Figs5_6.ipynb

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    "----\n",
    "# Comparing RS to established measures\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8b748901",
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   "outputs": [
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     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/statsmodels/compat/pandas.py:65: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.\n",
      "  from pandas import Int64Index as NumericIndex\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "import numpy as np\n",
    "import scipy as sc\n",
    "from itertools import product\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import PIL\n",
    "from numpy import log10\n",
    "import random\n",
    "from math import factorial\n",
    "import warnings\n",
    "import pandas as pd\n",
    "import re\n",
    "import os\n",
    "import math\n",
    "from collections import Counter\n",
    "\n",
    "from scipy.stats import linregress, gaussian_kde, skew\n",
    "from scipy.optimize import linear_sum_assignment\n",
    "from scipy.spatial import distance\n",
    "from scipy import stats\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from statsmodels.stats.outliers_influence import summary_table\n",
    "import statsmodels.api as sm\n",
    "\n",
    "\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "%config InlineBackend.figure_formats = ['svg']\n",
    "%config InlineBackend.print_figure_kwargs={'facecolor' : \"w\"}\n",
    "\n",
    "pd.set_option('display.max_columns', None)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "np.random.seed(0)\n",
    "\n",
    "# Given parameters\n",
    "n_obs = 1000\n",
    "n_bins = 40\n",
    "\n",
    "# Plotting histograms\n",
    "plt.figure(figsize=(8, 8))\n",
    "\n",
    "# Weibull parameters\n",
    "weibull_shape = 0.5\n",
    "# Generating data for different distributions\n",
    "data_weibull = np.random.weibull(weibull_shape, n_obs)\n",
    "# Calculating histogram\n",
    "hist_vals_weibull, bins_weibull = np.histogram(data_weibull, bins=n_bins, density=True)\n",
    "\n",
    "plt.subplot(2, 2, 1)\n",
    "plt.bar(bins_weibull[:-1], hist_vals_weibull, width=(bins_weibull[1]-bins_weibull[0]), align='edge')\n",
    "plt.xlabel('Bins')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Weibull Distribution')\n",
    "\n",
    "\n",
    "\n",
    "# Weibull parameters\n",
    "weibull_shape = 2\n",
    "# Generating data for different distributions\n",
    "data_weibull = np.random.weibull(weibull_shape, n_obs)\n",
    "# Calculating histogram\n",
    "hist_vals_weibull, bins_weibull = np.histogram(data_weibull, bins=n_bins, density=True)\n",
    "\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.bar(bins_weibull[:-1], hist_vals_weibull, width=(bins_weibull[1]-bins_weibull[0]), align='edge')\n",
    "plt.xlabel('Bins')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Weibull Distribution')\n",
    "\n",
    "\n",
    "# Weibull parameters\n",
    "weibull_shape = 3.5\n",
    "# Generating data for different distributions\n",
    "data_weibull = np.random.weibull(weibull_shape, n_obs)\n",
    "# Calculating histogram\n",
    "hist_vals_weibull, bins_weibull = np.histogram(data_weibull, bins=n_bins, density=True)\n",
    "\n",
    "plt.subplot(2, 2, 3)\n",
    "plt.bar(bins_weibull[:-1], hist_vals_weibull, width=(bins_weibull[1]-bins_weibull[0]), align='edge')\n",
    "plt.xlabel('Bins')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Weibull Distribution')\n",
