{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1e7c78d0-03ab-4303-890d-0b3b6b6391c0",
   "metadata": {},
   "source": [
    "# Exploring GCNS—Gaia Catalogue of Nearby Stars\n",
    "__Prelude: Demonstrating the Kolmogorov-Smirnov Test__\n",
    "\n",
    "The GCNS is described in an open access _A&A_ article by [Smart et al. (2021)](https://www.aanda.org/articles/aa/full_html/2021/05/aa39498-20/aa39498-20.html). This is believed to be a nearly complete compilation of  stars within 100 pc (0.1 kpc). [Table 2](https://www.aanda.org/articles/aa/full_html/2021/05/aa39498-20/T2.html) contains a detailed explanation of all the columns of data available in the catalog. Note that some of the header names are slightly different in the database than they are in this table. Why? To keep out the riffraff, I guess!\n",
    "\n",
    "FITS tables are available on [CDS](http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/649/A6#/browse). I found the connection a bit slow, but it worked with no hiccups. Click the FTP tab to get to the data tables. What you want is `table1c`, which is available in several formats. The plain text version is human-readable, and can be snarfed up using `pandas.read_table`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d1635195-8232-42bb-abb5-72a573e244a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm  # Simple way to display a progress bar for Python for loops."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "500b150f-ea20-4871-b526-b25010415828",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>GaiaEDR3</th>\n",
       "      <th>RAdeg</th>\n",
       "      <th>e_RAdeg</th>\n",
       "      <th>DEdeg</th>\n",
       "      <th>e_DEdeg</th>\n",
       "      <th>Plx</th>\n",
       "      <th>e_Plx</th>\n",
       "      <th>pmRA</th>\n",
       "      <th>e_pmRA</th>\n",
       "      <th>pmDE</th>\n",
       "      <th>...</th>\n",
       "      <th>e_Ksmag</th>\n",
       "      <th>WISE</th>\n",
       "      <th>W1mag</th>\n",
       "      <th>e_W1mag</th>\n",
       "      <th>W2mag</th>\n",
       "      <th>e_W2mag</th>\n",
       "      <th>W3mag</th>\n",
       "      <th>e_W3mag</th>\n",
       "      <th>W4mag</th>\n",
       "      <th>e_</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
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       "      <td>J000000.61-262155.2</td>\n",
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       "      <td>11.100</td>\n",
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       "      <th>1</th>\n",
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       "      <td>-19.498841</td>\n",
       "      <td>0.34734</td>\n",
       "      <td>26.798</td>\n",
       "      <td>0.50664</td>\n",
       "      <td>179.805</td>\n",
       "      <td>0.57186</td>\n",
       "      <td>-1.041</td>\n",
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       "      <td>0.016</td>\n",
       "      <td>6.704</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>530861741656374272</td>\n",
       "      <td>0.005637</td>\n",
       "      <td>0.00951</td>\n",
       "      <td>70.887364</td>\n",
       "      <td>0.00858</td>\n",
       "      <td>10.282</td>\n",
       "      <td>0.01075</td>\n",
       "      <td>-52.864</td>\n",
       "      <td>0.01210</td>\n",
       "      <td>17.787</td>\n",
       "      <td>...</td>\n",
       "      <td>0.022</td>\n",
       "      <td>J000001.37+705314.4</td>\n",
       "      <td>8.965</td>\n",
       "      <td>0.013</td>\n",
       "      <td>9.024</td>\n",
       "      <td>0.009</td>\n",
       "      <td>8.937</td>\n",
       "      <td>0.027</td>\n",
       "      <td>8.649</td>\n",
       "      <td>0.333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2745400068346761216</td>\n",
       "      <td>0.009336</td>\n",
       "      <td>0.03793</td>\n",
       "      <td>6.511017</td>\n",
       "      <td>0.03139</td>\n",
       "      <td>16.260</td>\n",
       "      <td>0.05893</td>\n",
       "      <td>117.495</td>\n",
       "      <td>0.06235</td>\n",
       "      <td>9.521</td>\n",
       "      <td>...</td>\n",
       "      <td>0.020</td>\n",
       "      <td>J000002.22+063039.7</td>\n",
       "      <td>11.866</td>\n",
