// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 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
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// POSSIBILITY OF SUCH DAMAGE.
//
// Author: keir@google.com (Keir Mierle)
#include "ceres/gradient_checking_cost_function.h"
#include <algorithm>
#include <cmath>
#include <numeric>
#include <string>
#include <vector>
#include "ceres/cost_function.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/parameter_block.h"
#include "ceres/problem.h"
#include "ceres/problem_impl.h"
#include "ceres/program.h"
#include "ceres/residual_block.h"
#include "ceres/dynamic_numeric_diff_cost_function.h"
#include "ceres/stringprintf.h"
#include "ceres/types.h"
#include "glog/logging.h"
namespace ceres {
namespace internal {
namespace {
// True if x and y have an absolute relative difference less than
// relative_precision and false otherwise. Stores the relative and absolute
// difference in relative/absolute_error if non-NULL.
bool IsClose(double x, double y, double relative_precision,
double *relative_error,
double *absolute_error) {
double local_absolute_error;
double local_relative_error;
if (!absolute_error) {
absolute_error = &local_absolute_error;
}
if (!relative_error) {
relative_error = &local_relative_error;
}
*absolute_error = fabs(x - y);
*relative_error = *absolute_error / max(fabs(x), fabs(y));
if (x == 0 || y == 0) {
// If x or y is exactly zero, then relative difference doesn't have any
// meaning. Take the absolute difference instead.
*relative_error = *absolute_error;
}
return fabs(*relative_error) < fabs(relative_precision);
}
class GradientCheckingCostFunction : public CostFunction {
public:
GradientCheckingCostFunction(const CostFunction* function,
double relative_step_size,
double relative_precision,
const string& extra_info)
: function_(function),
relative_precision_(relative_precision),
extra_info_(extra_info) {
DynamicNumericDiffCostFunction<CostFunction, CENTRAL>*
finite_diff_cost_function =
new DynamicNumericDiffCostFunction<CostFunction, CENTRAL>(
function,
DO_NOT_TAKE_OWNERSHIP,
relative_step_size);
const vector<int32>& parameter_block_sizes =
function->parameter_block_sizes();
for (int i = 0; i < parameter_block_sizes.size(); ++i) {
finite_diff_cost_function->AddParameterBlock(parameter_block_sizes[i]);
}
*mutable_parameter_block_sizes() = parameter_block_sizes;
set_num_residuals(function->num_residuals());
finite_diff_cost_function->SetNumResiduals(num_residuals());
finite_diff_cost_function_.reset(finite_diff_cost_function);
}
virtual ~GradientCheckingCostFunction() { }
virtual bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const {
if (!jacobians) {
// Nothing to check in this case; just forward.
return function_->Evaluate(parameters, residuals, NULL);
}
int num_residuals = function_->num_residuals();
// Make space for the jacobians of the two methods.
const vector<int32>& block_sizes = function_->parameter_block_sizes();
vector<Matrix> term_jacobians(block_sizes.size());
vector<Matrix> finite_difference_jacobians(block_sizes.size());
vector<double*> term_jacobian_pointers(block_sizes.size());
vector<double*> finite_difference_jacobian_pointers(block_sizes.size());
for (int i = 0; i < block_sizes.size(); i++) {
term_jacobians[i].resize(num_residuals, block_sizes[i]);
term_jacobian_pointers[i] = term_jacobians[i].data();
finite_difference_jacobians[i].resize(num_residuals, block_sizes[i]);
finite_difference_jacobian_pointers[i] =
finite_difference_jacobians[i].data();
}
// Evaluate the derivative using the user supplied code.
if (!function_->Evaluate(parameters,
residuals,
&term_jacobian_pointers[0])) {
LOG(WARNING) << "Function evaluation failed.";
return false;
}
// Evaluate the derivative using numeric derivatives.
finite_diff_cost_function_->Evaluate(
parameters,
residuals,
&finite_difference_jacobian_pointers[0]);
// See if any elements have relative error larger than the threshold.
int num_bad_jacobian_components = 0;
double 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 m;
for (int k = 0; k < block_sizes.size(); k++) {
// Copy the original jacobian blocks into the jacobians array.
if (jacobians[k] != NULL) {
MatrixRef(jacobians[k],
term_jacobians[k].rows(),
term_jacobians[k].cols()) = term_jacobians[k];
}
StringAppendF(&m,
"========== "
"Jacobian for " "block %d: (%ld by %ld)) "
"==========\n",
k,
static_cast<long>(term_jacobians[k].rows()),
static_cast<long>(term_jacobians[k].cols()));
// The funny spacing creates appropriately aligned column headers.