    "\n",
    "\n",
    "# Weibull parameters\n",
    "weibull_shape = 20\n",
    "# Generating data for different distributions\n",
    "data_weibull = np.random.weibull(weibull_shape, n_obs)\n",
    "# Calculating histogram\n",
    "hist_vals_weibull, bins_weibull = np.histogram(data_weibull, bins=n_bins, density=True)\n",
    "\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.bar(bins_weibull[:-1], hist_vals_weibull, width=(bins_weibull[1]-bins_weibull[0]), align='edge')\n",
    "plt.xlabel('Bins')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Weibull Distribution')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f13e90fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def histogram_intersection(p, q):\n",
    "    \n",
    "    # Calculate histogram intersection\n",
    "    \n",
    "    # q is the reference distribution\n",
    "    # p is the query distribution\n",
    "    \n",
    "    minima = np.minimum(p, q)\n",
    "    hi = np.true_divide(np.sum(minima), np.sum(p))\n",
    "    \n",
    "    if hi > 1 or hi < 0:\n",
    "        print('Error, HI =', hi)\n",
    "        print(p)\n",
    "        print(q)\n",
    "        return\n",
    "    return hi\n",
    "\n",
    "\n",
    "def chi_square_distance(p, q):\n",
    "    \n",
    "    # Calculate chi-square distance\n",
    "    \n",
    "    # q is the reference distribution\n",
    "    # p is the query distribution\n",
    "    \n",
    "    # The following uses 'add one smoothing'\n",
    "    p = np.array(p, dtype=float) + 1\n",
    "    q = np.array(q, dtype=float) + 1\n",
    "    p /= p.sum()\n",
    "    q /= q.sum()\n",
    "\n",
    "    return np.sum(((p - q)**2 / (p + q))) / 2\n",
    "\n",
    "\n",
    "def kl_divergence(p, q):\n",
    "    \n",
    "    # Calculate Kullback-Leibler Divergence\n",
    "    \n",
    "    # q is the reference distribution\n",
    "    # p is the query distribution\n",
    "    \n",
    "    # Ensure both lists are numpy arrays with dtype=float\n",
    "    \n",
    "    # The following uses 'add one smoothing'\n",
    "    p = np.array(p, dtype=float) + 1\n",
    "    q = np.array(q, dtype=float) + 1\n",
    "    p /= p.sum()\n",
    "    q /= q.sum()\n",
    "    \n",
    "    kl_div = np.sum(p * np.log(p / q))\n",
    "    return kl_div\n",
    "\n",
    "\n",
    "def earth_movers_distance(p, q):\n",
    "    \n",
    "    # Calculate Earth Mover's Distance\n",
    "    \n",
    "    # q is the reference distribution\n",
    "    # p is the query distribution\n",
    "    \n",
    "    # Ensure both lists are numpy arrays with dtype=float\n",
    "    p = np.array(p, dtype=float)\n",
    "    q = np.array(q, dtype=float)\n",
    "\n",
    "    # Normalize the distributions to ensure they sum to 1\n",
    "    p /= p.sum()\n",
    "    q /= q.sum()\n",
    "\n",
    "    # Calculate cumulative distributions\n",
    "    P = np.cumsum(p)\n",
    "    Q = np.cumsum(q)\n",
    "\n",
    "    # Calculate the cost matrix\n",
    "    C = np.abs(np.subtract.outer(P, Q))\n",
    "\n",
    "    # Solve the linear sum assignment problem\n",
    "    row_ind, col_ind = linear_sum_assignment(C)\n",
    "\n",
    "    # Calculate the Earth Mover's Distance\n",
    "    emd = C[row_ind, col_ind].sum()\n",
    "\n",
    "    return emd\n",
    "\n",
    "\n",
    "def kolmogorov_smirnov_distance(p, q):\n",
    "    \n",
    "    # Calculate KS distance\n",
    "    \n",
    "    # q is the reference distribution\n",
    "    # p is the query distribution\n",
    "    \n",
