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Diffstat (limited to 'extern/libmv/third_party/ceres/internal/ceres/polynomial.h')
| -rw-r--r-- | extern/libmv/third_party/ceres/internal/ceres/polynomial.h | 135 |
1 files changed, 0 insertions, 135 deletions
diff --git a/extern/libmv/third_party/ceres/internal/ceres/polynomial.h b/extern/libmv/third_party/ceres/internal/ceres/polynomial.h deleted file mode 100644 index 80ce77e6ae1..00000000000 --- a/extern/libmv/third_party/ceres/internal/ceres/polynomial.h +++ /dev/null @@ -1,135 +0,0 @@ -// Ceres Solver - A fast non-linear least squares minimizer -// Copyright 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: moll.markus@arcor.de (Markus Moll) -// sameeragarwal@google.com (Sameer Agarwal) - -#ifndef CERES_INTERNAL_POLYNOMIAL_SOLVER_H_ -#define CERES_INTERNAL_POLYNOMIAL_SOLVER_H_ - -#include <vector> -#include "ceres/internal/eigen.h" -#include "ceres/internal/port.h" - -namespace ceres { -namespace internal { - -// All polynomials are assumed to be the form -// -// sum_{i=0}^N polynomial(i) x^{N-i}. -// -// and are given by a vector of coefficients of size N + 1. - -// Evaluate the polynomial at x using the Horner scheme. -inline double EvaluatePolynomial(const Vector& polynomial, double x) { - double v = 0.0; - for (int i = 0; i < polynomial.size(); ++i) { - v = v * x + polynomial(i); - } - return v; -} - -// Use the companion matrix eigenvalues to determine the roots of the -// polynomial. -// -// This function returns true on success, false otherwise. -// Failure indicates that the polynomial is invalid (of size 0) or -// that the eigenvalues of the companion matrix could not be computed. -// On failure, a more detailed message will be written to LOG(ERROR). -// If real is not NULL, the real parts of the roots will be returned in it. -// Likewise, if imaginary is not NULL, imaginary parts will be returned in it. -bool FindPolynomialRoots(const Vector& polynomial, - Vector* real, - Vector* imaginary); - -// Return the derivative of the given polynomial. It is assumed that -// the input polynomial is at least of degree zero. -Vector DifferentiatePolynomial(const Vector& polynomial); - -// Find the minimum value of the polynomial in the interval [x_min, -// x_max]. The minimum is obtained by computing all the roots of the -// derivative of the input polynomial. All real roots within the -// interval [x_min, x_max] are considered as well as the end points -// x_min and x_max. Since polynomials are differentiable functions, -// this ensures that the true minimum is found. -void MinimizePolynomial(const Vector& polynomial, - double x_min, - double x_max, - double* optimal_x, - double* optimal_value); - -// Structure for storing sample values of a function. -// -// Clients can use this struct to communicate the value of the -// function and or its gradient at a given point x. -struct FunctionSample { - FunctionSample() - : x(0.0), - value(0.0), - value_is_valid(false), - gradient(0.0), - gradient_is_valid(false) { - } - string ToDebugString() const; - - double x; - double value; // value = f(x) - bool value_is_valid; - double gradient; // gradient = f'(x) - bool gradient_is_valid; -}; - -// Given a set of function value and/or gradient samples, find a -// polynomial whose value and gradients are exactly equal to the ones -// in samples. -// -// Generally speaking, -// -// degree = # values + # gradients - 1 -// -// Of course its possible to sample a polynomial any number of times, -// in which case, generally speaking the spurious higher order -// coefficients will be zero. -Vector FindInterpolatingPolynomial(const vector<FunctionSample>& samples); - -// Interpolate the function described by samples with a polynomial, -// and minimize it on the interval [x_min, x_max]. Depending on the -// input samples, it is possible that the interpolation or the root -// finding algorithms may fail due to numerical difficulties. But the -// function is guaranteed to return its best guess of an answer, by -// considering the samples and the end points as possible solutions. -void MinimizeInterpolatingPolynomial(const vector<FunctionSample>& samples, - double x_min, - double x_max, - double* optimal_x, - double* optimal_value); - -} // namespace internal -} // namespace ceres - -#endif // CERES_INTERNAL_POLYNOMIAL_SOLVER_H_ |