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// 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
// 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: keir@google.com (Keir Mierle)
//
// Based on the templated version in public/numeric_diff_cost_function.h.
#include "ceres/runtime_numeric_diff_cost_function.h"
#include <algorithm>
#include <numeric>
#include <vector>
#include "Eigen/Dense"
#include "ceres/cost_function.h"
#include "ceres/internal/scoped_ptr.h"
#include "glog/logging.h"
namespace ceres {
namespace internal {
namespace {
bool EvaluateJacobianForParameterBlock(const CostFunction* function,
int parameter_block_size,
int parameter_block,
RuntimeNumericDiffMethod method,
double relative_step_size,
double const* residuals_at_eval_point,
double** parameters,
double** jacobians) {
using Eigen::Map;
using Eigen::Matrix;
using Eigen::Dynamic;
using Eigen::RowMajor;
typedef Matrix<double, Dynamic, 1> ResidualVector;
typedef Matrix<double, Dynamic, 1> ParameterVector;
typedef Matrix<double, Dynamic, Dynamic, RowMajor> JacobianMatrix;
int num_residuals = function->num_residuals();
Map<JacobianMatrix> parameter_jacobian(jacobians[parameter_block],
num_residuals,
parameter_block_size);
// Mutate one element at a time and then restore.
Map<ParameterVector> x_plus_delta(parameters[parameter_block],
parameter_block_size);
ParameterVector x(x_plus_delta);
ParameterVector step_size = x.array().abs() * relative_step_size;
// To handle cases where a paremeter is exactly zero, instead use the mean
// step_size for the other dimensions.
double fallback_step_size = step_size.sum() / step_size.rows();
if (fallback_step_size == 0.0) {
// If all the parameters are zero, there's no good answer. Use the given
// relative step_size as absolute step_size and hope for the best.
fallback_step_size = relative_step_size;
}
// For each parameter in the parameter block, use finite differences to
// compute the derivative for that parameter.
for (int j = 0; j < parameter_block_size; ++j) {
if (step_size(j) == 0.0) {
// The parameter is exactly zero, so compromise and use the mean step_size
// from the other parameters. This can break in many cases, but it's hard
// to pick a good number without problem specific knowledge.
step_size(j) = fallback_step_size;
}
x_plus_delta(j) = x(j) + step_size(j);
ResidualVector residuals(num_residuals);
if (!function->Evaluate(parameters, &residuals[0], NULL)) {
// Something went wrong; bail.
return false;
}
// Compute this column of the jacobian in 3 steps:
// 1. Store residuals for the forward part.
// 2. Subtract residuals for the backward (or 0) part.
// 3. Divide out the run.
parameter_jacobian.col(j) = residuals;
double one_over_h = 1 / step_size(j);
if (method == CENTRAL) {
// Compute the function on the other side of x(j).
x_plus_delta(j) = x(j) - step_size(j);
if (!function->Evaluate(parameters, &residuals[0], NULL)) {
// Something went wrong; bail.
return false;
}
parameter_jacobian.col(j) -= residuals;
one_over_h /= 2;
} else {
// Forward difference only; reuse existing residuals evaluation.
parameter_jacobian.col(j) -=
Map<const ResidualVector>(residuals_at_eval_point, num_residuals);
}
x_plus_delta(j) = x(j); // Restore x_plus_delta.
// Divide out the run to get slope.
parameter_jacobian.col(j) *= one_over_h;
}
return true;
}
class RuntimeNumericDiffCostFunction : public CostFunction {
public:
RuntimeNumericDiffCostFunction(const CostFunction* function,
RuntimeNumericDiffMethod method,
double relative_step_size)
: function_(function),
method_(method),
relative_step_size_(relative_step_size) {
*mutable_parameter_block_sizes() = function->parameter_block_sizes();
set_num_residuals(function->num_residuals());
}
virtual ~RuntimeNumericDiffCostFunction() { }
virtual bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const {
// Get the function value (residuals) at the the point to evaluate.
bool success = function_->Evaluate(parameters, residuals, NULL);
if (!success) {
// Something went wrong; ignore the jacobian.
return false;
}
if (!jacobians) {
// Nothing to do; just forward.
return true;
}
const vector<int16>& block_sizes = function_->parameter_block_sizes();
CHECK(!block_sizes.empty());
// Create local space for a copy of the parameters which will get mutated.
int parameters_size = accumulate(block_sizes.begin(), block_sizes.end(), 0);
vector<double> parameters_copy(parameters_size);
vector<double*> parameters_references_copy(block_sizes.size());
parameters_references_copy[0] = ¶meters_copy[0];
for (int block = 1; block < block_sizes.size(); ++block) {
parameters_references_copy[block] = parameters_references_copy[block - 1]
+ block_sizes[block - 1];
}
// Copy the parameters into the local temp space.
for (int block = 0; block < block_sizes.size(); ++block) {
memcpy(parameters_references_copy[block],
parameters[block],
block_sizes[block] * sizeof(*parameters[block]));
}
for (int block = 0; block < block_sizes.size(); ++block) {
if (!jacobians[block]) {
// No jacobian requested for this parameter / residual pair.
continue;
}
if (!EvaluateJacobianForParameterBlock(function_,
block_sizes[block],
block,
method_,
relative_step_size_,
residuals,
¶meters_references_copy[0],
jacobians)) {
return false;
}
}
return true;
}
private:
const CostFunction* function_;
RuntimeNumericDiffMethod method_;
double relative_step_size_;
};
} // namespace
CostFunction* CreateRuntimeNumericDiffCostFunction(
const CostFunction* cost_function,
RuntimeNumericDiffMethod method,
double relative_step_size) {
return new RuntimeNumericDiffCostFunction(cost_function,
method,
relative_step_size);
}
} // namespace internal
} // namespace ceres
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