    "    # Ensure both lists are numpy arrays with dtype=float\n",
    "    p = np.array(p, dtype=float)\n",
    "    q = np.array(q, dtype=float)\n",
    "\n",
    "    # Normalize the distributions to ensure they sum to 1\n",
    "    p /= p.sum()\n",
    "    q /= q.sum()\n",
    "\n",
    "    # Calculate cumulative distributions\n",
    "    P = np.cumsum(p)\n",
    "    Q = np.cumsum(q)\n",
    "\n",
    "    # Calculate the KS distance\n",
    "    ks_distance = np.max(np.abs(P - Q))\n",
    "\n",
    "    return ks_distance\n",
    "\n",
    "\n",
    "def rank_probability_score(p, q):\n",
    "    \n",
    "    # Calculate the ranked probability score\n",
    "    \n",
    "    # q is the reference distribution\n",
    "    # p is the query distribution\n",
    "    \n",
    "    # Ensure both lists are numpy arrays with dtype=float\n",
    "    p = np.array(p, dtype=float)\n",
    "    q = np.array(q, dtype=float)\n",
    "\n",
    "    # Normalize the distributions to ensure they sum to 1\n",
    "    p /= p.sum()\n",
    "    q /= q.sum()\n",
    "\n",
    "    # Calculate cumulative distributions\n",
    "    P = np.cumsum(p)\n",
    "    Q = np.cumsum(q)\n",
    "\n",
    "    # Calculate Rank Probability Score\n",
    "    rps = np.sum((P - Q)**2)\n",
    "\n",
    "    return rps\n",
    "\n",
    "\n",
    "def RDS(p, q):\n",
    "    \n",
    "    # Calculate Relative distribution shift\n",
    "    \n",
    "    # q is the reference distribution\n",
    "    # p is the query distribution\n",
    "    p_bins = len(p)\n",
    "    p_obs = sum(p)\n",
    "    \n",
    "    q_bins = len(q)\n",
    "    q_obs = sum(q)\n",
    "    \n",
    "    z_p = (p_bins + 1)/p_bins\n",
    "    p = [sum(p[:ii+1])**(z_p) for ii in range(len(p))]\n",
    "    Sp = np.sum(np.array(p)/(p_obs**z_p)) - 1\n",
    "    Sp = Sp/(p_bins - 1)\n",
    "    \n",
    "    z_q = (q_bins + 1)/q_bins\n",
    "    q = [sum(q[:ii+1])**(z_q) for ii in range(len(q))]\n",
    "    Sq = np.sum(np.array(q)/(q_obs**z_q)) - 1\n",
    "    Sq = Sq/(q_bins - 1)\n",
    "    \n",
    "    return Sq - Sp\n",
    "    \n",
    "    \n",
    "def DS(p):\n",
    "    p_bins = len(p)\n",
    "    p_obs = sum(p)\n",
    "    \n",
    "    z_p = (p_bins + 1)/p_bins\n",
    "    p = [sum(p[:ii+1])**(z_p) for ii in range(len(p))]\n",
    "    Sp = np.sum(np.array(p)/(p_obs**z_p)) - 1\n",
    "    ds = Sp/(p_bins - 1)\n",
    "    return ds\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f5e8fc57",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_colored_grid(x_values, y_values, color_values):\n",
    "    \n",
    "    # Function to create a colored grid with text annotations\n",
    "    colors = np.zeros((4, 4), dtype=float)  # Initialize a 4x4 grid with zeros\n",
    "    \n",
    "    # Map x_values to grid coordinates\n",
    "    x_mapping = {x: i+1 for i, x in enumerate(sorted(set(x_values)))}\n",
    "    \n",
    "    # Assign color values to grid coordinates\n",
    "    for x, y, color in zip(x_values, y_values, color_values):\n",
    "        x_grid = x_mapping[x]\n",
    "        y_grid = y - min(y_values)  # Adjust y-values to start from 0\n",
    "        colors[y_grid, x_grid - 1] = color  \n",
    "\n",
    "    # Plot the colored grid\n",
    "    plt.imshow(colors, interpolation='nearest', cmap='gray_r', origin='lower', vmin=0, vmax=1)\n",
    "\n",
    "    # Add color bar\n",
    "    #plt.colorbar(label='Color Values', ticks=np.linspace(0, 1, 5))\n",
    "\n",
    "    # Add color value annotations inside each grid square\n",
