Basis: Basis

In nschaefer1211/OSE: Orthogonal Series Density Estimation

Description

This class creates a basis of length d, which generates a d-dimensional linear subspace of L^2[0,1]. Specifically, a trigonometric basis and a histogramm basis are provided as options.

Details

Note that the parent class Basis is merely there for construction purposes. An object generated by Basis$new(d) is not of much use to the user. Therefore one should always generat an object of a subclass of Basis, i.e. an object of class Trig_Basis or Hist_Basis

Usage

trig_bas <- Trig_Basis$new(d)
hist_bas <- Hist_Basis$new(d)


trig_bas$get_function(j)
trig_bas$dimension
hist_bas$get_function(j)
hist_bas$dimension

Arguments

d

a natural number which specifies the dimension of the subsapce generated by the object of class basis.

j

a natural number smaller or equal to d which specifies which basis function is returned.

Methods

$new() generates a new Basis object dependent on the input d.

$get_function() returns the jth basis function j.

$dimension returns the dimension of the vector space generated by the object of the class.

Examples

trig_bas <- Trig_Basis$new(10)
trig_bas$get_function(4)
trig_bas

hist_bas <- Hist_Basis$new(10)
hist_bas$get_function(5)
hist_bas

nschaefer1211/OSE documentation built on Dec. 31, 2020, 12:59 a.m.