manual_gp_toy.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iHt8kepLXOTG",
        "outputId": "946731f4-966a-4f5a-ad55-9a412c6d2da9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
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          ]
        }
      ],
      "source": [
        "!pip install jaxopt\n",
        "!pip install ott-jax"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "i3wErVmOdylu"
      },
      "outputs": [],
      "source": [
        "import jax\n",
        "from jax.scipy.sparse.linalg import gmres\n",
        "from jax.lax import custom_linear_solve\n",
        "from jax.numpy.linalg import slogdet\n",
        "import jax.numpy as jnp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j7ZlM04LLYrM"
      },
      "outputs": [],
      "source": [
        "# again, this only works on startup!\n",
        "from jax.config import config\n",
        "config.update(\"jax_enable_x64\", True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mDyyoNUMsdW5"
      },
      "source": [
        "## GP Process Regression"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "G8YHrf6scYa7"
      },
      "outputs": [],
      "source": [
        "def gp_regression_likelihood(Kxx, y, lbda):\n",
        "  \"\"\" Compute Gaussian Process regression.\n",
        "  \n",
        "  Source: https://math.stackexchange.com/questions/1030534/gradients-of-marginal-likelihood-of-gaussian-process-with-squared-exponential-co\n",
        "\n",
        "  -0.5 log det (K) - 0.5 y^t K_inv y - N/2 log 2pi\n",
        "  with K_inv = K^{-1}\n",
        "  \n",
        "  Consistency of K required to ensure the inverse exists.  \n",
        "  \"\"\"\n",
        "  # data fitting term\n",
        "  tol = 1e-7\n",
        "  maxiter = 5000\n",
        "\n",
        "  def matvec_Kxx(b):\n",
        "    return jnp.dot(Kxx, b) + (lbda**2)*b\n",
        "  \n",
        "  def solver_fun(matvec, b):\n",
        "    return jax.scipy.sparse.linalg.cg(matvec, b, tol=tol, maxiter=maxiter)[0]\n",
        "  \n",
        "  K_inv_y = custom_linear_solve(matvec_Kxx, y, solve=solver_fun, symmetric=True)\n",
        "  y_K_inv_y = - 0.5 * jnp.dot(y, K_inv_y)\n",
        "\n",
        "  # cste : play no role in optimization\n",
        "  N = y.shape[0]\n",
        "  cste = - 0.5 * N * jnp.log(2 * jnp.pi)\n",
        "\n",
        "  # regularization\n",
        "  # derivative: https://github.com/google/jax/blob/de464fcf22c8bf7a2931182f8095bc01530df9fe/jax/_src/numpy/linalg.py#L190\n",
        "  sign, log_abs_det = slogdet(Kxx + + (lbda**2)*jnp.eye(len(Kxx))) \n",
        "  log_det_value = - 0.5 * log_abs_det\n",
        "  \n",
        "  log_marginal_likelihood = log_det_value + y_K_inv_y + cste\n",
        "  return log_marginal_likelihood"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "THuLMnAK3wT8"
      },
      "outputs": [],
      "source": [
        "# Based on https://arxiv.org/pdf/2009.10862.pdf\n",
        "# \"An Intuitive Tutorial to Gaussian Processes Regression\"\n",
        "\n",
        "def gp_process_prediction(kernel_fun, kernel_params, X_train, X_test, Y_train, lbda):\n",
        "  \"\"\"Cheap implementation of GP prediction based on Kernel matrix inverse.\"\"\"\n",
        "  X = jnp.concatenate([X_train, X_test], axis=0)\n",
        "  K = kernel_fun(X, kernel_params)\n",
        "  train_sl = slice(None, len(X_train), None)\n",
        "  test_sl = slice(len(X_train), None, None)\n",
        "\n",
        "  Kxx = K[train_sl,train_sl] + (lbda**2)*jnp.eye(len(X_train))\n",
        "  inv_Kxx = jnp.linalg.inv(Kxx)\n",
        "  Kzx = K[test_sl,train_sl]\n",
        "  \n",
        "  Y_pred = Kzx @ (inv_Kxx @ Y_train)\n",
        "  Y_covar = K[test_sl,test_sl] - Kzx @ inv_Kxx @ Kzx.T\n",
        "  Y_var = jnp.diag(Y_covar)\n",
        "  return Y_pred, Y_var"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KBrBnbKtdF0P"
      },
      "outputs": [],
      "source": [
        "from jaxopt import OptaxSolver, LBFGS\n",
        "import optax\n",
        "from jaxopt.tree_util import tree_map, tree_sum, tree_sub, tree_scalar_mul, tree_add\n",
        "\n",
        "def log_barrier(params, bounds):\n",
        "  l_bounds, u_bounds = bounds\n",
        "  clipped = tree_map(jnp.clip, params, l_bounds, u_bounds)\n",
        "  eps_leaves = tree_scalar_mul(1e-3, tree_sub(u_bounds, l_bounds))\n",
        "  l_loss = tree_map(lambda leaf, l, eps: jnp.log(leaf - l + eps), clipped, l_bounds, eps_leaves)\n",
        "  u_loss = tree_map(lambda leaf, u, eps: jnp.log(u - leaf + eps), clipped, u_bounds, eps_leaves)\n",
        "  loss = tree_sum(tree_add(l_loss, u_loss))\n",
        "  return loss\n",
        "\n",
        "\n",
        "def optimize_gpr(kernel_fun, log_bounds, X_train, X_test, y_train, y_test, lbda,\n",
        "                 maxiter=1000, tol=1e-3, projected=False, verbose=False):\n",
        "  bounds = tuple(map(lambda d: {('log_'+k):jnp.log(v) for k, v in d.items()}, log_bounds))\n",
        "  kernel_params = kernel_fun.init_log_params()\n",
        "\n",
        "  def gpr_step(kernel_params):\n",
        "    if projected:\n",
        "      kernel_params = tree_map(jnp.clip, kernel_params, bounds[0], bounds[1])\n",
        "    Kxx = kernel_fun(X_train, kernel_params)\n",
        "    loss = -gp_regression_likelihood(Kxx, y_train, lbda)\n",
        "    return loss, Kxx\n",
        "\n",
        "  # optax_opt = optax.sgd(learning_rate=1e-2)\n",
        "  # opt = OptaxSolver(fun=gpr_step, opt=optax_opt, has_aux=True, maxiter=maxiter, tol=tol)\n",
        "  opt = LBFGS(fun=gpr_step, has_aux=True, maxiter=maxiter, tol=tol, maxls=20)\n",
        "  \n",
        "  if verbose:\n",
        "\n",
        "    state = opt.init_state(kernel_params)\n",
        "\n",
        "    @jax.jit\n",
        "    def opt_update(kernel_params, state):\n",
        "      return opt.update(kernel_params, state)\n",
        "\n",
        "    for step in range(maxiter):\n",
        "      kernel_params, state = opt_update(kernel_params, state)\n",
        "      if projected:\n",
        "        kernel_params = tree_map(jnp.clip, kernel_params, bounds[0], bounds[1])\n",
        "      Kxx = state.aux\n",
        "      preds, _ = gp_process_prediction(kernel_fun, kernel_params, X_train, X_test, y_train, lbda)\n",
        "      mse = jnp.mean((preds - y_test)**2)\n",
        "      print_params = {k: f\"{v:.3f}\" for k, v in kernel_fun.get_params(kernel_params).items()}\n",
        "      print(f\"[{step+1}] error={state.error:.3f} mse={mse:.3f} loss={state.value:.3f} params={print_params} CondNumber={jnp.linalg.cond(Kxx)}\")\n",
        "\n",
        "  else:\n",
        "    kernel_params, state = opt.run(kernel_params)\n",
        "    Kxx = state.aux\n",
        "    preds, _ = gp_process_prediction(kernel_fun, kernel_params, X_train, X_test, y_train, lbda)\n",
        "    mse = jnp.mean((preds - y_test)**2)\n",
        "    print_params = {k: f\"{v:.3f}\" for k, v in kernel_fun.get_params(kernel_params).items()}\n",
        "    print(f\"[{state.iter_num}] error={state.error:.3f} mse={mse:.3f} loss={state.value:.3f} params={print_params} CondNumber={jnp.linalg.cond(Kxx)}\")\n",
        "\n",
        "  return kernel_params"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hRx43HmisgbP"
      },
      "source": [
        "## Kernels"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ymWrxdUON-VP"
      },
      "outputs": [],
      "source": [
        "from os import X_OK\n",
        "from dataclasses import dataclass\n",
        "\n",
        "\n",
        "@dataclass\n",
        "class RBF_Kernel:\n",
        "  \"\"\" RBF Kernel class.\n",
        "\n",
        "  Attributes:\n",
        "    gamma: nature of gamma scaling (default: 'scale').\n",
        "      Mimic sklearn.svm.SVC behavior.\n",
        "      'scale': 1 / (X.var() * n_features)\n",
        "      'auto' : default value of 1\n",
        "  \"\"\"\n",
        "  gamma: str = 'scale'\n",
        "\n",
        "  def __post_init__(self):\n",
        "    if self.gamma not in ['auto', 'scale']:\n",
        "      raise ValueError(f\"Unrecognized value {self.gamma} for gamma\")\n",
        "\n",
        "  def init_log_params(self):\n",
        "    theta = jnp.array(0.)\n",
        "    inv_sigma = jnp.array(0.)\n",
        "    return {'log_theta': theta, 'log_sigma': inv_sigma}\n",
        "\n",
        "  def get_params(self, log_params):\n",
        "    return {k[len('log_'):]:jnp.exp(v) for k,v in log_params.items()}\n",
        "\n",
        "  def _set_diag_1(self, m):\n",
