286 lines
7.8 KiB
C++
286 lines
7.8 KiB
C++
/********************************************************
|
|
* ██████╗ ██████╗████████╗██╗
|
|
* ██╔════╝ ██╔════╝╚══██╔══╝██║
|
|
* ██║ ███╗██║ ██║ ██║
|
|
* ██║ ██║██║ ██║ ██║
|
|
* ╚██████╔╝╚██████╗ ██║ ███████╗
|
|
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
|
|
* Geophysical Computational Tools & Library (GCTL)
|
|
*
|
|
* Copyright (c) 2023 Yi Zhang (yizhang-geo@zju.edu.cn)
|
|
*
|
|
* GCTL is distributed under a dual licensing scheme. You can redistribute
|
|
* it and/or modify it under the terms of the GNU Lesser General Public
|
|
* License as published by the Free Software Foundation, either version 2
|
|
* of the License, or (at your option) any later version. You should have
|
|
* received a copy of the GNU Lesser General Public License along with this
|
|
* program. If not, see <http://www.gnu.org/licenses/>.
|
|
*
|
|
* If the terms and conditions of the LGPL v.2. would prevent you from using
|
|
* the GCTL, please consider the option to obtain a commercial license for a
|
|
* fee. These licenses are offered by the GCTL's original author. As a rule,
|
|
* licenses are provided "as-is", unlimited in time for a one time fee. Please
|
|
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
|
|
* to include some description of your company and the realm of its activities.
|
|
* Also add information on how to contact you by electronic and paper mail.
|
|
******************************************************/
|
|
|
|
#include "kde.h"
|
|
|
|
gctl::kde::kde(){}
|
|
|
|
gctl::kde::~kde(){}
|
|
|
|
gctl::kde::kde(double h, const array<double> &x)
|
|
{
|
|
init(h, x);
|
|
}
|
|
|
|
void gctl::kde::init(double h, const array<double> &x)
|
|
{
|
|
if (h <= 0) throw std::runtime_error("[gctl::kde2d] Invalid averaging width.");
|
|
if (x.size() < 2) throw std::runtime_error("[gctl::kde2d] Invalid sample size.");
|
|
|
|
h_ = h;
|
|
x_ = x;
|
|
xs_ = x.size();
|
|
return;
|
|
}
|
|
|
|
void gctl::kde::get_distribution(const array<double> &m, array<double> &d,
|
|
kde_kernel_e k_type)
|
|
{
|
|
double out;
|
|
int ms = m.size();
|
|
d.resize(xs_);
|
|
|
|
if (k_type == KDE_Gaussian)
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
out = 0;
|
|
for (size_t j = 0; j < ms; j++)
|
|
{
|
|
out += gaussian_kernel((x_[i] - m[j])/h_);
|
|
}
|
|
|
|
d[i] = out/(h_*ms);
|
|
}
|
|
}
|
|
else if (k_type == KDE_Epanechnikov)
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
out = 0;
|
|
for (size_t j = 0; j < ms; j++)
|
|
{
|
|
out += epanechnikov_kernel((x_[i] - m[j])/h_);
|
|
}
|
|
|
|
d[i] = out/(h_*ms);
|
|
}
|
|
}
|
|
else if (k_type == KDE_Rectangular)
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
out = 0;
|
|
for (size_t j = 0; j < ms; j++)
|
|
{
|
|
out += rectangular_kernel((x_[i] - m[j])/h_);
|
|
}
|
|
|
|
d[i] = out/(h_*ms);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
out = 0;
|
|
for (size_t j = 0; j < ms; j++)
|
|
{
|
|
out += triangular_kernel((x_[i] - m[j])/h_);
|
|
}
|
|
|
|
d[i] = out/(h_*ms);
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
|
|
void gctl::kde::get_gradient_at(size_t m_id, const array<double> &m,
|
|
array<double> &dm, kde_kernel_e k_type)
|
|
{
|
|
dm.resize(xs_);
|
|
int ms = m.size();
|
|
|
|
if (k_type == KDE_Gaussian)
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
dm[i] = ((x_[i] - m[m_id])/h_)*gaussian_kernel((x_[i] - m[m_id])/h_)/(h_*h_*ms);
|
|
}
|
|
}
|
|
else if (k_type == KDE_Epanechnikov)
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
dm[i] = -1.0*epanechnikov_kernel((x_[i] - m[m_id])/h_, true)/(h_*h_*ms);
|
|
}
|
|
}
|
|
else if (k_type == KDE_Rectangular)
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
