NumCpp  2.10.1
A Templatized Header Only C++ Implementation of the Python NumPy Library
romberg.hpp
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1 #pragma once
33 
34 #include <functional>
35 #include <vector>
36 
37 #include "NumCpp/Core/Types.hpp"
39 #include "NumCpp/NdArray.hpp"
40 #include "NumCpp/Utils/power.hpp"
41 
42 namespace nc::integrate
43 {
44  //============================================================================
45  // Method Description:
55  inline double romberg(const double low, const double high, const uint8 n, const std::function<double(double)>& f)
56  {
57  NdArray<double> rombergIntegral(n);
58 
59  // R(0,0) Start with trapezoidal integration with N = 1
60  rombergIntegral(0, 0) = trapazoidal(low, high, 1, f);
61 
62  double h = high - low;
63  for (uint8 step = 1; step < n; step++)
64  {
65  h *= 0.5;
66 
67  // R(step, 0) Improve trapezoidal integration with decreasing h
68  double trapezoidal_integration = 0.;
69  const uint32 stepEnd = utils::power(2, step - 1);
70  for (uint32 tzStep = 1; tzStep <= stepEnd; ++tzStep)
71  {
72  const double deltaX = (2. * static_cast<double>(tzStep - 1)) * h;
73  trapezoidal_integration += f(low + deltaX);
74  }
75 
76  rombergIntegral(step, 0) = 0.5 * rombergIntegral(step - 1, 0);
77  rombergIntegral(step, 0) += trapezoidal_integration * h;
78 
79  // R(m,n) Romberg integration with R(m,1) -> Simpson rule, R(m,2) -> Boole's rule
80  for (uint8 rbStep = 1; rbStep <= step; ++rbStep)
81  {
82  const double k = utils::power(4, rbStep);
83  rombergIntegral(step, rbStep) = k * rombergIntegral(step, rbStep - 1);
84  rombergIntegral(step, rbStep) -= rombergIntegral(step - 1, rbStep - 1);
85  rombergIntegral(step, rbStep) /= (k - 1.);
86  }
87  }
88 
89  return rombergIntegral.back();
90  }
91 } // namespace nc::integrate
const_reference back() const noexcept
Definition: NdArrayCore.hpp:2230
Definition: gauss_legendre.hpp:43
double romberg(const double low, const double high, const uint8 n, const std::function< double(double)> &f)
Definition: romberg.hpp:55
double trapazoidal(const double low, const double high, const uint32 n, const std::function< double(double)> &f) noexcept
Definition: trapazoidal.hpp:51
dtype f(GeneratorType &generator, dtype inDofN, dtype inDofD)
Definition: f.hpp:56
dtype power(dtype inValue, uint8 inPower) noexcept
Definition: Utils/power.hpp:46
std::uint8_t uint8
Definition: Types.hpp:42
std::uint32_t uint32
Definition: Types.hpp:40