25 #ifndef EIGEN_POLYNOMIAL_UTILS_H
26 #define EIGEN_POLYNOMIAL_UTILS_H
41 template <
typename Polynomials,
typename T>
45 T val=poly[poly.size()-1];
46 for(DenseIndex i=poly.size()-2; i>=0; --i ){
47 val = val*x + poly[i]; }
59 template <
typename Polynomials,
typename T>
63 typedef typename NumTraits<T>::Real Real;
65 if( internal::abs2( x ) <= Real(1) ){
71 for( DenseIndex i=1; i<poly.size(); ++i ){
72 val = val*inv_x + poly[i]; }
74 return std::pow(x,(T)(poly.size()-1)) * val;
88 template <
typename Polynomial>
90 typename NumTraits<typename Polynomial::Scalar>::Real
cauchy_max_bound(
const Polynomial& poly )
92 typedef typename Polynomial::Scalar Scalar;
93 typedef typename NumTraits<Scalar>::Real Real;
95 assert( Scalar(0) != poly[poly.size()-1] );
96 const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];
99 for( DenseIndex i=0; i<poly.size()-1; ++i ){
100 cb += internal::abs(poly[i]*inv_leading_coeff); }
110 template <
typename Polynomial>
112 typename NumTraits<typename Polynomial::Scalar>::Real
cauchy_min_bound(
const Polynomial& poly )
114 typedef typename Polynomial::Scalar Scalar;
115 typedef typename NumTraits<Scalar>::Real Real;
118 while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }
119 if( poly.size()-1 == i ){
122 const Scalar inv_min_coeff = Scalar(1)/poly[i];
124 for( DenseIndex j=i+1; j<poly.size(); ++j ){
125 cb += internal::abs(poly[j]*inv_min_coeff); }
139 template <
typename RootVector,
typename Polynomial>
143 typedef typename Polynomial::Scalar Scalar;
145 poly.setZero( rv.size()+1 );
146 poly[0] = -rv[0]; poly[1] = Scalar(1);
147 for( DenseIndex i=1; i< rv.size(); ++i )
149 for( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }
150 poly[0] = -rv[i]*poly[0];
156 #endif // EIGEN_POLYNOMIAL_UTILS_H