ROL
ROL_RaisedCosine.hpp
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43
44#ifndef ROL_RAISEDCOSINE_HPP
45#define ROL_RAISEDCOSINE_HPP
46
47#include "ROL_Distribution.hpp"
48#include "ROL_ParameterList.hpp"
49
50namespace ROL {
51
52template<class Real>
53class RaisedCosine : public Distribution<Real> {
54private:
55 Real mean_;
56 Real var_;
57
58 size_t factorial(const size_t m) const {
59 return (m==1 ? m : m * factorial(m-1));
60 }
61
62public:
63 RaisedCosine(const Real mean = 0.5, const Real var = 0.5)
64 : mean_(mean), var_(((var>0.) ? var : 0.5)) {}
65
66 RaisedCosine(ROL::ParameterList &parlist) {
67 mean_ = parlist.sublist("SOL").sublist("Distribution").sublist("Raised Cosine").get("Mean",0.5);
68 var_ = parlist.sublist("SOL").sublist("Distribution").sublist("Raised Cosine").get("Scale",0.5);
69 var_ = (var_ > 0.) ? var_ : 0.5;
70 }
71
72 Real evaluatePDF(const Real input) const {
73 Real a = mean_-var_, b = mean_+var_;
74 return ((input >= a && input <= b) ?
75 (1.+std::cos(ROL::ScalarTraits<Real>::pi()*(input-mean_)/var_))/(2.0*var_) : 0.);
76 }
77
78 Real evaluateCDF(const Real input) const {
79 Real a = mean_-var_, b = mean_+var_;
80 return ((input < a) ? 0. : ((input > b) ? 1. :
81 0.5*(1.+(input-mean_)/var_+std::sin(ROL::ScalarTraits<Real>::pi()*(input-mean_)/var_)/ROL::ScalarTraits<Real>::pi())));
82 }
83 Real integrateCDF(const Real input) const {
84 Real a = mean_-var_, b = mean_+var_;
85 Real v = input-mean_;
86 return ((input < a) ? 0. : ((input > b) ? input - var_ :
87 0.5*(v+0.5*v*v/var_-var_*((std::cos(ROL::ScalarTraits<Real>::pi()*v/var_)+1.) /
89 }
90 Real invertCDF(const Real input) const {
91 Real a = mean_-var_, b = mean_+var_, c = 0.;
92 Real fa = evaluateCDF(a) - input;
93 Real fc = 0.;
94 Real sa = ((fa < 0.) ? -1. : ((fa > 0.) ? 1. : 0.));
95 Real sc = 0.;
96 for (size_t i = 0; i < 100; i++) {
97 c = (a+b)*0.5;
98 fc = evaluateCDF(c) - input;
99 sc = ((fc < 0.) ? -1. : ((fc > 0.) ? 1. : 0.));
100 if ( fc == 0. || (b-a)*0.5 < ROL_EPSILON<Real>() ) {
101 break;
102 }
103 if ( sc == sa ) { a = c; fa = fc; sa = sc; }
104 else { b = c; }
105 }
106 return c;
107 }
108
109 Real moment(const size_t m) const {
110 Real a = mean_-var_, b = mean_+var_;
111 Real am = std::pow(a,m+1), bm = std::pow(b,m+1);
113 Real val_cos = 0., val_sin = 0.;
114 for (size_t k = 0; k < (m-1)/2; k++) {
115 val_cos += ((k%2==0) ? 1. : -1.)*factorial(m)/(factorial(m-2*k-1)*std::pow(omega,2+2*k))
116 *(std::pow(b,m-2*k-1)*std::cos(omega*b+phi)-std::pow(a,m-2*k-1)*std::cos(omega*a+phi));
117 }
118 for (size_t k = 0; k < m/2; k++) {
119 val_sin += ((k%2==0) ? 1. : -1.)*factorial(m)/(factorial(m-2*k)*std::pow(omega,1+2*k))
120 *(std::pow(b,m-2*k)*std::sin(omega*b+phi)-std::pow(a,m-2*k)*std::sin(omega*a+phi));
121 }
122 return 0.5*((bm-am)/((Real)m+1) + val_cos + val_sin)/var_;
123 }
124
125 Real lowerBound(void) const {
126 return mean_-var_;
127 }
128
129 Real upperBound(void) const {
130 return mean_+var_;
131 }
132
133 void test(std::ostream &outStream = std::cout ) const {
134 size_t size = 5;
135 std::vector<Real> X(size,0.);
136 std::vector<int> T(size,0);
137 X[0] = mean_-var_-4.*(Real)rand()/(Real)RAND_MAX;
138 T[0] = 0;
139 X[1] = mean_-var_;
140 T[1] = 1;
141 X[2] = (2.*var_)*(Real)rand()/(Real)RAND_MAX + (mean_-var_);
142 T[2] = 0;
143 X[3] = mean_+var_;
144 T[3] = 1;
145 X[4] = mean_+var_+4.*(Real)rand()/(Real)RAND_MAX;
146 T[4] = 0;
147 Distribution<Real>::test(X,T,outStream);
148 }
149};
150
151}
152
153#endif
virtual void test(std::ostream &outStream=std::cout) const
Real evaluateCDF(const Real input) const
Real evaluatePDF(const Real input) const
void test(std::ostream &outStream=std::cout) const
Real lowerBound(void) const
Real upperBound(void) const
size_t factorial(const size_t m) const
Real invertCDF(const Real input) const
RaisedCosine(ROL::ParameterList &parlist)
RaisedCosine(const Real mean=0.5, const Real var=0.5)
Real moment(const size_t m) const
Real integrateCDF(const Real input) const
static constexpr Real pi() noexcept