        "    i, j = jnp.diag_indices(len(m))\n",
        "    m = m.at[i,j].set(1.)\n",
        "    return m\n",
        "\n",
        "  def __call__(self, X, kernel_params):\n",
        "    if self.gamma == 'scale':\n",
        "      scale = jnp.var(X) * X.shape[1]  # sklearn.SVC behavior\n",
        "    elif self.gamma == 'auto':\n",
        "      scale = 1.\n",
        "    X = X / jnp.exp(kernel_params['log_sigma'])\n",
        "    energy = jnp.sum((X[:,jnp.newaxis,:] - X[jnp.newaxis,:,:])**2, axis=-1)\n",
        "    gamma = 0.5 / scale\n",
        "    K = jnp.exp(-energy * gamma)\n",
        "    K = self._set_diag_1(K)\n",
        "    K_scalar = (jnp.exp(kernel_params['log_theta'])**2) * K\n",
        "    return K_scalar"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IWG5H3T_tYVl"
      },
      "source": [
        "## GP regression tests"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "owR4FMYPtdRC",
        "outputId": "1aefac3f-43b9-45e1-d9f9-194858fb7695"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import numpy as onp\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "X = onp.linspace(start=0, stop=10, num=1_000).reshape(-1, 1)\n",
        "y = onp.squeeze(X * onp.sin(X))\n",
        "# y = (y - y.mean()) / y.std()\n",
        "\n",
        "plt.plot(X, y, label=r\"$f(x) = x \\sin(x)$\", linestyle=\"dotted\")\n",
        "plt.legend()\n",
        "plt.xlabel(\"$x$\")\n",
        "plt.ylabel(\"$f(x)$\")\n",
        "_ = plt.title(\"True generative process\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BKXOWz0bvN8p"
      },
      "outputs": [],
      "source": [
        "rng = onp.random.RandomState(1)\n",
        "training_indices = rng.choice(onp.arange(y.size), size=20, replace=False)\n",
        "X_train, y_train = X[training_indices], y[training_indices]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LfblPXAmFaal",
        "outputId": "3ff4cc0a-f5db-4844-fac7-62937731bb3b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/sklearn/gaussian_process/_gpr.py:610: ConvergenceWarning: lbfgs failed to converge (status=2):\n",
            "ABNORMAL_TERMINATION_IN_LNSRCH.\n",
            "\n",
            "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
            "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
            "  _check_optimize_result(\"lbfgs\", opt_res)\n",
            "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Condition number: 3.915460289332299e+17\n",
            "Params: 28.9**2 * RBF(length_scale=3.05)\n",
            "Log Marginal Likelihood: 67.04874239268894\n"
          ]
        }
      ],
      "source": [
        "from sklearn.gaussian_process import GaussianProcessRegressor\n",
        "from sklearn.gaussian_process.kernels import RBF\n",
        "\n",
        "sk_kernel = 1 * RBF(length_scale=1.0, length_scale_bounds=(1e-2, 1e2))\n",
        "gaussian_process = GaussianProcessRegressor(kernel=sk_kernel, n_restarts_optimizer=9)\n",
        "gaussian_process.fit(X_train, y_train)\n",
        "print('Condition number:', jnp.linalg.cond(gaussian_process.kernel_(X_train)))\n",
        "print('Params:', gaussian_process.kernel_)\n",
        "onp.set_printoptions(precision=6)\n",
        "if len(X_train) <= 10:\n",
        "  print('Kernel:', gaussian_process.kernel_(X_train))\n",
        "onp.set_printoptions(precision=4)\n",
        "print('Log Marginal Likelihood:', gaussian_process.log_marginal_likelihood_value_)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 372
        },
        "id": "ixNidTAi6xEq",
        "outputId": "1db0a975-f3e3-452d-c5be-69ad57038796"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] error=0.000 mse=4.422 loss=54.722 params={'sigma': '0.100', 'theta': '10.000'} CondNumber=9.380591633761729e+18\n"
          ]
        },
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
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            "\u001b[0;32m<ipython-input-5-d8b93db66544>\u001b[0m in \u001b[0;36moptimize_gpr\u001b[0;34m(kernel_fun, log_bounds, X_train, X_test, y_train, y_test, lbda, maxiter, tol, projected, verbose)\u001b[0m\n\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmaxiter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 40\u001b[0;31m       \u001b[0mkernel_params\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopt_update\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkernel_params\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     41\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0mprojected\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     42\u001b[0m         \u001b[0mkernel_params\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtree_map\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclip\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkernel_params\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/traceback_util.py\u001b[0m in \u001b[0;36mreraise_with_filtered_traceback\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    160\u001b[0m     \u001b[0m__tracebackhide__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    161\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 162\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    163\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    164\u001b[0m       \u001b[0mmode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfiltering_mode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/api.py\u001b[0m in \u001b[0;36mcache_miss\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    528\u001b[0m         \u001b[0mflat_fun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs_flat\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    529\u001b[0m         \u001b[0mdevice\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdevice\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbackend\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbackend\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mflat_fun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 530\u001b[0;31m         donated_invars=donated_invars, inline=inline, keep_unused=keep_unused)\n\u001b[0m\u001b[1;32m    531\u001b[0m     \u001b[0mout_pytree_def\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mout_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    532\u001b[0m     \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtree_unflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout_pytree_def\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_flat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mbind\u001b[0;34m(self, fun, *args, **params)\u001b[0m\n\u001b[1;32m   1935\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1936\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mbind\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1937\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mcall_bind\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1938\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1939\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mget_bind_params\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mcall_bind\u001b[0;34m(primitive, fun, *args, **params)\u001b[0m\n\u001b[1;32m   1951\u001b[0m   \u001b[0mtracers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtop_trace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfull_raise\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1952\u001b[0m   \u001b[0mfun_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mannotate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0min_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1953\u001b[0;31m   \u001b[0mouts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtop_trace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprocess_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprimitive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1954\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfull_lower\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mapply_todos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0menv_trace_todo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mouts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1955\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mprocess_call\u001b[0;34m(self, primitive, f, tracers, params)\u001b[0m\n\u001b[1;32m    685\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    686\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mprocess_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 687\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimpl\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    688\u001b[0m   \u001b[0mprocess_map\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprocess_call\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    689\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/dispatch.py\u001b[0m in \u001b[0;36m_xla_call_impl\u001b[0;34m(***failed resolving arguments***)\u001b[0m\n\u001b[1;32m    207\u001b[0m     \u001b[0marg_specs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'_device'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    208\u001b[0m   compiled_fun = xla_callable(fun, device, backend, name, donated_invars,\n\u001b[0;32m--> 209\u001b[0;31m                               keep_unused, *arg_specs)\n\u001b[0m\u001b[1;32m    210\u001b[0m   \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    211\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mcompiled_fun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/linear_util.py\u001b[0m in \u001b[0;36mmemoized_fun\u001b[0;34m(fun, *args)\u001b[0m\n\u001b[1;32m    293\u001b[0m       \u001b[0mfun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpopulate_stores\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstores\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    294\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 295\u001b[0;31m       \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    296\u001b[0m       \u001b[0mcache\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstores\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    297\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/dispatch.py\u001b[0m in \u001b[0;36m_xla_callable_uncached\u001b[0;34m(fun, device, backend, name, donated_invars, keep_unused, *arg_specs)\u001b[0m\n\u001b[1;32m    256\u001b[0m                            donated_invars, keep_unused, *arg_specs):\n\u001b[1;32m    257\u001b[0m   return lower_xla_callable(fun, device, backend, name, donated_invars, False,\n\u001b[0;32m--> 258\u001b[0;31m                             keep_unused, *arg_specs).compile().unsafe_call\n\u001b[0m\u001b[1;32m    259\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    260\u001b[0m \u001b[0mxla_callable\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_xla_callable_uncached\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/profiler.py\u001b[0m in \u001b[0;36mwrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    292\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    293\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mTraceAnnotation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mdecorator_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 294\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    295\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    296\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/dispatch.py\u001b[0m in \u001b[0;36mlower_xla_callable\u001b[0;34m(fun, device, backend, name, donated_invars, always_lower, keep_unused, *arg_specs)\u001b[0m\n\u001b[1;32m    301\u001b[0m                         \"for jit in {elapsed_time} sec\"):\n\u001b[1;32m    302\u001b[0m     jaxpr, out_type, consts = pe.trace_to_jaxpr_final2(\n\u001b[0;32m--> 303\u001b[0;31m         fun, pe.debug_info_final(fun, \"jit\"))\n\u001b[0m\u001b[1;32m    304\u001b[0m   \u001b[0mout_avals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkept_outputs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mutil\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munzip2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    305\u001b[0m   \u001b[0;32mif\u001b[0m \u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTracer\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mc\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mconsts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/profiler.py\u001b[0m in \u001b[0;36mwrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    292\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    293\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mTraceAnnotation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mdecorator_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 294\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    295\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    296\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/partial_eval.py\u001b[0m in \u001b[0;36mtrace_to_jaxpr_final2\u001b[0;34m(fun, debug_info)\u001b[0m\n\u001b[1;32m   2186\u001b[0m     \u001b[0mmain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjaxpr_stack\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# type: ignore\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2187\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_sublevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2188\u001b[0;31m       \u001b[0mjaxpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconsts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrace_to_subjaxpr_dynamic2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmain\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdebug_info\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2189\u001b[0m     \u001b[0;32mdel\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmain\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2190\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mjaxpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconsts\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/partial_eval.py\u001b[0m in \u001b[0;36mtrace_to_subjaxpr_dynamic2\u001b[0;34m(fun, main, debug_info)\u001b[0m\n\u001b[1;32m   2136\u001b[0m     \u001b[0min_tracers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_input_type_to_tracers\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_arg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0min_avals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2137\u001b[0m     \u001b[0min_tracers_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0min_tracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeep_inputs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mkeep\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2138\u001b[0;31m     \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcall_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0min_tracers_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2139\u001b[0m     \u001b[0mout_tracers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfull_raise\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mans\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2140\u001b[0m     \u001b[0mjaxpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconsts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mframe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_jaxpr2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout_tracers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/linear_util.py\u001b[0m in \u001b[0;36mcall_wrapped\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    166\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    167\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 168\u001b[0;31m       \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    169\u001b[0m     \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    170\u001b[0m       \u001b[0;31m# Some transformations yield from inside context managers, so we have to\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-5-d8b93db66544>\u001b[0m in \u001b[0;36mopt_update\u001b[0;34m(kernel_params, state)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mjax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjit\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mopt_update\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkernel_params\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mopt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkernel_params\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mstep\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmaxiter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jaxopt/_src/lbfgs.py\u001b[0m in \u001b[0;36mupdate\u001b[0;34m(self, params, state, *args, **kwargs)\u001b[0m\n\u001b[1;32m    260\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    261\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0muse_gamma\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 262\u001b[0;31m       \u001b[0mgamma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompute_gamma\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0ms_history\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0my_history\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprevious\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    