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-rw-r--r--eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h143
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diff --git a/eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h b/eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
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--- a/eigen/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
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@@ -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