Univariate Epanechnikov kernel PDF $k(x)=0.75(1-0.2x^2)/{2}$. More...

#include <pdf1d_weighted_epanech_kernel_pdf.h>

Inheritance diagram for pdf1d_weighted_epanech_kernel_pdf:

Public Member Functions
	pdf1d_weighted_epanech_kernel_pdf ()
	Dflt ctor.
	pdf1d_weighted_epanech_kernel_pdf (int n, double sep, double width)
	Define n kernels centred at i*sep (i=0..n-1).
virtual	~pdf1d_weighted_epanech_kernel_pdf ()
	Destructor.
virtual pdf1d_sampler *	new_sampler () const
	Create a sampler object on the heap.
virtual double	operator() (double x) const
	Probability density at x.
virtual double	log_p (double x) const
	Log of probability density at x.
virtual double	cdf (double x) const
	Cumulative Probability (P(x'<x) for x' drawn from the distribution).
virtual bool	cdf_is_analytic () const
	Return true if cdf() uses an analytic implementation.
virtual double	gradient (double x, double &p) const
	Gradient of PDF at x.
virtual double	nearest_plausible (double x, double log_p_min) const
	Compute nearest point to x which has a density above a threshold.
short	version_no () const
	Version number for I/O.
virtual vcl_string	is_a () const
	Name of the class.
virtual bool	is_class (vcl_string const &s) const
	Does the name of the class match the argument?.
virtual pdf1d_pdf *	clone () const
	Create a copy on the heap and return base class pointer.
void	set_weight (const vnl_vector< double > &weights)
	Set the weights.
void	swap_weight (vnl_vector< double > &weights)
	Swap in the weights values.
const vnl_vector< double > &	weight () const
	Weight of each kernel.
virtual void	set_centres (const vnl_vector< double > &x, double width)
	Initialise so all kernels have the same width.
virtual void	set_centres (const vnl_vector< double > &x, const vnl_vector< double > &width)
	Initialise so all kernels have given width.
virtual void	print_summary (vcl_ostream &os) const
	Print class to os.
virtual void	b_write (vsl_b_ostream &bfs) const
	Save class to binary file stream.
virtual void	b_read (vsl_b_istream &bfs)
	Load class from binary file stream.
const vnl_vector< double > &	centre () const
	Position of kernel centres.
const vnl_vector< double > &	width () const
	Width of each kernel.
bool	all_same_width () const
	True if all kernels have the same width.
virtual double	inverse_cdf (double P) const
	The inverse cdf.
double	mean () const
	Mean of distribution.
double	variance () const
	Variance of each dimension.
virtual int	n_peaks () const
	Number of peaks of distribution.
virtual double	peak (int) const
	Position of the i'th peak.
virtual double	log_prob_thresh (double pass_proportion) const
	Compute threshold for PDF to pass a given proportion.
virtual bool	is_valid_pdf () const
	Return true if the object represents a valid PDF.
void	get_samples (vnl_vector< double > &x) const
	Fill x with samples drawn from distribution.
bool	write_plot_file (const vcl_string &plot_file, double min_x, double max_x, int n) const
	Write values (x,p(x)) to text file suitable for plotting.
Static Public Member Functions
static void	pdf1d_weighted_kernel_mean_var (double &mean, double &var, const vnl_vector< double > &centres, const vnl_vector< double > &widths, const vnl_vector< double > &weights)
	calc the weighted mean and var of kernels.
Protected Member Functions
void	set_mean (double m)
void	set_variance (double v)
Protected Attributes
vnl_vector< double >	weight_
	Weight of each kernel.
double	sum_weights_
vnl_vector< double >	x_
	Position of kernel centres.
vnl_vector< double >	width_
	Width of each kernel.
vcl_vector< int >	index_
	Workspace.
bool	all_same_width_
	True if all kernels have the same width.
Friends
class	pdf1d_weighted_epanech_kernel_sampler

Detailed Description

Univariate Epanechnikov kernel PDF $k(x)=0.75(1-0.2x^2)/{2}$.

Definition at line 14 of file pdf1d_weighted_epanech_kernel_pdf.h.

Constructor & Destructor Documentation

pdf1d_weighted_epanech_kernel_pdf::pdf1d_weighted_epanech_kernel_pdf ( )

Dflt ctor.

Definition at line 19 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

pdf1d_weighted_epanech_kernel_pdf::pdf1d_weighted_epanech_kernel_pdf	(	int	n,
		double	sep,
		double	width
	)

Define n kernels centred at i*sep (i=0..n-1).

Definition at line 25 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

pdf1d_weighted_epanech_kernel_pdf::~pdf1d_weighted_epanech_kernel_pdf ( ) [virtual]

Destructor.

Definition at line 38 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

Member Function Documentation

bool pdf1d_kernel_pdf::all_same_width ( ) const [inline, inherited]

True if all kernels have the same width.

Definition at line 61 of file pdf1d_kernel_pdf.h.

void pdf1d_weighted_kernel_pdf::b_read ( vsl_b_istream & bfs ) [virtual, inherited]

Load class from binary file stream.

Reimplemented from pdf1d_kernel_pdf.

