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.cc b/internal/ceres/gradient_checker.cc
new file mode 100644
index 0000000..411a67f
--- /dev/null
+++ b/internal/ceres/gradient_checker.cc
@@ -0,0 +1,277 @@
+// 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.
+//
+// Authors: wjr@google.com (William Rucklidge),
+//          keir@google.com (Keir Mierle),
+//          dgossow@google.com (David Gossow)
+
+#include "ceres/gradient_checker.h"
+
+#include <algorithm>
+#include <cmath>
+#include <cstdint>
+#include <numeric>
+#include <string>
+#include <vector>
+
+#include "ceres/is_close.h"
+#include "ceres/stringprintf.h"
+#include "ceres/types.h"
+
+namespace ceres {
+
+using internal::IsClose;
+using internal::StringAppendF;
+using internal::StringPrintf;
+using std::string;
+using std::vector;
+
+namespace {
+// Evaluate the cost function and transform the returned Jacobians to
+// the local space of the respective local parameterizations.
+bool EvaluateCostFunction(
+    const ceres::CostFunction* function,
+    double const* const * parameters,
+    const std::vector<const ceres::LocalParameterization*>&
+        local_parameterizations,
+    Vector* residuals,
+    std::vector<Matrix>* jacobians,
+    std::vector<Matrix>* local_jacobians) {
+  CHECK(residuals != nullptr);
+  CHECK(jacobians != nullptr);
+  CHECK(local_jacobians != nullptr);
+
+  const vector<int32_t>& block_sizes = function->parameter_block_sizes();
+  const int num_parameter_blocks = block_sizes.size();
+
+  // Allocate Jacobian matrices in local space.
+  local_jacobians->resize(num_parameter_blocks);
+  vector<double*> local_jacobian_data(num_parameter_blocks);
+  for (int i = 0; i < num_parameter_blocks; ++i) {
+    int block_size = block_sizes.at(i);
+    if (local_parameterizations.at(i) != NULL) {
+      block_size = local_parameterizations.at(i)->LocalSize();
+    }
+    local_jacobians->at(i).resize(function->num_residuals(), block_size);
+    local_jacobians->at(i).setZero();
+    local_jacobian_data.at(i) = local_jacobians->at(i).data();
+  }
+
+  // Allocate Jacobian matrices in global space.
+  jacobians->resize(num_parameter_blocks);
+  vector<double*> jacobian_data(num_parameter_blocks);
+  for (int i = 0; i < num_parameter_blocks; ++i) {
+    jacobians->at(i).resize(function->num_residuals(), block_sizes.at(i));
+    jacobians->at(i).setZero();
+    jacobian_data.at(i) = jacobians->at(i).data();
+  }
+
+  // Compute residuals & jacobians.
+  CHECK_NE(0, function->num_residuals());
+  residuals->resize(function->num_residuals());
+  residuals->setZero();
+  if (!function->Evaluate(parameters, residuals->data(),
+                          jacobian_data.data())) {
+    return false;
+  }
+
+  // Convert Jacobians from global to local space.
+  for (size_t i = 0; i < local_jacobians->size(); ++i) {
+    if (local_parameterizations.at(i) == NULL) {
+      local_jacobians->at(i) = jacobians->at(i);
+    } else {
+      int global_size = local_parameterizations.at(i)->GlobalSize();
+      int local_size = local_parameterizations.at(i)->LocalSize();
+      CHECK_EQ(jacobians->at(i).cols(), global_size);
+      Matrix global_J_local(global_size, local_size);
+      local_parameterizations.at(i)->ComputeJacobian(
+          parameters[i], global_J_local.data());
+      local_jacobians->at(i).noalias() = jacobians->at(i) * global_J_local;
+    }
+  }
+  return true;
+}
+} // namespace
+
+GradientChecker::GradientChecker(
+      const CostFunction* function,
+      const vector<const LocalParameterization*>* local_parameterizations,
+      const NumericDiffOptions& options) :
+        function_(function) {
+  CHECK(function != nullptr);
+  if (local_parameterizations != NULL) {
+    local_parameterizations_ = *local_parameterizations;
+  } else {
+    local_parameterizations_.resize(function->parameter_block_sizes().size(),
+                                    NULL);
+  }
+  DynamicNumericDiffCostFunction<CostFunction, CENTRAL>*
+      finite_diff_cost_function =
+      new DynamicNumericDiffCostFunction<CostFunction, CENTRAL>(
+          function, DO_NOT_TAKE_OWNERSHIP, options);
+  finite_diff_cost_function_.reset(finite_diff_cost_function);
+
+  const vector<int32_t>& parameter_block_sizes =
+      function->parameter_block_sizes();
+  const int num_parameter_blocks = parameter_block_sizes.size();
+  for (int i = 0; i < num_parameter_blocks; ++i) {
+    finite_diff_cost_function->AddParameterBlock(parameter_block_sizes[i]);
+  }
+  finite_diff_cost_function->SetNumResiduals(function->num_residuals());
+}
+
+bool GradientChecker::Probe(double const* const * parameters,
+                            double relative_precision,
+                            ProbeResults* results_param) const {
+  int num_residuals = function_->num_residuals();
+
+  // Make sure that we have a place to store results, no matter if the user has
+  // provided an output argument.
