Weighted sum of Dirac Measures
using TensorDec
Series with 3 variables
x = @ring x1 x2 x3
n = length(x)
r = 4;
Random weights in $[0,1]$
w0 = rand(Float64,r)
4-element Array{Float64,1}:
0.10310570990285539
0.659237146402671
0.42854695858385483
0.9028954619877378
Random points in $[0,1]^n$
Xi0 = rand(Float64,n,r)
3×4 Array{Float64,2}:
0.894353 0.723909 0.847517 0.243868
0.621765 0.474676 0.889351 0.234888
0.448695 0.324577 0.0910113 0.929199
Moment function of the sum of the Dirac measures of the points $\Xi_0$ with weights $\omega_0$ and its generating series up to degree 3.
mt = moment(w0, Xi0)
s = series(mt, monoms(x, 3))
0.4339257411626396dx1*dx3 + 0.9702397337601841dx2 + 1.1382083719944895dx3 + 0.6585957641575078dx1*dx2 + 0.756553791183631dx3^3 + 0.14323371231850154dx2^2dx3 + 0.5978228622857406dx1^3 + 0.40844393047707755dx2^3 + 0.36208356970237654dx2*dx3 + 0.5016353149729792dx1^2dx2 + 0.17670723666808152dx1*dx2*dx3 + 0.7894555317442516dx1^2 + 0.8733277036829585dx3^2 + 1.1528284153895243dx1 + 0.5771697834203546dx2^2 + 0.22704558514092504dx1^2dx3 + 0.2619613422143817dx1*dx3^2 + 0.4425968864300194dx1*dx2^2 + 0.2321415223320108dx2*dx3^2 + 2.093785276877119
Decomposition of the series from its terms up to degree 3.
w, Xi = decompose(s);
w
4-element Array{Float64,1}:
0.4285469585838939
0.10310570990277962
0.6592371464026707
0.9028954619877747
Xi
3×4 Array{Float64,2}:
0.847517 0.894353 0.723909 0.243868
0.889351 0.621765 0.474676 0.234888
0.0910113 0.448695 0.324577 0.929199