       "      <td>0.013</td>\n",
       "      <td>11.660</td>\n",
       "      <td>0.009</td>\n",
       "      <td>11.630</td>\n",
       "      <td>0.218</td>\n",
       "      <td>8.881</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2855176271335676800</td>\n",
       "      <td>0.013536</td>\n",
       "      <td>0.02864</td>\n",
       "      <td>29.277896</td>\n",
       "      <td>0.01968</td>\n",
       "      <td>10.295</td>\n",
       "      <td>0.04369</td>\n",
       "      <td>51.287</td>\n",
       "      <td>0.05345</td>\n",
       "      <td>46.282</td>\n",
       "      <td>...</td>\n",
       "      <td>0.018</td>\n",
       "      <td>J000003.24+291640.4</td>\n",
       "      <td>11.907</td>\n",
       "      <td>0.012</td>\n",
       "      <td>11.743</td>\n",
       "      <td>0.008</td>\n",
       "      <td>11.589</td>\n",
       "      <td>0.218</td>\n",
       "      <td>9.077</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>22.624</td>\n",
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       "      <td>-73.354</td>\n",
       "      <td>0.05561</td>\n",
       "      <td>-84.683</td>\n",
       "      <td>...</td>\n",
       "      <td>0.022</td>\n",
       "      <td>J235958.43+122233.9</td>\n",
       "      <td>11.516</td>\n",
       "      <td>0.012</td>\n",
       "      <td>11.288</td>\n",
       "      <td>0.008</td>\n",
       "      <td>11.161</td>\n",
       "      <td>0.164</td>\n",
       "      <td>8.734</td>\n",
       "      <td>0.505</td>\n",
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       "    <tr>\n",
       "      <th>331308</th>\n",
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       "      <td>0.22628</td>\n",
       "      <td>18.053030</td>\n",
       "      <td>0.14174</td>\n",
       "      <td>14.321</td>\n",
       "      <td>0.27067</td>\n",
       "      <td>261.914</td>\n",
       "      <td>0.33586</td>\n",
       "      <td>-99.384</td>\n",
       "      <td>...</td>\n",
       "      <td>0.035</td>\n",
       "      <td>J235958.54+180310.9</td>\n",
       "      <td>13.521</td>\n",
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       "      <td>13.331</td>\n",
       "      <td>0.012</td>\n",
       "      <td>12.667</td>\n",
       "      <td></td>\n",
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       "    <tr>\n",
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       "      <td>18.105</td>\n",
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       "      <td>57.761</td>\n",
       "      <td>0.01537</td>\n",
       "      <td>96.078</td>\n",
       "      <td>...</td>\n",
       "      <td>0.025</td>\n",
       "      <td>J235958.73-531056.2</td>\n",
       "      <td>10.857</td>\n",
       "      <td>0.012</td>\n",
       "      <td>10.679</td>\n",
       "      <td>0.008</td>\n",
       "      <td>10.482</td>\n",
       "      <td>0.068</td>\n",
       "      <td>8.853</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>331310</th>\n",
       "      <td>2011682661920690304</td>\n",
       "      <td>359.995813</td>\n",
       "      <td>0.46508</td>\n",
       "      <td>60.918306</td>\n",
       "      <td>0.34315</td>\n",
       "      <td>9.094</td>\n",
       "      <td>0.53559</td>\n",
       "      <td>-24.265</td>\n",
       "      <td>0.58406</td>\n",
       "      <td>-25.545</td>\n",
       "      <td>...</td>\n",
       "      <td>0.029</td>\n",
       "      <td>J235959.00+605505.8</td>\n",
       "      <td>12.739</td>\n",
       "      <td>0.014</td>\n",
       "      <td>12.590</td>\n",
       "      <td>0.009</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>331311</th>\n",
       "      <td>2314850075324449408</td>\n",
       "      <td>359.999926</td>\n",
       "      <td>0.24543</td>\n",
       "      <td>-30.024529</td>\n",
       "      <td>0.23446</td>\n",
       "      <td>11.352</td>\n",
       "      <td>0.33888</td>\n",
       "      <td>295.092</td>\n",
       "      <td>0.30139</td>\n",
       "      <td>-306.598</td>\n",
       "      <td>...</td>\n",
       "      <td>0.089</td>\n",
       "      <td>J235959.97-300128.2</td>\n",
       "      <td>14.456</td>\n",
       "      <td>0.015</td>\n",
