polynomialutils.cpp File Reference

#include "main.h"
#include <unsupported/Eigen/Polynomials>
#include <iostream>

Classes
struct	Eigen::internal::increment_if_fixed_size< Size >

Namespaces
	Eigen
	Namespace containing all symbols from the Eigen library.
	Eigen::internal
	Namespace containing low-level routines from the Eigen library.

Functions
template<typename Scalar_ , int Deg_>
void	realRoots_to_monicPolynomial_test (int deg)
template<typename Scalar_ >
void	realRoots_to_monicPolynomial_scalar ()
template<typename Scalar_ , int Deg_>
void	CauchyBounds (int deg)
template<typename Scalar_ >
void	CauchyBounds_scalar ()
	EIGEN_DECLARE_TEST (polynomialutils)

Function Documentation

CauchyBounds()

template<typename Scalar_ , int Deg_>

void CauchyBounds

(

int

deg

)

                           {
  typedef internal::increment_if_fixed_size<Deg_> Dim;
  typedef Matrix<Scalar_, Dim::ret, 1> PolynomialType;
  typedef Matrix<Scalar_, Deg_, 1> EvalRootsType;
 
  PolynomialType pols(deg + 1);
  EvalRootsType roots = EvalRootsType::Random(deg);
  roots_to_monicPolynomial(roots, pols);
  Scalar_ M = cauchy_max_bound(pols);
  Scalar_ m = cauchy_min_bound(pols);
  Scalar_ Max = roots.array().abs().maxCoeff();
  Scalar_ min = roots.array().abs().minCoeff();
  bool eval = (M >= Max) && (m <= min);
  if (!eval) {
    cerr << "Roots: " << roots << endl;
    cerr << "Bounds: (" << m << ", " << M << ")" << endl;
    cerr << "Min,Max: (" << min << ", " << Max << ")" << endl;
  }
  VERIFY(eval);
}

References Eigen::cauchy_max_bound(), Eigen::cauchy_min_bound(), Global_Variables::Dim, eval(), m, min, Eigen::roots_to_monicPolynomial(), and VERIFY.

CauchyBounds_scalar()

template<typename Scalar_ >

void CauchyBounds_scalar

(

)

                           {
  CALL_SUBTEST_2((CauchyBounds<Scalar_, 2>(2)));
  CALL_SUBTEST_3((CauchyBounds<Scalar_, 3>(3)));
  CALL_SUBTEST_4((CauchyBounds<Scalar_, 4>(4)));
  CALL_SUBTEST_5((CauchyBounds<Scalar_, 5>(5)));
  CALL_SUBTEST_6((CauchyBounds<Scalar_, 6>(6)));
  CALL_SUBTEST_7((CauchyBounds<Scalar_, 7>(7)));
  CALL_SUBTEST_8((CauchyBounds<Scalar_, 17>(17)));
 
  CALL_SUBTEST_9((CauchyBounds<Scalar_, Dynamic>(internal::random<int>(18, 26))));
}

References CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, CALL_SUBTEST_7, CALL_SUBTEST_8, and CALL_SUBTEST_9.

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

polynomialutils

)

                                    {
  for (int i = 0; i < g_repeat; i++) {
    realRoots_to_monicPolynomial_scalar<double>();
    realRoots_to_monicPolynomial_scalar<float>();
    CauchyBounds_scalar<double>();
    CauchyBounds_scalar<float>();
  }
}

References Eigen::g_repeat, and i.

realRoots_to_monicPolynomial_scalar()

template<typename Scalar_ >

void realRoots_to_monicPolynomial_scalar

(

)

                                           {
  CALL_SUBTEST_2((realRoots_to_monicPolynomial_test<Scalar_, 2>(2)));
  CALL_SUBTEST_3((realRoots_to_monicPolynomial_test<Scalar_, 3>(3)));
  CALL_SUBTEST_4((realRoots_to_monicPolynomial_test<Scalar_, 4>(4)));
  CALL_SUBTEST_5((realRoots_to_monicPolynomial_test<Scalar_, 5>(5)));
  CALL_SUBTEST_6((realRoots_to_monicPolynomial_test<Scalar_, 6>(6)));
  CALL_SUBTEST_7((realRoots_to_monicPolynomial_test<Scalar_, 7>(7)));
  CALL_SUBTEST_8((realRoots_to_monicPolynomial_test<Scalar_, 17>(17)));
 
  CALL_SUBTEST_9((realRoots_to_monicPolynomial_test<Scalar_, Dynamic>(internal::random<int>(18, 26))));
}

References CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, CALL_SUBTEST_7, CALL_SUBTEST_8, and CALL_SUBTEST_9.

realRoots_to_monicPolynomial_test()

template<typename Scalar_ , int Deg_>

void realRoots_to_monicPolynomial_test

(

int

deg

)

                                                {
  typedef internal::increment_if_fixed_size<Deg_> Dim;
  typedef Matrix<Scalar_, Dim::ret, 1> PolynomialType;
  typedef Matrix<Scalar_, Deg_, 1> EvalRootsType;
 
  PolynomialType pols(deg + 1);
  EvalRootsType roots = EvalRootsType::Random(deg);
  roots_to_monicPolynomial(roots, pols);
 
  EvalRootsType evr(deg);
  for (int i = 0; i < roots.size(); ++i) {
    evr[i] = std::abs(poly_eval(pols, roots[i]));
  }
 
  bool evalToZero = evr.isZero(test_precision<Scalar_>());
  if (!evalToZero) {
    cerr << evr.transpose() << endl;
  }
  VERIFY(evalToZero);
}

References abs(), Global_Variables::Dim, i, Eigen::poly_eval(), Eigen::roots_to_monicPolynomial(), and VERIFY.