NumCpp  2.12.1
A Templatized Header Only C++ Implementation of the Python NumPy Library
gaussNewtonNlls.hpp
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1
30#pragma once
31
32#include <array>
33#include <functional>
34#include <type_traits>
35#include <utility>
36
40#include "NumCpp/Core/Shape.hpp"
41#include "NumCpp/Core/Types.hpp"
43#include "NumCpp/Linalg/inv.hpp"
44#include "NumCpp/NdArray.hpp"
45
46namespace nc::linalg
47{
48 //============================================================================
49 // Method Description:
71 template<typename dtype,
72 typename... Params,
73 std::enable_if_t<std::is_arithmetic_v<dtype>, int> = 0,
74 std::enable_if_t<all_arithmetic_v<Params...>, int> = 0,
75 std::enable_if_t<all_same_v<dtype, Params...>, int> = 0>
76 std::pair<NdArray<double>, double>
77 gaussNewtonNlls(const uint32 numIterations,
78 const NdArray<dtype>& coordinates,
79 const NdArray<dtype>& measurements,
80 const std::function<dtype(const NdArray<dtype>&, const NdArray<dtype>&)>& function,
81 const std::array<std::function<dtype(const NdArray<dtype>&, const NdArray<dtype>&)>,
82 sizeof...(Params)>& derivatives,
83 Params... initialGuess)
84 {
86
87 const auto coordinatesShape = coordinates.shape();
88
89 if (coordinatesShape.rows != measurements.size())
90 {
91 THROW_INVALID_ARGUMENT_ERROR("coordinates number of rows, and measurements size must be the same.");
92 }
93
94 NdArray<double> beta = NdArray<dtype>({ initialGuess... }).template astype<double>().transpose();
95 NdArray<double> residuals(coordinatesShape.rows, 1);
96 NdArray<double> jacobian(coordinatesShape.rows, sizeof...(Params));
97
98 const auto colSlice = coordinates.cSlice();
99 for (uint32 iteration = 1; iteration <= numIterations; ++iteration)
100 {
101 for (uint32 measIdx = 0; measIdx < coordinatesShape.rows; ++measIdx)
102 {
103 const auto coordinate = coordinates(measIdx, colSlice);
104
105 residuals[measIdx] =
106 static_cast<double>(measurements[measIdx]) - static_cast<double>(function(coordinate, beta));
107
108 for (uint32 paramIdx = 0; paramIdx < sizeof...(Params); ++paramIdx)
109 {
110 const auto& derivative = derivatives[paramIdx];
111 jacobian(measIdx, paramIdx) = static_cast<double>(derivative(coordinate, beta));
112 }
113 }
114
115 // perform the gauss-newton linear algebra
116 const auto jacobianT = jacobian.transpose();
117 const auto jacobianPsuedoInverse = linalg::inv(jacobianT.dot(jacobian));
118 const auto intermediate = jacobianPsuedoInverse.dot(jacobianT);
119 const auto deltaBeta = intermediate.dot(residuals);
120 beta += deltaBeta;
121 }
122
123 // calculate the final rms of the residuals
124 for (uint32 measIdx = 0; measIdx < coordinatesShape.rows; ++measIdx)
125 {
126 const auto coordinate = coordinates(measIdx, colSlice);
127
128 residuals[measIdx] =
129 static_cast<double>(measurements[measIdx]) - static_cast<double>(function(coordinate, beta));
130 }
131
132 return std::make_pair(beta.flatten(), rms(residuals).item());
133 }
134} // namespace nc::linalg
#define THROW_INVALID_ARGUMENT_ERROR(msg)
Definition: Error.hpp:37
#define STATIC_ASSERT_ARITHMETIC(dtype)
Definition: StaticAsserts.hpp:39
Holds 1D and 2D arrays, the main work horse of the NumCpp library.
Definition: NdArrayCore.hpp:139
size_type size() const noexcept
Definition: NdArrayCore.hpp:4524
self_type transpose() const
Definition: NdArrayCore.hpp:4882
const Shape & shape() const noexcept
Definition: NdArrayCore.hpp:4511
Slice cSlice(index_type inStartIdx=0, size_type inStepSize=1) const
Definition: NdArrayCore.hpp:1008
Definition: cholesky.hpp:41
NdArray< double > inv(const NdArray< dtype > &inArray)
Definition: inv.hpp:54
std::pair< NdArray< double >, double > gaussNewtonNlls(const uint32 numIterations, const NdArray< dtype > &coordinates, const NdArray< dtype > &measurements, const std::function< dtype(const NdArray< dtype > &, const NdArray< dtype > &)> &function, const std::array< std::function< dtype(const NdArray< dtype > &, const NdArray< dtype > &)>, sizeof...(Params)> &derivatives, Params... initialGuess)
Definition: gaussNewtonNlls.hpp:77
dtype beta(GeneratorType &generator, dtype inAlpha, dtype inBeta)
Definition: Random/beta.hpp:61
constexpr bool all_arithmetic_v
Definition: TypeTraits.hpp:67
constexpr bool all_same_v
Definition: TypeTraits.hpp:101
NdArray< double > rms(const NdArray< dtype > &inArray, Axis inAxis=Axis::NONE)
Definition: rms.hpp:51
std::uint32_t uint32
Definition: Types.hpp:40