learn_radius.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Import necessary libraries\n",
    "import jax.numpy as jnp\n",
    "from jax import random, grad, jit, lax, jacrev\n",
    "from jax.scipy.linalg import inv, svd, eigh, det\n",
    "from jax.numpy.linalg import norm\n",
    "from tqdm.auto import tqdm\n",
    "from sklearn.datasets import make_spd_matrix\n",
    "from jax_models import visualize_observations, Lorenz96, KuramotoSivashinsky, generate_true_states, generate_localization_matrix\n",
    "from jax_filters import ensrf_steps, kalman_filter_process, ensrf_step\n",
    "import jax\n",
    "import matplotlib.pyplot as plt\n",
    "from jax.tree_util import Partial\n",
    "from functools import partial\n",
    "from jax_vi import KL_gaussian, log_likelihood, KL_sum\n",
    "jax.config.update(\"jax_enable_x64\", True)\n",
    "#jax.config.update(\"jax_debug_nans\", True)\n",
    "\n",
    "N = 10 # number of Monte Carlo samples\n",
    "F = 8.0\n",
    "dt = 0.05\n",
    "num_steps = 250  # Number of time steps\n",
    "J0 = 0\n",
    "n = 40   # Number of state variables\n",
    "key = random.PRNGKey(0)  # Random key for reproducibility\n",
    "x0 = random.normal(key, (n,))\n",
    "initial_state  = x0\n",
    "# Noise covariances\n",
    "Q = 0.03 * jnp.eye(n)  # Process noise covariance\n",
    "R = 0.5 * jnp.eye(n)  # Observation noise covariance\n",
    "# Observation matrix (identity matrix for direct observation of all state variables)\n",
    "H = jnp.eye(n)\n",
    "\n",
    "n_ensemble = 5\n",
    "observation_interval = 1\n",
    "initial_state = random.normal(random.PRNGKey(0), (n,))  # Initial state\n",
    "m0 = initial_state\n",
    "C0 = Q\n",
    "\n",
    "\n",
    "l96_model = Lorenz96(dt = dt, F = 8)\n",
    "l96_step = Partial(l96_model.step)\n",
    "# Generate true states and observations using the Lorenz '96 model\n",
    "\n",
    "state_transition_function = l96_model.step\n",
    "\n",
    "jacobian_function = jacrev(l96_step, argnums=0)\n",
    "jac_func = Partial(jacobian_function)\n",
    "\n",
    "observations, true_states = generate_true_states(key, num_steps, n, initial_state, H, Q, R, l96_step, observation_interval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.QuadMesh at 0x7fd608878090>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolormesh(generate_localization_matrix(40, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "@jit\n",
    "def var_cost(radius, inflation, model, ensemble_init, observations, H, Q, R, key, J, J0):\n",
    "    localization_matrix = generate_localization_matrix(n, radius)\n",
    "    pred_states, pred_covar, states, covariances = ensrf_steps(l96_step, ensemble_init, num_steps, observations, observation_interval, H, Q, R, localization_matrix, inflation, key)\n",
    "    ensemble_mean = jnp.mean(states, axis=-1)  # Taking the mean across the ensemble members dimension\n",
    "    pred_mean = jnp.mean(pred_states, axis = -1)\n",
    "    key, *subkeys = random.split(key, num=N+1)\n",
    "    kl_sum = KL_sum(pred_mean, pred_covar, ensemble_mean, covariances, n, l96_step, Q, key)\n",
    "\n",
    "    def inner_map(subkey):\n",
    "        return log_likelihood(random.multivariate_normal(subkey, ensemble_mean, covariances), observations, H, R, num_steps, J0)  \n",
    "    cost = kl_sum - jnp.nanmean(jax.lax.map(inner_map, jnp.vstack(subkeys)))\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "inflation = 1.5  # Fixed starting value for inflation\n",
    "radius_opt = 1.0\n",
    "alpha = 1e-4  # Learning rate\n",
    "key = random.PRNGKey(0)  # Random key\n",
    "N = 10  # Number of MC samples\n",
    "m0 = initial_state\n",
    "C0 = Q  # Initial covariance, assuming Q is your process noise covariance\n",
    "ensemble_init = random.multivariate_normal(key, initial_state, Q, (n_ensemble,)).T\n",
    "localization_matrix = generate_localization_matrix(n, radius_opt)\n",
    "\n",
    "pred_states, pred_covariances, states, covariances = ensrf_steps(l96_step, ensemble_init, num_steps, observations, observation_interval, H, Q, R, localization_matrix, inflation, key)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# var_cost_single_obs(radius_opt, inflation, n_ensemble, ensemble_init, observations[0], H, Q, R, key, n, J0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(19371.94949537, dtype=float64)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "key, subkey = random.split(key)\n",
