ROL
ROL_Parabolic.hpp
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43
44#ifndef ROL_PARABOLIC_HPP
45#define ROL_PARABOLIC_HPP
46
47#include "ROL_Distribution.hpp"
48#include "ROL_ParameterList.hpp"
49
50namespace ROL {
51
52template<class Real>
53class Parabolic : public Distribution<Real> {
54private:
55 Real a_;
56 Real b_;
57
58public:
59 Parabolic(const Real a = 0., const Real b = 1.)
60 : a_(std::min(a,b)), b_(std::max(a,b)) {}
61
62 Parabolic(ROL::ParameterList &parlist) {
63 a_ = parlist.sublist("SOL").sublist("Distribution").sublist("Parabolic").get("Lower Bound",0.);
64 b_ = parlist.sublist("SOL").sublist("Distribution").sublist("Parabolic").get("Upper Bound",1.);
65 Real tmp = a_;
66 a_ = std::min(a_,b_);
67 b_ = std::max(b_,tmp);
68 }
69
70 Real evaluatePDF(const Real input) const {
71 Real scale = 6.0/std::pow(b_-a_,3.0);
72 return ((input >= a_ && input <= b_) ? scale*(input-a_)*(b_-input) : 0.);
73 }
74
75 Real evaluateCDF(const Real input) const {
76 Real d1 = b_-a_, d2 = d1*d1, d3 = d2*d1;
77 Real v1 = input-a_, v2 = v1*v1, v3 = v1*v2;
78 return ((input < a_) ? 0. : ((input > b_) ? 1. :
79 3.0*v2/d2 - 2.0*v3/d3));
80 }
81
82 Real integrateCDF(const Real input) const {
83 Real d0 = b_+a_, d1 = b_-a_, d2 = d1*d1, d3 = d2*d1;
84 Real v1 = input-a_, v2 = v1*v1, v3 = v1*v2, v4 = v1*v3;
85 return ((input < a_) ? 0. :
86 ((input > b_) ? input - 0.5*d0 :
87 v3/d2 - 0.5*v4/d3));
88 }
89
90 Real invertCDF(const Real input) const {
91 Real a = a_-b_, b = a_+b_, 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 p = (Real)m;
111 Real a1 = std::pow(a_,p+1), b1 = std::pow(b_,p+1);
112 Real a2 = a1*a_, b2 = b1*b_;
113 Real a3 = a2*a_, b3 = b2*b_;
114 return 6./std::pow(b_-a_,3)
115 * (-(b3-a3)/(p+3) + (a_+b_)*(b2-a2)/(p+2) - a_*b_*(b1-a1)/(p+1));
116 }
117
118 Real lowerBound(void) const {
119 return a_;
120 }
121
122 Real upperBound(void) const {
123 return b_;
124 }
125
126 void test(std::ostream &outStream = std::cout ) const {
127 size_t size = 5;
128 std::vector<Real> X(size,0.);
129 std::vector<int> T(size,0);
130 X[0] = a_-4.0*(Real)rand()/(Real)RAND_MAX;
131 T[0] = 0;
132 X[1] = a_;
133 T[1] = 1;
134 X[2] = (b_-a_)*(Real)rand()/(Real)RAND_MAX + a_;
135 T[2] = 0;
136 X[3] = b_;
137 T[3] = 1;
138 X[4] = b_+4.0*(Real)rand()/(Real)RAND_MAX;
139 T[4] = 0;
140 Distribution<Real>::test(X,T,outStream);
141 }
142};
143
144}
145
146#endif
virtual void test(std::ostream &outStream=std::cout) const
Real moment(const size_t m) const
Real lowerBound(void) const
Real upperBound(void) const
Real invertCDF(const Real input) const
void test(std::ostream &outStream=std::cout) const
Real evaluatePDF(const Real input) const
Parabolic(const Real a=0., const Real b=1.)
Real integrateCDF(const Real input) const
Parabolic(ROL::ParameterList &parlist)
Real evaluateCDF(const Real input) const