partitioned_matrix_view_2_3_4.cc revision 0ae28bd5885b5daa526898fcf7c323dc2c3e1963 
1// Ceres Solver - A fast non-linear least squares minimizer
2// Copyright 2012 Google Inc. All rights reserved.
3// http://code.google.com/p/ceres-solver/
4//
5// Redistribution and use in source and binary forms, with or without
6// modification, are permitted provided that the following conditions are met:
7//
8// * Redistributions of source code must retain the above copyright notice,
9//   this list of conditions and the following disclaimer.
10// * Redistributions in binary form must reproduce the above copyright notice,
11//   this list of conditions and the following disclaimer in the documentation
12//   and/or other materials provided with the distribution.
13// * Neither the name of Google Inc. nor the names of its contributors may be
14//   used to endorse or promote products derived from this software without
15//   specific prior written permission.
16//
17// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
18// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27// POSSIBILITY OF SUCH DAMAGE.
28//
29// Author: moll.markus@arcor.de (Markus Moll)
30
31#ifndef CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
32#define CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
33
34#include "ceres/internal/eigen.h"
35
36namespace ceres {
37namespace internal {
38
39// Use the companion matrix eigenvalues to determine the roots of the polynomial
40//
41//   sum_{i=0}^N polynomial(i) x^{N-i}.
42//
43// This function returns true on success, false otherwise.
44// Failure indicates that the polynomial is invalid (of size 0) or
45// that the eigenvalues of the companion matrix could not be computed.
46// On failure, a more detailed message will be written to LOG(ERROR).
47// If real is not NULL, the real parts of the roots will be returned in it.
48// Likewise, if imaginary is not NULL, imaginary parts will be returned in it.
49bool FindPolynomialRoots(const Vector& polynomial,
50                         Vector* real,
51                         Vector* imaginary);
52
53// Evaluate the polynomial at x using the Horner scheme.
54inline double EvaluatePolynomial(const Vector& polynomial, double x) {
55  double v = 0.0;
56  for (int i = 0; i < polynomial.size(); ++i) {
57    v = v * x + polynomial(i);
58  }
59  return v;
60}
61
62}  // namespace internal
63}  // namespace ceres
64
65#endif  // CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
66