    "var_cost(radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(Array(19371.94949537, dtype=float64), Array(106432.99820942, dtype=float64))\n"
     ]
    }
   ],
   "source": [
    "print(jax.value_and_grad(var_cost) (radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# for radius_opt in jnp.arange(0.1, 3, 0.1):\n",
    "#     print(radius_opt, jax.value_and_grad(var_cost) (radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(40, 5)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ensemble_init.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "radius_range = jnp.arange(1, 20, 1)  # from 3 to 40 with step size 1\n",
    "inflation = 1.5\n",
    "radius_values = []\n",
    "cost_values = []\n",
    "\n",
    "for radius_opt in radius_range:\n",
    "    cost = var_cost(radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0)\n",
    "    radius_values.append(radius_opt)\n",
    "    cost_values.append(cost)\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(radius_values, cost_values, label='Cost', marker='o')\n",
    "plt.title('Cost vs Radius')\n",
    "plt.xlabel('Radius')\n",
    "plt.ylabel('Cost')\n",
    "plt.grid(True)\n",
    "\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(1002.34075499, dtype=float64)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_cost_grad = grad(var_cost, argnums=0)\n",
    "radius_opt = 5.5\n",
    "var_cost_grad(radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "base_m, base_C, base_K = kalman_filter_process(l96_step, jac_func, m0, C0, observations, H, Q, R)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_ensemble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "45b294c448754987b613b7b2f95b7077",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.972451134271991 3027.5488657280093 0.5150113943426026\n",
      "3.1817317991007275 790.7193351712633 0.49264432814224657\n",
      "2.516732687578985 664.9991115217425 0.47461395977595966\n",
      "1.5217963734233755 994.9363141556097 0.4422777563119548\n",
      "0.47697956030604294 1044.8168131173325 0.43575014657133704\n",
      "0.5114891771693617 -34.50961686331871 0.43564239654377085\n",
      "0.5659495491958345 -54.46037202647281 0.4352961244458655\n",
      "0.5964787740911373 -30.52922489530272 0.4350062013943892\n",
      "0.5691580135081189 27.32076058301834 0.4352676404723275\n",
      "0.5606371041310894 8.520909377029511 0.43534156253310197\n",
      "0.5740176772366575 -13.380573105568203 0.43522317927644266\n",
      "0.6167876875473677 -42.77001031071012 0.434820596029137\n",
      "0.4908720405976096 125.91564694975807 0.435713530654477\n",
      "0.4964849010979384 -5.6128605003288214 0.4356964275412801\n",
      "0.49056418794817047 5.92071314976792 0.43571442660557386\n",
      "0.4663656287354622 24.19855921270826 0.4357736080331193\n",
      "0.4406138347526492 25.75179398281304 0.43581793642980404\n",
      "0.4546529482702411 -14.039113517591915 0.43579578464512014\n",
      "0.4737691725596794 -19.11622428943825 0.43575761365097443\n",
      "0.502692962205208 -28.923789645528657 0.43567566135798635\n",
      "0.5359453204905453 -33.25235828533738 0.4355198132783843\n",
      "0.4975129781209282 38.43234236961712 0.435693129125282\n",
      "0.4818482944847415 15.664683636186709 0.43573815141077926\n",
      "0.4691735854963914 12.67470898835009 0.43576773466210433\n",
      "0.5046947301487251 -35.52114465233373 0.4356685092488356\n",
      "0.4632136595144611 41.48107063426406 0.4357799347040341\n",
      "0.4728493707031361 -9.635711188675003 0.4357596916466667\n",
      "0.46825950233781655 4.589868365319575 0.43576967177985865\n",
      "0.48218893265360485 -13.92943031578831 0.4357372802890797\n",
      "0.4929501035401767 -10.761170886571847 0.4357073711262552\n",
      "0.49289507325179815 0.0550302883785605 0.43570753678950613\n",
      "0.5337858726926237 -40.89079944082546 0.4355326928624836\n",
      "0.5254700238099235 8.315848882700152 0.43557837814968065\n",
      "0.5265307044851749 -1.06068067525149 0.4355728868409018\n",
      "0.500451675220298 26.079029264876908 0.43568339805100154\n",
      "0.5425863280333383 -42.134652813040304 0.43547747820993915\n",
      "0.570933632270421 -28.347304237082767 0.43525156913199375\n",
      "0.6077510997615196 -36.817467491098625 0.43489966811395064\n",
      "0.5634400271602533 44.311072601266346 0.43531786846344733\n",
      "0.6004905735015704 -37.050546341317045 0.43496755626749456\n",
      "0.39216282391207036 208.32774958950006 0.43586423767763227\n",
