pdf1d_epanech_kernel_pdf Class Reference

#include <pdf1d_epanech_kernel_pdf.h>

Inheritance diagram for pdf1d_epanech_kernel_pdf:

Detailed Description

Univariate Epanechnikov kernel PDF $k(x)=0.75(1-0.2x^2)/ {5}$.

Definition at line 15 of file pdf1d_epanech_kernel_pdf.h.

Public Member Functions

pdf1d_epanech_kernel_pdf ()

Dflt ctor.

pdf1d_epanech_kernel_pdf (int n, double sep, double width)

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

virtual ~pdf1d_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.

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.

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.

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.

Protected Member Functions

void set_mean (double m)

void set_variance (double v)

Protected Attributes

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.

Constructor & Destructor Documentation

pdf1d_epanech_kernel_pdf::pdf1d_epanech_kernel_pdf ( )

Dflt ctor.

Definition at line 19 of file pdf1d_epanech_kernel_pdf.cxx.

pdf1d_epanech_kernel_pdf::pdf1d_epanech_kernel_pdf ( int n,

double sep,

double width

)

Define n kernels centred at i*sep (i=0.
.n-1).
Definition at line 24 of file pdf1d_epanech_kernel_pdf.cxx.

pdf1d_epanech_kernel_pdf::~pdf1d_epanech_kernel_pdf ( ) [virtual]

Destructor.

Definition at line 34 of file pdf1d_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_epanech_kernel_pdf::b_read ( vsl_b_istream & bfs ) [virtual]

Load class from binary file stream.

Reimplemented from pdf1d_kernel_pdf.
Definition at line 211 of file pdf1d_epanech_kernel_pdf.cxx.

void pdf1d_epanech_kernel_pdf::b_write ( vsl_b_ostream & bfs ) const [virtual]

Save class to binary file stream.

Reimplemented from pdf1d_kernel_pdf.
Definition at line 200 of file pdf1d_epanech_kernel_pdf.cxx.

double pdf1d_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 81 of file pdf1d_epanech_kernel_pdf.cxx.

bool pdf1d_epanech_kernel_pdf::cdf_is_analytic ( ) const [virtual]

Return true if cdf() uses an analytic implementation.

Reimplemented from pdf1d_pdf.
Definition at line 104 of file pdf1d_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_epanech_kernel_pdf::clone ( ) const [virtual]

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

Implements pdf1d_pdf.
Definition at line 180 of file pdf1d_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 131 of file pdf1d_pdf.cxx.

double pdf1d_epanech_kernel_pdf::gradient ( double x,

double & p

) const [virtual]

Gradient of PDF at x.

Implements pdf1d_pdf.
Definition at line 112 of file pdf1d_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.
Reimplemented from pdf1d_pdf.
Definition at line 68 of file pdf1d_kernel_pdf.cxx.

vcl_string pdf1d_epanech_kernel_pdf::is_a ( ) const [virtual]

Name of the class.

Reimplemented from pdf1d_kernel_pdf.
Definition at line 152 of file pdf1d_epanech_kernel_pdf.cxx.

bool pdf1d_epanech_kernel_pdf::is_class ( vcl_string const & s ) const [virtual]

Does the name of the class match the argument?.

Reimplemented from pdf1d_kernel_pdf.
Definition at line 162 of file pdf1d_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 125 of file pdf1d_pdf.cxx.

double pdf1d_epanech_kernel_pdf::log_p ( double x ) const [virtual]

Log of probability density at x.

Implements pdf1d_pdf.
Definition at line 74 of file pdf1d_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_exponential, pdf1d_flat, and pdf1d_gaussian.
Definition at line 67 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_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 141 of file pdf1d_epanech_kernel_pdf.cxx.

pdf1d_sampler * pdf1d_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 41 of file pdf1d_epanech_kernel_pdf.cxx.

double pdf1d_epanech_kernel_pdf::operator() ( double x ) const [virtual]

Probability density at x.

Reimplemented from pdf1d_pdf.
Definition at line 52 of file pdf1d_epanech_kernel_pdf.cxx.

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

Position of the i'th peak.

Definition at line 51 of file pdf1d_pdf.h.

void pdf1d_epanech_kernel_pdf::print_summary ( vcl_ostream & os ) const [virtual]

Print class to os.

Reimplemented from pdf1d_kernel_pdf.
Definition at line 190 of file pdf1d_epanech_kernel_pdf.cxx.

void pdf1d_kernel_pdf::set_centres ( const vnl_vector< double > & x,

const vnl_vector< double > & width

) [virtual, inherited]

Initialise so all kernels have given width.

Reimplemented in pdf1d_weighted_kernel_pdf.
Definition at line 49 of file pdf1d_kernel_pdf.cxx.

void pdf1d_kernel_pdf::set_centres ( const vnl_vector< double > & x,

double width

) [virtual, inherited]

Initialise so all kernels have the same width.

Reimplemented in pdf1d_weighted_kernel_pdf.
Definition at line 34 of file pdf1d_kernel_pdf.cxx.

void pdf1d_pdf::set_mean ( double m ) [inline, protected, inherited]

Reimplemented in pdf1d_gaussian.
Definition at line 31 of file pdf1d_pdf.h.

void pdf1d_pdf::set_variance ( double v ) [inline, protected, inherited]

Definition at line 32 of file pdf1d_pdf.h.

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

Variance of each dimension.

Definition at line 45 of file pdf1d_pdf.h.

short pdf1d_epanech_kernel_pdf::version_no ( ) const

Version number for I/O.

Reimplemented from pdf1d_kernel_pdf.
Definition at line 171 of file pdf1d_epanech_kernel_pdf.cxx.

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

Width of each kernel.

Definition at line 58 of file pdf1d_kernel_pdf.h.

bool pdf1d_pdf::write_plot_file ( const vcl_string & plot_file,

double min_x,

double max_x,

int n

) const [inherited]

Write values (x,p(x)) to text file suitable for plotting.
Evaluate pdf at n points in range [min_x,max_x] and write a text file, each line of which is {x p(x)}, suitable for plotting with many graph packages
Definition at line 141 of file pdf1d_pdf.cxx.

Member Data Documentation

bool pdf1d_kernel_pdf::all_same_width_ [protected, inherited]

True if all kernels have the same width.

Definition at line 38 of file pdf1d_kernel_pdf.h.

vcl_vector<int> pdf1d_kernel_pdf::index_ [mutable, protected, inherited]

Workspace.
If non-empty x_(index[i]) <= x_(index[i+1])
Definition at line 35 of file pdf1d_kernel_pdf.h.

vnl_vector<double> pdf1d_kernel_pdf::width_ [protected, inherited]

Width of each kernel.

Definition at line 31 of file pdf1d_kernel_pdf.h.

vnl_vector<double> pdf1d_kernel_pdf::x_ [protected, inherited]

Position of kernel centres.

Definition at line 28 of file pdf1d_kernel_pdf.h.

The documentation for this class was generated from the following files:

contrib/mul/pdf1d/pdf1d_epanech_kernel_pdf.h
contrib/mul/pdf1d/pdf1d_epanech_kernel_pdf.cxx

Generated on Thu Jan 10 14:43:20 2008 for contrib/mul/pdf1d by

1.4.4


Public Member Functions
	pdf1d_epanech_kernel_pdf ()
	Dflt ctor.
	pdf1d_epanech_kernel_pdf (int n, double sep, double width)
	Define n kernels centred at i*sep (i=0.
virtual	~pdf1d_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.
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.
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.
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.
Protected Member Functions
void	set_mean (double m)
void	set_variance (double v)
Protected Attributes
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.