notebooks/L63 Timings.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "cf4673d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "35ea1c3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"..\")\n",
    "import time\n",
    "import warnings\n",
    "from pathlib import Path\n",
    "from copy import copy\n",
    "\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "from falkon.kernels import GaussianKernel\n",
    "from falkon import FalkonOptions\n",
    "from nyskoop.data.lorenz import Lorenz63\n",
    "from experiment_helpers import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "c2c4599a",
   "metadata": {},
   "outputs": [],
   "source": [
    "set_matplotlib_rc(18, 20, 22)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "fc7a6298",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_l63_fulldata(n_train: int, n_test: int, num_test_sets: int, max_q: int, **kwargs):\n",
    "    ics = np.array([1, 1, 1])\n",
    "    lorenz63_dset = Lorenz63(ics[0], ics[1], ics[2], sigma=10, rho=28, beta=8/3, **kwargs)\n",
    "    full_data = lorenz63_dset.solve(n_train + num_test_sets * n_test + max_q * (num_test_sets + 1))\n",
    "    full_data = torch.from_numpy(full_data)\n",
    "    return full_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "d7262043",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig_path = Path(\"outputs/timings\")\n",
    "fig_path.mkdir(exist_ok=True, parents=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "197e2961",
   "metadata": {},
   "source": [
    "**Generate the whole dataset. Max 10k training points**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "ea073273",
   "metadata": {},
   "outputs": [],
   "source": [
    "q = 40  # How many steps-ahead for predictions\n",
    "num_test_sets = 5\n",
    "n_test = 10_000\n",
    "full_data = gen_l63_fulldata(\n",
    "    100_000, n_test, num_test_sets, max_q=q, dt=0.01, burnin=5, l63_version='normal'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30a63159",
   "metadata": {},
   "source": [
    "**Helper functions to run the experiments**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "30cbaac2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "id": "312dc1fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_data_get_error(n_train, n_reps, dtype, **model_hps):\n",
    "    X_train, Y_train, all_test_sets = gen_lagged(\n",
    "        full_data, n_train, n_test, num_test_sets, q, dtype=dtype\n",
    "    )\n",
    "    errs, times = [], []\n",
    "    for i in range(n_reps):\n",
    "        t_start = time.time()\n",
    "        if \"M\" in model_hps:\n",
    "            model_hps[\"M\"] = int(5 * np.sqrt(n_train))\n",
    "        if \"penalty\" in model_hps:\n",
    "            model_hps[\"penalty\"] = 1 / np.sqrt(n)\n",
    "        est = train_est(X_train, Y_train, **model_hps)\n",
    "        t_end = time.time()\n",
    "        times.append(t_end - t_start)\n",
    "        err = nrmse(est, all_test_sets, variable='all')[0].mean()\n",
    "        errs.append(err.item())\n",
    "    return (\n",
    "        np.median(errs),\n",
    "        np.percentile(errs, 90),\n",
    "        np.percentile(errs, 10),\n",
    "        np.min(times)\n",
    "   )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "55eca15d",
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def hp_search_inner(hp_dict, fn, out_df: pd.DataFrame, pbar: tqdm, **kwargs):\n",
    "    new_dict = copy(hp_dict)\n",
    "    \n",
    "    final_hp_key, hp_list = None, []\n",
    "    for hp_key in list(new_dict.keys()):\n",
    "        hp_list = new_dict.pop(hp_key)\n",
    "        # Allow to specify different HP values for different 'kind' of algorithms\n",
    "        if isinstance(hp_list, dict):\n",
    "            hp_list = hp_list.get(kwargs['kind'], [])\n",
    "        if len(hp_list) > 0:\n",
    "            final_hp_key = hp_key\n",
