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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2013 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: sameeragarwal@google.com (Sameer Agarwal)
// mierle@gmail.com (Keir Mierle)
//
// Finite differencing routine used by NumericDiffCostFunction.
#ifndef CERES_PUBLIC_INTERNAL_NUMERIC_DIFF_H_
#define CERES_PUBLIC_INTERNAL_NUMERIC_DIFF_H_
#include <cstring>
#include "Eigen/Dense"
#include "ceres/cost_function.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/internal/variadic_evaluate.h"
#include "ceres/types.h"
#include "glog/logging.h"
namespace ceres {
namespace internal {
// Helper templates that allow evaluation of a variadic functor or a
// CostFunction object.
template <typename CostFunctor,
int N0, int N1, int N2, int N3, int N4,
int N5, int N6, int N7, int N8, int N9 >
bool EvaluateImpl(const CostFunctor* functor,
double const* const* parameters,
double* residuals,
const void* /* NOT USED */) {
return VariadicEvaluate<CostFunctor,
double,
N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>::Call(
*functor,
parameters,
residuals);
}
template <typename CostFunctor,
int N0, int N1, int N2, int N3, int N4,
int N5, int N6, int N7, int N8, int N9 >
bool EvaluateImpl(const CostFunctor* functor,
double const* const* parameters,
double* residuals,
const CostFunction* /* NOT USED */) {
return functor->Evaluate(parameters, residuals, NULL);
}
// This is split from the main class because C++ doesn't allow partial template
// specializations for member functions. The alternative is to repeat the main
// class for differing numbers of parameters, which is also unfortunate.
template <typename CostFunctor,
NumericDiffMethod kMethod,
int kNumResiduals,
int N0, int N1, int N2, int N3, int N4,
int N5, int N6, int N7, int N8, int N9,
int kParameterBlock,
int kParameterBlockSize>
struct NumericDiff {
// Mutates parameters but must restore them before return.
static bool EvaluateJacobianForParameterBlock(
const CostFunctor* functor,
double const* residuals_at_eval_point,
const double relative_step_size,
int num_residuals,
double **parameters,
double *jacobian) {
using Eigen::Map;
using Eigen::Matrix;
using Eigen::RowMajor;
using Eigen::ColMajor;
const int NUM_RESIDUALS =
(kNumResiduals != ceres::DYNAMIC ? kNumResiduals : num_residuals);
typedef Matrix<double, kNumResiduals, 1> ResidualVector;
typedef Matrix<double, kParameterBlockSize, 1> ParameterVector;
// The convoluted reasoning for choosing the Row/Column major
// ordering of the matrix is an artifact of the restrictions in
// Eigen that prevent it from creating RowMajor matrices with a
// single column. In these cases, we ask for a ColMajor matrix.
typedef Matrix<double,
kNumResiduals,
kParameterBlockSize,
(kParameterBlockSize == 1) ? ColMajor : RowMajor>
JacobianMatrix;
Map<JacobianMatrix> parameter_jacobian(jacobian,
NUM_RESIDUALS,
kParameterBlockSize);
// Mutate 1 element at a time and then restore.
Map<ParameterVector> x_plus_delta(parameters[kParameterBlock],
kParameterBlockSize);
ParameterVector x(x_plus_delta);
ParameterVector step_size = x.array().abs() * relative_step_size;
// To handle cases where a parameter is exactly zero, instead use
// the mean step_size for the other dimensions. If all the
// parameters are zero, there's no good answer. Take
// relative_step_size as a guess and hope for the best.
const double fallback_step_size =
(step_size.sum() == 0)
? relative_step_size
: step_size.sum() / step_size.rows();
// For each parameter in the parameter block, use finite differences to
// compute the derivative for that parameter.
ResidualVector residuals(NUM_RESIDUALS);
for (int j = 0; j < kParameterBlockSize; ++j) {
const double delta =
(step_size(j) == 0.0) ? fallback_step_size : step_size(j);
x_plus_delta(j) = x(j) + delta;
if (!EvaluateImpl<CostFunctor, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(
functor, parameters, residuals.data(), functor)) {
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_delta = 1.0 / delta;
if (kMethod == CENTRAL) {
// Compute the function on the other side of x(j).
x_plus_delta(j) = x(j) - delta;
if (!EvaluateImpl<CostFunctor, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(
functor, parameters, residuals.data(), functor)) {
return false;
}
parameter_jacobian.col(j) -= residuals;
one_over_delta /= 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_delta;
}
return true;
}
};
template <typename CostFunctor,
NumericDiffMethod kMethod,
int kNumResiduals,
int N0, int N1, int N2, int N3, int N4,
int N5, int N6, int N7, int N8, int N9,
int kParameterBlock>
struct NumericDiff<CostFunctor, kMethod, kNumResiduals,
N0, N1, N2, N3, N4, N5, N6, N7, N8, N9,
kParameterBlock, 0> {
// Mutates parameters but must restore them before return.
static bool EvaluateJacobianForParameterBlock(
const CostFunctor* functor,
double const* residuals_at_eval_point,
const double relative_step_size,
const int num_residuals,
double **parameters,
double *jacobian) {
LOG(FATAL) << "Control should never reach here.";
return true;
}
};
} // namespace internal
} // namespace ceres
#endif // CERES_PUBLIC_INTERNAL_NUMERIC_DIFF_H_
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