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261 lines
11 KiB
261 lines
11 KiB
1 month ago
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2023 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: keir@google.com (Keir Mierle)
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// sameeragarwal@google.com (Sameer Agarwal)
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//
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// Create CostFunctions as needed by the least squares framework with jacobians
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// computed via numeric (a.k.a. finite) differentiation. For more details see
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// http://en.wikipedia.org/wiki/Numerical_differentiation.
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//
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// To get an numerically differentiated cost function, you must define
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// a class with a operator() (a functor) that computes the residuals.
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//
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// The function must write the computed value in the last argument
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// (the only non-const one) and return true to indicate success.
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// Please see cost_function.h for details on how the return value
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// maybe used to impose simple constraints on the parameter block.
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//
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// For example, consider a scalar error e = k - x'y, where both x and y are
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// two-dimensional column vector parameters, the prime sign indicates
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// transposition, and k is a constant. The form of this error, which is the
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// difference between a constant and an expression, is a common pattern in least
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// squares problems. For example, the value x'y might be the model expectation
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// for a series of measurements, where there is an instance of the cost function
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// for each measurement k.
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//
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// The actual cost added to the total problem is e^2, or (k - x'k)^2; however,
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// the squaring is implicitly done by the optimization framework.
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//
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// To write an numerically-differentiable cost function for the above model,
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// first define the object
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//
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// class MyScalarCostFunctor {
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// explicit MyScalarCostFunctor(double k): k_(k) {}
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//
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// bool operator()(const double* const x,
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// const double* const y,
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// double* residuals) const {
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// residuals[0] = k_ - x[0] * y[0] - x[1] * y[1];
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// return true;
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// }
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//
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// private:
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// double k_;
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// };
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//
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// Note that in the declaration of operator() the input parameters x
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// and y come first, and are passed as const pointers to arrays of
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// doubles. If there were three input parameters, then the third input
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// parameter would come after y. The output is always the last
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// parameter, and is also a pointer to an array. In the example above,
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// the residual is a scalar, so only residuals[0] is set.
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//
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// Then given this class definition, the numerically differentiated
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// cost function with central differences used for computing the
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// derivative can be constructed as follows.
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//
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// CostFunction* cost_function
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// = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, 1, 2, 2>(
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// new MyScalarCostFunctor(1.0)); ^ ^ ^ ^
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// | | | |
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// Finite Differencing Scheme -+ | | |
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// Dimension of residual ------------+ | |
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// Dimension of x ----------------------+ |
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// Dimension of y -------------------------+
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//
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// In this example, there is usually an instance for each measurement of k.
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//
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// In the instantiation above, the template parameters following
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// "MyScalarCostFunctor", "1, 2, 2", describe the functor as computing
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// a 1-dimensional output from two arguments, both 2-dimensional.
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//
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// NumericDiffCostFunction also supports cost functions with a
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// runtime-determined number of residuals. For example:
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//
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// clang-format off
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//
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// CostFunction* cost_function
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// = new NumericDiffCostFunction<MyScalarCostFunctor, CENTRAL, DYNAMIC, 2, 2>(
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// new CostFunctorWithDynamicNumResiduals(1.0), ^ ^ ^
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// TAKE_OWNERSHIP, | | |
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// runtime_number_of_residuals); <----+ | | |
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// | | | |
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// | | | |
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// Actual number of residuals ------+ | | |
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// Indicate dynamic number of residuals --------------------+ | |
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// Dimension of x ------------------------------------------------+ |
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// Dimension of y ---------------------------------------------------+
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// clang-format on
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//
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//
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// The central difference method is considerably more accurate at the cost of
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// twice as many function evaluations than forward difference. Consider using
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// central differences begin with, and only after that works, trying forward
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// difference to improve performance.
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//
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// WARNING #1: A common beginner's error when first using
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// NumericDiffCostFunction is to get the sizing wrong. In particular,
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// there is a tendency to set the template parameters to (dimension of
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// residual, number of parameters) instead of passing a dimension
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// parameter for *every parameter*. In the example above, that would
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// be <MyScalarCostFunctor, 1, 2>, which is missing the last '2'
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// argument. Please be careful when setting the size parameters.
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//
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////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////
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//
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// ALTERNATE INTERFACE
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//
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// For a variety of reasons, including compatibility with legacy code,
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// NumericDiffCostFunction can also take CostFunction objects as
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// input. The following describes how.