    "    for i in range(4):\n",
    "        for j in range(4):\n",
    "            # Determine font color based on color value\n",
    "            font_color = 'white' if colors[i, j] >= 0.35 else 'black'\n",
    "            plt.text(j, i, f'{colors[i, j]:.2f}', ha='center', va='center', color=font_color)\n",
    "\n",
    "    # Add gridlines for clarity\n",
    "    # plt.grid(True, which='both', color='black', linewidth=1.5)\n",
    "\n",
    "    # Hide ticks\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "\n",
    "    # Show plot\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d8842b22",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_distributions(N, n, k, model, param):\n",
    "    dists = []\n",
    "    while len(dists) < N:\n",
    "        \n",
    "        if model == 'Poisson':\n",
    "            data = np.random.poisson(param, n)\n",
    "        \n",
    "        elif model == 'Gaussian':\n",
    "            data = np.random.normal(0, param, n)\n",
    "        \n",
    "        elif model == 'Negative binomial':\n",
    "            data = np.random.negative_binomial(1, param, n)\n",
    "        \n",
    "        elif model == 'Lognormal':\n",
    "            data = np.random.lognormal(0, param, n)\n",
    "        \n",
    "        elif model == 'Weibull':\n",
    "            data = np.random.weibull(param, n)\n",
    "        \n",
    "        else:\n",
    "            raise ValueError(\"Unsupported model type\")\n",
    "\n",
    "        hist_vals, bins = np.histogram(data, bins=k, density=False)\n",
    "        dists.append(hist_vals.tolist())\n",
    "\n",
    "    return dists\n",
    "\n",
    "\n",
    "def get_r2(measure_vals, RDS_vals):\n",
    "    xv = []\n",
    "    yv = []\n",
    "    for i, val in enumerate(measure_vals):\n",
    "        if val > 0 and val < 10**10:\n",
    "            xv.append(val)\n",
    "            yv.append(RDS_vals[i])\n",
    "\n",
    "    slope, intercept, r_val, p_val, std_err = linregress(xv, np.abs(yv))\n",
    "    return round(r_val**2, 2)\n",
    "    "
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   "execution_count": 6,
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      "20\n",
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   "source": [
    "rds_r2s = []\n",
    "csd_r2s = []\n",
    "ksd_r2s = []\n",
    "hni_r2s = []\n",
    "kld_r2s = []\n",
    "emd_r2s = []\n",
    "rps_r2s = []\n",
    "\n",
    "rds_vals1 = []\n",
    "csd_vals1 = []\n",
    "ksd_vals1 = []\n",
    "hni_vals1 = []\n",
    "kld_vals1 = []\n",
    "emd_vals1 = []\n",
    "rps_vals1 = []\n",
    "\n",
    "N = 10**5\n",
    "n_obs = 100\n",
    "\n",
    "n_bins_ls = [5, 10, 20, 40,\n",
    "             5, 10, 20, 40,\n",
    "             5, 10, 20, 40,\n",
    "             5, 10, 20, 40,\n",
    "            ]\n",
    "\n",
    "param_values = [0.5, 0.5, 0.5, 0.5,\n",
    "                1, 1, 1, 1,\n",
    "                3.5, 3.5, 3.5, 3.5,\n",
    "                20, 20, 20, 20,\n",
    "               ]\n",
    "\n",
    "for i, n_bins in enumerate(n_bins_ls):        \n",
    "    \n",
    "    rds_vals2 = []\n",
    "    csd_vals2 = []\n",
    "    ksd_vals2 = []\n",
    "    hni_vals2 = []\n",
    "    kld_vals2 = []\n",
    "    emd_vals2 = []\n",
    "    rps_vals2 = []\n",
    "        \n",
    "    shape = param_values[i]\n",
    "    print(shape)\n",
    "        \n",
    "    num = 0\n",
    "    while num < N:\n",
    "        data = np.random.weibull(shape, n_obs)\n",
