internal/ceres/polynomial_solver.h

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// Author: moll.markus@arcor.de (Markus Moll)

#ifndef CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
#define CERES_INTERNAL_POLYNOMIAL_SOLVER_H_

#include "ceres/internal/eigen.h"

namespace ceres {
namespace internal {

// Use the companion matrix eigenvalues to determine the roots of the polynomial
//
//   sum_{i=0}^N polynomial(i) x^{N-i}.
//
// 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);

// 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;
}

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_POLYNOMIAL_SOLVER_H_