{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bc14beac",
   "metadata": {},
   "source": [
    "# Wasserstein Barycenters of Gaussian Mixture Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7152202",
   "metadata": {},
   "source": [
    "In this notebook we demonstrate how we can compute {class}`~ott.solvers.linear.continuous_barycenter.WassersteinBarycenter` of mixtures of {class}`~ott.tools.gaussian_mixture.gaussian.Gaussian`s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88cd6ac2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "if \"google.colab\" in sys.modules:\n",
    "    !pip install -q git+https://github.com/ott-jax/ott@main"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d2799c24",
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import LogNorm\n",
    "\n",
    "from ott.geometry import costs\n",
    "from ott.problems.linear import barycenter_problem\n",
    "from ott.solvers.linear import continuous_barycenter\n",
    "from ott.tools.gaussian_mixture import gaussian_mixture"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "603a2cd7",
   "metadata": {},
   "source": [
    "## Generate the Gaussian Mixture Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f867aca0",
   "metadata": {},
   "source": [
    "First, we randomly generate the $d$ dimensional mixtures of Gaussians. \n",
    "\n",
    "For each GMM we chose a ridge $c \\in \\mathbb{R}^d$ for the means of the components and a parameter $s>0$ that affects the covariance matrices of the components.\n",
    "\n",
    "The means of the components of a GMM are generated as:\n",
    "\n",
    "$$\\mu = mu + c,$$\n",
    "\n",
    "where $u$ is obtained as $d$ samples from the normal distribution, $c \\in \\mathbb{R}^d$ and $m=0.1\\frac{1}{d} \\sum_{i=1}^d c_i$. \n",
    "\n",
    "The covariance matrices are generated using the eigendecomposition:\n",
    "\n",
    "$$C=U \\Lambda U^{\\top},$$\n",
    "\n",
    "where $U \\in \\mathbb{R}^{d \\times d}$ is a randomly generated orthogonal matrix and $\\Lambda$ is the diagonal matrix with elements of the diagonal the randomly generated eigenvalues:\n",
    "\n",
    "$$\\lambda = s e^h,$$\n",
    "\n",
    "where $h$ is obtained as $d$ samples from the normal distribution and $s>0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9ce4856",
   "metadata": {},
   "source": [
    "The weights of the $K$ components of the GMM are generated as:\n",
    "\n",
    "$$w_k = \\frac{e^{a_k}}{\\sum_{k=1}^K e^{a_k}} \\forall k,$$\n",
    "\n",
    "where $a_k=0.1*v_K$ and $v_k$ follows the normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e25d363",
   "metadata": {},
   "source": [
    "We generate three GMMs, each composed of a different number of components. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b9ccbb51",
   "metadata": {},
   "outputs": [],
   "source": [
    "dim = 2  # the dimension of the Gaussians\n",
    "n_components = (2, 3, 5)  # the number of components of the GMMs\n",
    "# the number of GMMs whose barycenter will be computed\n",
    "n_gmms = len(n_components)\n",
    "epsilon = 0.1  # the entropy regularization parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89a59ccb",
   "metadata": {},
   "source": [
    "The barycentric weights determine how much each {class}`~ott.tools.gaussian_mixture.gaussian_mixture.GaussianMixture` will contribute to the {class}`~ott.solvers.linear.continuous_barycenter.WassersteinBarycenter` computation. Since these weights must sum to one, we generate them by sampling Dirichlet random values. Larger values of the concentration parameter $\\alpha$ lead to barycentric weights that are more uniform. Smaller values of $\\alpha$ will result to certain GMMs contributing significantly more than others to the barycenter computation.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "53bf20b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    }
   ],
   "source": [
    "# generate the pseudo-random keys that will be needed\n",
    "key = jax.random.PRNGKey(seed=0)\n",
    "keys = jax.random.split(key, num=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d48c7e8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 50.0  # the concentration parameter of Dirichlet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bc7f8af4",
   "metadata": {},
   "outputs": [],
   "source": [
    "barycentric_weights = jax.random.dirichlet(\n",
    "    keys[0], alpha=jnp.ones(n_gmms) * alpha\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3e2b2cd6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the seeds for the random generation of each measure.\n",
