108 lines
3.7 KiB
C++
108 lines
3.7 KiB
C++
// Copyright (c) 2007, 2008, 2009 libmv authors.
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to
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// deal in the Software without restriction, including without limitation the
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// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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// sell copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in
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// all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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// IN THE SOFTWARE.
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#ifndef LIBMV_NUMERIC_DERIVATIVE_H
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#define LIBMV_NUMERIC_DERIVATIVE_H
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#include <cmath>
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#include "libmv/numeric/numeric.h"
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#include "libmv/logging/logging.h"
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namespace libmv {
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// Numeric derivative of a function.
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// TODO(keir): Consider adding a quadratic approximation.
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enum NumericJacobianMode {
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CENTRAL,
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FORWARD,
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};
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template<typename Function, NumericJacobianMode mode = CENTRAL>
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class NumericJacobian {
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public:
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typedef typename Function::XMatrixType Parameters;
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typedef typename Function::XMatrixType::RealScalar XScalar;
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typedef typename Function::FMatrixType FMatrixType;
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typedef Matrix<typename Function::FMatrixType::RealScalar,
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Function::FMatrixType::RowsAtCompileTime,
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Function::XMatrixType::RowsAtCompileTime>
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JMatrixType;
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NumericJacobian(const Function &f) : f_(f) {}
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// TODO(keir): Perhaps passing the jacobian back by value is not a good idea.
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JMatrixType operator()(const Parameters &x) {
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// Empirically determined constant.
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Parameters eps = x.array().abs() * XScalar(1e-5);
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// To handle cases where a paremeter is exactly zero, instead use the mean
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// eps for the other dimensions.
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XScalar mean_eps = eps.sum() / eps.rows();
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if (mean_eps == XScalar(0)) {
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// TODO(keir): Do something better here.
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mean_eps = 1e-8; // ~sqrt(machine precision).
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}
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// TODO(keir): Elimininate this needless function evaluation for the
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// central difference case.
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FMatrixType fx = f_(x);
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const int rows = fx.rows();
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const int cols = x.rows();
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JMatrixType jacobian(rows, cols);
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Parameters x_plus_delta = x;
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for (int c = 0; c < cols; ++c) {
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if (eps(c) == XScalar(0)) {
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eps(c) = mean_eps;
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}
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x_plus_delta(c) = x(c) + eps(c);
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jacobian.col(c) = f_(x_plus_delta);
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XScalar one_over_h = 1 / eps(c);
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if (mode == CENTRAL) {
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x_plus_delta(c) = x(c) - eps(c);
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jacobian.col(c) -= f_(x_plus_delta);
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one_over_h /= 2;
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} else {
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jacobian.col(c) -= fx;
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}
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x_plus_delta(c) = x(c);
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jacobian.col(c) = jacobian.col(c) * one_over_h;
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}
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return jacobian;
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}
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private:
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const Function &f_;
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};
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template<typename Function, typename Jacobian>
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bool CheckJacobian(const Function &f, const typename Function::XMatrixType &x) {
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Jacobian j_analytic(f);
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NumericJacobian<Function> j_numeric(f);
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typename NumericJacobian<Function>::JMatrixType J_numeric = j_numeric(x);
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typename NumericJacobian<Function>::JMatrixType J_analytic = j_analytic(x);
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LG << J_numeric - J_analytic;
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return true;
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}
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} // namespace libmv
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#endif // LIBMV_NUMERIC_DERIVATIVE_H
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