PolynomialUtils.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_POLYNOMIAL_UTILS_H
11 #define EIGEN_POLYNOMIAL_UTILS_H
12 
13 namespace Eigen {
14 
26 template <typename Polynomials, typename T>
27 inline
28 T poly_eval_horner( const Polynomials& poly, const T& x )
29 {
30  T val=poly[poly.size()-1];
31  for(DenseIndex i=poly.size()-2; i>=0; --i ){
32  val = val*x + poly[i]; }
33  return val;
34 }
35 
44 template <typename Polynomials, typename T>
45 inline
46 T poly_eval( const Polynomials& poly, const T& x )
47 {
48  typedef typename NumTraits<T>::Real Real;
49 
50  if( internal::abs2( x ) <= Real(1) ){
51  return poly_eval_horner( poly, x ); }
52  else
53  {
54  T val=poly[0];
55  T inv_x = T(1)/x;
56  for( DenseIndex i=1; i<poly.size(); ++i ){
57  val = val*inv_x + poly[i]; }
58 
59  return std::pow(x,(T)(poly.size()-1)) * val;
60  }
61 }
62 
73 template <typename Polynomial>
74 inline
76 {
77  typedef typename Polynomial::Scalar Scalar;
78  typedef typename NumTraits<Scalar>::Real Real;
79 
80  assert( Scalar(0) != poly[poly.size()-1] );
81  const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];
82  Real cb(0);
83 
84  for( DenseIndex i=0; i<poly.size()-1; ++i ){
85  cb += internal::abs(poly[i]*inv_leading_coeff); }
86  return cb + Real(1);
87 }
88 
95 template <typename Polynomial>
96 inline
98 {
99  typedef typename Polynomial::Scalar Scalar;
100  typedef typename NumTraits<Scalar>::Real Real;
101 
102  DenseIndex i=0;
103  while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }
104  if( poly.size()-1 == i ){
105  return Real(1); }
106 
107  const Scalar inv_min_coeff = Scalar(1)/poly[i];
108  Real cb(1);
109  for( DenseIndex j=i+1; j<poly.size(); ++j ){
110  cb += internal::abs(poly[j]*inv_min_coeff); }
111  return Real(1)/cb;
112 }
113 
124 template <typename RootVector, typename Polynomial>
125 void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )
126 {
127 
128  typedef typename Polynomial::Scalar Scalar;
129 
130  poly.setZero( rv.size()+1 );
131  poly[0] = -rv[0]; poly[1] = Scalar(1);
132  for( DenseIndex i=1; i< rv.size(); ++i )
133  {
134  for( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }
135  poly[0] = -rv[i]*poly[0];
136  }
137 }
138 
139 } // end namespace Eigen
140 
141 #endif // EIGEN_POLYNOMIAL_UTILS_H