10#ifndef EIGEN_POLYNOMIAL_UTILS_H
11#define EIGEN_POLYNOMIAL_UTILS_H
26template <
typename Polynomials,
typename T>
30 T val=poly[poly.size()-1];
31 for(DenseIndex i=poly.size()-2; i>=0; --i ){
32 val = val*x + poly[i]; }
44template <
typename Polynomials,
typename T>
50 if( numext::abs2( x ) <= Real(1) ){
56 for( DenseIndex i=1; i<poly.size(); ++i ){
57 val = val*inv_x + poly[i]; }
59 return numext::pow(x,(T)(poly.size()-1)) * val;
73template <
typename Polynomial>
78 typedef typename Polynomial::Scalar Scalar;
81 eigen_assert( Scalar(0) != poly[poly.size()-1] );
82 const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];
85 for( DenseIndex i=0; i<poly.size()-1; ++i ){
86 cb +=
abs(poly[i]*inv_leading_coeff); }
96template <
typename Polynomial>
101 typedef typename Polynomial::Scalar Scalar;
105 while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }
106 if( poly.size()-1 == i ){
109 const Scalar inv_min_coeff = Scalar(1)/poly[i];
111 for( DenseIndex j=i+1; j<poly.size(); ++j ){
112 cb +=
abs(poly[j]*inv_min_coeff); }
126template <
typename RootVector,
typename Polynomial>
130 typedef typename Polynomial::Scalar Scalar;
132 poly.setZero( rv.size()+1 );
133 poly[0] = -rv[0]; poly[1] = Scalar(1);
134 for( DenseIndex i=1; i< rv.size(); ++i )
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];
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)