    "        d1, bins = np.histogram(data, bins=n_bins, density=False)\n",
    "        data = np.random.weibull(shape, n_obs)\n",
    "        d2, bins = np.histogram(data, bins=n_bins, density=False)\n",
    "            \n",
    "        # Relative distributional shift\n",
    "        j = RDS(d1, d2)\n",
    "        rds_vals2.append(j)\n",
    "\n",
    "        # KS distance\n",
    "        j = kolmogorov_smirnov_distance(d1, d2)\n",
    "        ksd_vals2.append(j)\n",
    "\n",
    "        # Histogram intersection\n",
    "        j = histogram_intersection(d1, d2)\n",
    "        hni_vals2.append(1-j)\n",
    "\n",
    "        # chi-square distance\n",
    "        j = chi_square_distance(d1, d2)\n",
    "        csd_vals2.append(np.sqrt(j))\n",
    "\n",
    "        # KL divergence\n",
    "        j = kl_divergence(d1, d2)\n",
    "        kld_vals2.append(np.sqrt(j))\n",
    "\n",
    "        # Rank probability score\n",
    "        j = rank_probability_score(d1, d2)\n",
    "        rps_vals2.append(np.sqrt(j))\n",
    "\n",
    "        # Earth movers distance\n",
    "        j = earth_movers_distance(d1, d2)\n",
    "        emd_vals2.append(j)\n",
    "\n",
    "        num += 1\n",
    "\n",
    "        \n",
    "    if shape == 1 and n_bins == 40:\n",
    "        rds_vals1 = list(rds_vals2)\n",
    "        csd_vals1 = list(csd_vals2)\n",
    "        ksd_vals1 = list(ksd_vals2)\n",
    "        hni_vals1 = list(hni_vals2)\n",
    "        kld_vals1 = list(kld_vals2)\n",
    "        emd_vals1 = list(emd_vals2)\n",
    "        rps_vals1 = list(rps_vals2)\n",
    "        \n",
    "        \n",
    "    r2 = get_r2(csd_vals2, rds_vals2)\n",
    "    csd_r2s.append(r2)\n",
    "    \n",
    "    r2 = get_r2(ksd_vals2, rds_vals2)\n",
    "    ksd_r2s.append(r2)\n",
    "    \n",
    "    r2 = get_r2(hni_vals2, rds_vals2)\n",
    "    hni_r2s.append(r2)\n",
    "    \n",
    "    r2 = get_r2(kld_vals2, rds_vals2)\n",
    "    kld_r2s.append(r2)\n",
    "    \n",
    "    r2 = get_r2(emd_vals2, rds_vals2)\n",
    "    emd_r2s.append(r2)\n",
    "    \n",
    "    r2 = get_r2(rps_vals2, rds_vals2)\n",
    "    rps_r2s.append(r2)\n",
    "\n",
    "R2s = [emd_r2s, rps_r2s, ksd_r2s, kld_r2s, hni_r2s, csd_r2s]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "41518d9e",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 576x864 with 6 Axes>"
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   "source": [
    "\n",
    "def plot_colored_grid(x_values, y_values, color_values, ax):\n",
    "    # Initialize a 4x4 grid with zeros\n",
    "    colors = np.zeros((4, 4), dtype=float)\n",
    "    \n",
    "    # Map x_values to grid coordinates\n",
    "    x_mapping = {x: i+1 for i, x in enumerate(sorted(set(x_values)))}\n",
    "    \n",
    "    # Map y_values to grid coordinates\n",
    "    y_mapping = {y: i+1 for i, y in enumerate(sorted(set(y_values)))}\n",
    "\n",
    "    # Assign color values to grid coordinates\n",
    "    for x, y, color in zip(x_values, y_values, color_values):\n",
    "        x_grid = x_mapping[x]\n",
    "        y_grid = y_mapping[y]\n",
    "        colors[y_grid - 1, x_grid - 1] = color  \n",
    "\n",
    "    # Plot the colored grid\n",
    "    ax.imshow(colors, interpolation='nearest', cmap='gray_r', origin='lower', vmin=0, vmax=1)\n",
    "\n",
    "    # Add color value annotations inside each grid square\n",
    "    for i in range(4):\n",
    "        for j in range(4):\n",
    "            # Determine font color based on color value\n",