    "seeds = jax.random.randint(keys[1], shape=(n_gmms,), minval=0, maxval=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12a43944",
   "metadata": {},
   "source": [
    "We set the offsets $c$ for each GMM to be different so that they can be easily visualized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2cbb4efe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Offsets for the means of each GMM\n",
    "cs = jnp.array([[-20, -15], [60, -15], [50, 65]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3c2d0cec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0c7829ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "ms = 0.1 * jnp.mean(cs, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "86ab5b36",
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameter that controls the covariance matrices\n",
    "ss = jnp.array([4, 3, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9bd26384",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert cs.shape[0] == n_gmms\n",
    "assert ss.size == n_gmms\n",
    "assert seeds.size == n_gmms\n",
    "assert len(n_components) == n_gmms\n",
    "assert jnp.mean(cs, axis=1).all() > 0\n",
    "assert ss.all() > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "82a461e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "gmm_generators = [\n",
    "    gaussian_mixture.GaussianMixture.from_random(\n",
    "        jax.random.PRNGKey(seeds[i]),\n",
    "        n_components=n_components[i],\n",
    "        n_dimensions=dim,\n",
    "        stdev_cov=ss[i],\n",
    "        stdev_mean=ms[i],\n",
    "        ridge=cs[i],\n",
    "    )\n",
    "    for i in range(n_gmms)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1c7566e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the means and covariances of the GMMs\n",
    "means_covs = [\n",
    "    (gmm_generators[i].loc, gmm_generators[i].covariance) for i in range(n_gmms)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6cafd87d",
   "metadata": {},
   "outputs": [],
   "source": [
    "means_and_covs_to_x = jax.vmap(costs.mean_and_cov_to_x, in_axes=[0, 0, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5d746c32",
   "metadata": {},
   "outputs": [],
   "source": [
    "# stack the concatenated means and (raveled) covariances of the pointclouds\n",
    "ys = jnp.vstack(\n",
    "    means_and_covs_to_x(means_covs[i][0], means_covs[i][1], dim)\n",
    "    for i in range(n_gmms)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "eb718f6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the weights of the randomly generated GMMs\n",
    "weights = [gmm_generators[i].component_weight_ob.probs() for i in range(n_gmms)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "91700d09",
   "metadata": {},
   "outputs": [],
   "source": [
    "# stack the weights of the GMMs\n",
    "bs = jnp.hstack(jnp.asarray(weights[i]) for i in range(n_gmms))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a87beb4",
   "metadata": {},
   "source": [
    "## Compute the Wasserstein barycenter of the GMMs\n",
    "\n",
    "We can now compute the barycenter of the input GMMs. We determine the size of the barycenter and solve the barycenter problem. We must ensure that the initialization of the {class}`~ott.problems.linear.barycenter_problem.BarycenterProblem` is such that its covariance matrices are positive semidefinite. We therefore initialize the barycenter as a random {class}`~ott.tools.gaussian_mixture.gaussian_mixture.GaussianMixture`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1c178f92",
   "metadata": {},
   "outputs": [],
   "source": [
    "# determine the size of the barycenter.\n",
    "bar_size = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d4bfa77c",
   "metadata": {},
   "outputs": [],
   "source": [
    "gmm_generator = gaussian_mixture.GaussianMixture.from_random(\n",
    "    keys[2], n_components=bar_size, n_dimensions=dim\n",
    ")\n",
    "\n",
    "x_init_means = gmm_generator.loc\n",
    "x_init_covs = gmm_generator.covariance\n",
    "\n",
    "x_init = means_and_covs_to_x(x_init_means, x_init_covs, dim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "85428ed6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create an instance of the Bures cost class.\n",
    "b_cost = costs.Bures(dimension=dim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bd016819",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a barycenter problem.\n",
