Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files(the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions :
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
#include <cstdlib>
#include <iostream>
void wikipediaExample()
{
{
const double s = coordinates.
at(0);
const double beta1 = betas.at(0);
const double beta2 = betas.at(1);
return (beta1 * s) / (beta2 + s);
};
{
const double s = coordinates.
at(0);
const double beta2 = betas.at(1);
return s / (beta2 + s);
};
{
const double s = coordinates.
at(0);
const double beta1 = betas.at(0);
const double beta2 = betas.at(1);
};
const double beta1Guess = 0.9;
const double beta2Guess = 0.2;
#ifdef __cpp_structured_bindings
function, {delFdelBeta1, delFdelBeta2}, beta1Guess, beta2Guess);
#else
function, {delFdelBeta1, delFdelBeta2}, beta1Guess, beta2Guess);
auto& betas = results.first;
auto&
rms = results.second;
#endif
std::cout << "==========Wikipedia Example==========\n";
std::cout << "beta values = " << betas;
std::cout <<
"RMS = " <<
rms <<
'\n';
}
void exponentialExample()
{
{
const double t = coordinates.
at(0);
const double beta1 = betas.at(0);
const double beta2 = betas.at(1);
};
{
const double t = coordinates.
at(0);
const double beta2 = betas.at(1);
};
{
const double t = coordinates.
at(0);
const double beta1 = betas.at(0);
const double beta2 = betas.at(1);
return beta1 * t *
nc::exp(beta2 * t);
};
const double beta1Guess = 6.0;
const double beta2Guess = 0.3;
#ifdef __cpp_structured_bindings
exponentialFunction, {delFdelBeta1, delFdelBeta2}, beta1Guess, beta2Guess);
#else
exponentialFunction, {delFdelBeta1, delFdelBeta2}, beta1Guess, beta2Guess);
auto& betas = results.first;
auto&
rms = results.second;
#endif
std::cout << "==========Exponential Population Example==========\n";
std::cout << "beta values = " << betas;
std::cout <<
"RMS = " <<
rms <<
'\n';
}
void sinusoidalExample()
{
nc::NdArray<double> temperature = { 61.0, 65.0, 72.0, 78.0, 85.0, 90.0, 92.0, 92.0, 88.0, 81.0, 72.0, 63.0 };
{
const double t = coordinates.
at(0);
const double beta1 = betas.at(0);
const double beta2 = betas.at(1);
const double beta3 = betas.at(2);
const double beta4 = betas.at(3);
return beta1 *
nc::sin(beta2 * t + beta3) + beta4;
};
{
const double t = coordinates.
at(0);
const double beta2 = betas.at(1);
const double beta3 = betas.at(2);
};
{
const double t = coordinates.
at(0);
const double beta1 = betas.at(0);
const double beta2 = betas.at(1);
const double beta3 = betas.at(2);
return beta1 * t *
nc::cos(beta2 * t + beta3);
};
{
const double t = coordinates.
at(0);
const double beta1 = betas.at(0);
const double beta2 = betas.at(1);
const double beta3 = betas.at(2);
return beta1 *
nc::cos(beta2 * t + beta3);
};
{
return 1.0;
};
const double beta1Guess = 17.0;
const double beta2Guess = 0.5;
const double beta3Guess = 10.5;
const double beta4Guess = 77.0;
#ifdef __cpp_structured_bindings
sinusodialFunction, {delFdelBeta1, delFdelBeta2, delFdelBeta3, delFdelBeta4},
beta1Guess, beta2Guess, beta3Guess, beta4Guess);
#else
sinusodialFunction, {delFdelBeta1, delFdelBeta2, delFdelBeta3, delFdelBeta4},
beta1Guess, beta2Guess, beta3Guess, beta4Guess);
auto& betas = results.first;
auto&
rms = results.second;
#endif
std::cout << "==========Sinusodial Temperature Example==========\n";
std::cout << "beta values = " << betas;
std::cout <<
"RMS = " <<
rms <<
'\n';
}
{
const auto x = coordinates.
at(0);
const auto y = coordinates.
at(1);
const auto a = betas.
at(0);
const auto x0 = betas.
at(2);
const auto y0 = betas.
at(3);
const auto sigmaX = betas.
at(4);
const auto sigmaY = betas.
at(5);
}
{
const auto dcOffset = betas.
at(1);
return baseGaussianFunction(coordinates, betas) + dcOffset;
}
void twoDimensionalGaussianExample()
{
auto coords = nc::arange<double>(-3.0, 3.1, 0.1);
#ifdef __cpp_structured_bindings
auto [y, x] = nc::meshgrid<double>(coords, coords);
#else
auto grid = nc::meshgrid<double>(coords, coords);
auto& y = grid.first;
auto& x = grid.second;
#endif
const auto aTruth = nc::random::randFloat<double>(900.0, 1100.0);
const auto dcOffsetTruth = nc::random::randFloat<double>(90.0, 100.0);
const auto x0Truth = nc::random::randFloat<double>(-0.5, 0.5);
const auto y0Truth = nc::random::randFloat<double>(-0.5, 0.5);
const auto sigmaXTruth = nc::random::randFloat<double>(0.9, 1.1);
const auto sigmaYTruth = nc::random::randFloat<double>(0.9, 1.1);
nc::NdArray<double> betasTruth = { aTruth, dcOffsetTruth, x0Truth, y0Truth, sigmaXTruth, sigmaYTruth };
const auto cSlice = coordinates.
