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Diffstat (limited to 'eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h')
-rw-r--r-- | eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h | 143 |
1 files changed, 0 insertions, 143 deletions
diff --git a/eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h b/eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h deleted file mode 100644 index 394e857..0000000 --- a/eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h +++ /dev/null @@ -1,143 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -#ifndef EIGEN_POLYNOMIAL_UTILS_H -#define EIGEN_POLYNOMIAL_UTILS_H - -namespace Eigen { - -/** \ingroup Polynomials_Module - * \returns the evaluation of the polynomial at x using Horner algorithm. - * - * \param[in] poly : the vector of coefficients of the polynomial ordered - * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial - * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. - * \param[in] x : the value to evaluate the polynomial at. - * - * \note for stability: - * \f$ |x| \le 1 \f$ - */ -template <typename Polynomials, typename T> -inline -T poly_eval_horner( const Polynomials& poly, const T& x ) -{ - T val=poly[poly.size()-1]; - for(DenseIndex i=poly.size()-2; i>=0; --i ){ - val = val*x + poly[i]; } - return val; -} - -/** \ingroup Polynomials_Module - * \returns the evaluation of the polynomial at x using stabilized Horner algorithm. - * - * \param[in] poly : the vector of coefficients of the polynomial ordered - * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial - * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. - * \param[in] x : the value to evaluate the polynomial at. - */ -template <typename Polynomials, typename T> -inline -T poly_eval( const Polynomials& poly, const T& x ) -{ - typedef typename NumTraits<T>::Real Real; - - if( numext::abs2( x ) <= Real(1) ){ - return poly_eval_horner( poly, x ); } - else - { - T val=poly[0]; - T inv_x = T(1)/x; - for( DenseIndex i=1; i<poly.size(); ++i ){ - val = val*inv_x + poly[i]; } - - return numext::pow(x,(T)(poly.size()-1)) * val; - } -} - -/** \ingroup Polynomials_Module - * \returns a maximum bound for the absolute value of any root of the polynomial. - * - * \param[in] poly : the vector of coefficients of the polynomial ordered - * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial - * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. - * - * \pre - * the leading coefficient of the input polynomial poly must be non zero - */ -template <typename Polynomial> -inline -typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly ) -{ - using std::abs; - typedef typename Polynomial::Scalar Scalar; - typedef typename NumTraits<Scalar>::Real Real; - - eigen_assert( Scalar(0) != poly[poly.size()-1] ); - const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1]; - Real cb(0); - - for( DenseIndex i=0; i<poly.size()-1; ++i ){ - cb += abs(poly[i]*inv_leading_coeff); } - return cb + Real(1); -} - -/** \ingroup Polynomials_Module - * \returns a minimum bound for the absolute value of any non zero root of the polynomial. - * \param[in] poly : the vector of coefficients of the polynomial ordered - * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial - * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$. - */ -template <typename Polynomial> -inline -typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly ) -{ - using std::abs; - typedef typename Polynomial::Scalar Scalar; - typedef typename NumTraits<Scalar>::Real Real; - - DenseIndex i=0; - while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; } - if( poly.size()-1 == i ){ - return Real(1); } - - const Scalar inv_min_coeff = Scalar(1)/poly[i]; - Real cb(1); - for( DenseIndex j=i+1; j<poly.size(); ++j ){ - cb += abs(poly[j]*inv_min_coeff); } - return Real(1)/cb; -} - -/** \ingroup Polynomials_Module - * Given the roots of a polynomial compute the coefficients in the - * monomial basis of the monic polynomial with same roots and minimal degree. - * If RootVector is a vector of complexes, Polynomial should also be a vector - * of complexes. - * \param[in] rv : a vector containing the roots of a polynomial. - * \param[out] poly : the vector of coefficients of the polynomial ordered - * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial - * e.g. \f$ 3 + x^2 \f$ is stored as a vector \f$ [ 3, 0, 1 ] \f$. - */ -template <typename RootVector, typename Polynomial> -void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly ) -{ - - typedef typename Polynomial::Scalar Scalar; - - poly.setZero( rv.size()+1 ); - poly[0] = -rv[0]; poly[1] = Scalar(1); - for( DenseIndex i=1; i< rv.size(); ++i ) - { - for( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; } - poly[0] = -rv[i]*poly[0]; - } -} - -} // end namespace Eigen - -#endif // EIGEN_POLYNOMIAL_UTILS_H |