    "bar_p = barycenter_problem.BarycenterProblem(\n",
    "    y=ys,\n",
    "    b=bs,\n",
    "    weights=barycentric_weights,\n",
    "    num_per_segment=n_components,\n",
    "    cost_fn=b_cost,\n",
    "    epsilon=epsilon,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5dba3154",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a Wasserstein barycenter solver.\n",
    "solver = continuous_barycenter.WassersteinBarycenter(lse_mode=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5702e303",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the barycenter.\n",
    "out = solver(bar_p, bar_size=bar_size, x_init=x_init)\n",
    "barycenter = out.x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "587f463a",
   "metadata": {},
   "source": [
    "Now that we have computed the barycenter, we can extract the means and the covariances of its components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1162408b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract the means and covariances of the barycenter.\n",
    "means_bary, covs_bary = costs.x_to_means_and_covs(barycenter, dim)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80741af9",
   "metadata": {},
   "source": [
    "## Visualize the results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "742a6785",
   "metadata": {},
   "source": [
    "We consider a discretization grid in 2D in order to plot the negative probabilities of points under the considered GMMs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e2d51265",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the grid\n",
    "x1 = np.linspace(-30.0, 90.0)\n",
    "x2 = np.linspace(-30.0, 90.0)\n",
    "x, y = np.meshgrid(x1, x2)\n",
    "grid = np.array([x.ravel(), y.ravel()]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "101063de",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the negative log probabilities of the GMMs at the grid.\n",
    "n_log_probs = jnp.asarray(\n",
    "    [-gmm_generators[i].log_prob(grid) for i in range(n_gmms)]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "1f779128",
   "metadata": {},
   "outputs": [],
   "source": [
    "weights_bary = jnp.ones(bar_size) / bar_size"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49af2e5f",
   "metadata": {},
   "source": [
    "We now create a {class}`~ott.tools.gaussian_mixture.gaussian_mixture.GaussianMixture` object using the means and covarinces of the computed barycenter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "67b141a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the negative log probabilities at the grid under the barycenter GMM.\n",
    "gmm_generator_bary = (\n",
    "    gaussian_mixture.GaussianMixture.from_mean_cov_component_weights(\n",
    "        mean=means_bary, cov=covs_bary, component_weights=weights_bary\n",
    "    )\n",
    ")\n",
    "\n",
    "# compute the negative log probabilities of the barycenter at the grid.\n",
    "n_log_prob_bary = -gmm_generator_bary.log_prob(grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b249681b",
   "metadata": {},
   "source": [
    "We visualize the three GMMs and their barycenter by plotting the negative log probabilities at the considered grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c7403b2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# reshape the log probabilities in order to plot.\n",
    "n_log_probs = n_log_probs.reshape((n_gmms, x.shape[0], x.shape[1]))\n",
    "n_log_prob_bary = n_log_prob_bary.reshape((x.shape[0], x.shape[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1258a9ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "for i in range(n_gmms):\n",
    "    _ = plt.contour(\n",
    "        x,\n",
    "        y,\n",
    "        n_log_probs[i, :, :],\n",
    "        norm=LogNorm(vmin=1.0, vmax=10.0),\n",
    "        levels=np.logspace(0, 1, 10),\n",
    "    )\n",
    "_ = plt.contour(\n",
    "    x,\n",
    "    y,\n",
    "    n_log_prob_bary,\n",
    "    norm=LogNorm(vmin=1.0, vmax=10.0),\n",
    "    levels=np.logspace(0, 1, 10),\n",
    ")\n",
    "plt.annotate(\"First GMM\", (-25, 0), fontsize=16)\n",
    "plt.annotate(\"Second GMM\", (50, -8), fontsize=16)\n",
    "plt.annotate(\"Third GMM\", (40, 78), fontsize=16)\n",
    "plt.annotate(\"Barycenter\", (20, 30), fontsize=16)\n",
    "\n",
    "plt.title(\"Three GMMs and their barycenter\", fontsize=20)\n",
    "plt.axis(\"tight\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}