{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted sum of Dirac Measures "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using TensorDec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Series with 3 variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = @ring x1 x2 x3\n",
    "n = length(x)\n",
    "r = 4;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random weights in $[0,1]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " 0.10310570990285539\n",
       " 0.659237146402671  \n",
       " 0.42854695858385483\n",
       " 0.9028954619877378 "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w0 = rand(Float64,r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random points in $[0,1]^n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×4 Array{Float64,2}:\n",
       " 0.894353  0.723909  0.847517   0.243868\n",
       " 0.621765  0.474676  0.889351   0.234888\n",
       " 0.448695  0.324577  0.0910113  0.929199"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xi0 = rand(Float64,n,r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "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"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mt = moment(w0, Xi0)\n",
    "s = series(mt, monoms(x, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decomposition of the series from its terms up to degree 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "w, Xi = decompose(s);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " 0.4285469585838939 \n",
       " 0.10310570990277962\n",
       " 0.6592371464026707 \n",
       " 0.9028954619877747 "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×4 Array{Float64,2}:\n",
       " 0.847517   0.894353  0.723909  0.243868\n",
       " 0.889351   0.621765  0.474676  0.234888\n",
       " 0.0910113  0.448695  0.324577  0.929199"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "name": "julia-1.0"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
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