    "            font_color = 'white' if colors[i, j] >= 0.35 else 'black'\n",
    "            ax.text(j, i, f'{colors[i, j]:.2f}', \n",
    "                    ha='center', \n",
    "                    va='center', \n",
    "                    fontsize=12,\n",
    "                    color=font_color)\n",
    "\n",
    "    \n",
    "    xticks = sorted(list(set(x_values)))\n",
    "    yticks = sorted(list(set(y_values)))\n",
    "    ax.set_xticks(np.arange(len(xticks)))\n",
    "    ax.set_xticklabels(xticks)\n",
    "    ax.set_yticks(np.arange(len(yticks)))\n",
    "    ax.set_yticklabels(yticks)\n",
    "    ax.set_xlabel('No. of bins', fontsize=16)\n",
    "    ax.set_ylabel(r'$\\alpha$', fontsize=18)\n",
    "    \n",
    "    \n",
    "\n",
    "# Function to create a 3x2 figure with subplots for each measure\n",
    "def create_figure(n_bins_ls, param_values, R2s):\n",
    "    measures = ['EMD', r\"$\\sqrt{RPS}$\", 'KSD', r\"$\\sqrt{KLD}$\", '1 - HI', r\"$\\sqrt{CSD}$\"]\n",
    "    fig, axs = plt.subplots(3, 2, figsize=(8, 12))\n",
    "\n",
    "    for i, measure in enumerate(measures):\n",
    "        row = i // 2\n",
    "        col = i % 2\n",
    "\n",
    "        ax = axs[row, col]\n",
    "\n",
    "        # Generate x_values, y_values, and color_values for the subplot\n",
    "        x_values = n_bins_ls\n",
    "        y_values = param_values\n",
    "        color_values = R2s[i]\n",
    "\n",
    "        # Plot colored grid for the measure subplot\n",
    "        ax.set_title(measure, fontsize=18)\n",
    "        plot_colored_grid(x_values, y_values, color_values, ax)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    fig.patch.set_facecolor('white')\n",
    "    plt.subplots_adjust(hspace=0.45, wspace=0.4)\n",
    "    plt.savefig('Final_Figs/manuscript/Fig5.jpg', bbox_inches='tight', format='jpg', dpi=600)\n",
    "    plt.savefig('Final_Figs/manuscript/Fig5.pdf', bbox_inches='tight', format='pdf', dpi=600)\n",
    "    plt.show()\n",
    "\n",
    "# Call the function to create the figure\n",
    "create_figure(n_bins_ls, param_values, R2s)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5db991c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_pts_within_radius(x, y, radius, scale=0):\n",
    "    \"\"\"Count the number of points within a fixed radius in 2D space\"\"\"\n",
    "    \n",
    "    raw_data = np.array([x, y])\n",
    "    x = np.array(x)\n",
    "    y = np.array(y)\n",
    "    raw_data = raw_data.transpose()\n",
    "    \n",
    "    # Get unique data points by adding each pair of points to a set\n",
    "    unique_points = set()\n",
    "    for xval, yval in raw_data:\n",
    "        unique_points.add((xval, yval))\n",
    "    \n",
    "    count_data = []\n",
    "    for a, b in unique_points:\n",
    "        if scale == 'sqrt':\n",
    "            num_neighbors = len(x[((sqrt(x) - sqrt(a)) ** 2 +\n",
    "                                   (sqrt(y) - sqrt(b)) ** 2) <= sqrt(radius) ** 2])\n",
    "        else:        \n",
    "            num_neighbors = len(x[((x - a) ** 2 + (y - b) ** 2) <= radius ** 2])\n",
    "        count_data.append((a, b, num_neighbors))\n",
    "    return count_data\n",
    "\n",
    "\n",
    "\n",
    "def plot_color_by_pt_dens(x, y, radius, loglog=0, scale=0, plot_obj=None, point_size=10):\n",
    "    \n",
    "    \"\"\"Plot bivariate relationships with large n using color for point density\n",
    "\n",
    "    Inputs:\n",
    "    x & y -- variables to be plotted\n",