m += " block row col user dx/dy num diff dx/dy "
"abs error relative error parameter residual\n";
for (int i = 0; i < term_jacobians[k].rows(); i++) {
for (int j = 0; j < term_jacobians[k].cols(); j++) {
double term_jacobian = term_jacobians[k](i, j);
double finite_jacobian = finite_difference_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(&m, "%6d %4d %4d %17g %17g %17g %17g %17g %17g",
k, i, j,
term_jacobian, finite_jacobian,
absolute_error, relative_error,
parameters[k][j],
residuals[i]);
if (bad_jacobian_entry) {
num_bad_jacobian_components++;
StringAppendF(
&m, " ------ (%d,%d,%d) Relative error worse than %g",
k, i, j, relative_precision_);
}
m += "\n";
}
}
}
// Since there were some bad errors, dump comprehensive debug info.
if (num_bad_jacobian_components) {
string header = StringPrintf("Detected %d bad jacobian component(s). "
"Worst relative error was %g.\n",
num_bad_jacobian_components,
worst_relative_error);
if (!extra_info_.empty()) {
header += "Extra info for this residual: " + extra_info_ + "\n";
}
LOG(WARNING) << "\n" << header << m;
}
return true;
}
private:
const CostFunction* function_;
internal::scoped_ptr<CostFunction> finite_diff_cost_function_;
double relative_precision_;
string extra_info_;
};
} // namespace
CostFunction *CreateGradientCheckingCostFunction(
const CostFunction *cost_function,
double relative_step_size,
double relative_precision,
const string& extra_info) {
return new GradientCheckingCostFunction(cost_function,
relative_step_size,
relative_precision,
extra_info);
}
ProblemImpl* CreateGradientCheckingProblemImpl(ProblemImpl* problem_impl,
double relative_step_size,
double relative_precision) {
// We create new CostFunctions by wrapping the original CostFunction
// in a gradient checking CostFunction. So its okay for the
// ProblemImpl to take ownership of it and destroy it. The
// LossFunctions and LocalParameterizations are reused and since
// they are owned by problem_impl, gradient_checking_problem_impl
// should not take ownership of it.
Problem::Options gradient_checking_problem_options;
gradient_checking_problem_options.cost_function_ownership = TAKE_OWNERSHIP;
gradient_checking_problem_options.loss_function_ownership =
DO_NOT_TAKE_OWNERSHIP;
gradient_checking_problem_options.local_parameterization_ownership =
DO_NOT_TAKE_OWNERSHIP;
ProblemImpl* gradient_checking_problem_impl = new ProblemImpl(
gradient_checking_problem_options);
Program* program = problem_impl->mutable_program();
// For every ParameterBlock in problem_impl, create a new parameter
// block with the same local parameterization and constancy.
const vector<ParameterBlock*>& parameter_blocks = program->parameter_blocks();
for (int i = 0; i < parameter_blocks.size(); ++i) {
ParameterBlock* parameter_block = parameter_blocks[i];
gradient_checking_problem_impl->AddParameterBlock(
parameter_block->mutable_user_state(),
parameter_block->Size(),
parameter_block->mutable_local_parameterization());
if (parameter_block->IsConstant()) {
gradient_checking_problem_impl->SetParameterBlockConstant(
parameter_block->mutable_user_state());
}
}
// For every ResidualBlock in problem_impl, create a new
// ResidualBlock by wrapping its CostFunction inside a
// GradientCheckingCostFunction.
const vector<ResidualBlock*>& residual_blocks = program->residual_blocks();
for (int i = 0; i < residual_blocks.size(); ++i) {
ResidualBlock* residual_block = residual_blocks[i];
// Build a human readable string which identifies the
// ResidualBlock. This is used by the GradientCheckingCostFunction
// when logging debugging information.
string extra_info = StringPrintf(
"Residual block id %d; depends on parameters [", i);
vector<double*> parameter_blocks;
for (int j = 0; j < residual_block->NumParameterBlocks(); ++j) {
ParameterBlock* parameter_block = residual_block->parameter_blocks()[j];
parameter_blocks.push_back(parameter_block->mutable_user_state());
StringAppendF(&extra_info, "%p", parameter_block->mutable_user_state());
extra_info += (j < residual_block->NumParameterBlocks() - 1) ? ", " : "]";
}
// Wrap the original CostFunction in a GradientCheckingCostFunction.
CostFunction* gradient_checking_cost_function =
CreateGradientCheckingCostFunction(residual_block->cost_function(),
relative_step_size,
relative_precision,
extra_info);
// The const_cast is necessary because
// ProblemImpl::AddResidualBlock can potentially take ownership of
// the LossFunction, but in this case we are guaranteed that this
// will not be the case, so this const_cast is harmless.
gradient_checking_problem_impl->AddResidualBlock(
gradient_checking_cost_function,
const_cast<LossFunction*>(residual_block->loss_function()),
parameter_blocks);
}
return gradient_checking_problem_impl;
}
} // namespace internal
} // namespace ceres