    "            break\n",
    "    \n",
    "    if len(new_dict) == 0 and final_hp_key is None:  # base case??\n",
    "        err, err_high, err_low, t_elapsed = fn(**kwargs)\n",
    "        kwargs[\"err\"] = err\n",
    "        kwargs[\"err_high\"] = err_high\n",
    "        kwargs[\"err_low\"] = err_low\n",
    "        kwargs[\"time\"] = t_elapsed\n",
    "        pbar.update(1)\n",
    "        return pd.DataFrame.from_dict([kwargs])\n",
    "    \n",
    "    hp_dfs = []\n",
    "    for hp_val in hp_list:\n",
    "        kwargs[final_hp_key] = hp_val\n",
    "        try:\n",
    "            hp_dfs.append(hp_search_inner(new_dict, fn, out_df, pbar, **kwargs))\n",
    "        except Exception as e:\n",
    "            warnings.warn(f\"{kwargs} failed.\")\n",
    "            raise\n",
    "    return pd.concat([out_df] + hp_dfs)\n",
    "\n",
    "def hp_search(hp_dict, fn, out_df, **kwargs):\n",
    "    np.random.seed(42)\n",
    "    torch.manual_seed(42)\n",
    "    # Calculate total iterations taking into account the special dict case\n",
    "    total = 0\n",
    "    for algo_kind in hp_dict[\"kind\"]:\n",
    "        subtotal = 1\n",
    "        for k, v, in hp_dict.items():\n",
    "            if k == \"kind\": continue\n",
    "            if isinstance(v, dict):\n",
    "                subtotal *= len(v.get(algo_kind, [1]))\n",
    "            elif isinstance(v, list) or isinstance(v, tuple):\n",
    "                subtotal *= len(v)\n",
    "        total += subtotal\n",
    "    with tqdm(desc='HP Search', total=total, mininterval=1.0) as pbar:\n",
    "        return hp_search_inner(hp_dict, fn, out_df, pbar, **kwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43fc8e9c",
   "metadata": {},
   "source": [
    "**Define hyperparameters**\n",
    "\n",
    "The `kind` key defines which estimators will run.\n",
    "\n",
    "The other keys are hyperparameters for either the estimators or the data generation.\n",
    "\n",
    "Remember to set the **exp_name** variable appropriately!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "id": "86c9e180",
   "metadata": {},
   "outputs": [],
   "source": [
    "pcr_hps_n = {\n",
    "    \"kind\": [\"pcr\", \"rrr\", \"krr\"],#[\"full_rrr\", \"rrr\", \"full_pcr\", \"pcr\", ],\n",
    "    \"M\": {\"pcr\": [250], \"rrr\": [250], \"krr\": [250]},\n",
    "    \"kernel\": [GaussianKernel(3.5, opt=FalkonOptions(use_cpu=True))],\n",
    "    \"num_components\": {\n",
    "        \"pcr\": [25],\n",
    "        \"full_rrr\": [25],\n",
    "        \"rrr\": [25],\n",
    "        \"full_pcr\": [25],\n",
    "    },\n",
    "    # 'n_train' is the x-axis for this experiment: time/error as n_train increases.\n",
    "    \"n_train\": {\n",
    "        \"full_rrr\": np.logspace(2, 4, 10, dtype=int)[:-2],  # takes too long if we go up to 10**4\n",
    "        \"rrr\": np.logspace(2, 4.8, 20, dtype=int),\n",
    "        \"full_pcr\": np.logspace(2, 4, 10, dtype=int),\n",
    "        \"pcr\": np.logspace(2, 4.8, 20, dtype=int),\n",
    "        \"krr\": np.logspace(2, 4.8, 20, dtype=int),\n",
    "    },\n",
    "    \"n_reps\": {\n",
    "        \"full_rrr\": [2],  # only 2 reps since there is no variability in error (only in timings)\n",
    "        \"full_pcr\": [2],\n",
    "        \"rrr\": [20],\n",
    "        \"pcr\": [20],\n",
    "        \"krr\": [20]\n",
    "    },\n",
    "    \"dtype\": [torch.float32],\n",
    "    \"penalty\": {\"rrr\": [1e-4], \"full_rrr\": [1e-4], \"krr\": [1e-2]},\n",
    "}\n",
    "exp_name = \"l63_varym_varyn_5sqrtn\"\n",
    "pcr_n_df_path = Path(f\"outputs/timings/{exp_name}.csv\")\n",
    "pcr_n_df_path.parent.mkdir(parents=True, exist_ok=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "95812314",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f7da3e4c",
   "metadata": {},
   "source": [
