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Speed-Improvemend for 2D-KDE calculation by reordering loops and allowing for inlined function calls

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jkriege2 2024-03-18 12:10:38 +01:00
parent 7292dd5c54
commit 6ca2e6ea3c
2 changed files with 113 additions and 77 deletions
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54
lib/jkqtmath/jkqtpstatkde.cpp
View File

@ -22,64 +22,10 @@
#include "jkqtmath/jkqtpstatkde.h"
double jkqtpstatKernel1DGaussian(double t) {
return exp(-0.5*t*t)/JKQTPSTATISTICS_SQRT_2PI;
}
double jkqtpstatKernel1DCauchy(double t) {
return 1.0/(JKQTPSTATISTICS_PI*(1.0+t*t));
}
double jkqtpstatKernel1DPicard(double t) {
return exp(-0.5*fabs(t))/2.0;
}
double jkqtpstatKernel1DEpanechnikov(double t) {
return (fabs(t)<1.0)?(0.75*(1.0-t*t)):0.0;
}
double jkqtpstatKernel1DUniform(double t) {
return (fabs(t)<=1.0)?0.5:0.0;
}
double jkqtpstatKernel1DTriangle(double t) {
return (fabs(t)<=1.0)?(1.0-fabs(t)):0.0;
}
double jkqtpstatKernel1DQuartic(double t) {
return (fabs(t)<=1.0)?(15.0/16.0*jkqtp_sqr(1.0-t*t)):0.0;
}
double jkqtpstatKernel1DTriweight(double t) {
return (fabs(t)<1.0)?(35.0/32.0*jkqtp_cube(1.0-t*t)):0.0;
}
double jkqtpstatKernel1DTricube(double t) {
return (fabs(t)<1.0)?(70.0/81.0*jkqtp_cube(1.0-jkqtp_cube(fabs(t)))):0.0;
}
double jkqtpstatKernel1DCosine(double t) {
return (fabs(t)<1.0)?(JKQTPSTATISTICS_PI/4.0*cos(t*JKQTPSTATISTICS_PI/2.0)):0.0;
}
double jkqtpstatKernel2DGaussian(double tx, double ty)
{
return exp(-0.5*(tx*tx+ty*ty))/(2.0*JKQTPSTATISTICS_PI);
}
double jkqtpstatKernel2DUniform(double tx, double ty) {
return (fabs(tx)<1.0 && fabs(ty)<=1.0)?0.25:0.0;
}