263\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    264\u001b[0m       \u001b[0mgamma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/tree_util.py\u001b[0m in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    203\u001b[0m   \u001b[0mleaves\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtreedef\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtree_flatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtree\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_leaf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    204\u001b[0m   \u001b[0mall_leaves\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mleaves\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mtreedef\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten_up_to\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrest\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 205\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0mtreedef\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mxs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mxs\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mall_leaves\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    206\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    207\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbuild_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtreedef\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jaxopt/_src/lbfgs.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(s_history, y_history)\u001b[0m\n\u001b[1;32m    114\u001b[0m   \u001b[0;31m# Note that unlike BFGS, the initialization can change on every iteration.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    115\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 116\u001b[0;31m   \u001b[0mfun\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0ms_history\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_history\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtree_vdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_history\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mlast\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms_history\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mlast\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    117\u001b[0m   \u001b[0mnum\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtree_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtree_map\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms_history\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_history\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    118\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_rewriting_take\u001b[0;34m(arr, idx, indices_are_sorted, unique_indices, mode, fill_value)\u001b[0m\n\u001b[1;32m   3605\u001b[0m   \u001b[0mtreedef\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstatic_idx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic_idx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_split_index_for_jit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0midx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3606\u001b[0m   return _gather(arr, treedef, static_idx, dynamic_idx, indices_are_sorted,\n\u001b[0;32m-> 3607\u001b[0;31m                  unique_indices, mode, fill_value)\n\u001b[0m\u001b[1;32m   3608\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3609\u001b[0m \u001b[0;31m# TODO(phawkins): re-enable jit after fixing excessive recompilation for\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_gather\u001b[0;34m(arr, treedef, static_idx, dynamic_idx, indices_are_sorted, unique_indices, mode, fill_value)\u001b[0m\n\u001b[1;32m   3613\u001b[0m             unique_indices, mode, fill_value):\n\u001b[1;32m   3614\u001b[0m   \u001b[0midx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_merge_static_and_dynamic_indices\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtreedef\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstatic_idx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdynamic_idx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3615\u001b[0;31m   \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_index_to_gather\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0midx\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# shared with _scatter_update\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3616\u001b[0m   \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3617\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_index_to_gather\u001b[0;34m(x_shape, idx, normalize_indices)\u001b[0m\n\u001b[1;32m   3813\u001b[0m         \u001b[0;31m# XLA gives error when indexing into an axis of size 0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3814\u001b[0m         \u001b[0;32mraise\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"index is out of bounds for axis {x_axis} with size 0\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3815\u001b[0;31m       \u001b[0mi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_normalize_index\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_shape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mx_axis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnormalize_indices\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3816\u001b[0m       \u001b[0mi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconvert_element_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex_dtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3817\u001b[0m       \u001b[0mgather_indices\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgather_indices_shape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_normalize_index\u001b[0;34m(index, axis_size)\u001b[0m\n\u001b[1;32m   3488\u001b[0m   return lax.select(\n\u001b[1;32m   3489\u001b[0m     \u001b[0mlax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_lax_const\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3490\u001b[0;31m     \u001b[0mlax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis_size_val\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3491\u001b[0m     index)\n\u001b[1;32m   3492\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/lax/lax.py\u001b[0m in \u001b[0;36madd\u001b[0;34m(x, y)\u001b[0m\n\u001b[1;32m    442\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    443\u001b[0m   \u001b[0;34mr\"\"\"Elementwise addition: :math:`x + y`.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 444\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0madd_p\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbind\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    445\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    446\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0msub\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mbind\u001b[0;34m(self, *args, **params)\u001b[0m\n\u001b[1;32m    322\u001b[0m     assert (not config.jax_enable_checks or\n\u001b[1;32m    323\u001b[0m             all(isinstance(arg, Tracer) or valid_jaxtype(arg) for arg in args)), args\n\u001b[0;32m--> 324\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbind_with_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfind_top_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    325\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    326\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mbind_with_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mbind_with_trace\u001b[0;34m(self, trace, args, params)\u001b[0m\n\u001b[1;32m    325\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    326\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mbind_with_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 327\u001b[0;31m     \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprocess_primitive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfull_raise\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    328\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfull_lower\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiple_results\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mfull_lower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    329\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/partial_eval.py\u001b[0m in \u001b[0;36mprocess_primitive\u001b[0;34m(self, primitive, tracers, params)\u001b[0m\n\u001b[1;32m   1815\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mprimitive\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcustom_staging_rules\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1816\u001b[0m       \u001b[0;32mreturn\u001b[0m \u001b[0mcustom_staging_rules\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mprimitive\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1817\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdefault_process_primitive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprimitive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1818\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1819\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mdefault_process_primitive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/partial_eval.py\u001b[0m in \u001b[0;36mdefault_process_primitive\u001b[0;34m(self, primitive, tracers, params)\u001b[0m\n\u001b[1;32m   1819\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mdefault_process_primitive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1820\u001b[0m     \u001b[0mavals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maval\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1821\u001b[0;31m     \u001b[0mout_avals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0meffects\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabstract_eval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mavals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1822\u001b[0m     \u001b[0mout_avals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mout_avals\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiple_results\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mout_avals\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1823\u001b[0m     \u001b[0msource_info\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msource_info_util\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mabstract_eval_\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    358\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_effect_free_abstract_eval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mabstract_eval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    359\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mabstract_eval_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 360\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mabstract_eval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mno_effects\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    361\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mabstract_eval_\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    362\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/lax/utils.py\u001b[0m in \u001b[0;36mstandard_abstract_eval\u001b[0;34m(prim, shape_rule, dtype_rule, weak_type_rule, named_shape_rule, *avals, **kwargs)\u001b[0m\n\u001b[1;32m     65\u001b[0m   \u001b[0;32melif\u001b[0m \u001b[0mleast_specialized\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mShapedArray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     66\u001b[0m     return core.ShapedArray(shape_rule(*avals, **kwargs),\n\u001b[0;32m---> 67\u001b[0;31m                             \u001b[0mdtype_rule\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mavals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweak_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mweak_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     68\u001b[0m                             named_shape=named_shape_rule(*avals, **kwargs))\n\u001b[1;32m     69\u001b[0m   \u001b[0;32melif\u001b[0m \u001b[0mleast_specialized\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDShapedArray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/lax/lax.py\u001b[0m in \u001b[0;36mnaryop_dtype_rule\u001b[0;34m(result_dtype, accepted_dtypes, name, *avals, **kwargs)\u001b[0m\n\u001b[1;32m   1471\u001b[0m   \u001b[0maval_dtypes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0maval\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mavals\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1472\u001b[0m   \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0maval_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtypes\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maval_dtypes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccepted_dtypes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1473\u001b[0;31m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0missubdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maval_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtypes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1474\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0maval_dtype\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfloat0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1475\u001b[0m         raise TypeError(\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/lax/lax.py\u001b[0m in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   1471\u001b[0m   \u001b[0maval_dtypes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0maval\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mavals\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1472\u001b[0m   \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0maval_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtypes\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maval_dtypes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccepted_dtypes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1473\u001b[0;31m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0missubdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maval_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtypes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1474\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0maval_dtype\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfloat0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1475\u001b[0m         raise TypeError(\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/dtypes.py\u001b[0m in \u001b[0;36missubdtype\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m    234\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    235\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0missubdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 236\u001b[0;31m   \u001b[0;32mif\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"bfloat16\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    237\u001b[0m     \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbfloat16\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    238\u001b[0m   \u001b[0;32mif\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mbfloat16\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ],
      "source": [
        "kernel = RBF_Kernel(gamma='scale')\n",
        "lbda = 0.05**0.5\n",
        "log_bounds = {'theta': jnp.array(1e-2), 'sigma': jnp.array(1e-1)}, {'theta': jnp.array(1e1), 'sigma': jnp.array(1e2)}\n",
        "kernel_params = optimize_gpr(kernel, log_bounds, X_train, X, y_train, y, lbda=lbda, maxiter=100, verbose=True, projected=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2liYHos2LveQ"
      },
      "outputs": [],
      "source": [
        "Kxx = kernel(X_train, kernel_params)\n",
        "print('Condition number:', jnp.linalg.cond(Kxx))\n",
        "print('Params:', kernel_params)\n",
        "onp.set_printoptions(precision=6)\n",
        "if len(Kxx) <= 10:\n",
        "  print('Kernel:', Kxx)\n",
        "onp.set_printoptions(precision=4)\n",
        "print('[JAX    ] Log Marginal Likelihood:', gp_regression_likelihood(Kxx, y_train, lbda=lbda))\n",
        "print('[SKLEARN] Log Marginal Likelihood:', gp_regression_likelihood(gaussian_process.kernel_(X_train), y_train, lbda=lbda))\n",
        "delta = jnp.abs(gaussian_process.kernel_(X_train) - Kxx) / gaussian_process.kernel_(X_train)\n",
        "print(f\"Max Rel Error={jnp.max(delta)*100:.2f}%\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4a4bX9vc7dim"
      },
      "outputs": [],
      "source": [
        "mean_prediction, var_prediction = gp_process_prediction(kernel, kernel_params, X_train, X, y_train, lbda=lbda)\n",
        "std_prediction = var_prediction ** 0.5"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "If50MlnT8X1E"
      },
      "outputs": [],
      "source": [
        "plt.plot(X, y, label=r\"$f(x) = x \\sin(x)$\", linestyle=\"dotted\")\n",
        "plt.scatter(X_train, y_train, label=\"Observations\")\n",
        "plt.plot(X, mean_prediction, label=\"Mean prediction\")\n",
        "plt.fill_between(\n",
        "    X.ravel(),\n",
        "    mean_prediction - 1.96 * std_prediction,\n",
        "    mean_prediction + 1.96 * std_prediction,\n",
        "    alpha=0.5,\n",
        "    label=r\"95% confidence interval\",\n",
        ")\n",
        "plt.legend()\n",
        "plt.xlabel(\"$x$\")\n",
        "plt.ylabel(\"$f(x)$\")\n",