cSlice();
for (
nc::uint32 i = 0; i < measurements.size(); ++i)
{
measurements[i] = gaussianFunction(coordinates(i, cSlice), betasTruth);
}
auto noise = nc::random::randN<double>(measurements.shape()) * 10.0;
measurements += noise;
{
const auto a = betas.
at(0);
return baseGaussianFunction(coordinates, betas) / a;
};
{
return 1.0;
};
{
const auto x = coordinates.
at(0);
const auto x0 = betas.
at(2);
const auto sigmaX = betas.
at(4);
return (x - x0) /
nc::square(sigmaX) * baseGaussianFunction(coordinates, betas);
};
{
const auto y = coordinates.
at(1);
const auto y0 = betas.
at(3);
const auto sigmaY = betas.
at(5);
return (y - y0) /
nc::square(sigmaY) * baseGaussianFunction(coordinates, betas);
};
{
const auto x = coordinates.
at(0);
const auto x0 = betas.
at(2);
const auto sigmaX = betas.
at(4);
};
{
const auto y = coordinates.
at(1);
const auto y0 = betas.
at(2);
const auto sigmaY = betas.
at(4);
};
const double aGuess = aTruth + nc::random::randN<double>() * 5.0;
const double dcOffsetGuess = dcOffsetTruth + nc::random::randN<double>() * 5.0;
const double x0Guess = x0Truth + nc::random::randN<double>() * 0.2;
const double y0Guess = y0Truth + nc::random::randN<double>() * 0.2;
const double sigmaXGuess = sigmaXTruth + nc::random::randN<double>() * 0.2;
const double sigmaYGuess = sigmaYTruth + nc::random::randN<double>() * 0.2;
#ifdef __cpp_structured_bindings
FunctionType(gaussianFunction), {delFdelA, delFdelDcOffset, delFdelX0, delFdelY0, delFdelSigmaX, delFdelSigmaY},
aGuess, dcOffsetGuess, x0Guess, y0Guess, sigmaXGuess, sigmaYGuess);
#else
FunctionType(gaussianFunction), {delFdelA, delFdelDcOffset, delFdelX0, delFdelY0, delFdelSigmaX, delFdelSigmaY},
aGuess, dcOffsetGuess, x0Guess, y0Guess, sigmaXGuess, sigmaYGuess);
auto& betas = results.first;
auto&
rms = results.second;
#endif
nc::NdArray<double> initialGuess = { aGuess, dcOffsetGuess, x0Guess, y0Guess, sigmaXGuess, sigmaYGuess };
std::cout << "==========2D Gaussian Example==========\n";
std::cout << "truth values = " << betasTruth;
std::cout << "initial guess = " << initialGuess;
std::cout << "beta values = " << betas;
std::cout <<
"RMS = " <<
rms <<
'\n';
}
int main()
{
wikipediaExample();
exponentialExample();
sinusoidalExample();
twoDimensionalGaussianExample();
return EXIT_SUCCESS;
}
Slice cSlice(int32 inStartIdx=0, uint32 inStepSize=1) const noexcept
Definition: NdArrayCore.hpp:969
Shape shape() const noexcept
Definition: NdArrayCore.hpp:4276
reference at(int32 inIndex)
Definition: NdArrayCore.hpp:995
NdArray< dtype > transpose() const
Definition: NdArrayCore.hpp:4650
uint32 rows
Definition: Core/Shape.hpp:44
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:79
void seed(int inSeed)
Definition: generator.hpp:48
constexpr dtype power(dtype inValue, uint8 inExponent) noexcept
Definition: Functions/power.hpp:52
constexpr dtype square(dtype inValue) noexcept
Definition: square.hpp:47
auto sin(dtype inValue) noexcept
Definition: sin.hpp:49
NdArray< double > rms(const NdArray< dtype > &inArray, Axis inAxis=Axis::NONE)
Definition: rms.hpp:51
NdArray< dtype > vstack(std::initializer_list< NdArray< dtype >> inArrayList)
Definition: vstack.hpp:48
auto cos(dtype inValue) noexcept
Definition: cos.hpp:49
NdArray< dtype > transpose(const NdArray< dtype > &inArray)
Definition: transpose.hpp:45
auto exp(dtype inValue) noexcept
Definition: exp.hpp:49
std::uint32_t uint32
Definition: Types.hpp:40