      "0.3921418800842421 0.020943827828247663 0.43586424931537365\n",
      "0.38849016078792425 3.6517192963178395 0.435866188645378\n",
      "0.39545263658822954 -6.962475800305288 0.4358623342787955\n",
      "0.4033658121322674 -7.91317554403787 0.43585711110942404\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[14], line 33\u001b[0m\n\u001b[1;32m     31\u001b[0m current_cost \u001b[38;5;241m=\u001b[39m var_cost(radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0)\n\u001b[1;32m     32\u001b[0m costs\u001b[38;5;241m.\u001b[39mappend(current_cost)\n\u001b[0;32m---> 33\u001b[0m grad_radius \u001b[38;5;241m=\u001b[39m var_cost_grad(radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0)\n\u001b[1;32m     34\u001b[0m radius_opt \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m=\u001b[39m alpha \u001b[38;5;241m*\u001b[39m grad_radius  \u001b[38;5;66;03m# Update inflation parameter\u001b[39;00m\n\u001b[1;32m     35\u001b[0m radii\u001b[38;5;241m.\u001b[39mappend(radius_opt)\n",
      "    \u001b[0;31m[... skipping hidden 1 frame]\u001b[0m\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/api.py:659\u001b[0m, in \u001b[0;36mgrad.<locals>.grad_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    656\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(fun, docstr\u001b[38;5;241m=\u001b[39mdocstr, argnums\u001b[38;5;241m=\u001b[39margnums)\n\u001b[1;32m    657\u001b[0m \u001b[38;5;129m@api_boundary\u001b[39m\n\u001b[1;32m    658\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad_f\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m--> 659\u001b[0m   _, g \u001b[38;5;241m=\u001b[39m value_and_grad_f(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    660\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m g\n",
      "    \u001b[0;31m[... skipping hidden 1 frame]\u001b[0m\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/api.py:735\u001b[0m, in \u001b[0;36mvalue_and_grad.<locals>.value_and_grad_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    733\u001b[0m   _check_input_dtype_grad(holomorphic, allow_int, leaf)\n\u001b[1;32m    734\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_aux:\n\u001b[0;32m--> 735\u001b[0m   ans, vjp_py \u001b[38;5;241m=\u001b[39m _vjp(f_partial, \u001b[38;5;241m*\u001b[39mdyn_args, reduce_axes\u001b[38;5;241m=\u001b[39mreduce_axes)\n\u001b[1;32m    736\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    737\u001b[0m   ans, vjp_py, aux \u001b[38;5;241m=\u001b[39m _vjp(\n\u001b[1;32m    738\u001b[0m       f_partial, \u001b[38;5;241m*\u001b[39mdyn_args, has_aux\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, reduce_axes\u001b[38;5;241m=\u001b[39mreduce_axes)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/api.py:2223\u001b[0m, in \u001b[0;36m_vjp\u001b[0;34m(fun, has_aux, reduce_axes, *primals)\u001b[0m\n\u001b[1;32m   2221\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_aux:\n\u001b[1;32m   2222\u001b[0m   flat_fun, out_tree \u001b[38;5;241m=\u001b[39m flatten_fun_nokwargs(fun, in_tree)\n\u001b[0;32m-> 2223\u001b[0m   out_primal, out_vjp \u001b[38;5;241m=\u001b[39m ad\u001b[38;5;241m.\u001b[39mvjp(\n\u001b[1;32m   2224\u001b[0m       flat_fun, primals_flat, reduce_axes\u001b[38;5;241m=\u001b[39mreduce_axes)\n\u001b[1;32m   2225\u001b[0m   out_tree \u001b[38;5;241m=\u001b[39m out_tree()\n\u001b[1;32m   2226\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/interpreters/ad.py:142\u001b[0m, in \u001b[0;36mvjp\u001b[0;34m(traceable, primals, has_aux, reduce_axes)\u001b[0m\n\u001b[1;32m    140\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(traceable, primals, has_aux\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m, reduce_axes\u001b[38;5;241m=\u001b[39m()):\n\u001b[1;32m    141\u001b[0m   \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_aux:\n\u001b[0;32m--> 142\u001b[0m     out_primals, pvals, jaxpr, consts \u001b[38;5;241m=\u001b[39m linearize(traceable, \u001b[38;5;241m*\u001b[39mprimals)\n\u001b[1;32m    143\u001b[0m   \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    144\u001b[0m     out_primals, pvals, jaxpr, consts, aux \u001b[38;5;241m=\u001b[39m linearize(traceable, \u001b[38;5;241m*\u001b[39mprimals, has_aux\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/interpreters/ad.py:131\u001b[0m, in \u001b[0;36mlinearize\u001b[0;34m(traceable, *primals, **kwargs)\u001b[0m\n\u001b[1;32m    129\u001b[0m _, in_tree \u001b[38;5;241m=\u001b[39m tree_flatten(((primals, primals), {}))\n\u001b[1;32m    130\u001b[0m jvpfun_flat, out_tree \u001b[38;5;241m=\u001b[39m flatten_fun(jvpfun, in_tree)\n\u001b[0;32m--> 131\u001b[0m jaxpr, out_pvals, consts \u001b[38;5;241m=\u001b[39m pe\u001b[38;5;241m.