        "_ = plt.title(\"Gaussian process regression on noise-free dataset\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xpKRP9Q1sj8K"
      },
      "source": [
        "## Sinkhorn Mu-GP"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OrmWXOQ7ovZU"
      },
      "outputs": [],
      "source": [
        "from typing import Any, Optional\n",
        "from dataclasses import dataclass\n",
        "\n",
        "from jaxopt.tree_util import tree_l2_norm\n",
        "\n",
        "from ott.geometry import pointcloud\n",
        "import ott.core.sinkhorn as sinkhorn\n",
        "\n",
        "\n",
        "@dataclass\n",
        "class SinkhornMuGPR:\n",
        "  \"\"\" Gaussian Process Regression with Sinkhorn Mu Kernel.\n",
        "\n",
        "  Attributes:\n",
        "    sinkhorn_epsilon: (float) regularization in Sinkhorn. Default: 1e-2.\n",
        "    kernel_fun: function that takes an array of shape (n, f) and return an array of shape (n, n)\n",
        "      kernel_fun(x)_ij = K(x_i, x_j) is the covariance matrix of the GP.\n",
        "    log_bounds bounds for Kernel parmateres\n",
        "  \"\"\"\n",
        "  maxiter: int = 1000\n",
        "  tol: float = 1e-3\n",
        "  sinkhorn_epsilon: float = 1e-1\n",
        "  kernel_fun: Any = RBF_Kernel\n",
        "  log_bounds: Optional[Any] = None\n",
        "  debug: bool = False\n",
        "  verbose: bool = False\n",
        "  lbda: float = 1e-1\n",
        "\n",
        "  def __post_init__(self):\n",
        "    if self.log_bounds is not None:\n",
        "      self.bounds = tuple(map(lambda d: {('log_'+k):jnp.log(v) for k, v in d.items()}, log_bounds))\n",
        "    else:\n",
        "      self.bounds = None\n",
        "\n",
        "  def compute_sinkhorn_embeddings(self, coordinates, weights, mu):\n",
        "    mu_cloud, mu_weights = mu\n",
        "\n",
        "    def sinkhorn_single_cloud(cloud_coords, cloud_weight):\n",
        "      geom = pointcloud.PointCloud(cloud_coords, mu_cloud,\n",
        "                                   epsilon=self.sinkhorn_epsilon)\n",
        "      out = sinkhorn.sinkhorn(geom, cloud_weight, mu_weights,\n",
        "                              lse_mode=True, implicit_differentiation=False)\n",
        "      return out.g\n",
        "\n",
        "    parallel_sinkhorn = jax.vmap(sinkhorn_single_cloud,\n",
        "                                 in_axes=(0, 0),\n",
        "                                 out_axes=0)\n",
        "    \n",
        "    g_mu_embeddings = parallel_sinkhorn(coordinates, weights)\n",
        "    return g_mu_embeddings\n",
        "\n",
        "  def _project_gp_params(self, gp_params):\n",
        "    if self.bounds is not None:\n",
        "      kernel_params = gp_params['kernel_params']\n",
        "      kernel_params = tree_map(jnp.clip, kernel_params, self.bounds[0], self.bounds[1])\n",
        "      gp_params = {'kernel_params':kernel_params, 'mu':gp_params['mu']}  # project params\n",
        "    return gp_params\n",
        "\n",
        "  def _g_mu(self, padded_cloud_X_train, gp_params):\n",
        "    coordinates, weights = padded_cloud_X_train\n",
        "    if self.debug:\n",
        "      return jnp.sum(coordinates * weights[:,:,jnp.newaxis], axis=1)\n",
        "    g_mu = self.compute_sinkhorn_embeddings(coordinates, weights, mu=gp_params['mu'])\n",
        "    return g_mu\n",
        "  \n",
        "  def gpr_mu(self, padded_cloud_X_train, y, gp_params):\n",
        "    \"\"\"GP regression for clouds.\n",
        "\n",
        "    N   : number of clouds\n",
        "    n   : maximum number of points in a cloud\n",
        "    d   : dimension of the space\n",
        "    mu  : support measure\n",
        "    K   : number of points in mu\n",
        "\n",
        "    Args:\n",
        "      padded_cloud_X_train: tuple of\n",
        "        coordinates: array of shape (N, n, d) and,\n",
        "        weights: array of shape (N, n)\n",
        "      y              : array of shape (N,)\n",
        "      gp_params      : parameters of Gaussian process\n",
        "\n",
        "    mu : array of shape (K, d)\n",
        "    \"\"\"\n",
        "    gp_params = self._project_gp_params(gp_params)\n",
        "    g_mu = self._g_mu(padded_cloud_X_train, gp_params)\n",
        "    Kxx  = self.kernel_fun(g_mu, gp_params['kernel_params'])\n",
        "    loss = -gp_regression_likelihood(Kxx, y, self.lbda)\n",
        "    return loss, Kxx\n",
        "\n",
        "  def pad_point_clouds(self, data):\n",
        "    # +1 for unified processing of all clouds including biggest one\n",
        "    max_cloud_size = max([cloud.shape[0] for cloud in data]) + 1\n",
        "\n",
        "    def pad_cloud(cloud):\n",
        "      delta = max_cloud_size - cloud.shape[0]\n",
        "      uniform = jnp.ones(cloud.shape[0]) / cloud.shape[0]\n",
        "      zeros = jnp.zeros(delta)\n",
        "      weights = jnp.concatenate([uniform, zeros], axis=0)\n",
        "      cloud = jnp.pad(cloud, pad_width=((0, delta), (0,0)), mode='mean')\n",
        "      return cloud, weights\n",
        "\n",
        "    data = list(map(pad_cloud, data))\n",
        "    coordinates = jnp.stack([t[0] for t in data])\n",
        "    weights = jnp.stack([t[1] for t in data])\n",
        "    return coordinates, weights\n",
        "\n",
        "  def init_mu(self, coordinates):\n",
        "    # mu_cloud = jnp.mean(coordinates, axis=1)  # Euclidean Barycenter\n",
        "    # mu_cloud = jnp.zeros((coordinates.shape[0], coordinates.shape[-1]))\n",
        "    mu_cloud = jnp.array([[0.25, 0.5], [0.75, 0.5], [0.5, 0.25], [0.5, 0.75], [0.5, 0.5]])\n",
        "    mu_weight = None\n",
        "    return mu_cloud, mu_weight\n",
        "\n",
        "  def _plot_step(self, step, padded_cloud_X_train, padded_cloud_X_test, y_train, y_test, gp_params, state):\n",
        "    X_train = self._g_mu(padded_cloud_X_train, gp_params)\n",
        "    X_test = self._g_mu(padded_cloud_X_test, gp_params)\n",
        "    Kxx = state.aux if state.aux is not None else self.kernel_fun(X_train, gp_params['kernel_params'])\n",
        "    preds, _ = gp_process_prediction(self.kernel_fun, gp_params['kernel_params'], X_train, X_test, y_train, lbda=self.lbda)\n",
        "    mse = jnp.mean((preds - y_test)**2)\n",
        "    print_params = {k: f\"{v:.3f}\" for k, v in self.kernel_fun.get_params(gp_params['kernel_params']).items()}\n",
        "    print(f\"[{step}] error={state.error:.3f} mse={mse:.6f} loss={state.value:.3f} params={print_params} CondNumber={jnp.linalg.cond(Kxx):,.1f}\")\n",
        "\n",
        "  def optimize_gpr(self, cloud_X_train, cloud_X_test, y_train, y_test):\n",
        "    \"\"\"GP regression for clouds.\n",
        "\n",
        "    N   : number of clouds\n",
        "    n_i : number of points in cloud i\n",
        "    d   : dimension of the space\n",
        "    mu  : support measure\n",
        "    K   : number of points in mu\n",
        "\n",
        "    Args:\n",
        "      cloud_X_train  : list of length N of arrays of shape (n_i, d)\n",
        "      cloud_X_test   : list of length N' of arrays of shape (n'_i, d)\n",
        "      y_train        : array of shape (N,)\n",
        "      y_test         : array of shape (N',)\n",
        "\n",
        "    mu : array of shape (K, d)\n",
        "\n",
        "    \"\"\"\n",
        "    padded_cloud_X_train = self.pad_point_clouds(cloud_X_train)\n",
        "    padded_cloud_X_test = self.pad_point_clouds(cloud_X_test)\n",
        "\n",
        "    kernel_params = self.kernel_fun.init_log_params()\n",
        "    mu_init = self.init_mu(padded_cloud_X_train[0])\n",
        "\n",
        "    gp_params = {'kernel_params': kernel_params, 'mu': mu_init}\n",
        "\n",
        "    def gpr_mu_step(gp_params):\n",
        "      return self.gpr_mu(padded_cloud_X_train, y_train, gp_params)\n",
        "\n",
        "    opt = LBFGS(fun=gpr_mu_step, has_aux=True, maxiter=self.maxiter, tol=self.tol, maxls=20)\n",
        "\n",
        "    mu_hist = [mu_init[0]]\n",
        "    if self.verbose:\n",
        "\n",
        "      state = opt.init_state(gp_params)\n",
        "      state = state._replace(value=gpr_mu_step(gp_params)[0], error=tree_l2_norm(opt.optimality_fun(gp_params)))\n",
        "      self._plot_step(0, padded_cloud_X_train, padded_cloud_X_test, y_train, y_test, gp_params, state)\n",
        "\n",
        "      @jax.jit\n",
        "      def opt_update(gp_params, state):\n",
        "        return opt.update(gp_params, state)\n",
        "\n",
