1] = 2;
+  std::vector<int> local_parameter_sizes(2);
+  local_parameter_sizes[0] = 2;
+  local_parameter_sizes[1] = 2;
+
+  // Test cost function for correctness.
+  Eigen::Matrix<double, 3, 3, Eigen::RowMajor> j1_out;
+  Eigen::Matrix<double, 3, 2, Eigen::RowMajor> j2_out;
+  Eigen::Vector3d residual;
+  std::vector<const double*> parameters(2);
+  parameters[0] = param0.data();
+  parameters[1] = param1.data();
+  std::vector<double*> jacobians(2);
+  jacobians[0] = j1_out.data();
+  jacobians[1] = j2_out.data();
+  cost_function.Evaluate(parameters.data(), residual.data(), jacobians.data());
+
+  Matrix residual_expected = residual_offset + j0 * param0 + j1 * param1;
+
+  ExpectMatricesClose(j1_out, j0, std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(j2_out, j1, std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(residual, residual_expected, kTolerance);
+
+  // Create local parameterization.
+  Eigen::Matrix<double, 3, 2, Eigen::RowMajor> global_J_local;
+  global_J_local.row(0) << 1.5, 2.5;
+  global_J_local.row(1) << 3.5, 4.5;
+  global_J_local.row(2) << 5.5, 6.5;
+
+  MatrixParameterization parameterization;
+  parameterization.global_J_local = global_J_local;
+
+  // Test local parameterization for correctness.
+  Eigen::Vector3d x(7.0, 8.0, 9.0);
+  Eigen::Vector2d delta(10.0, 11.0);
+
+  Eigen::Matrix<double, 3, 2, Eigen::RowMajor> global_J_local_out;
+  parameterization.ComputeJacobian(x.data(), global_J_local_out.data());
+  ExpectMatricesClose(global_J_local_out,
+                      global_J_local,
+                      std::numeric_limits<double>::epsilon());
+
+  Eigen::Vector3d x_plus_delta;
+  parameterization.Plus(x.data(), delta.data(), x_plus_delta.data());
+  Eigen::Vector3d x_plus_delta_expected = x + (global_J_local * delta);
+  ExpectMatricesClose(x_plus_delta, x_plus_delta_expected, kTolerance);
+
+  // Now test GradientChecker.
+  std::vector<const LocalParameterization*> parameterizations(2);
+  parameterizations[0] = &parameterization;
+  parameterizations[1] = NULL;
+  NumericDiffOptions numeric_diff_options;
+  GradientChecker::ProbeResults results;
+  GradientChecker gradient_checker(
+      &cost_function, &parameterizations, numeric_diff_options);
+
+  Problem::Options problem_options;
+  problem_options.cost_function_ownership = DO_NOT_TAKE_OWNERSHIP;
+  problem_options.local_parameterization_ownership = DO_NOT_TAKE_OWNERSHIP;
+  Problem problem(problem_options);
+  Eigen::Vector3d param0_solver;
+  Eigen::Vector2d param1_solver;
+  problem.AddParameterBlock(param0_solver.data(), 3, &parameterization);
+  problem.AddParameterBlock(param1_solver.data(), 2);
+  problem.AddResidualBlock(
+      &cost_function, NULL, param0_solver.data(), param1_solver.data());
+  Solver::Options solver_options;
+  solver_options.check_gradients = true;
+  solver_options.initial_trust_region_radius = 1e10;
+  Solver solver;
+  Solver::Summary summary;
+
+  // First test case: everything is correct.
+  EXPECT_TRUE(gradient_checker.Probe(parameters.data(), kTolerance, NULL));
+  EXPECT_TRUE(gradient_checker.Probe(parameters.data(), kTolerance, &results))
+      << results.error_log;
+
+  // Check that results contain correct data.
+  ASSERT_EQ(results.return_value, true);
+  ExpectMatricesClose(
+      results.residuals, residual, std::numeric_limits<double>::epsilon());
+  CheckDimensions(results, parameter_sizes, local_parameter_sizes, 3);
+  ExpectMatricesClose(
+      results.local_jacobians.at(0), j0 * global_J_local, kTolerance);
+  ExpectMatricesClose(results.local_jacobians.at(1),
+                      j1,
+                      std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(
+      results.local_numeric_jacobians.at(0), j0 * global_J_local, kTolerance);
+  ExpectMatricesClose(results.local_numeric_jacobians.at(1), j1, kTolerance);
+  ExpectMatricesClose(
+      results.jacobians.at(0), j0, std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(
+      results.jacobians.at(1), j1, std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(results.numeric_jacobians.at(0), j0, kTolerance);
+  ExpectMatricesClose(results.numeric_jacobians.at(1), j1, kTolerance);
+  EXPECT_GE(results.maximum_relative_error, 0.0);
+  EXPECT_TRUE(results.error_log.empty());
+
+  // Test interaction with the 'check_gradients' option in Solver.