\u001b[39mtrace_to_jaxpr_nounits(jvpfun_flat, in_pvals)\n\u001b[1;32m    132\u001b[0m out_primals_pvals, out_tangents_pvals \u001b[38;5;241m=\u001b[39m tree_unflatten(out_tree(), out_pvals)\n\u001b[1;32m    133\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m \u001b[38;5;28mall\u001b[39m(out_primal_pval\u001b[38;5;241m.\u001b[39mis_known() \u001b[38;5;28;01mfor\u001b[39;00m out_primal_pval \u001b[38;5;129;01min\u001b[39;00m out_primals_pvals)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/profiler.py:336\u001b[0m, in \u001b[0;36mannotate_function.<locals>.wrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    333\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(func)\n\u001b[1;32m    334\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mwrapper\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m    335\u001b[0m   \u001b[38;5;28;01mwith\u001b[39;00m TraceAnnotation(name, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mdecorator_kwargs):\n\u001b[0;32m--> 336\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m func(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    337\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m wrapper\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/interpreters/partial_eval.py:774\u001b[0m, in \u001b[0;36mtrace_to_jaxpr_nounits\u001b[0;34m(fun, pvals, instantiate)\u001b[0m\n\u001b[1;32m    772\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m core\u001b[38;5;241m.\u001b[39mnew_main(JaxprTrace, name_stack\u001b[38;5;241m=\u001b[39mcurrent_name_stack) \u001b[38;5;28;01mas\u001b[39;00m main:\n\u001b[1;32m    773\u001b[0m   fun \u001b[38;5;241m=\u001b[39m trace_to_subjaxpr_nounits(fun, main, instantiate)\n\u001b[0;32m--> 774\u001b[0m   jaxpr, (out_pvals, consts, env) \u001b[38;5;241m=\u001b[39m fun\u001b[38;5;241m.\u001b[39mcall_wrapped(pvals)\n\u001b[1;32m    775\u001b[0m   \u001b[38;5;28;01massert\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m env\n\u001b[1;32m    776\u001b[0m   \u001b[38;5;28;01mdel\u001b[39;00m main, fun, env\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/linear_util.py:191\u001b[0m, in \u001b[0;36mWrappedFun.call_wrapped\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    188\u001b[0m gen \u001b[38;5;241m=\u001b[39m gen_static_args \u001b[38;5;241m=\u001b[39m out_store \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m    190\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 191\u001b[0m   ans \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mf(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;28mdict\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mparams, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs))\n\u001b[1;32m    192\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m:\n\u001b[1;32m    193\u001b[0m   \u001b[38;5;66;03m# Some transformations yield from inside context managers, so we have to\u001b[39;00m\n\u001b[1;32m    194\u001b[0m   \u001b[38;5;66;03m# interrupt them before reraising the exception. Otherwise they will only\u001b[39;00m\n\u001b[1;32m    195\u001b[0m   \u001b[38;5;66;03m# get garbage-collected at some later time, running their cleanup tasks\u001b[39;00m\n\u001b[1;32m    196\u001b[0m   \u001b[38;5;66;03m# only after this exception is handled, which can corrupt the global\u001b[39;00m\n\u001b[1;32m    197\u001b[0m   \u001b[38;5;66;03m# state.\u001b[39;00m\n\u001b[1;32m    198\u001b[0m   \u001b[38;5;28;01mwhile\u001b[39;00m stack:\n",
      "    \u001b[0;31m[... skipping hidden 1 frame]\u001b[0m\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/pjit.py:257\u001b[0m, in \u001b[0;36m_cpp_pjit.<locals>.cache_miss\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    255\u001b[0m \u001b[38;5;129m@api_boundary\u001b[39m\n\u001b[1;32m    256\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mcache_miss\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m--> 257\u001b[0m   outs, out_flat, out_tree, args_flat, jaxpr \u001b[38;5;241m=\u001b[39m _python_pjit_helper(\n\u001b[1;32m    258\u001b[0m       fun, infer_params_fn, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    259\u001b[0m   executable \u001b[38;5;241m=\u001b[39m _read_most_recent_pjit_call_executable(jaxpr)\n\u001b[1;32m    260\u001b[0m   fastpath_data \u001b[38;5;241m=\u001b[39m _get_fastpath_data(executable, out_tree, args_flat, out_flat)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/pjit.py:168\u001b[0m, in \u001b[0;36m_python_pjit_helper\u001b[0;34m(fun, infer_params_fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m    166\u001b[0m   dispatch\u001b[38;5;241m.