Definition at line 140 of file pdf1d_weighted_kernel_pdf.cxx.

void pdf1d_weighted_kernel_pdf::b_write ( vsl_b_ostream & bfs ) const [virtual, inherited]

Save class to binary file stream.

Reimplemented from pdf1d_kernel_pdf.

Definition at line 130 of file pdf1d_weighted_kernel_pdf.cxx.

double pdf1d_weighted_epanech_kernel_pdf::cdf ( double x0 ) const [virtual]

Cumulative Probability (P(x'<x) for x' drawn from the distribution).

CDF of $k(x) = 0.75x(1-x^2/15)/\sqrt{5} + 0.5$ if $x^2<5$

Reimplemented from pdf1d_pdf.

Definition at line 87 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

bool pdf1d_weighted_epanech_kernel_pdf::cdf_is_analytic ( ) const [virtual]

Return true if cdf() uses an analytic implementation.

Reimplemented from pdf1d_pdf.

Definition at line 112 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

const vnl_vector<double>& pdf1d_kernel_pdf::centre ( ) const [inline, inherited]

Position of kernel centres.

Definition at line 55 of file pdf1d_kernel_pdf.h.

pdf1d_pdf * pdf1d_weighted_epanech_kernel_pdf::clone ( ) const [virtual]

Create a copy on the heap and return base class pointer.

Implements pdf1d_pdf.

Definition at line 181 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

void pdf1d_pdf::get_samples ( vnl_vector< double > & x ) const [inherited]

Fill x with samples drawn from distribution.

Utility function. This calls new_sampler() to do the work, then deletes the sampler again. If you intend calling this repeatedly, create a sampler yourself.

Definition at line 132 of file pdf1d_pdf.cxx.

double pdf1d_weighted_epanech_kernel_pdf::gradient	(	double	x,
		double &	p
	)		const `[virtual]`

Gradient of PDF at x.

Implements pdf1d_pdf.

Definition at line 119 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

double pdf1d_kernel_pdf::inverse_cdf ( double P ) const [virtual, inherited]

The inverse cdf.

The value of x: P(x'<x) = P for x' drawn from distribution pdf. Uses Newton-Raphson.

The value of x: P(x'<x) = P for x' drawn from distribution pdf.

Reimplemented from pdf1d_pdf.

Definition at line 69 of file pdf1d_kernel_pdf.cxx.

vcl_string pdf1d_weighted_epanech_kernel_pdf::is_a ( ) const [virtual]

Name of the class.

Reimplemented from pdf1d_weighted_kernel_pdf.

Definition at line 159 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

bool pdf1d_weighted_epanech_kernel_pdf::is_class ( vcl_string const & s ) const [virtual]

Does the name of the class match the argument?.

Reimplemented from pdf1d_weighted_kernel_pdf.

Definition at line 167 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

bool pdf1d_pdf::is_valid_pdf ( ) const [virtual, inherited]

Return true if the object represents a valid PDF.

This will return false, if n_dims() is 0, for example just ofter default construction.

Reimplemented in pdf1d_mixture.

Definition at line 126 of file pdf1d_pdf.cxx.

double pdf1d_weighted_epanech_kernel_pdf::log_p ( double x ) const [virtual]

Log of probability density at x.

Implements pdf1d_pdf.

Definition at line 79 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

double pdf1d_pdf::log_prob_thresh ( double pass_proportion ) const [virtual, inherited]

Compute threshold for PDF to pass a given proportion.

Reimplemented in pdf1d_flat, pdf1d_gaussian, and pdf1d_exponential.

Definition at line 68 of file pdf1d_pdf.cxx.

double pdf1d_pdf::mean ( ) const [inline, inherited]

Mean of distribution.

Definition at line 42 of file pdf1d_pdf.h.

virtual int pdf1d_pdf::n_peaks ( ) const [inline, virtual, inherited]

Number of peaks of distribution.

Definition at line 48 of file pdf1d_pdf.h.

double pdf1d_weighted_epanech_kernel_pdf::nearest_plausible	(	double	x,
		double	log_p_min
	)		const `[virtual]`

Compute nearest point to x which has a density above a threshold.

If log_p(x)>log_p_min then x returned unchanged. Otherwise x is moved (typically up the gradient) until log_p(x)>=log_p_min.

Parameters:

x	This may be modified to the nearest plausible position.
log_p_min	lower threshold for log_p(x)

Implements pdf1d_pdf.

Definition at line 150 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

pdf1d_sampler * pdf1d_weighted_epanech_kernel_pdf::new_sampler ( ) const [virtual]

Create a sampler object on the heap.

Caller is responsible for deletion.

Implements pdf1d_pdf.

Definition at line 44 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

double pdf1d_weighted_epanech_kernel_pdf::operator() ( double x ) const [virtual]

Probability density at x.

Reimplemented from pdf1d_pdf.

Definition at line 55 of file pdf1d_weighted_epanech_kernel_pdf.cxx.

void pdf1d_weighted_kernel_pdf::pdf1d_weighted_kernel_mean_var	(	double &	mean,
		double &	var,
		const vnl_vector< double > &	centres,
		const vnl_vector< double > &	widths,
		const vnl_vector< double > &	weights
	)		`[static, inherited]`