136
lib/jkqtmath/jkqtpstatkde.h
View File

@ -49,64 +49,84 @@
\f[ k(t):=\frac{1}{\sqrt{2\pi}}\exp \left(-\frac{1}{2}t^2\right) \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DGaussian(double t);
inline double jkqtpstatKernel1DGaussian(double t) {
return exp(-0.5*t*t)/JKQTPSTATISTICS_SQRT_2PI;
}
/*! \brief a 1D Cauchy kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t):=\frac{1}{\pi(1+t^2)} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DCauchy(double t);
inline double jkqtpstatKernel1DCauchy(double t) {
return 1.0/(JKQTPSTATISTICS_PI*(1.0+t*t));
}
/*! \brief a 1D Picard kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t):=\frac{1}{2}\exp(-|t|) \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DPicard(double t);
inline double jkqtpstatKernel1DPicard(double t) {
return exp(-0.5*fabs(t))/2.0;
}
/*! \brief a 1D Epanechnikov kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t) :=\begin{cases}\frac{3}{4} ( 1- t^2 ), & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DEpanechnikov(double t);
inline double jkqtpstatKernel1DEpanechnikov(double t) {
return (fabs(t)<1.0)?(0.75*(1.0-t*t)):0.0;
}
/*! \brief a 1D uniform kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t) :=\begin{cases}0.5, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DUniform(double t);
inline double jkqtpstatKernel1DUniform(double t) {
return (fabs(t)<=1.0)?0.5:0.0;
}
/*! \brief a 1D Epanechnikov kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t) :=\begin{cases}1-|t|, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DTriangle(double t);
inline double jkqtpstatKernel1DTriangle(double t) {
return (fabs(t)<=1.0)?(1.0-fabs(t)):0.0;
}
/*! \brief a 1D quartic kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t) :=\begin{cases}\frac{15}{16}(1-t^2)^2, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DQuartic(double t);
inline double jkqtpstatKernel1DQuartic(double t) {
return (fabs(t)<=1.0)?(15.0/16.0*jkqtp_sqr(1.0-t*t)):0.0;
}
/*! \brief a 1D triweight kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t) :=\begin{cases}\frac{35}{32}(1-t^2)^3, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DTriweight(double t);
inline double jkqtpstatKernel1DTriweight(double t) {
return (fabs(t)<1.0)?(35.0/32.0*jkqtp_cube(1.0-t*t)):0.0;
}
/*! \brief a 1D tricube kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t) :=\begin{cases}\frac{70}{81}(1-|t|^3)^3, & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DTricube(double t);
inline double jkqtpstatKernel1DTricube(double t) {
return (fabs(t)<1.0)?(70.0/81.0*jkqtp_cube(1.0-jkqtp_cube(fabs(t)))):0.0;
}
/*! \brief a 1D cosine kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_1dkde_kernels
\f[ k(t) :=\begin{cases}\frac{\pi}{4}\cos\left(\frac{\pi}{2}t\right), & \text{if }t\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel1DCosine(double t);
inline double jkqtpstatKernel1DCosine(double t) {
return (fabs(t)<1.0)?(JKQTPSTATISTICS_PI/4.0*cos(t*JKQTPSTATISTICS_PI/2.0)):0.0;
}
@ -125,14 +145,19 @@ jkqtmath_LIB_EXPORT double jkqtpstatKernel1DCosine(double t);
\f[ k(t_x, t_y):=\frac{1}{2\pi}\exp \left(-\frac{t_x^2+t_y^2}{2}\right) \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel2DGaussian(double tx, double ty);
inline double jkqtpstatKernel2DGaussian(double tx, double ty)
{
return exp(-0.5*(tx*tx+ty*ty))/(2.0*JKQTPSTATISTICS_PI);
}
/*! \brief a 2D Uniform kernel function, e.g. for Kernel Density Estimation
\ingroup jkqtptools_math_statistics_2dkde_kernels
\f[ k(t_x, t_y):=\begin{cases}\frac{1}{4}, & \text{if }t_x,t_y\in [-1;1]\\0, & \text{else}\end{cases} \f]
*/
jkqtmath_LIB_EXPORT double jkqtpstatKernel2DUniform(double tx, double ty);
inline double jkqtpstatKernel2DUniform(double tx, double ty) {
return (fabs(tx)<1.0 && fabs(ty)<=1.0)?0.25:0.0;
}
@ -473,6 +498,45 @@ inline double jkqtpstatEvaluateKernelSum2D(double x, double y, InputItX firstX,
/*! \brief stores a part-result of the Kernel Density Estimator (KDE) at a given position
\ingroup jkqtptools_math_statistics_2dkde
\internal
Iterates over all datapoints in firstX..lastX and firstY..lastY, for each one determines whether the floating-point values are valid
and the calls fStore, which is a functor that is supposed to iterate over the KDE 2D array and over calls sum up the KDE.
This is internally used by jkqtpstatKDE2D(). The construction is not as straight-forward, as iterating over all positions in the 2D-KJDE
and the calling jkqtpstatEvaluateKernelSum2D(), bt by reordering the loops it is significatyl faster (~20%)
\tparam InputItX standard iterator type of \a firstX and \a lastX.
\tparam InputItY standard iterator type of \a firstY and \a lastY.
\tparam FF functor
\param x where to evaluate the kernel sum, x-coordinate
\param y where to evaluate the kernel sum, y-coordinate
\param firstX iterator pointing to the first x-position item in the dataset to use \f$ X_1 \f$
\param lastX iterator pointing behind the last x-position item in the dataset to use \f$ X_N \f$
\param firstY iterator pointing to the first y-position item in the dataset to use \f$ Y_1 \f$
\param lastY iterator pointing behind the last y-position item in the dataset to use \f$ Y_N \f$
\param kernel the kernel function to use (e.g. jkqtpstatKernel1DGaussian() )
\param bandwidthX x-bandwidth used for the KDE
\param bandwidthY y-bandwidth used for the KDE
*/
template <class InputItX, class InputItY, class FF>
inline int jkqtpstatStoreKernelSum2D(FF&& fStore, InputItX firstX, InputItX lastX, InputItY firstY, InputItY lastY, const std::function<double(double,double)>& kernel, double bandwidthX, double bandwidthY) {
auto itX=firstX;
auto itY=firstY;
int cnt=0;
for (; (itX!=lastX)&&(itY!=lastY); ++itX, ++itY) {
const double vx=jkqtp_todouble(*itX);
const double vy=jkqtp_todouble(*itY);
if (JKQTPIsOKFloat(vx) && JKQTPIsOKFloat(vy)) {
fStore(vx,vy, kernel,bandwidthX, bandwidthY);
cnt++;
}
}
return cnt;
}
/*! \brief calculate an autoranged 2-dimensional Kernel Density Estimation (KDE) from the given data range \a firstX / \a firstY ... \a lastY / \a lastY
\ingroup jkqtptools_math_statistics_2dkde
@ -504,18 +568,44 @@ inline void jkqtpstatKDE2D(InputItX firstX, InputItX lastX, InputItY firstY, Inp
const double binwx=fabs(xmax-xmin)/static_cast<double>(xbins);
const double binwy=fabs(ymax-ymin)/static_cast<double>(ybins);
double y=ymin;
auto itOut=histogramImgOut;
for (size_t by=0; by<ybins; by++) {
double x=xmin;
for (size_t bx=0; bx<xbins; bx++) {
const double vv=jkqtpstatEvaluateKernelSum2D(x,y, firstX, lastX,firstY,lastY, kernel, bandwidthX,bandwidthY);
*itOut=vv;
//std::cout<<x<<","<<y<<","<<vv<<*itOut<<std::endl;
x+=binwx;
++itOut;
{
auto itOut=histogramImgOut;
for (size_t by=0; by<ybins; by++) {
for (size_t bx=0; bx<xbins; bx++) {
*itOut=0;
++itOut;
}
}
}
const double cnt=jkqtpstatStoreKernelSum2D([&](double vx, double vy, const std::function<double(double,double)>& kernel, double bandwidthX, double bandwidthY){
double y=ymin;
auto itOut=histogramImgOut;
for (size_t by=0; by<ybins; by++) {
double x=xmin;
for (size_t bx=0; bx<xbins; bx++) {
const double vvx=(x-vx)/bandwidthX;
const double vvy=(y-vy)/bandwidthY;
*itOut+=kernel(vvx,vvy)/sqrt(bandwidthX*bandwidthY);
//std::cout<<x<<","<<y<<","<<vv<<*itOut<<std::endl;
x+=binwx;
++itOut;
}
y+=binwy;
}
}, firstX, lastX, firstY, lastY, kernel, bandwidthX, bandwidthY);
{
auto itOut=histogramImgOut;
for (size_t by=0; by<ybins; by++) {
for (size_t bx=0; bx<xbins; bx++) {
*itOut/=cnt;
++itOut;
}
}
y+=binwy;
}
}