+  param0_solver = param0;
+  param1_solver = param1;
+  solver.Solve(solver_options, &problem, &summary);
+  EXPECT_EQ(CONVERGENCE, summary.termination_type);
+  EXPECT_LE(summary.final_cost, 1e-12);
+
+  // Second test case: Mess up reported derivatives with respect to 3rd
+  // component of 1st parameter. Check should fail.
+  Eigen::Matrix<double, 3, 3, Eigen::RowMajor> j0_offset;
+  j0_offset.setZero();
+  j0_offset.col(2).setConstant(0.001);
+  cost_function.SetJacobianOffset(0, j0_offset);
+  EXPECT_FALSE(gradient_checker.Probe(parameters.data(), kTolerance, NULL));
+  EXPECT_FALSE(gradient_checker.Probe(parameters.data(), kTolerance, &results))
+      << results.error_log;
+
+  // Check that results contain correct data.
+  ASSERT_EQ(results.return_value, true);
+  ExpectMatricesClose(
+      results.residuals, residual, std::numeric_limits<double>::epsilon());
+  CheckDimensions(results, parameter_sizes, local_parameter_sizes, 3);
+  ASSERT_EQ(results.local_jacobians.size(), 2);
+  ASSERT_EQ(results.local_numeric_jacobians.size(), 2);
+  ExpectMatricesClose(results.local_jacobians.at(0),
+                      (j0 + j0_offset) * global_J_local,
+                      kTolerance);
+  ExpectMatricesClose(results.local_jacobians.at(1),
+                      j1,
+                      std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(
+      results.local_numeric_jacobians.at(0), j0 * global_J_local, kTolerance);
+  ExpectMatricesClose(results.local_numeric_jacobians.at(1), j1, kTolerance);
+  ExpectMatricesClose(results.jacobians.at(0), j0 + j0_offset, kTolerance);
+  ExpectMatricesClose(
+      results.jacobians.at(1), j1, std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(results.numeric_jacobians.at(0), j0, kTolerance);
+  ExpectMatricesClose(results.numeric_jacobians.at(1), j1, kTolerance);
+  EXPECT_GT(results.maximum_relative_error, 0.0);
+  EXPECT_FALSE(results.error_log.empty());
+
+  // Test interaction with the 'check_gradients' option in Solver.
+  param0_solver = param0;
+  param1_solver = param1;
+  solver.Solve(solver_options, &problem, &summary);
+  EXPECT_EQ(FAILURE, summary.termination_type);
+
+  // Now, zero out the local parameterization Jacobian of the 1st parameter
+  // with respect to the 3rd component. This makes the combination of
+  // cost function and local parameterization return correct values again.
+  parameterization.global_J_local.row(2).setZero();
+
+  // Verify that the gradient checker does not treat this as an error.
+  EXPECT_TRUE(gradient_checker.Probe(parameters.data(), kTolerance, &results))
+      << results.error_log;
+
+  // Check that results contain correct data.
+  ASSERT_EQ(results.return_value, true);
+  ExpectMatricesClose(
+      results.residuals, residual, std::numeric_limits<double>::epsilon());
+  CheckDimensions(results, parameter_sizes, local_parameter_sizes, 3);
+  ASSERT_EQ(results.local_jacobians.size(), 2);
+  ASSERT_EQ(results.local_numeric_jacobians.size(), 2);
+  ExpectMatricesClose(results.local_jacobians.at(0),
+                      (j0 + j0_offset) * parameterization.global_J_local,
+                      kTolerance);
+  ExpectMatricesClose(results.local_jacobians.at(1),
+                      j1,
+                      std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(results.local_numeric_jacobians.at(0),
+                      j0 * parameterization.global_J_local,
+                      kTolerance);
+  ExpectMatricesClose(results.local_numeric_jacobians.at(1), j1, kTolerance);
+  ExpectMatricesClose(results.jacobians.at(0), j0 + j0_offset, kTolerance);
+  ExpectMatricesClose(
+      results.jacobians.at(1), j1, std::numeric_limits<double>::epsilon());
+  ExpectMatricesClose(results.numeric_jacobians.at(0), j0, kTolerance);
+  ExpectMatricesClose(results.numeric_jacobians.at(1), j1, kTolerance);
+  EXPECT_GE(results.maximum_relative_error, 0.0);
+  EXPECT_TRUE(results.error_log.empty());
+
+  // Test interaction with the 'check_gradients' option in Solver.
+  param0_solver = param0;
+  param1_solver = param1;
+  solver.Solve(solver_options, &problem, &summary);
+  EXPECT_EQ(CONVERGENCE, summary.termination_type);
+  EXPECT_LE(summary.final_cost, 1e-12);
+}
+
+}  // namespace internal
+}  // namespace ceres