{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Session: Entropic Optimal Transport\n",
    "\n",
    "In this practical session, we will consider the problem of optimal transport with entropic regularization. We will implement the Sinkhorn algorithm and apply it to some simple examples.\n",
    "\n",
    "**Instructions**\n",
    "- You should submit one single Jupyter notebook with the name **`2025-OT-2-Name1-Name2-Name3.ipynb`**, where **Name1**, **Name2**, and **Name3** are the last names of the three members of your trinom. \n",
    "- You need to submit it by email before **November 18th 2025, 13:59:59** with the subject **`2025-OT-2-Name1-Name2-Name3`** at **`samuel.vaiter@cnrs.fr`**. *No other subject allowed (otherwise grade = 0.)*\n",
    "- You are required to write your code in Python, using the NumPy library, and the theoretical questions should be answered using LaTeX.\n",
    "- (If this rule is not followed ⇒ **grade = 0**.) You **can** use ChatGPT or other AI assistants, but are **required** to state it clearly, e.g,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We are going to use Numpy and Matplotlib for this practical.\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropic Optimal Transport: Definitions and Notation\n",
    "\n",
    "Given two histograms $(a, b) \\in \\Sigma_n \\times \\Sigma_m$ (the sets of histograms of size $n, m$), the problem of entropic optimal transport can be expressed as finding a coupling matrix $P \\in \\mathbb{R}^{n \\times n}$ that minimizes the cost function:\n",
    "\n",
    "$$ \\min_{P \\in U(a, b)} \\langle C, P \\rangle - \\epsilon H(P), $$\n",
    "\n",
    "where:\n",
    "- $U(a, b)$ represents the set of couplings between $a$ and $b$,\n",
    "- $C_{ij}$ denotes the cost matrix,\n",
    "- $\\langle C, P \\rangle = \\sum_{i=1}^n \\sum_{j=1}^n P_{ij} C_{ij}$ is the scalar product between $C$ and $P$,\n",
    "- $H(P) = - \\sum_{i=1}^n \\sum_{j=1}^n P_{ij} \\log P_{ij}$ is the entropy of the coupling matrix $P$, with the convention $0 \\log 0 = 0$.\n",
    "- $\\epsilon > 0$ is a regularization parameter controlling the influence of entropy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Point cloud transportation\n",
    "\n",
    "**Question 1** Generate two 2D point clouds $(x_i)_i, (y_j)_j$ of different sizes $n, m$ such that one point cloud lies inside the other. Plot both point clouds to visualize their relative positions.\n",
    "\n",
    "You _could_ generate the inner one with a uniform law, and the outer one on annulus (uniform law on the radius and the angle)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2**\n",
    "\n",
    "1. Compute the Euclidean cost matrix $C$ between the two point clouds. The cost between two points $x_i$ and $y_j$ can be defined as the Euclidean distance between them.\n",
    "\n",
    "2. Define the **empirical** histograms $a, b$ associated with the two point clouds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3** Write a function `sinkhorn` that takes as input the cost matrix $C$, the histograms $a,b$, the regularization parameter $\\epsilon$, and the number of iterations `n_iter`, and returns the optimal coupling matrix $P$ and the dual variables $u, v$.\n",
    "\n",
    "You should also (optionally) keep in memory the constraints violations at each iteration $\\|Pu - a\\|_1$ and $\\|P^T v - b\\|_1$. Display a plot of these two quantities as a function of the iteration number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 4** Display the optimal coupling matrix $P$ as an image. Do it for several values of $\\epsilon$. What do you observe? What can you say about the structure of the optimal coupling matrix?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 5** Keep only the highest entries of the coupling matrix and use them to draw a map between the two clouds. First, draw \"strong\" connections, i.e., links $(i, j)$ corresponding to large values of $P_{i,j}$. Then, draw weaker connections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimal transport between Gaussian histograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 6**  Write a Python code snippet to create two normalized Gaussian distributions, centered at different locations with added noise for regularization. Each distribution should be normalized so that their sum equals 1. Use $\\sigma = 0.06$ for the standard deviation, and the Gaussian distributions should be centered at 0.25 and 0.8. Add a minimum value of 0.02 times the maximum of each distribution before normalization. Display them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 7** Using as Gibbs kernel the Gaussian kernel, implement the Sinkhorn algorithm for the optimal transport problem with the two Gaussian distributions defined above. Plot the optimal coupling matrix for different values of $\\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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