\u001b[39mcheck_arg(arg)\n\u001b[1;32m    167\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 168\u001b[0m   out_flat \u001b[38;5;241m=\u001b[39m pjit_p\u001b[38;5;241m.\u001b[39mbind(\u001b[38;5;241m*\u001b[39margs_flat, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mparams)\n\u001b[1;32m    169\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m pxla\u001b[38;5;241m.\u001b[39mDeviceAssignmentMismatchError \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[1;32m    170\u001b[0m   fails, \u001b[38;5;241m=\u001b[39m e\u001b[38;5;241m.\u001b[39margs\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/core.py:2740\u001b[0m, in \u001b[0;36mAxisPrimitive.bind\u001b[0;34m(self, *args, **params)\u001b[0m\n\u001b[1;32m   2736\u001b[0m axis_main \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmax\u001b[39m((axis_frame(a)\u001b[38;5;241m.\u001b[39mmain_trace \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m used_axis_names(\u001b[38;5;28mself\u001b[39m, params)),\n\u001b[1;32m   2737\u001b[0m                 default\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, key\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mlambda\u001b[39;00m t: \u001b[38;5;28mgetattr\u001b[39m(t, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlevel\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m))\n\u001b[1;32m   2738\u001b[0m top_trace \u001b[38;5;241m=\u001b[39m (top_trace \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m axis_main \u001b[38;5;129;01mor\u001b[39;00m axis_main\u001b[38;5;241m.\u001b[39mlevel \u001b[38;5;241m<\u001b[39m top_trace\u001b[38;5;241m.\u001b[39mlevel\n\u001b[1;32m   2739\u001b[0m              \u001b[38;5;28;01melse\u001b[39;00m axis_main\u001b[38;5;241m.\u001b[39mwith_cur_sublevel())\n\u001b[0;32m-> 2740\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbind_with_trace(top_trace, args, params)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/core.py:447\u001b[0m, in \u001b[0;36mPrimitive.bind_with_trace\u001b[0;34m(self, trace, args, params)\u001b[0m\n\u001b[1;32m    446\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mbind_with_trace\u001b[39m(\u001b[38;5;28mself\u001b[39m, trace, args, params):\n\u001b[0;32m--> 447\u001b[0m   out \u001b[38;5;241m=\u001b[39m trace\u001b[38;5;241m.\u001b[39mprocess_primitive(\u001b[38;5;28mself\u001b[39m, \u001b[38;5;28mmap\u001b[39m(trace\u001b[38;5;241m.\u001b[39mfull_raise, args), params)\n\u001b[1;32m    448\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mmap\u001b[39m(full_lower, out) \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmultiple_results \u001b[38;5;28;01melse\u001b[39;00m full_lower(out)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/interpreters/ad.py:318\u001b[0m, in \u001b[0;36mJVPTrace.process_primitive\u001b[0;34m(self, primitive, tracers, params)\u001b[0m\n\u001b[1;32m    316\u001b[0m   msg \u001b[38;5;241m=\u001b[39m \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mDifferentiation rule for \u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mprimitive\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m not implemented\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    317\u001b[0m   \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(msg)\n\u001b[0;32m--> 318\u001b[0m primal_out, tangent_out \u001b[38;5;241m=\u001b[39m jvp(primals_in, tangents_in, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mparams)\n\u001b[1;32m    319\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m primitive\u001b[38;5;241m.\u001b[39mmultiple_results:\n\u001b[1;32m    320\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m [JVPTracer(\u001b[38;5;28mself\u001b[39m, x, t) \u001b[38;5;28;01mfor\u001b[39;00m x, t \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(primal_out, tangent_out)]\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/pjit.py:1558\u001b[0m, in \u001b[0;36m_pjit_jvp\u001b[0;34m(primals_in, tangents_in, jaxpr, in_shardings, out_shardings, resource_env, donated_invars, name, keep_unused, inline)\u001b[0m\n\u001b[1;32m   1556\u001b[0m _filter_zeros_in \u001b[38;5;241m=\u001b[39m partial(_filter_zeros, is_nz_tangents_in)\n\u001b[1;32m   1557\u001b[0m _filter_zeros_out \u001b[38;5;241m=\u001b[39m partial(_filter_zeros, is_nz_tangents_out)\n\u001b[0;32m-> 1558\u001b[0m outputs \u001b[38;5;241m=\u001b[39m pjit_p\u001b[38;5;241m.