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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
13namespace Eigen {
14
26template <typename Polynomials, typename T>
27inline
28T 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
44template <typename Polynomials, typename T>
45inline
46T poly_eval( const Polynomials& poly, const T& x )
47{
48 typedef typename NumTraits<T>::Real Real;
49
50 if( numext::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 numext::pow(x,(T)(poly.size()-1)) * val;
60 }
61}
62
73template <typename Polynomial>
74inline
76{
77 using std::abs;
78 typedef typename Polynomial::Scalar Scalar;
79 typedef typename NumTraits<Scalar>::Real Real;
80
81 eigen_assert( Scalar(0) != poly[poly.size()-1] );
82 const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];
83 Real cb(0);
84
85 for( DenseIndex i=0; i<poly.size()-1; ++i ){
86 cb += abs(poly[i]*inv_leading_coeff); }
87 return cb + Real(1);
88}
89
96template <typename Polynomial>
97inline
99{
100 using std::abs;
101 typedef typename Polynomial::Scalar Scalar;
102 typedef typename NumTraits<Scalar>::Real Real;
103
104 DenseIndex i=0;
105 while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }
106 if( poly.size()-1 == i ){
107 return Real(1); }
108
109 const Scalar inv_min_coeff = Scalar(1)/poly[i];
110 Real cb(1);
111 for( DenseIndex j=i+1; j<poly.size(); ++j ){
112 cb += abs(poly[j]*inv_min_coeff); }
113 return Real(1)/cb;
114}
115
126template <typename RootVector, typename Polynomial>
127void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )
128{
129
130 typedef typename Polynomial::Scalar Scalar;
131
132 poly.setZero( rv.size()+1 );
133 poly[0] = -rv[0]; poly[1] = Scalar(1);
134 for( DenseIndex i=1; i< rv.size(); ++i )
135 {
136 for( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }
137 poly[0] = -rv[i]*poly[0];
138 }
139}
140
141} // end namespace Eigen
142
143#endif // EIGEN_POLYNOMIAL_UTILS_H
NumTraits< typenamePolynomial::Scalar >::Real cauchy_max_bound(const Polynomial &poly)
Definition: PolynomialUtils.h:75
T poly_eval_horner(const Polynomials &poly, const T &x)
Definition: PolynomialUtils.h:28
NumTraits< typenamePolynomial::Scalar >::Real cauchy_min_bound(const Polynomial &poly)
Definition: PolynomialUtils.h:98
T poly_eval(const Polynomials &poly, const T &x)
Definition: PolynomialUtils.h:46
void roots_to_monicPolynomial(const RootVector &rv, Polynomial &poly)
Definition: PolynomialUtils.h:127
Namespace containing all symbols from the Eigen library.
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)