// 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 <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_NOTNULL(residuals);
CHECK_NOTNULL(jacobians);
CHECK_NOTNULL(local_jacobians);
const vector<int32>& 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) = 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_NOTNULL(function);
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>& 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