\u001b[39mbind(\n\u001b[1;32m   1559\u001b[0m     \u001b[38;5;241m*\u001b[39mprimals_in, \u001b[38;5;241m*\u001b[39m_filter_zeros_in(tangents_in),\n\u001b[1;32m   1560\u001b[0m     jaxpr\u001b[38;5;241m=\u001b[39mjaxpr_jvp,\n\u001b[1;32m   1561\u001b[0m     in_shardings\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m*\u001b[39min_shardings, \u001b[38;5;241m*\u001b[39m_filter_zeros_in(in_shardings)),\n\u001b[1;32m   1562\u001b[0m     out_shardings\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m*\u001b[39mout_shardings, \u001b[38;5;241m*\u001b[39m_filter_zeros_out(out_shardings)),\n\u001b[1;32m   1563\u001b[0m     resource_env\u001b[38;5;241m=\u001b[39mresource_env,\n\u001b[1;32m   1564\u001b[0m     donated_invars\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m*\u001b[39mdonated_invars, \u001b[38;5;241m*\u001b[39m_filter_zeros_in(donated_invars)),\n\u001b[1;32m   1565\u001b[0m     name\u001b[38;5;241m=\u001b[39mname,\n\u001b[1;32m   1566\u001b[0m     keep_unused\u001b[38;5;241m=\u001b[39mkeep_unused,\n\u001b[1;32m   1567\u001b[0m     inline\u001b[38;5;241m=\u001b[39minline)\n\u001b[1;32m   1569\u001b[0m primals_out, tangents_out \u001b[38;5;241m=\u001b[39m split_list(outputs, [\u001b[38;5;28mlen\u001b[39m(jaxpr\u001b[38;5;241m.\u001b[39mjaxpr\u001b[38;5;241m.\u001b[39moutvars)])\n\u001b[1;32m   1570\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(primals_out) \u001b[38;5;241m==\u001b[39m \u001b[38;5;28mlen\u001b[39m(jaxpr\u001b[38;5;241m.\u001b[39mjaxpr\u001b[38;5;241m.\u001b[39moutvars)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/core.py:2740\u001b[0m, in \u001b[0;36mAxisPrimitive.bind\u001b[0;34m(self, *args, **params)\u001b[0m\n\u001b[1;32m   2736\u001b[0m axis_main \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmax\u001b[39m((axis_frame(a)\u001b[38;5;241m.\u001b[39mmain_trace \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m used_axis_names(\u001b[38;5;28mself\u001b[39m, params)),\n\u001b[1;32m   2737\u001b[0m                 default\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, key\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mlambda\u001b[39;00m t: \u001b[38;5;28mgetattr\u001b[39m(t, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlevel\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m))\n\u001b[1;32m   2738\u001b[0m top_trace \u001b[38;5;241m=\u001b[39m (top_trace \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m axis_main \u001b[38;5;129;01mor\u001b[39;00m axis_main\u001b[38;5;241m.\u001b[39mlevel \u001b[38;5;241m<\u001b[39m top_trace\u001b[38;5;241m.\u001b[39mlevel\n\u001b[1;32m   2739\u001b[0m              \u001b[38;5;28;01melse\u001b[39;00m axis_main\u001b[38;5;241m.\u001b[39mwith_cur_sublevel())\n\u001b[0;32m-> 2740\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbind_with_trace(top_trace, args, params)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/core.py:447\u001b[0m, in \u001b[0;36mPrimitive.bind_with_trace\u001b[0;34m(self, trace, args, params)\u001b[0m\n\u001b[1;32m    446\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mbind_with_trace\u001b[39m(\u001b[38;5;28mself\u001b[39m, trace, args, params):\n\u001b[0;32m--> 447\u001b[0m   out \u001b[38;5;241m=\u001b[39m trace\u001b[38;5;241m.\u001b[39mprocess_primitive(\u001b[38;5;28mself\u001b[39m, \u001b[38;5;28mmap\u001b[39m(trace\u001b[38;5;241m.\u001b[39mfull_raise, args), params)\n\u001b[1;32m    448\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mmap\u001b[39m(full_lower, out) \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmultiple_results \u001b[38;5;28;01melse\u001b[39;00m full_lower(out)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/interpreters/partial_eval.py:212\u001b[0m, in \u001b[0;36mJaxprTrace.process_primitive\u001b[0;34m(self, primitive, tracers, params)\u001b[0m\n\u001b[1;32m    210\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mprocess_primitive\u001b[39m(\u001b[38;5;28mself\u001b[39m, primitive, tracers, params):\n\u001b[1;32m    211\u001b[0m   \u001b[38;5;28;01mif\u001b[39;00m primitive \u001b[38;5;129;01min\u001b[39;00m custom_partial_eval_rules:\n\u001b[0;32m--> 212\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m custom_partial_eval_rules[primitive](\u001b[38;5;28mself\u001b[39m, \u001b[38;5;241m*\u001b[39mtracers, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mparams)\n\u001b[1;32m    213\u001b[0m   \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    214\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mdefault_process_primitive(primitive, tracers, params)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/pjit.py:1635\u001b[0m, in \u001b[0;36m_pjit_partial_eval\u001b[0;34m(trace, jaxpr, in_shardings, out_shardings, resource_env, donated_invars, name, keep_unused, inline, *in_tracers)\u001b[0m\n\u001b[1;32m   1633\u001b[0m \u001b[38;5;66;03m# Bind known things to pjit_p.