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66 lines
2.8 KiB
C++
66 lines
2.8 KiB
C++
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2012 Google Inc. All rights reserved.
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// http://code.google.com/p/ceres-solver/
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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: moll.markus@arcor.de (Markus Moll)
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#ifndef CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
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#define CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
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#include "ceres/internal/eigen.h"
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namespace ceres {
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namespace internal {
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// Use the companion matrix eigenvalues to determine the roots of the polynomial
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//
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// sum_{i=0}^N polynomial(i) x^{N-i}.
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//
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// This function returns true on success, false otherwise.
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// Failure indicates that the polynomial is invalid (of size 0) or
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// that the eigenvalues of the companion matrix could not be computed.
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// On failure, a more detailed message will be written to LOG(ERROR).
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// If real is not NULL, the real parts of the roots will be returned in it.
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// Likewise, if imaginary is not NULL, imaginary parts will be returned in it.
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bool FindPolynomialRoots(const Vector& polynomial,
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Vector* real,
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Vector* imaginary);
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// Evaluate the polynomial at x using the Horner scheme.
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inline double EvaluatePolynomial(const Vector& polynomial, double x) {
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double v = 0.0;
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for (int i = 0; i < polynomial.size(); ++i) {
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v = v * x + polynomial(i);
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}
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return v;
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}
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
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