dm[i] = -1.0*rectangular_kernel((x_[i] - m[m_id])/h_, true)/(h_*h_*ms);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (size_t i = 0; i < xs_; i++)
|
|
{
|
|
dm[i] = -1.0*triangular_kernel((x_[i] - m[m_id])/h_, true)/(h_*h_*ms);
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
|
|
double gctl::kde::gaussian_kernel(double x)
|
|
{
|
|
return exp(-0.5*x*x)/sqrt(2*M_PI);
|
|
}
|
|
|
|
double gctl::kde::epanechnikov_kernel(double x, bool gradient)
|
|
{
|
|
if (gradient)
|
|
{
|
|
if (fabs(x) >= 1) return 0;
|
|
else return -1.5*x;
|
|
}
|
|
|
|
if (fabs(x) >= 1) return 0;
|
|
else return 0.75*(1 - x*x);
|
|
}
|
|
|
|
double gctl::kde::rectangular_kernel(double x, bool gradient)
|
|
{
|
|
if (gradient) return 0;
|
|
|
|
if (fabs(x) >= 1) return 0;
|
|
else return 0.5;
|
|
}
|
|
|
|
double gctl::kde::triangular_kernel(double x, bool gradient)
|
|
{
|
|
if (gradient)
|
|
{
|
|
if (fabs(x) >= 1) return 0;
|
|
else if (x >= 0) return -1.0;
|
|
else return 1.0;
|
|
}
|
|
|
|
if (fabs(x) >= 1) return 0;
|
|
else return (1 - fabs(x));
|
|
}
|
|
|
|
gctl::kde2d::kde2d(){}
|
|
|
|
gctl::kde2d::~kde2d(){}
|
|
|
|
gctl::kde2d::kde2d(double hx, double hy, const array<double> &x, const array<double> &y)
|
|
{
|
|
init(hx, hy, x, y);
|
|
}
|
|
|
|
void gctl::kde2d::init(double hx, double hy, const array<double> &x, const array<double> &y)
|
|
{
|
|
if (hx <= 0 || hy <= 0) throw std::runtime_error("[gctl::kde2d] Invalid averaging width.");
|
|
if (x.size() < 2 || y.size() < 2) throw std::runtime_error("[gctl::kde2d] Invalid sample size.");
|
|
|
|
hx_ = hx;
|
|
hy_ = hy;
|
|
xs_ = x.size();
|
|
ys_ = y.size();
|
|
x_ = x;
|
|
y_ = y;
|
|
return;
|
|
}
|
|
|
|
void gctl::kde2d::get_distribution(const array<double> &mx,
|
|
const array<double> &my, array<double> &dxy, kde_kernel_e k_type)
|
|
{
|
|
if (mx.size() != my.size()) throw std::runtime_error("[gctl::kde2d] Invalid evaluating size.");;
|
|
int ms = mx.size();
|
|
|
|
dxy.resize(xs_*ys_);
|
|
|
|
double out;
|
|
if (k_type == KDE_Gaussian)
|
|
{
|
|
for (size_t i = 0; i < ys_; i++)
|
|
{
|
|
for (size_t j = 0; j < xs_; j++)
|
|
{
|
|
out = 0.0;
|
|
for (size_t k = 0; k < ms; k++)
|
|
{
|
|
out += gaussian_kernel((x_[j] - mx[k])/hx_, (y_[i] - my[k])/hy_);
|
|
}
|
|
|
|
dxy[i*xs_ + j] = out/(hx_*hy_*ms);
|
|
}
|
|
}
|
|
}
|
|
else throw std::runtime_error("[gctl::kde2d] Invalid kernel type.");
|
|
return;
|
|
}
|
|
|
|
void gctl::kde2d::get_gradient_x_at(size_t mx_id, size_t my_id,
|
|
const array<double> &mx, const array<double> &my,
|
|
array<double> &dmx, kde_kernel_e k_type)
|
|
{
|
|
if (mx.size() != my.size()) throw std::runtime_error("[gctl::kde2d] Invalid evaluating size.");;
|
|
int ms = mx.size();
|
|
|
|
dmx.resize(xs_*ys_);
|
|
|
|
if (k_type == KDE_Gaussian)
|
|
{
|
|
for (size_t i = 0; i < ys_; i++)
|
|
{
|
|
for (size_t j = 0; j < xs_; j++)
|
|
{
|
|
dmx[i*xs_ + j] = ((x_[j] - mx[mx_id])/hx_)*gaussian_kernel((x_[j] - mx[mx_id])/hx_, (y_[i] - my[my_id])/hy_)/(hx_*hx_*hy_*ms);
|
|
}
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
|
|
void gctl::kde2d::get_gradient_y_at(size_t mx_id, size_t my_id,
|
|
const array<double> &mx, const array<double> &my,
|
|
array<double> &dmy, kde_kernel_e k_type)
|
|
{
|
|
if (mx.size() != my.size()) throw std::runtime_error("[gctl::kde2d] Invalid evaluating size.");;
|
|
int ms = mx.size();
|
|
|
|
dmy.resize(xs_*ys_);
|
|
|
|
if (k_type == KDE_Gaussian)
|
|
{
|
|
for (size_t i = 0; i < ys_; i++)
|
|
{
|
|
for (size_t j = 0; j < xs_; j++)
|
|
{
|
|
dmy[i*xs_ + j] = ((y_[i] - my[my_id])/hy_)*gaussian_kernel((x_[j] - mx[mx_id])/hx_, (y_[i] - my[my_id])/hy_)/(hy_*hy_*hx_*ms);
|
|
}
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
|
|
double gctl::kde2d::gaussian_kernel(double x, double y)
|
|
{
|
|
return exp(-0.5*(x*x + y*y))/(2*M_PI);
|
|
} |