    "    radius -- the linear distance within which to count points as neighbors\n",
    "    scale -- a flag to indicate the use of a scale plot (scale = 1)\n",
    "\n",
    "    The color of each point in the plot is determined by the logarithm (base 10)\n",
    "    of the number of points that occur with a given radius of the focal point,\n",
    "    with hotter colors indicating more points. The number of neighboring points\n",
    "    is determined in linear space regardless of whether a scale plot is\n",
    "    presented.\n",
    "    \"\"\"\n",
    "    \n",
    "    plot_data = count_pts_within_radius(x, y, radius, scale)\n",
    "    sorted_plot_data = np.array(sorted(plot_data, key=lambda point: point[2]))\n",
    "\n",
    "    if plot_obj == None:\n",
    "        plot_obj = plt.axes()\n",
    "        \n",
    "    plot_obj.scatter(sorted_plot_data[:, 0],\n",
    "            sorted_plot_data[:, 1],\n",
    "            facecolors='none',\n",
    "            s = point_size, \n",
    "            edgecolors='0.1', \n",
    "            linewidths=1., \n",
    "            #cmap='Greys'\n",
    "            )\n",
    "    \n",
    "    # plot points\n",
    "    c = np.array(sorted_plot_data[:, 2])**0.25\n",
    "    c = np.max(c) - c\n",
    "    plot_obj.scatter(sorted_plot_data[:, 0],\n",
    "                    sorted_plot_data[:, 1],\n",
    "                    c = c,\n",
    "                    s = point_size, \n",
    "                    edgecolors='k', \n",
    "                    linewidths=0.0, \n",
    "                    cmap='Greys_r',\n",
    "                    #alpha = 0.5,\n",
    "                    )\n",
    "        \n",
    "    return plot_obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a7746e55",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "X_lists = [ksd_vals1, \n",
    "           emd_vals1, \n",
    "           rps_vals1,\n",
    "           csd_vals1, \n",
    "           hni_vals1, \n",
    "           kld_vals1,\n",
    "          ]\n",
    "\n",
    "x_labs = ['KSD',\n",
    "          'EMD',\n",
    "          r\"$\\sqrt{RPS}$\",\n",
    "          r\"$\\sqrt{CSD}$\",\n",
    "          '1 - HI',\n",
    "          r\"$\\sqrt{KLD}$\",\n",
    "          ]\n",
    "\n",
    "fig = plt.figure(figsize=(11, 11))\n",
    "\n",
    "text_x_vals = [0.038, 0.25, 0.05, \n",
    "               0.12, 0.095, 0.18]\n",
    "\n",
    "for i, x_ls in enumerate(X_lists):\n",
    "    \n",
    "    xv = []\n",
    "    yv = []\n",
    "    ct = 0\n",
    "    for ii, val in enumerate(x_ls):\n",
    "        \n",
    "        if val > 0 and val < 10**10:\n",
    "            xv.append(val)\n",
    "            yv.append(rds_vals1[ii])\n",
    "    \n",
    "    if len(xv) < 10:\n",
    "        continue\n",
    "        \n",
    "    plot_color_by_pt_dens(xv, yv, radius=0.05, loglog=0, plot_obj=plt.subplot(3, 3, i+1), point_size=10)\n",
    "    slope, intercept, r_val, p_val, std_err = linregress(xv, np.abs(yv))\n",
    "    fitted_vals = slope * np.array(xv) + intercept\n",
    "    s = r'$r^{2}$' + ' = ' + str(round(r_val**2, 2))\n",
    "    \n",
    "    plt.text(text_x_vals[i], 0.9*np.nanmax(yv), s, fontsize=12)\n",
    "    plt.xlabel(x_labs[i], fontsize= 12)\n",
    "    plt.ylabel('RDS', fontsize= 12)\n",
    "    plt.tick_params(axis='both', labelsize=10)\n",
    "    \n",
    "fig.patch.set_facecolor('white')\n",
    "plt.subplots_adjust(hspace=0.4, wspace=0.5)\n",
    "plt.savefig('Final_Figs/manuscript/Fig6.pdf', bbox_inches='tight', format='pdf', dpi=600)\n",