\u001b[39;00m\n\u001b[1;32m   1634\u001b[0m known_inputs \u001b[38;5;241m=\u001b[39m [pv\u001b[38;5;241m.\u001b[39mget_known() \u001b[38;5;28;01mfor\u001b[39;00m pv \u001b[38;5;129;01min\u001b[39;00m in_pvals \u001b[38;5;28;01mif\u001b[39;00m pv\u001b[38;5;241m.\u001b[39mis_known()]\n\u001b[0;32m-> 1635\u001b[0m all_known_outs \u001b[38;5;241m=\u001b[39m pjit_p\u001b[38;5;241m.\u001b[39mbind(\u001b[38;5;241m*\u001b[39mknown_inputs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mknown_params)\n\u001b[1;32m   1636\u001b[0m all_known_outs \u001b[38;5;241m=\u001b[39m subs_list2(in_fwd, out_fwd, known_inputs, all_known_outs,\n\u001b[1;32m   1637\u001b[0m                             all_known_outs)\n\u001b[1;32m   1639\u001b[0m known_out_vals, residual_vals \u001b[38;5;241m=\u001b[39m \\\n\u001b[1;32m   1640\u001b[0m     split_list(all_known_outs, [\u001b[38;5;28mlen\u001b[39m(all_known_outs) \u001b[38;5;241m-\u001b[39m num_residuals])\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/core.py:2740\u001b[0m, in \u001b[0;36mAxisPrimitive.bind\u001b[0;34m(self, *args, **params)\u001b[0m\n\u001b[1;32m   2736\u001b[0m axis_main \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmax\u001b[39m((axis_frame(a)\u001b[38;5;241m.\u001b[39mmain_trace \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m used_axis_names(\u001b[38;5;28mself\u001b[39m, params)),\n\u001b[1;32m   2737\u001b[0m                 default\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, key\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mlambda\u001b[39;00m t: \u001b[38;5;28mgetattr\u001b[39m(t, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlevel\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m))\n\u001b[1;32m   2738\u001b[0m top_trace \u001b[38;5;241m=\u001b[39m (top_trace \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m axis_main \u001b[38;5;129;01mor\u001b[39;00m axis_main\u001b[38;5;241m.\u001b[39mlevel \u001b[38;5;241m<\u001b[39m top_trace\u001b[38;5;241m.\u001b[39mlevel\n\u001b[1;32m   2739\u001b[0m              \u001b[38;5;28;01melse\u001b[39;00m axis_main\u001b[38;5;241m.\u001b[39mwith_cur_sublevel())\n\u001b[0;32m-> 2740\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbind_with_trace(top_trace, args, params)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/core.py:447\u001b[0m, in \u001b[0;36mPrimitive.bind_with_trace\u001b[0;34m(self, trace, args, params)\u001b[0m\n\u001b[1;32m    446\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mbind_with_trace\u001b[39m(\u001b[38;5;28mself\u001b[39m, trace, args, params):\n\u001b[0;32m--> 447\u001b[0m   out \u001b[38;5;241m=\u001b[39m trace\u001b[38;5;241m.\u001b[39mprocess_primitive(\u001b[38;5;28mself\u001b[39m, \u001b[38;5;28mmap\u001b[39m(trace\u001b[38;5;241m.\u001b[39mfull_raise, args), params)\n\u001b[1;32m    448\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mmap\u001b[39m(full_lower, out) \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmultiple_results \u001b[38;5;28;01melse\u001b[39;00m full_lower(out)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/core.py:935\u001b[0m, in \u001b[0;36mEvalTrace.process_primitive\u001b[0;34m(self, primitive, tracers, params)\u001b[0m\n\u001b[1;32m    934\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mprocess_primitive\u001b[39m(\u001b[38;5;28mself\u001b[39m, primitive, tracers, params):\n\u001b[0;32m--> 935\u001b[0m   \u001b[38;5;28;01mreturn\u001b[39;00m primitive\u001b[38;5;241m.\u001b[39mimpl(\u001b[38;5;241m*\u001b[39mtracers, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mparams)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.11/site-packages/jax/_src/pjit.py:1245\u001b[0m, in \u001b[0;36m_pjit_call_impl\u001b[0;34m(jaxpr, in_shardings, out_shardings, resource_env, donated_invars, name, keep_unused, inline, *args)\u001b[0m\n\u001b[1;32m   1242\u001b[0m donated_argnums \u001b[38;5;241m=\u001b[39m [i \u001b[38;5;28;01mfor\u001b[39;00m i, d \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(donated_invars) \u001b[38;5;28;01mif\u001b[39;00m d]\n\u001b[1;32m   1243\u001b[0m has_explicit_sharding \u001b[38;5;241m=\u001b[39m _pjit_explicit_sharding(\n\u001b[1;32m   1244\u001b[0m     in_shardings, out_shardings, \u001b[38;5;28;01mNone\u001b[39;00m, \u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[0;32m-> 1245\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m xc\u001b[38;5;241m.