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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #include "main.h"
11 #include <unsupported/Eigen/Polynomials>
12 #include <iostream>
13 
14 using namespace std;
15 
16 namespace Eigen {
17 namespace internal {
18 template<int Size>
19 struct increment_if_fixed_size
20 {
21   enum {
22     ret = (Size == Dynamic) ? Dynamic : Size+1
23   };
24 };
25 }
26 }
27 
28 template<typename _Scalar, int _Deg>
realRoots_to_monicPolynomial_test(int deg)29 void realRoots_to_monicPolynomial_test(int deg)
30 {
31   typedef internal::increment_if_fixed_size<_Deg>            Dim;
32   typedef Matrix<_Scalar,Dim::ret,1>                  PolynomialType;
33   typedef Matrix<_Scalar,_Deg,1>                      EvalRootsType;
34 
35   PolynomialType pols(deg+1);
36   EvalRootsType roots = EvalRootsType::Random(deg);
37   roots_to_monicPolynomial( roots, pols );
38 
39   EvalRootsType evr( deg );
40   for( int i=0; i<roots.size(); ++i ){
41     evr[i] = std::abs( poly_eval( pols, roots[i] ) ); }
42 
43   bool evalToZero = evr.isZero( test_precision<_Scalar>() );
44   if( !evalToZero ){
45     cerr << evr.transpose() << endl; }
46   VERIFY( evalToZero );
47 }
48 
realRoots_to_monicPolynomial_scalar()49 template<typename _Scalar> void realRoots_to_monicPolynomial_scalar()
50 {
51   CALL_SUBTEST_2( (realRoots_to_monicPolynomial_test<_Scalar,2>(2)) );
52   CALL_SUBTEST_3( (realRoots_to_monicPolynomial_test<_Scalar,3>(3)) );
53   CALL_SUBTEST_4( (realRoots_to_monicPolynomial_test<_Scalar,4>(4)) );
54   CALL_SUBTEST_5( (realRoots_to_monicPolynomial_test<_Scalar,5>(5)) );
55   CALL_SUBTEST_6( (realRoots_to_monicPolynomial_test<_Scalar,6>(6)) );
56   CALL_SUBTEST_7( (realRoots_to_monicPolynomial_test<_Scalar,7>(7)) );
57   CALL_SUBTEST_8( (realRoots_to_monicPolynomial_test<_Scalar,17>(17)) );
58 
59   CALL_SUBTEST_9( (realRoots_to_monicPolynomial_test<_Scalar,Dynamic>(
60           internal::random<int>(18,26) )) );
61 }
62 
63 
64 
65 
66 template<typename _Scalar, int _Deg>
CauchyBounds(int deg)67 void CauchyBounds(int deg)
68 {
69   typedef internal::increment_if_fixed_size<_Deg>            Dim;
70   typedef Matrix<_Scalar,Dim::ret,1>                  PolynomialType;
71   typedef Matrix<_Scalar,_Deg,1>                      EvalRootsType;
72 
73   PolynomialType pols(deg+1);
74   EvalRootsType roots = EvalRootsType::Random(deg);
75   roots_to_monicPolynomial( roots, pols );
76   _Scalar M = cauchy_max_bound( pols );
77   _Scalar m = cauchy_min_bound( pols );
78   _Scalar Max = roots.array().abs().maxCoeff();
79   _Scalar min = roots.array().abs().minCoeff();
80   bool eval = (M >= Max) && (m <= min);
81   if( !eval )
82   {
83     cerr << "Roots: " << roots << endl;
84     cerr << "Bounds: (" << m << ", " << M << ")" << endl;
85     cerr << "Min,Max: (" << min << ", " << Max << ")" << endl;
86   }
87   VERIFY( eval );
88 }
89 
CauchyBounds_scalar()90 template<typename _Scalar> void CauchyBounds_scalar()
91 {
92   CALL_SUBTEST_2( (CauchyBounds<_Scalar,2>(2)) );
93   CALL_SUBTEST_3( (CauchyBounds<_Scalar,3>(3)) );
94   CALL_SUBTEST_4( (CauchyBounds<_Scalar,4>(4)) );
95   CALL_SUBTEST_5( (CauchyBounds<_Scalar,5>(5)) );
96   CALL_SUBTEST_6( (CauchyBounds<_Scalar,6>(6)) );
97   CALL_SUBTEST_7( (CauchyBounds<_Scalar,7>(7)) );
98   CALL_SUBTEST_8( (CauchyBounds<_Scalar,17>(17)) );
99 
100   CALL_SUBTEST_9( (CauchyBounds<_Scalar,Dynamic>(
101           internal::random<int>(18,26) )) );
102 }
103 
test_polynomialutils()104 void test_polynomialutils()
105 {
106   for(int i = 0; i < g_repeat; i++)
107   {
108     realRoots_to_monicPolynomial_scalar<double>();
109     realRoots_to_monicPolynomial_scalar<float>();
110     CauchyBounds_scalar<double>();
111     CauchyBounds_scalar<float>();
112   }
113 }
114