// 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/
//
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//
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//
// Author: keir@google.com (Keir Mierle)
// sameeragarwal@google.com (Sameer Agarwal)
//
// Create CostFunctions as needed by the least squares framework with jacobians
// computed via numeric (a.k.a. finite) differentiation. For more details see
// http://en.wikipedia.org/wiki/Numerical_differentiation.
//
// To get an numerically differentiated cost function, you must define
// a class with a operator() (a functor) that computes the residuals.
//
// The function must write the computed value in the last argument
// (the only non-const one) and return true to indicate success.
// Please see cost_function.h for details on how the return value
// maybe used to impose simple constraints on the parameter block.
//
// For example, consider a scalar error e = k - x'y, where both x and y are
// two-dimensional column vector parameters, the prime sign indicates
// transposition, and k is a constant. The form of this error, which is the
// difference between a constant and an expression, is a common pattern in least
// squares problems. For example, the value x'y might be the model expectation
// for a series of measurements, where there is an instance of the cost function
// for each measurement k.
//
// The actual cost added to the total problem is e^2, or (k - x'k)^2; however,
// the squaring is implicitly done by the optimization framework.
//
// To write an numerically-differentiable cost function for the above model, first
// define the object
//
// class MyScalarCostFunctor {
// MyScalarCostFunctor(double k): k_(k) {}
//
// bool operator()(const double* const x,
// const double* const y,
// double* residuals) const {
// residuals[0] = k_ - x[0] * y[0] + x[1] * y[1];
// return true;
// }
//
// private:
// double k_;
// };
//
// Note that in the declaration of operator() the input parameters x
// and y come first, and are passed as const pointers to arrays of
// doubles. If there were three input parameters, then the third input
// parameter would come after y. The output is always the last
// parameter, and is also a pointer to an array. In the example above,
// the residual is a scalar, so only residuals[0] is set.
//
// Then given this class definition, the numerically differentiated
// cost function with central differences used for computing the
// derivative can be constructed as follows.
//
// CostFunction* cost_function
// = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, 1, 2, 2>(
// new MyScalarCostFunctor(1.0)); ^ ^ ^ ^
// | | | |
// Finite Differencing Scheme -+ | | |
// Dimension of residual ------------+ | |
// Dimension of x ----------------------+ |
// Dimension of y -------------------------+
//
// In this example, there is usually an instance for each measurement of k.
//
// In the instantiation above, the template parameters following
// "MyScalarCostFunctor", "1, 2, 2", describe the functor as computing
// a 1-dimensional output from two arguments, both 2-dimensional.
//
// NumericDiffCostFunction also supports cost functions with a
// runtime-determined number of residuals. For example:
//
// CostFunction* cost_function
// = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, DYNAMIC, 2, 2>(
// new CostFunctorWithDynamicNumResiduals(1.0), ^ ^ ^
// TAKE_OWNERSHIP, | | |
// runtime_number_of_residuals); <----+ | | |
// | | | |
// | | | |
// Actual number of residuals ------+ | | |
// Indicate dynamic number of residuals --------------------+ | |
// Dimension of x ------------------------------------------------+ |
// Dimension of y ---------------------------------------------------+
//
// The framework can currently accommodate cost functions of up to 10
// independent variables, and there is no limit on the dimensionality
// of each of them.
//
// The central difference method is considerably more accurate at the cost of
// twice as many function evaluations than forward difference. Consider using
// central differences begin with, and only after that works, trying forward
// difference to improve performance.
//
// WARNING #1: A common beginner's error when first using
// NumericDiffCostFunction is to get the sizing wrong. In particular,
// there is a tendency to set the template parameters to (dimension of
// residual, number of parameters) instead of passing a dimension
// parameter for *every parameter*. In the example above, that would
// be <MyScalarCostFunctor, 1, 2>, which is missing the last '2'
// argument. Please be careful when setting the size parameters.
//
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//
// ALTERNATE INTERFACE
//
// For a variety of reason, including compatibility with legacy code,
// NumericDiffCostFunction can also take CostFunction objects as
// input. The following describes how.
//
// To get a numerically differentiated cost function, define a
// subclass of CostFunction such that the Evaluate() function ignores
// the jacobian parameter. The numeric differentiation wrapper will
// fill in the jacobian parameter if necessary by repeatedly calling
// the Evaluate() function with small changes to the appropriate
// parameters, and computing the slope. For performance, the numeric
// differentiation wrapper class is templated on the concrete cost
// function, even though it could be implemented only in terms of the
// virtual CostFunction interface.
//
// The numerically differentiated version of a cost function for a cost function
// can be constructed as follows:
//
// CostFunction* cost_function
// = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>(
// new MyCostFunction(...), TAKE_OWNERSHIP);
//
// where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8
// respectively. Look at the tests for a more detailed example.
//
// TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives.
#ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
#define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
#include "Eigen/Dense"
#include "ceres/cost_function.h"
#include "ceres/internal/numeric_diff.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/sized_cost_function.h"
#include "ceres/types.h"
#include "glog/logging.h"
namespace ceres {
template <typename CostFunctor,
NumericDiffMethod method = CENTRAL,
int kNumResiduals = 0, // Number of residuals, or ceres::DYNAMIC
int N0 = 0, // Number of parameters in block 0.
int N1 = 0, // Number of parameters in block 1.
int N2 = 0, // Number of parameters in block 2.
int N3 = 0, // Number of parameters in block 3.
int N4 = 0, // Number of parameters in block 4.
int N5 = 0, // Number of parameters in block 5.
int N6 = 0, // Number of parameters in block 6.
int N7 = 0, // Number of parameters in block 7.
int N8 = 0, // Number of parameters in block 8.
int N9 = 0> // Number of parameters in block 9.
class NumericDiffCostFunction
: public SizedCostFunction<kNumResiduals,
N0, N1, N2, N3, N4,
N5, N6, N7, N8, N9> {
public:
NumericDiffCostFunction(CostFunctor* functor,
Ownership ownership = TAKE_OWNERSHIP,
int num_residuals = kNumResiduals,
const double relative_step_size = 1e-6)
:functor_(functor),
ownership_(ownership),
relative_step_size_(relative_step_size) {
if (kNumResiduals == DYNAMIC) {
SizedCostFunction<kNumResiduals,
N0, N1, N2, N3, N4,
N5, N6, N7, N8, N9>
::set_num_residuals(num_residuals);
}
}
~NumericDiffCostFunction() {
if (ownership_ != TAKE_OWNERSHIP) {
functor_.release();
}
}
virtual bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const {
using internal::FixedArray;
using internal::NumericDiff;
const int kNumParameters = N0 + N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9;
const int kNumParameterBlocks =
(N0 > 0) + (N1 > 0) + (N2 > 0) + (N3 > 0) + (N4 > 0) +
(N5 > 0) + (N6 > 0) + (N7 > 0) + (N8 > 0) + (N9 > 0);
// Get the function value (residuals) at the the point to evaluate.
if (!internal::EvaluateImpl<CostFunctor,
N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>(
functor_.get(),
parameters,
residuals,
functor_.get())) {
return false;
}
if (jacobians == NULL) {
return true;
}
// Create a copy of the parameters which will get mutated.
FixedArray<double> parameters_copy(kNumParameters);
FixedArray<double*> parameters_reference_copy(kNumParameterBlocks);
parameters_reference_copy[0] = parameters_copy.get();
if (N1) parameters_reference_copy[1] = parameters_reference_copy[0] + N0;
if (N2) parameters_reference_copy[2] = parameters_reference_copy[1] + N1;
if (N3) parameters_reference_copy[3] = parameters_reference_copy[2] + N2;
if (N4) parameters_reference_copy[4] = parameters_reference_copy[3] + N3;
if (N5) parameters_reference_copy[5] = parameters_reference_copy[4] + N4;
if (N6) parameters_reference_copy[6] = parameters_reference_copy[5] + N5;
if (N7) parameters_reference_copy[7] = parameters_reference_copy[6] + N6;
if (N8) parameters_reference_copy[8] = parameters_reference_copy[7] + N7;
if (N9) parameters_reference_copy[9] = parameters_reference_copy[8] + N8;
#define COPY_PARAMETER_BLOCK(block) \
if (N ## block) memcpy(parameters_reference_copy[block], \
parameters[block], \
sizeof(double) * N ## block); // NOLINT
COPY_PARAMETER_BLOCK(0);
COPY_PARAMETER_BLOCK(1);
COPY_PARAMETER_BLOCK(2);
COPY_PARAMETER_BLOCK(3);
COPY_PARAMETER_BLOCK(4);
COPY_PARAMETER_BLOCK(5);
COPY_PARAMETER_BLOCK(6);
COPY_PARAMETER_BLOCK(7);
COPY_PARAMETER_BLOCK(8);
COPY_PARAMETER_BLOCK(9);
#undef COPY_PARAMETER_BLOCK
#define EVALUATE_JACOBIAN_FOR_BLOCK(block) \
if (N ## block && jacobians[block] != NULL) { \
if (!NumericDiff<CostFunctor, \
method, \
kNumResiduals, \
N0, N1, N2, N3, N4, N5, N6, N7, N8, N9, \
block, \
N ## block >::EvaluateJacobianForParameterBlock( \
functor_.get(), \
residuals, \
relative_step_size_, \
SizedCostFunction<kNumResiduals, \
N0, N1, N2, N3, N4, \
N5, N6, N7, N8, N9>::num_residuals(), \
parameters_reference_copy.get(), \
jacobians[block])) { \
return false; \
} \
}
EVALUATE_JACOBIAN_FOR_BLOCK(0);
EVALUATE_JACOBIAN_FOR_BLOCK(1);
EVALUATE_JACOBIAN_FOR_BLOCK(2);
EVALUATE_JACOBIAN_FOR_BLOCK(3);
EVALUATE_JACOBIAN_FOR_BLOCK(4);
EVALUATE_JACOBIAN_FOR_BLOCK(5);
EVALUATE_JACOBIAN_FOR_BLOCK(6);
EVALUATE_JACOBIAN_FOR_BLOCK(7);
EVALUATE_JACOBIAN_FOR_BLOCK(8);
EVALUATE_JACOBIAN_FOR_BLOCK(9);
#undef EVALUATE_JACOBIAN_FOR_BLOCK
return true;
}
private:
internal::scoped_ptr<CostFunctor> functor_;
Ownership ownership_;
const double relative_step_size_;
};
} // namespace ceres
#endif // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_