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//
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// To get a numerically differentiated cost function, define a
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// subclass of CostFunction such that the Evaluate() function ignores
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// the jacobian parameter. The numeric differentiation wrapper will
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// fill in the jacobian parameter if necessary by repeatedly calling
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// the Evaluate() function with small changes to the appropriate
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// parameters, and computing the slope. For performance, the numeric
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// differentiation wrapper class is templated on the concrete cost
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// function, even though it could be implemented only in terms of the
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// virtual CostFunction interface.
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//
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// The numerically differentiated version of a cost function for a cost function
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// can be constructed as follows:
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//
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// CostFunction* cost_function
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// = new NumericDiffCostFunction<MyCostFunction, CENTRAL, 1, 4, 8>(
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// new MyCostFunction(...), TAKE_OWNERSHIP);
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//
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// where MyCostFunction has 1 residual and 2 parameter blocks with sizes 4 and 8
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// respectively. Look at the tests for a more detailed example.
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//
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// TODO(keir): Characterize accuracy; mention pitfalls; provide alternatives.
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#ifndef CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
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#define CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
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#include <array>
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#include <memory>
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#include "Eigen/Dense"
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#include "ceres/cost_function.h"
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#include "ceres/internal/numeric_diff.h"
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#include "ceres/internal/parameter_dims.h"
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#include "ceres/numeric_diff_options.h"
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#include "ceres/sized_cost_function.h"
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#include "ceres/types.h"
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#include "glog/logging.h"
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namespace ceres {
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template <typename CostFunctor,
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NumericDiffMethodType kMethod = CENTRAL,
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int kNumResiduals = 0, // Number of residuals, or ceres::DYNAMIC
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int... Ns> // Parameters dimensions for each block.
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class NumericDiffCostFunction final
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: public SizedCostFunction<kNumResiduals, Ns...> {
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public:
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explicit NumericDiffCostFunction(
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CostFunctor* functor,
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Ownership ownership = TAKE_OWNERSHIP,
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int num_residuals = kNumResiduals,
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const NumericDiffOptions& options = NumericDiffOptions())
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: functor_(functor), ownership_(ownership), options_(options) {
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if (kNumResiduals == DYNAMIC) {
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SizedCostFunction<kNumResiduals, Ns...>::set_num_residuals(num_residuals);
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}
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}
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NumericDiffCostFunction(NumericDiffCostFunction&& other)
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: functor_(std::move(other.functor_)), ownership_(other.ownership_) {}
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virtual ~NumericDiffCostFunction() {
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if (ownership_ != TAKE_OWNERSHIP) {
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functor_.release();
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}
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}
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bool Evaluate(double const* const* parameters,
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double* residuals,
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double** jacobians) const override {
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using internal::FixedArray;
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using internal::NumericDiff;
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using ParameterDims =
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typename SizedCostFunction<kNumResiduals, Ns...>::ParameterDims;
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constexpr int kNumParameters = ParameterDims::kNumParameters;
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constexpr int kNumParameterBlocks = ParameterDims::kNumParameterBlocks;
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// Get the function value (residuals) at the the point to evaluate.
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if (!internal::VariadicEvaluate<ParameterDims>(
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*functor_, parameters, residuals)) {
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return false;
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}
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if (jacobians == nullptr) {
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return true;
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}
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// Create a copy of the parameters which will get mutated.
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FixedArray<double> parameters_copy(kNumParameters);
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std::array<double*, kNumParameterBlocks> parameters_reference_copy =
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ParameterDims::GetUnpackedParameters(parameters_copy.data());
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for (int block = 0; block < kNumParameterBlocks; ++block) {
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memcpy(parameters_reference_copy[block],
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parameters[block],
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sizeof(double) * ParameterDims::GetDim(block));
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}
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internal::EvaluateJacobianForParameterBlocks<ParameterDims>::
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template Apply<kMethod, kNumResiduals>(
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functor_.get(),
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residuals,
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options_,
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SizedCostFunction<kNumResiduals, Ns...>::num_residuals(),
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parameters_reference_copy.data(),
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jacobians);
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return true;
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}
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const CostFunctor& functor() const { return *functor_; }
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private:
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std::unique_ptr<CostFunctor> functor_;
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Ownership ownership_;
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NumericDiffOptions options_;
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};
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} // namespace ceres
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#endif // CERES_PUBLIC_NUMERIC_DIFF_COST_FUNCTION_H_
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