        "      for step in range(self.maxiter):\n",
        "        gp_params, state = opt_update(gp_params, state)\n",
        "        gp_params = self._project_gp_params(gp_params)\n",
        "        mu_hist.append(gp_params['mu'][0])\n",
        "        print(' '.join([f'[{mu_p[0]:.3f}, {mu_p[1]:.3f}]' for mu_p in gp_params['mu'][0]]))\n",
        "        self._plot_step(step+1, padded_cloud_X_train, padded_cloud_X_test, y_train, y_test, gp_params, state)\n",
        "    else:\n",
        "      gp_params, state = opt.run(gp_params)\n",
        "      gp_params = self._project_gp_params(gp_params)\n",
        "      mu_hist.append(gp_params['mu'])\n",
        "      self._plot_step(state.iter_num, padded_cloud_X_train, padded_cloud_X_test, y_train, y_test, gp_params, state)\n",
        "    \n",
        "    return gp_params, mu_hist"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ba2JvmtFIYbd"
      },
      "source": [
        "## Test on Toy Example"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kEbSqspIxi8G"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"figure.figsize\"] = (16,9)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lnMCQa8yBvIo"
      },
      "outputs": [],
      "source": [
        "import numpy as onp\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "\n",
        "def targets_ground_truth(points, sigmas):\n",
        "  m1, m2 = points[:,0], points[:,1]\n",
        "  targets = (m1 - m2**2) / (1 + jnp.squeeze(sigmas))\n",
        "  return targets\n",
        "\n",
        "def generate_meta_dataset(key, ds_size, sigmas_bounds):\n",
        "  key_1, key_2 = jax.random.split(key)\n",
        "  min_sigma, max_sigma = sigmas_bounds\n",
        "  means = jax.random.uniform(key_1, shape=(ds_size, 2), minval=0.2, maxval=0.8)\n",
        "  sigmas = jax.random.uniform(key_2, shape=(ds_size, 1), minval=min_sigma, maxval=max_sigma)\n",
        "  targets = targets_ground_truth(means, sigmas)\n",
        "  return targets, (means, sigmas)\n",
        "\n",
        "def generate_sample_dataset(key, ds_size, num_points, sigmas_bounds):\n",
        "  key_1, key_2 = jax.random.split(key)\n",
        "  targets, (means, sigmas) = generate_meta_dataset(key_1, ds_size, sigmas_bounds)\n",
        "  sample = means[:,jnp.newaxis,:] + jax.random.normal(key_2, shape=(ds_size, num_points, 2)) * sigmas[:,jnp.newaxis,:]\n",
        "  return sample, targets"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SaSjaF1MBnAQ"
      },
      "outputs": [],
      "source": [
        "key = jax.random.PRNGKey(61378)\n",
        "ds_size = 100\n",
        "num_points = 50 #50 * 50\n",
        "min_sigma = 0.01\n",
        "max_sigma = 0.02 \n",
        "sample_ds, target_ds = generate_sample_dataset(key, ds_size, num_points, (min_sigma, max_sigma))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5MuN8ARMBnFL"
      },
      "outputs": [],
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "test_size = 0.6\n",
        "sample_train, sample_test, target_train, target_test = train_test_split(sample_ds, target_ds, test_size=test_size, shuffle=True, random_state=89)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Oq2TtnIEBnHP"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import ott\n",
        "\n",
        "resolution = 50\n",
        "x_thicks = jnp.linspace(0, 1, resolution)\n",
        "y_thicks = jnp.linspace(0, 1, resolution)\n",
        "x_grid, y_grid = jnp.meshgrid(x_thicks, y_thicks)\n",
        "grid = jnp.stack([x_grid.ravel(), y_grid.ravel()], axis=-1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hixVNdhMxliy"
      },
      "outputs": [],
      "source": [
        "def plot_ground_truth(sigmas):\n",
        "  targets_grid = targets_ground_truth(grid, sigmas)\n",
        "  plt.imshow(targets_grid.reshape((resolution, resolution)), origin='lower')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 537
        },
        "id": "xKCEnSKQqoEP",
        "outputId": "21c2e4a6-50f2-4d8a-fa31-47f7fee69113"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x648 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import matplotlib.cm as cm\n",
        "\n",
        "def plot_ds(sample_train, target_train):\n",
        "  min_sample, max_sample = target_train.min(), target_train.max()\n",
        "  for sample, target in zip(sample_train, target_train):\n",
        "    r = (target - min_sample) / (max_sample - min_sample)\n",
        "    color = cm.viridis(r)\n",
        "    s = jnp.exp(target) / 20\n",
        "    plt.scatter(sample[:,0], sample[:,1], s=s, color=color)\n",
        "plot_ds(sample_train, target_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "39af07c5-1884-45af-8ccc-8b3428557288",
        "id": "2PdbscVUXyo1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0] error=9.691 mse=0.000022 loss=-115.578 params={'theta': '1.000', 'sigma': '1.000'} CondNumber=2,078,093,731,183.5\n",
            "[0.159, 2.149] [0.576, -1.767] [2.549, -1.261] [-1.187, 2.558] [1.140, -0.241]\n",
            "[1] error=5.352 mse=0.000044 loss=-117.332 params={'sigma': '4.606', 'theta': '0.400'} CondNumber=2,078,101,087,389.0\n",
            "[0.212, 2.175] [0.511, -1.835] [2.566, -1.238] [-1.199, 2.563] [1.147, -0.224]\n",
            "[2] error=7.006 mse=0.000039 loss=-117.460 params={'sigma': '4.328', 'theta': '0.459'} CondNumber=131,147,578,705.2\n",
            "[0.219, 2.148] [0.508, -1.801] [2.530, -1.208] [-1.169, 2.531] [1.136, -0.208]\n",
            "[3] error=4.868 mse=0.000038 loss=-117.728 params={'sigma': '4.454', 'theta': '0.457'} CondNumber=82,757,451,791.5\n",
            "[0.226, 2.127] [0.504, -1.776] [2.503, -1.184] [-1.147, 2.506] [1.128, -0.195]\n",
            "[4] error=3.824 mse=0.000038 loss=-117.847 params={'sigma': '4.518', 'theta': '0.457'} CondNumber=111,842,640,815.5\n",
            "[0.239, 2.103] [0.494, -1.751] [2.470, -1.153] [-1.120, 2.476] [1.118, -0.177]\n",
            "[5] error=3.112 mse=0.000038 loss=-117.955 params={'sigma': '4.573', 'theta': '0.458'} CondNumber=134,011,561,658.5\n",
            "[0.274, 2.053] [0.466, -1.703] [2.397, -1.081] [-1.064, 2.409] [1.098, -0.133]\n",
            "[6] error=2.682 mse=0.000038 loss=-118.139 params={'sigma': '4.631', 'theta': '0.462'} CondNumber=161,971,407,757.9\n",
            "[0.426, 1.869] [0.343, -1.540] [2.123, -0.796] [-0.852, 2.154] [1.022, 0.041]\n",
            "[7] error=3.487 mse=0.000037 loss=-118.702 params={'sigma': '4.675', 'theta': '0.481'} CondNumber=228,159,070,902.6\n",
            "[0.739, 1.514] [0.089, -1.239] [1.599, -0.235] [-0.461, 1.655] [0.883, 0.397]\n",
            "[8] error=5.622 mse=0.000029 loss=-119.566 params={'sigma': '4.666', 'theta': '0.585'} CondNumber=855,943,543,709.5\n",
            "[0.686, 1.581] [0.137, -1.305] [1.711, -0.345] [-0.558, 1.755] [0.915, 0.338]\n",
            "[9] error=5.987 mse=0.000027 loss=-119.750 params={'sigma': '4.640', 'theta': '0.752'} CondNumber=6,004,750,746,281.6\n",
            "[0.752, 1.500] [0.087, -1.237] [1.603, -0.228] [-0.484, 1.650] [0.886, 0.417]\n",
            "[10] error=2.600 mse=0.000026 loss=-120.052 params={'sigma': '4.706', 'theta': '0.731'} CondNumber=3,521,872,933,903.9\n",
            "[0.765, 1.479] [0.081, -1.219] [1.579, -0.204] [-0.470, 1.629] [0.878, 0.434]\n",
            "[11] error=1.755 mse=0.000026 loss=-120.087 params={'sigma': '4.744', 'theta': '0.731'} CondNumber=6,415,874,970,037.8\n",
            "[0.765, 1.479] [0.081, -1.219] [1.579, -0.204] [-0.470, 1.628] [0.878, 0.434]\n",
            "[12] error=1.751 mse=0.000026 loss=-120.088 params={'sigma': '4.744', 'theta': '0.731'} CondNumber=7,716,318,601,882.0\n",
            "[0.765, 1.479] [0.081, -1.219] [1.579, -0.204] [-0.470, 1.628] [0.878, 0.434]\n",
            "[13] error=1.751 mse=0.000026 loss=-120.088 params={'sigma': '4.744', 'theta': '0.731'} CondNumber=7,728,254,206,055.3\n",
            "[0.765, 1.479] [0.081, -1.219] [1.579, -0.204] [-0.470, 1.628] [0.878, 0.434]\n",
            "[14] error=1.751 mse=0.000026 loss=-120.088 params={'sigma': '4.744', 'theta': '0.731'} CondNumber=7,728,954,799,250.5\n",
            "[0.765, 1.479] [0.081, -1.219] [1.579, -0.204] [-0.470, 1.628] [0.878, 0.434]\n",
            "[15] error=1.751 mse=0.000026 loss=-120.088 params={'sigma': '4.744', 'theta': '0.731'} CondNumber=7,729,112,718,554.6\n",
            "[0.792, 1.351] [0.138, -1.146] [1.463, -0.149] [-0.433, 1.612] [0.817, 0.510]\n",
            "[16] error=3.812 mse=0.000024 loss=-120.147 params={'sigma': '5.077', 'theta': '0.786'} CondNumber=7,728,945,297,776.0\n",
            "[0.788, 1.370] [0.131, -1.158] [1.482, -0.158] [-0.440, 1.616] [0.826, 0.499]\n",