    "**Run experiment with increasing training set size**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "id": "2a6cd12a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "HP Search:  33%|██████████▋                     | 20/60 [01:32<09:23, 14.09s/it]/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr', 'M': 250, 'kernel': GaussianKernel(sigma=Parameter containing:\n",
      "tensor([3.5000], dtype=torch.float64)), 'num_components': 25, 'n_train': 100, 'n_reps': 20, 'dtype': torch.float32, 'penalty': 0.0001} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr', 'M': 250, 'kernel': GaussianKernel(sigma=Parameter containing:\n",
      "tensor([3.5000], dtype=torch.float64)), 'num_components': 25, 'n_train': 100, 'n_reps': 20, 'dtype': torch.float32} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr', 'M': 250, 'kernel': GaussianKernel(sigma=Parameter containing:\n",
      "tensor([3.5000], dtype=torch.float64)), 'num_components': 25, 'n_train': 100, 'n_reps': 20} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr', 'M': 250, 'kernel': GaussianKernel(sigma=Parameter containing:\n",
      "tensor([3.5000], dtype=torch.float64)), 'num_components': 25, 'n_train': 100} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr', 'M': 250, 'kernel': GaussianKernel(sigma=Parameter containing:\n",
      "tensor([3.5000], dtype=torch.float64)), 'num_components': 25} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr', 'M': 250, 'kernel': GaussianKernel(sigma=Parameter containing:\n",
      "tensor([3.5000], dtype=torch.float64))} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr', 'M': 250} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "/tmp/ipykernel_2868/1204261774.py:29: UserWarning: {'kind': 'rrr'} failed.\n",
      "  warnings.warn(f\"{kwargs} failed.\")\n",
      "HP Search:  33%|██████████▋                     | 20/60 [01:32<03:04,  4.62s/it]\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'n' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[301], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m pcr_n_df \u001b[38;5;241m=\u001b[39m \u001b[43mhp_search\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m      2\u001b[0m \u001b[43m    \u001b[49m\u001b[43mpcr_hps_n\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[43m    \u001b[49m\u001b[43mgen_data_get_error\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      4\u001b[0m \u001b[43m    \u001b[49m\u001b[43mpd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mDataFrame\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      5\u001b[0m \u001b[43m)\u001b[49m\n\u001b[1;32m      6\u001b[0m pcr_n_df[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msigma\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m pcr_n_df[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mkernel\u001b[39m\u001b[38;5;124m\"\u001b[39m]\u001b[38;5;241m.\u001b[39mapply(\u001b[38;5;28;01mlambda\u001b[39;00m r: r\u001b[38;5;241m.\u001b[39msigma\u001b[38;5;241m.\u001b[39mitem())\n\u001b[1;32m      7\u001b[0m pcr_n_df \u001b[38;5;241m=\u001b[39m pcr_n_df\u001b[38;5;241m.\u001b[39mdrop(columns\u001b[38;5;241m=\u001b[39m[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mkernel\u001b[39m\u001b[38;5;124m\"\u001b[39m])\n",
      "Cell \u001b[0;32mIn[146], line 48\u001b[0m, in \u001b[0;36mhp_search\u001b[0;34m(hp_dict, fn, out_df, **kwargs)\u001b[0m\n\u001b[1;32m     46\u001b[0m     total \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m subtotal\n\u001b[1;32m     47\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m tqdm(desc\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mHP Search\u001b[39m\u001b[38;5;124m'\u001b[39m, total\u001b[38;5;241m=\u001b[39mtotal, mininterval\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1.0\u001b[39m) \u001b[38;5;28;01mas\u001b[39;00m pbar:\n\u001b[0;32m---> 48\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mhp_search_inner\u001b[49m\u001b[43m(\u001b[49m\u001b[43mhp_dict\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mout_df\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpbar\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[0;32mIn[146], line 27\u001b[0m, in \u001b[0;36mhp_search_inner\u001b[0;34m(hp_dict, fn, out_df, pbar, **kwargs)\u001b[0m\n\u001b[1;32m     25\u001b[0m kwargs[final_hp_key] \u001b[38;5;241m=\u001b[39m hp_val\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 27\u001b[0m     hp_dfs\u001b[38;5;241m.