+  ProbeResults* results;
+  ProbeResults results_local;
+  if (results_param != NULL) {
+    results = results_param;
+    results->residuals.resize(0);
+    results->jacobians.clear();
+    results->numeric_jacobians.clear();
+    results->local_jacobians.clear();
+    results->local_numeric_jacobians.clear();
+    results->error_log.clear();
+  } else {
+    results = &results_local;
+  }
+  results->maximum_relative_error = 0.0;
+  results->return_value = true;
+
+  // Evaluate the derivative using the user supplied code.
+  vector<Matrix>& jacobians = results->jacobians;
+  vector<Matrix>& local_jacobians = results->local_jacobians;
+  if (!EvaluateCostFunction(function_, parameters, local_parameterizations_,
+                       &results->residuals, &jacobians, &local_jacobians)) {
+    results->error_log = "Function evaluation with Jacobians failed.";
+    results->return_value = false;
+  }
+
+  // Evaluate the derivative using numeric derivatives.
+  vector<Matrix>& numeric_jacobians = results->numeric_jacobians;
+  vector<Matrix>& local_numeric_jacobians = results->local_numeric_jacobians;
+  Vector finite_diff_residuals;
+  if (!EvaluateCostFunction(finite_diff_cost_function_.get(), parameters,
+                            local_parameterizations_, &finite_diff_residuals,
+                            &numeric_jacobians, &local_numeric_jacobians)) {
+    results->error_log += "\nFunction evaluation with numerical "
+        "differentiation failed.";
+    results->return_value = false;
+  }
+
+  if (!results->return_value) {
+    return false;
+  }
+
+  for (int i = 0; i < num_residuals; ++i) {
+    if (!IsClose(
+        results->residuals[i],
+        finite_diff_residuals[i],
+        relative_precision,
+        NULL,
+        NULL)) {
+      results->error_log = "Function evaluation with and without Jacobians "
+          "resulted in different residuals.";
+      LOG(INFO) << results->residuals.transpose();
+      LOG(INFO) << finite_diff_residuals.transpose();
+      return false;
+    }
+  }
+
+  // See if any elements have relative error larger than the threshold.
+  int num_bad_jacobian_components = 0;
+  double& worst_relative_error = results->maximum_relative_error;
+  worst_relative_error = 0;
+
+  // Accumulate the error message for all the jacobians, since it won't get
+  // output if there are no bad jacobian components.
+  string error_log;
+  for (int k = 0; k < function_->parameter_block_sizes().size(); k++) {
+    StringAppendF(&error_log,
+                  "========== "
+                  "Jacobian for " "block %d: (%ld by %ld)) "
+                  "==========\n",
+                  k,
+                  static_cast<long>(local_jacobians[k].rows()),
+                  static_cast<long>(local_jacobians[k].cols()));
+    // The funny spacing creates appropriately aligned column headers.
+    error_log +=
+        " block  row  col        user dx/dy    num diff dx/dy         "
+        "abs error    relative error         parameter          residual\n";
+
+    for (int i = 0; i < local_jacobians[k].rows(); i++) {
+      for (int j = 0; j < local_jacobians[k].cols(); j++) {
+        double term_jacobian = local_jacobians[k](i, j);
+        double finite_jacobian = local_numeric_jacobians[k](i, j);
+        double relative_error, absolute_error;
+        bool bad_jacobian_entry =
+            !IsClose(term_jacobian,
+                     finite_jacobian,
+                     relative_precision,
+                     &relative_error,
+                     &absolute_error);
+        worst_relative_error = std::max(worst_relative_error, relative_error);
+
+        StringAppendF(&error_log,
+                      "%6d %4d %4d %17g %17g %17g %17g %17g %17g",
+                      k, i, j,
+                      term_jacobian, finite_jacobian,
+                      absolute_error, relative_error,
+                      parameters[k][j],
+                      results->residuals[i]);
+
+        if (bad_jacobian_entry) {
+          num_bad_jacobian_components++;
+          StringAppendF(
+              &error_log,
+              " ------ (%d,%d,%d) Relative error worse than %g",
+              k, i, j, relative_precision);
+        }
+        error_log += "\n";
+      }
+    }
+  }
+
+  // Since there were some bad errors, dump comprehensive debug info.
+  if (num_bad_jacobian_components) {
+    string header = StringPrintf("\nDetected %d bad Jacobian component(s). "
+        "Worst relative error was %g.\n",
+        num_bad_jacobian_components,
+        worst_relative_error);
+     results->error_log = header + "\n" + error_log;
+    return false;
+  }
+  return true;
+}
+
+}  // namespace ceres