v0.3.19/examples/OneDimension.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# One-Dimensional Cases\n",
    "\n",
    "*You are seeing the\n",
    "notebook output generated by\n",
    "[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n",
    "[Julia source file](https://github.com/JuliaOptimalTransport/OptimalTransport.jl/blob/master/examples/OneDimension/script.jl).\n",
    "The rendered HTML can be viewed [in the docs](https://juliaoptimaltransport.github.io/OptimalTransport.jl/dev/examples/OneDimension/).*"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The 1D case in Optimal Transport is a special case where one can\n",
    "easily obtain closed form solutions efficiently\n",
    "when the cost function is convex. In this situation,\n",
    "one does no need to use Linear Programming solvers\n",
    "to obtain the exact solution to the problem."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Packages\n",
    "\n",
    "We load the following packages into our environment:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using OptimalTransport\n",
    "using Distances\n",
    "using Distributions\n",
    "using StatsPlots\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "\n",
    "Random.seed!(1234);"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Continuous Distribution\n",
    "\n",
    "In the 1D case, when the source measure $\\mu$ is continuous and the cost function\n",
    "has the form ``c(x, y) = h(|x - y|)`` where ``h`` is a convex function,\n",
    "the optimal transport plan is the Monge map\n",
    "$$\n",
    "T = F_\\nu^{-1} \\circ F_\\mu\n",
    "$$\n",
    "where ``F_\\mu`` is the cumulative distribution function of `μ` and ``F_\\nu^{-1}`` is the\n",
    "quantile function of `ν`.\n",
    "In this setting, the optimal transport cost can be computed as\n",
    "$$\n",
    "\\int_0^1 c(F_\\mu^{-1}(x), F_\\nu^{-1}(x)) \\mathrm{d}x\n",
    "$$\n",
    "where ``F_\\mu^{-1}`` and ``F_\\nu^{-1}`` are the quantile functions of `μ` and `ν`,\n",
    "respectively.\n",
    "\n",
    "We start by defining the distributions."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "μ = Normal(0, 1)\n",
    "\n",
    "N = 10\n",
    "ν = Poisson(N);"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "Nest, we define a cost function."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "c(x, y) = (abs(x - y))^2 # could have used `sqeuclidean` from `Distances.jl`\n",
    "\n",
    "T = ot_plan(c, μ, ν);"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "`T` is the Monge Map. Let's visualize it."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=3}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "p1 = plot(μ; label='μ')\n",
    "p1 = plot!(ν; marker=:circle, label='ν')\n",
    "p2 = plot(-2:0.1:2, T(-2:0.1:2); label=\"Monge map\", color=:green, legend=:topleft)\n",
    "plot(p1, p2)"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "The optimal transport cost can be computed with"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "104.72027014853339"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "ot_cost(c, μ, ν)"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "If instead you want the 2-Wasserstein distance (which is the square root\n",
    "of the optimal transport with the Square Euclidean distatce, then use"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "10.233292243874079"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "cell_type": "code",
   "source": [
    "wasserstein(μ, ν; p=2)"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Finite Discrete Distributions\n",
    "\n",
    "If the source and target measures are 1D finite discrete distributions\n",
    "(sometimes referred as empirical distributions, or as sample distributions),\n",
    "and if the cost function is convex, then the optimal\n",
    "transport plan can be written as a sorting algorithm,\n",
    "where the utmost left probability mass of the source is transported\n",
    "to the closest probability mass of the target, until everything is transported.\n",
    "\n",
    "Define your measures as DiscreteNonParametric, which is a type in Distributions.jl.\n",
    "Also, let's assume both point masses with equal weights and let's\n",
    "use the `sqeuclidean` function instead of creating our own cost function."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "M = 15\n",
    "μ = DiscreteNonParametric(1.5rand(M), fill(1 / M, M))\n",
    "\n",
    "N = 10\n",
    "ν = DiscreteNonParametric(1.5rand(N) .+ 2, fill(1 / N, N))\n",
    "\n",
    "γ = ot_plan(sqeuclidean, μ, ν);"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "This time γ is a sparse matrix containing the transport plan. Let's visualize the results.\n",
    "We create a function `curve` just as a helper to draw the transport plan."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌ Warning: Assignment to `p` in soft scope is ambiguous because a global variable by the same name exists: `p` will be treated as a new local. Disambiguate by using `local p` to suppress this warning or `global p` to assign to the existing global variable.\n",
      "└ @ string:15\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=26}",
      "image/png": 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       "  1832.62,446.9 1844.38,448.373 1856.15,450.201 1867.91,452.383 1879.68,454.919 1891.44,457.81 1903.21,461.054 1914.97,464.653 1926.74,468.606 1938.5,472.914 \n",
       "  1950.27,477.575 1962.03,482.591 1973.79,487.961 1985.56,493.685 1997.32,499.763 2009.09,506.196 2020.85,512.983 2032.62,520.124 2044.38,527.619 2056.15,535.469 \n",
       "  2067.91,543.673 2079.68,552.231 2091.44,561.143 2103.21,570.409 2114.97,580.03 2126.74,590.005 2138.5,600.334 2150.26,611.017 2162.03,622.055 2173.79,633.446 \n",
       "  2185.56,645.192 2197.32,657.292 2209.09,669.747 2220.85,682.556 2232.62,695.718 2244.38,709.235 2256.15,723.107 2267.91,737.332 2279.68,751.912 2291.44,766.846 \n",
       "  \n",
       "  \"/>\n",
       "<path clip-path=\"url(#clip230)\" d=\"\n",
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      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "function curve(x1, x2, y1, y2)\n",
    "    a = min(y1, y2)\n",
    "    b = (y1 - y2 + a * (x1^2 - x2^2)) / (x1 - x2)\n",
    "    c = y1 + a * x1^2 - b * x1\n",
    "    f(x) = -a * x^2 + b * x + c\n",
    "    return f\n",
    "end\n",
    "\n",
    "p = plot(μ; marker=:circle, label='μ')\n",
    "p = plot!(ν; marker=:circle, label='ν', ylims=(0, 0.2))\n",
    "for i in 1:M, j in 1:N\n",
    "    if γ[i, j] > 0\n",
    "        transport = curve(μ.support[i], ν.support[j], 1 / M, 1 / N)\n",
    "        x = range(μ.support[i], ν.support[j]; length=100)\n",
    "        p = plot!(x, transport.(x); color=:green, label=nothing, alpha=0.5)\n",
    "    end\n",
    "end\n",
    "p"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "Again, the optimal transport cost can be calculated with"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "3.2925430197981305"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "cell_type": "code",
   "source": [
    "ot_cost(sqeuclidean, μ, ν)"
   ],
   "metadata": {},
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
 ],
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