\u001b[39mappend(\u001b[43mhp_search_inner\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnew_dict\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mout_df\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpbar\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[1;32m     29\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mwarn(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mkwargs\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m failed.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "Cell \u001b[0;32mIn[146], line 27\u001b[0m, in \u001b[0;36mhp_search_inner\u001b[0;34m(hp_dict, fn, out_df, pbar, **kwargs)\u001b[0m\n\u001b[1;32m     25\u001b[0m kwargs[final_hp_key] \u001b[38;5;241m=\u001b[39m hp_val\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 27\u001b[0m     hp_dfs\u001b[38;5;241m.\u001b[39mappend(\u001b[43mhp_search_inner\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnew_dict\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mout_df\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpbar\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[1;32m     29\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mwarn(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mkwargs\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m failed.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "    \u001b[0;31m[... skipping similar frames: hp_search_inner at line 27 (5 times)]\u001b[0m\n",
      "Cell \u001b[0;32mIn[146], line 27\u001b[0m, in \u001b[0;36mhp_search_inner\u001b[0;34m(hp_dict, fn, out_df, pbar, **kwargs)\u001b[0m\n\u001b[1;32m     25\u001b[0m kwargs[final_hp_key] \u001b[38;5;241m=\u001b[39m hp_val\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 27\u001b[0m     hp_dfs\u001b[38;5;241m.\u001b[39mappend(\u001b[43mhp_search_inner\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnew_dict\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mout_df\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpbar\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[1;32m     29\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mwarn(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mkwargs\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m failed.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "Cell \u001b[0;32mIn[146], line 15\u001b[0m, in \u001b[0;36mhp_search_inner\u001b[0;34m(hp_dict, fn, out_df, pbar, **kwargs)\u001b[0m\n\u001b[1;32m     12\u001b[0m         \u001b[38;5;28;01mbreak\u001b[39;00m\n\u001b[1;32m     14\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(new_dict) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m final_hp_key \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:  \u001b[38;5;66;03m# base case??\u001b[39;00m\n\u001b[0;32m---> 15\u001b[0m     err, err_high, err_low, t_elapsed \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     16\u001b[0m     kwargs[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124merr\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m err\n\u001b[1;32m     17\u001b[0m     kwargs[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124merr_high\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m err_high\n",