    "plt.savefig('Final_Figs/manuscript/Fig6.jpg', bbox_inches='tight', format='jpg', dpi=600)\n",
    "plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ba1a062",
   "metadata": {},
   "source": [
    "## Check for symmetry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3d8a3fad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RDS is symmetrical\n",
      "RPS is symmetrical\n",
      "CSD is symmetrical\n",
      "KSD is symmetrical\n",
      "EMD is symmetrical\n",
      "1 - HI is symmetrical\n",
      "KLD is not symmetrical\n"
     ]
    }
   ],
   "source": [
    "num = 0\n",
    "N = 10**3\n",
    "n_obs = 100\n",
    "n_bins = 40\n",
    "\n",
    "rds_sym = 'RDS is symmetrical'\n",
    "emd_sym = 'EMD is symmetrical'\n",
    "kld_sym = 'KLD is symmetrical'\n",
    "ksd_sym = 'KSD is symmetrical'\n",
    "csd_sym = 'CSD is symmetrical'\n",
    "hni_sym = '1 - HI is symmetrical'\n",
    "rps_sym = 'RPS is symmetrical'\n",
    "\n",
    "while num < N:\n",
    "    n_bins = np.random.randint(4, 40)\n",
    "    n_obs = np.random.randint(50, 200)\n",
    "    \n",
    "    shape1 = np.random.uniform(0.5, 20)\n",
    "    shape2 = np.random.uniform(0.5, 20)\n",
    "    \n",
    "    data = np.random.weibull(shape1, n_obs)\n",
    "    d1, bins = np.histogram(data, bins=n_bins, density=False)\n",
    "    \n",
    "    data = np.random.weibull(shape2, n_obs)\n",
    "    d2, bins = np.histogram(data, bins=n_bins, density=False)\n",
    "            \n",
    "    # Relative distributional shift\n",
    "    rds1 = RDS(d1, d2)\n",
    "    rds2 = RDS(d2, d1)\n",
    "    if np.abs(rds1) != np.abs(rds2):\n",
    "        rds_sym = 'RDS is not symmetrical'\n",
    "    \n",
    "    \n",
    "    # KS distance\n",
    "    j1 = kolmogorov_smirnov_distance(d1, d2)\n",
    "    j2 = kolmogorov_smirnov_distance(d2, d1)\n",
    "    if j1 != j2:\n",
    "        ksd_sym = 'KSD is not symmetrical'\n",
    "    \n",
    "    # Histogram intersection\n",
    "    j1 = histogram_intersection(d1, d2)\n",
    "    j2 = histogram_intersection(d2, d1)\n",
    "    if j1 != j2:\n",
    "        hni_sym = '1 - HI is not symmetrical'\n",
    "        \n",
    "    # chi-square distance\n",
    "    j1 = chi_square_distance(d1, d2)\n",
    "    j2 = chi_square_distance(d2, d1)\n",
    "    if j1 != j2:\n",
    "        csd_sym = 'CSD is not symmetrical'\n",
    "        \n",
    "    # KL divergence\n",
    "    j1 = kl_divergence(d1, d2)\n",
    "    j2 = kl_divergence(d2, d1)\n",
    "    if j1 != j2:\n",
    "        kld_sym = 'KLD is not symmetrical'\n",
    "        \n",
    "    # Rank probability score\n",
    "    j1 = rank_probability_score(d1, d2)\n",
    "    j2 = rank_probability_score(d2, d1)\n",
    "    if j1 != j2:\n",
    "        rps_sym = 'RPS is not symmetrical'\n",
    "        \n",
    "    # Earth movers distance\n",
    "    j1 = earth_movers_distance(d1, d2)\n",
    "    j2 = earth_movers_distance(d2, d1)\n",
    "    if round(j1, 6) != round(j2,6):\n",
    "        emd_sym = 'EMD is not symmetrical'\n",
    "        print(j1, j2)\n",
    "        break\n",
    "        \n",
    "    num += 1\n",
    "    \n",
    "print(rds_sym)\n",
    "print(rps_sym)\n",
    "print(csd_sym)\n",
    "print(ksd_sym)\n",
    "print(emd_sym)\n",
    "print(hni_sym)\n",
    "print(kld_sym)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a683f382",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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