\u001b[39m_xla\u001b[38;5;241m.\u001b[39mpjit(name, f, call_impl_cache_miss, [], [], donated_argnums,\n\u001b[1;32m   1246\u001b[0m                     tree_util\u001b[38;5;241m.\u001b[39mdispatch_registry,\n\u001b[1;32m   1247\u001b[0m                     _get_cpp_global_cache(has_explicit_sharding))(\u001b[38;5;241m*\u001b[39margs)\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "import properscoring\n",
    "from IPython.display import clear_output\n",
    "from jax import grad\n",
    "from tqdm.notebook import tqdm\n",
    "import jax.numpy as jnp\n",
    "from jax import random\n",
    "\n",
    "\n",
    "var_cost_grad = grad(var_cost, argnums=0)\n",
    "\n",
    "inflation = 1.05  # Fixed starting value for inflation\n",
    "radius_opt = 7.0\n",
    "alpha = 1e-3  # Learning rate\n",
    "key = random.PRNGKey(0)  # Random key\n",
    "N = 10  # Number of MC samples\n",
    "m0 = initial_state\n",
    "C0 = Q  # Initial covariance, assuming Q is your process noise covariance\n",
    "ensemble_init = random.multivariate_normal(key, initial_state, Q, (n_ensemble,)).T\n",
    "\n",
    "crpss = []\n",
    "radii = []\n",
    "rmses=[]\n",
    "true_div = []\n",
    "costs = []\n",
    "\n",
    "\n",
    "for i in tqdm(range(100)):\n",
    "    key, subkey = random.split(key)\n",
    "        \n",
    "    # Gradient descent step for inflation parameter\n",
    "    current_cost = var_cost(radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0)\n",
    "    costs.append(current_cost)\n",
    "    grad_radius = var_cost_grad(radius_opt, inflation, l96_step, ensemble_init, observations, H, Q, R, subkey, num_steps, J0)\n",
    "    radius_opt -= alpha * grad_radius  # Update inflation parameter\n",
    "    radii.append(radius_opt)\n",
    "    localization_matrix = generate_localization_matrix(n, radius_opt)\n",
    "\n",
    "    predicted_states, pred_covariances, states, covariances = ensrf_steps(l96_step, ensemble_init, num_steps, observations, observation_interval, H, Q, R, localization_matrix, inflation, key)\n",
    "    ensemble_mean = jnp.mean(states, axis=-1)  # Taking the mean across the ensemble members dimension\n",
    "    rmse = jnp.sqrt(jnp.mean((ensemble_mean - true_states)**2))\n",
    "    print(radius_opt, grad_radius, rmse)\n",
    "    rmses.append(rmse)\n",
    "    crps = properscoring.crps_ensemble(true_states, states).mean(axis=1).mean()\n",
    "    crpss.append(crps)\n",
    "    total_kl_divergence = 0\n",
    "    for t in range(num_steps):  \n",
    "        kl_div_t = KL_gaussian(n, ensemble_mean[t], covariances[t],  base_m[t], base_C[t])\n",
    "        total_kl_divergence += kl_div_t \n",
    "    true_div.append(total_kl_divergence / num_steps)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2ce4e6a210>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2ce514b410>]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rmses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(10, 6))\n",
    "\n",
    "# Plotting the RMSE and CRPS on the primary y-axis\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('Iteration')\n",
    "ax1.set_ylabel('RMSE / CRPS', color=color)\n",
    "ln1 = ax1.plot(rmses, label='RMSE', color='tab:orange', linestyle='-')\n",
    "ln2 = ax1.plot(crpss, label='CRPS', color='tab:red', linestyle='--')\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "# Create a twin y-axis for the inflation parameter\n",
    "ax2 = ax1.twinx()\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('Localization Radius', color=color)\n",
    "ln3 = ax2.plot(radii, label='Radius', color=color, linestyle=':')\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "# Combine legends from both axes\n",
    "lns = ln1 + ln2 + ln3\n",
    "labs = [l.get_label() for l in lns]\n",
    "ax1.legend(lns, labs, loc='upper right')\n",
    "\n",
    "plt.title('RMSE, CRPS, and Radius Parameter over Iterations')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([3, 6, 12, 25, 50, 100, 200], [2.3, 5.75, 7.8, 11.6, 16, 26.8, 44.2])\n",
    "plt.xlabel(\"Ensemble size\")\n",
    "plt.ylabel(\"Optimal localization radius\")\n",
    "plt.savefig(\"localization_radii.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}