      "Cell \u001b[0;32mIn[299], line 11\u001b[0m, in \u001b[0;36mgen_data_get_error\u001b[0;34m(n_train, n_reps, dtype, **model_hps)\u001b[0m\n\u001b[1;32m      9\u001b[0m     model_hps[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mM\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mint\u001b[39m(\u001b[38;5;241m5\u001b[39m \u001b[38;5;241m*\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(n_train))\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpenalty\u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;129;01min\u001b[39;00m model_hps:\n\u001b[0;32m---> 11\u001b[0m     model_hps[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpenalty\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m \u001b[38;5;241m/\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(\u001b[43mn\u001b[49m)\n\u001b[1;32m     12\u001b[0m est \u001b[38;5;241m=\u001b[39m train_est(X_train, Y_train, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mmodel_hps)\n\u001b[1;32m     13\u001b[0m t_end \u001b[38;5;241m=\u001b[39m time\u001b[38;5;241m.\u001b[39mtime()\n",
      "\u001b[0;31mNameError\u001b[0m: name 'n' is not defined"
     ]
    }
   ],
   "source": [
    "pcr_n_df = hp_search(\n",
    "    pcr_hps_n, \n",
    "    gen_data_get_error,\n",
    "    pd.DataFrame()\n",
    ")\n",
    "pcr_n_df[\"sigma\"] = pcr_n_df[\"kernel\"].apply(lambda r: r.sigma.item())\n",
    "pcr_n_df = pcr_n_df.drop(columns=[\"kernel\"])\n",
    "pcr_n_df.to_csv(pcr_n_df_path, index=False)\n",
    "print(f\"Saved experiment statistics at {pcr_n_df_path}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "id": "d6807d79",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting results from experiment at outputs/timings/l63_varym_varyn_5sqrtn.csv\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f\"Plotting results from experiment at {pcr_n_df_path}\")\n",
    "plot_time = False\n",
    "plot_fit = True\n",
    "if plot_time:\n",
    "    fig, ax = plt.subplots(ncols=2, figsize=(8, 4))\n",
    "else:\n",
    "    fig, ax = plt.subplots(ncols=1, figsize=(6, 4))\n",
    "    ax = [ax]\n",
    "models = [\n",
    "#     (\"full_rrr\", \"FullRRR\", IBM_COLORS[3], \"-\", f\"outputs/timings/l63_varyn_m250_all.csv\"),\n",
    "    (\"rrr\", \"NysRRR\", IBM_COLORS[1], \"--\",      f\"outputs/timings/l63_varym_varyn_5sqrtn.csv\"),\n",
    "#     (\"full_pcr\", \"FullPCR\", IBM_COLORS[0], \"-\", f\"outputs/timings/l63_varyn_m250_all.csv\"),\n",
    "    (\"pcr\", \"NysPCR\", IBM_COLORS[2], \"--\",      f\"outputs/timings/l63_varym_varyn_5sqrtn.csv\"),\n",
    "    (\"krr\", \"NysKRR\", IBM_COLORS[0], \"--\",      f\"outputs/timings/l63_varym_varyn_5sqrtn.csv\"),\n",
    "]\n",
    "\n",
    "for kind, lbl, c, ls, path in models:\n",
    "    df = pd.read_csv(path)\n",
    "    # Error\n",
    "    ax[0].plot(\n",
    "        df[df[\"kind\"] == kind][\"n_train\"],\n",
    "        df[df[\"kind\"] == kind][\"err\"], label=lbl, \n",
    "        c=c, marker='o', lw=2, linestyle=ls\n",
    "    )\n",
    "    ax[0].fill_between(\n",
    "        df[df[\"kind\"] == kind][\"n_train\"],\n",
    "        df[df[\"kind\"] == kind][\"err_low\"],\n",
    "        df[df[\"kind\"] == kind][\"err_high\"],\n",
    "        color=c, alpha=0.3,\n",
    "    )\n",
    "    if plot_fit:\n",
    "        fitx = np.linspace(100, ax[0].get_xlim()[1], 1000)\n",
    "#         coefs = np.polyfit(df[df[\"kind\"] == kind][\"err\"], 1 / np.sqrt(df[df[\"kind\"] == kind][\"n_train\"]), deg=1)\n",
    "#         print(df[df[\"kind\"] == kind][\"err\"])\n",
    "#         print(1 / np.sqrt(df[df[\"kind\"] == kind][\"n_train\"]))\n",
    "#         print(coefs)\n",
    "        ax[0].plot(fitx, 9.5 / np.sqrt(fitx) + 0.52)\n",
    "    if plot_time:\n",
    "        ax[1].plot(\n",
    "            df[df[\"kind\"] == kind][\"n_train\"],\n",
    "            df[df[\"kind\"] == kind][\"time\"], \n",
    "            c=c, marker='o', lw=2, linestyle=ls\n",
    "        )\n",
    "\n",
    "ax[0].set_xlabel('Number of samples')\n",
    "ax[0].set_ylabel(\"nRMSE\")\n",
    "ax[0].set_xscale('log')\n",