            "[17] error=4.472 mse=0.000023 loss=-120.173 params={'sigma': '5.021', 'theta': '0.985'} CondNumber=18,423,421,683,031.1\n",
            "[0.798, 1.326] [0.151, -1.136] [1.441, -0.139] [-0.424, 1.614] [0.805, 0.525]\n",
            "[18] error=1.544 mse=0.000023 loss=-120.333 params={'sigma': '5.134', 'theta': '0.950'} CondNumber=16,170,243,512,967.2\n",
            "[0.801, 1.309] [0.160, -1.131] [1.427, -0.133] [-0.416, 1.617] [0.797, 0.534]\n",
            "[19] error=0.787 mse=0.000023 loss=-120.352 params={'sigma': '5.174', 'theta': '0.943'} CondNumber=20,926,767,070,730.6\n",
            "[0.803, 1.297] [0.168, -1.130] [1.418, -0.129] [-0.410, 1.624] [0.791, 0.541]\n",
            "[20] error=0.641 mse=0.000023 loss=-120.361 params={'sigma': '5.194', 'theta': '0.945'} CondNumber=22,854,586,949,110.3\n",
            "[0.810, 1.257] [0.196, -1.135] [1.395, -0.119] [-0.389, 1.656] [0.773, 0.563]\n",
            "[21] error=0.632 mse=0.000023 loss=-120.384 params={'sigma': '5.210', 'theta': '0.952'} CondNumber=23,821,953,471,220.9\n",
            "[0.827, 1.161] [0.253, -1.141] [1.369, -0.095] [-0.355, 1.733] [0.733, 0.613]\n",
            "[22] error=0.784 mse=0.000024 loss=-120.416 params={'sigma': '5.215', 'theta': '0.970'} CondNumber=25,487,418,215,901.2\n",
            "[0.843, 1.108] [0.277, -1.137] [1.392, -0.074] [-0.360, 1.767] [0.712, 0.639]\n",
            "[23] error=0.800 mse=0.000025 loss=-120.445 params={'sigma': '5.221', 'theta': '0.996'} CondNumber=27,412,756,234,687.7\n",
            "[0.869, 1.019] [0.320, -1.132] [1.409, -0.039] [-0.356, 1.823] [0.675, 0.684]\n",
            "[24] error=0.684 mse=0.000026 loss=-120.464 params={'sigma': '5.255', 'theta': '0.997'} CondNumber=24,607,117,199,826.8\n",
            "[0.901, 0.960] [0.344, -1.132] [1.453, 0.000] [-0.375, 1.854] [0.646, 0.714]\n",
            "[25] error=0.773 mse=0.000027 loss=-120.485 params={'sigma': '5.270', 'theta': '1.006'} CondNumber=22,751,800,405,035.6\n",
            "[0.952, 0.883] [0.373, -1.143] [1.487, 0.062] [-0.380, 1.892] [0.610, 0.756]\n",
            "[26] error=0.760 mse=0.000028 loss=-120.508 params={'sigma': '5.305', 'theta': '1.001'} CondNumber=18,267,420,189,175.5\n",
            "[1.123, 0.655] [0.473, -1.237] [1.568, 0.289] [-0.362, 2.003] [0.508, 0.883]\n",
            "[27] error=2.181 mse=0.000031 loss=-120.548 params={'sigma': '5.370', 'theta': '0.997'} CondNumber=27,452,441,028,185.8\n",
            "[1.061, 0.762] [0.424, -1.211] [1.532, 0.210] [-0.365, 1.940] [0.556, 0.823]\n",
            "[28] error=1.723 mse=0.000030 loss=-120.555 params={'sigma': '5.570', 'theta': '0.969'} CondNumber=20,409,326,417,527.6\n",
            "[1.172, 0.664] [0.472, -1.305] [1.571, 0.366] [-0.341, 1.975] [0.512, 0.878]\n",
            "[29] error=1.875 mse=0.000031 loss=-120.589 params={'sigma': '5.492', 'theta': '0.995'} CondNumber=65,817,020,278,795.8\n",
            "[1.141, 0.711] [0.453, -1.292] [1.556, 0.324] [-0.345, 1.951] [0.533, 0.852]\n",
            "[30] error=0.407 mse=0.000030 loss=-120.613 params={'sigma': '5.581', 'theta': '0.980'} CondNumber=22,096,213,802,940.1\n"
          ]
        }
      ],
      "source": [
        "rbf = RBF_Kernel(gamma='auto')\n",
        "lbda = 1e-2\n",
        "sinkhorn_epsilon = 1e-2\n",
        "log_bounds = {'theta': jnp.array(1e-2), 'sigma': jnp.array(1e-2)}, {'theta': jnp.array(1e2), 'sigma': jnp.array(1e2)}\n",
        "mu_gpr = SinkhornMuGPR(kernel_fun=rbf, debug=False, verbose=True, maxiter=30, log_bounds=log_bounds, lbda=lbda, sinkhorn_epsilon=sinkhorn_epsilon)\n",
        "gp_params, mu_hist = mu_gpr.optimize_gpr(list(sample_train), list(sample_test), target_train, target_test)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 537
        },
        "id": "ETXsiS_FXyo6",
        "outputId": "a9d76ad5-b196-4c3e-f4b7-f29642d5b31b"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x648 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "for i in range(len(mu_hist[0])):\n",
        "  x = [mu[i,0] for mu in mu_hist]\n",
        "  y = [mu[i,1] for mu in mu_hist]\n",
        "  plt.plot(x,y,'-*')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f832a4d6-5f66-4b97-8d75-7fe665371a36",
        "id": "HvJeJlXrXyo-"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Condition number: 30946298691.93739\n",
            "Params: 0.402**2 * RBF(length_scale=2.23)\n",
            "Log Marginal Likelihood: 3.340129642660507\n",
            "[SKLEARN] TrainSetSize=40 mae=0.04194 rmse=0.05853 evs=0.94016\n",
            "[MEAN] TrainSetSize=40 mae=0.19332 rmse=0.23865 evs=-0.00000\n"
          ]
        }
      ],
      "source": [
        "from sklearn.gaussian_process import GaussianProcessRegressor\n",
        "from sklearn.gaussian_process.kernels import RBF\n",
        "from sklearn.metrics import mean_squared_error, mean_absolute_error, explained_variance_score\n",
        "\n",
        "X_train = mu_gpr._g_mu(mu_gpr.pad_point_clouds(sample_train), gp_params)\n",
        "X_test = mu_gpr._g_mu(mu_gpr.pad_point_clouds(sample_test), gp_params)\n",
        "\n",
        "sk_kernel = 1 * RBF(length_scale=1.0, length_scale_bounds=(5e-2, 1e2))\n",
        "gaussian_process = GaussianProcessRegressor(kernel=sk_kernel, n_restarts_optimizer=10, alpha=lbda**0.5)\n",
        "gaussian_process.fit(X_train, target_train)\n",
        "print('Condition number:', jnp.linalg.cond(gaussian_process.kernel_(X_train)))\n",
        "print('Params:', gaussian_process.kernel_)\n",
        "onp.set_printoptions(precision=6)\n",
        "if len(X_train) <= 10:\n",
        "  print('Kernel:', gaussian_process.kernel_(X_train))\n",
        "onp.set_printoptions(precision=4)\n",
        "print('Log Marginal Likelihood:', gaussian_process.log_marginal_likelihood_value_)\n",
        "test_pred = gaussian_process.predict(X_test)\n",
        "evs = explained_variance_score(target_test, test_pred)\n",
        "rmse = mean_squared_error(target_test, test_pred, squared=False)\n",
        "mae = mean_absolute_error(target_test, test_pred)\n",
        "msg = f\"[SKLEARN] TrainSetSize={len(X_train)} mae={mae:.5f} rmse={rmse:.5f} evs={evs:.5f}\"\n",
        "print(msg)\n",
        "test_pred = jnp.mean(target_test) * jnp.ones_like(target_test)\n",
        "evs = explained_variance_score(target_test, test_pred)\n",
        "rmse = mean_squared_error(target_test, test_pred, squared=False)\n",
        "mae = mean_absolute_error(target_test, test_pred)\n",
        "msg = f\"[MEAN] TrainSetSize={len(X_train)} mae={mae:.5f} rmse={rmse:.5f} evs={evs:.5f}\"\n",
        "print(msg)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d6445bbf-ccb8-4dab-a46b-1debbaf7b543",
        "id": "Dt0-i8vLXypB"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Condition number: 32771967472747.4\n",
            "Params: {'sigma': '5.581', 'theta': '0.980'}\n",
            "[JAX    ] Log Marginal Likelihood: 120.61339064270985\n",
            "[SKLEARN] Log Marginal Likelihood: 115.72334169744468\n",
            "Max Rel Error=1224.46%\n",
            "[JAX] TrainSetSize=40 mae=0.00406 rmse=0.00548 evs=0.99947\n"
          ]
        }
      ],
      "source": [
        "Kxx = mu_gpr.kernel_fun(X_train, gp_params['kernel_params'])\n",
        "print('Condition number:', jnp.linalg.cond(Kxx))\n",
        "print('Params:', {k: f\"{v:.3f}\" for k, v in mu_gpr.kernel_fun.get_params(gp_params['kernel_params']).items()})\n",
        "onp.set_printoptions(precision=6)\n",
        "if len(Kxx) <= 10:\n",
        "  print('Kernel:', Kxx)\n",
        "onp.set_printoptions(precision=4)\n",
        "print('[JAX    ] Log Marginal Likelihood:', gp_regression_likelihood(Kxx, target_train, lbda=lbda))\n",
        "print('[SKLEARN] Log Marginal Likelihood:', gp_regression_likelihood(gaussian_process.kernel_(X_train), target_train, lbda=lbda))\n",
        "delta = jnp.abs(gaussian_process.kernel_(X_train) - Kxx) / gaussian_process.kernel_(X_train)\n",
        "print(f\"Max Rel Error={jnp.max(delta)*100:.2f}%\")\n",
        "test_pred, _ = gp_process_prediction(mu_gpr.kernel_fun, gp_params['kernel_params'], X_train, X_test, target_train, lbda=lbda)\n",
        "evs = explained_variance_score(target_test, test_pred)\n",
        "rmse = mean_squared_error(target_test, test_pred, squared=False)\n",
        "mae = mean_absolute_error(target_test, test_pred)\n",
        "msg = f\"[JAX] TrainSetSize={len(X_train)} mae={mae:.5f} rmse={rmse:.5f} evs={evs:.5f}\"\n",
        "print(msg)"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "fqHhp_qnLBSY"
      },
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}