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Stokhos_KL_OneDExponentialCovarianceFunction.hpp
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41
42#ifndef STOKHOS_KL_ONE_D_EXPONENTIAL_COVARIANCE_FUNCTION_HPP
43#define STOKHOS_KL_ONE_D_EXPONENTIAL_COVARIANCE_FUNCTION_HPP
44
45#include <string>
46#include <cmath>
47#include "Teuchos_ParameterList.hpp"
48#include "Teuchos_ScalarTraits.hpp"
50
51namespace Stokhos {
52
53 namespace KL {
54
118 template <typename value_type>
120 public:
121
122 typedef ExponentialOneDEigenFunction<value_type> eigen_function_type;
123 typedef OneDEigenPair<eigen_function_type> eigen_pair_type;
124
127 const value_type& a,
128 const value_type& b,
129 const value_type& L,
130 const int dim_name,
131 Teuchos::ParameterList& solverParams);
132
135
137 value_type evaluateCovariance(const value_type& x,
138 const value_type& xp) const {
139 return std::exp(-std::abs(x-xp)/L);
140 }
141
143 const Teuchos::Array<eigen_pair_type>& getEigenPairs() const {
144 return eig_pair;
145 }
146
147 private:
148
151
154
155 protected:
156
157 typedef typename Teuchos::ScalarTraits<value_type>::magnitudeType magnitude_type;
158
160 value_type L;
161
163 Teuchos::Array<eigen_pair_type> eig_pair;
164
166 template <class Func>
167 value_type newton(const Func& func, const value_type& a,
168 const value_type& b, magnitude_type tol,
169 int max_num_its);
170
172 template <class Func>
173 value_type bisection(const Func& func, const value_type& a,
174 const value_type& b, magnitude_type tol,
175 int max_num_its);
176
181 struct EigFuncSin {
182 const value_type& alpha;
183 EigFuncSin(const value_type& alpha_) : alpha(alpha_) {}
184 value_type eval(const value_type& u) const {
185 return alpha*std::tan(u) + u; }
186 value_type deriv(const value_type& u) const {
187 return alpha/(std::cos(u)*std::cos(u)) + 1.0; }
188 };
189
194 struct EigFuncCos {
195 const value_type& alpha;
196 EigFuncCos(const value_type& alpha_) : alpha(alpha_) {}
197 value_type eval(const value_type& u) const {
198 return alpha - u*std::tan(u); }
199 value_type deriv(const value_type& u) const {
200 return -std::tan(u) - u/(std::cos(u)*std::cos(u)); }
201 };
202
203 }; // class OneDExponentialCovarianceFunction
204
205 } // namespace KL
206
207} // namespace Stokhos
208
209// Include template definitions
211
212#endif // STOKHOS_KL_ONE_D_EXPONENTIAL_COVARIANCE_FUNCTION_HPP
Class representing an exponential covariance function and its KL eigevalues/eigenfunctions.
value_type bisection(const Func &func, const value_type &a, const value_type &b, magnitude_type tol, int max_num_its)
A basic root finder based on bisection.
value_type evaluateCovariance(const value_type &x, const value_type &xp) const
Evaluate covariance.
const Teuchos::Array< eigen_pair_type > & getEigenPairs() const
Get eigenpairs.
Teuchos::ScalarTraits< value_type >::magnitudeType magnitude_type
OneDExponentialCovarianceFunction(const OneDExponentialCovarianceFunction &)
Prohibit copying.
value_type newton(const Func &func, const value_type &a, const value_type &b, magnitude_type tol, int max_num_its)
A basic root finder based on Newton's method.
OneDExponentialCovarianceFunction & operator=(const OneDExponentialCovarianceFunction &)
Prohibit copying.
OneDExponentialCovarianceFunction(int M, const value_type &a, const value_type &b, const value_type &L, const int dim_name, Teuchos::ParameterList &solverParams)
Constructor.
Top-level namespace for Stokhos classes and functions.
Nonlinear function whose roots define eigenvalues for cos() eigenfunction.
Nonlinear function whose roots define eigenvalues for sin() eigenfunction.