    "# ax[0].set_xlim(100, 10000)\n",
    "\n",
    "if plot_time:\n",
    "    ax[1].set_xlabel('Number of samples')\n",
    "    ax[1].set_ylabel('Time (s)')\n",
    "    ax[1].set_xscale('log')\n",
    "    ax[1].set_yscale('log')\n",
    "    ax[1].set_xlim(100, 10000)\n",
    "    ax[1].set_yticks([1e-2, 1e-1, 1, 1e1, 1e2])\n",
    "\n",
    "ax[0].set_ylim([0, 2.0])\n",
    "\n",
    "ax[0].grid()\n",
    "# fig.legend(ncols=len(models), loc='upper center', bbox_to_anchor=(0.5, 1))\n",
    "ax[0].legend(loc='best')\n",
    "fig.tight_layout()\n",
    "# fig.subplots_adjust(top=0.88)\n",
    "fig.savefig(pcr_n_df_path.with_suffix('.png'), dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "id": "f6d94d70",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefs=array([0.98773111, 0.0083463 ])\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13])\n",
    "y = 1 / np.sqrt(x) + np.random.randn(len(x)) * 0.01\n",
    "coefs = np.polyfit(y, 1 / np.sqrt(x), deg=1)\n",
    "print(f\"{coefs=}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "id": "f9761bec",
   "metadata": {},
   "outputs": [],
   "source": [
    "# y ~ a / sqrt(x) + b\n",
    "# y ~ c * x**2 + d * x + e\n",
    "\n",
    "# y - b ~ a / sqrt(x)\n",
    "# (y - b)**2 ~ a**2 / x\n",
    "# x ~ [a / (y-b)]**2 = a ** 2 / (y**2 - 2by + b ** 2) = (a / y) ** 2\n",
    "# sqrt(x) ~ a / (y - b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "id": "2a156f3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc5e4dc8490>]"
      ]
     },
     "execution_count": 226,
     "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": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(x, y)\n",
    "ax.plot(np.linspace(1, 13, 100), (coefs[0] / np.sqrt(np.linspace(1, 13, 100)) + coefs[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "id": "0b4a9dbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc5e3141d50>]"
      ]
     },
     "execution_count": 276,
     "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": [
    "fitx = np.linspace(100, 60_000, 100)\n",
    "coefs = np.polyfit(\n",
    "    df[df[\"kind\"] == kind][\"err\"], \n",
    "    1 / np.sqrt(df[df[\"kind\"] == kind][\"n_train\"]),\n",
    "    deg=1\n",
    ")\n",
    "# print(df[df[\"kind\"] == kind][\"err\"])\n",
    "# print(1 / np.sqrt(df[df[\"kind\"] == kind][\"n_train\"]))\n",
    "# print(coefs)\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(\n",
    "    df[df[\"kind\"] == kind][\"n_train\"], \n",
    "    df[df[\"kind\"] == kind][\"err\"]\n",
    ")\n",
    "ax.plot(fitx, 2/(fitx ** (1/2))+0.7)#(13 / (1 * np.sqrt(fitx))) + 0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "id": "d98fe95f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.08593261, -0.05943817])"
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "id": "917acc50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.08 / np.sqrt(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "id": "96a9f9fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40    0.100000\n",
       "41    0.084515\n",
       "42    0.071247\n",
       "43    0.060193\n",
       "44    0.050767\n",
       "45    0.042835\n",
       "46    0.036155\n",
       "47    0.030500\n",
       "48    0.025743\n",
       "49    0.021724\n",
       "50    0.018331\n",
       "51    0.015471\n",
       "52    0.013055\n",
       "53    0.011018\n",
       "54    0.009299\n",
       "55    0.007848\n",
       "56    0.006623\n",
       "57    0.005589\n",
       "58    0.004717\n",
       "59    0.003981\n",
       "Name: n_train, dtype: float64"
      ]
     },
     "execution_count": 282,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / np.sqrt(df[df[\"kind\"] == kind][\"n_train\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44a6e9ce",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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