       "      <td>14.244</td>\n",
       "      <td>0.019</td>\n",
       "      <td>11.771</td>\n",
       "      <td></td>\n",
       "      <td>8.202</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>331312 rows × 74 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   GaiaEDR3       RAdeg  e_RAdeg      DEdeg  e_DEdeg     Plx  \\\n",
       "0       2334666126716440064    0.002565  0.03305 -26.365350  0.02500  14.697   \n",
       "1       2341871673090078592    0.005121  0.42837 -19.498841  0.34734  26.798   \n",
       "2        530861741656374272    0.005637  0.00951  70.887364  0.00858  10.282   \n",
       "3       2745400068346761216    0.009336  0.03793   6.511017  0.03139  16.260   \n",
       "4       2855176271335676800    0.013536  0.02864  29.277896  0.01968  10.295   \n",
       "...                     ...         ...      ...        ...      ...     ...   \n",
       "331307  2766925825958528512  359.993523  0.03391  12.376062  0.02638  22.624   \n",
       "331308  2773791481503524992  359.994028  0.22628  18.053030  0.14174  14.321   \n",
       "331309  6521388186590534272  359.994771  0.01233 -53.182288  0.01463  18.105   \n",
       "331310  2011682661920690304  359.995813  0.46508  60.918306  0.34315   9.094   \n",
       "331311  2314850075324449408  359.999926  0.24543 -30.024529  0.23446  11.352   \n",
       "\n",
       "          e_Plx     pmRA   e_pmRA     pmDE  ...  e_Ksmag  \\\n",
       "0       0.03698   23.497  0.03680  -62.339  ...    0.026   \n",
       "1       0.50664  179.805  0.57186   -1.041  ...    0.018   \n",
       "2       0.01075  -52.864  0.01210   17.787  ...    0.022   \n",
       "3       0.05893  117.495  0.06235    9.521  ...    0.020   \n",
       "4       0.04369   51.287  0.05345   46.282  ...    0.018   \n",
       "...         ...      ...      ...      ...  ...      ...   \n",
       "331307  0.04461  -73.354  0.05561  -84.683  ...    0.022   \n",
       "331308  0.27067  261.914  0.33586  -99.384  ...    0.035   \n",
       "331309  0.02083   57.761  0.01537   96.078  ...    0.025   \n",
       "331310  0.53559  -24.265  0.58406  -25.545  ...    0.029   \n",
       "331311  0.33888  295.092  0.30139 -306.598  ...    0.089   \n",
       "\n",
       "                        WISE    W1mag  e_W1mag    W2mag  e_W2mag    W3mag  \\\n",
       "0       J000000.61-262155.2    11.799    0.012   11.606    0.009   11.100   \n",
       "1       J000001.23-192955.7     6.868    0.021    6.800    0.009    6.722   \n",
       "2       J000001.37+705314.4     8.965    0.013    9.024    0.009    8.937   \n",
       "3       J000002.22+063039.7    11.866    0.013   11.660    0.009   11.630   \n",
       "4       J000003.24+291640.4    11.907    0.012   11.743    0.008   11.589   \n",
       "...                      ...      ...      ...      ...      ...      ...   \n",
       "331307  J235958.43+122233.9    11.516    0.012   11.288    0.008   11.161   \n",
       "331308  J235958.54+180310.9    13.521    0.015   13.331    0.012   12.667   \n",
       "331309  J235958.73-531056.2    10.857    0.012   10.679    0.008   10.482   \n",
       "331310  J235959.00+605505.8    12.739    0.014   12.590    0.009            \n",
       "331311  J235959.97-300128.2    14.456    0.015   14.244    0.019   11.771   \n",
       "\n",
       "        e_W3mag    W4mag     e_  \n",
       "0         0.128    9.074    NaN  \n",
       "1         0.016    6.704  0.077  \n",
       "2         0.027    8.649  0.333  \n",
       "3         0.218    8.881    NaN  \n",
       "4         0.218    9.077    NaN  \n",
       "...         ...      ...    ...  \n",
       "331307    0.164    8.734  0.505  \n",
       "331308             9.057    NaN  \n",
       "331309    0.068    8.853    NaN  \n",
       "331310                      NaN  \n",
       "331311             8.202    NaN  \n",
       "\n",
       "[331312 rows x 74 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load catalogue into a Pandas dataframe.\n",
    "import pandas as pd\n",
    "df = pd.read_table('J_A+A_649_A6_table1c.dat.gz.txt', sep='|',\n",
    "                   header=5,            # header is in row 5.\n",
    "                   skiprows=[6,331319]) # Skip horizontal rules in the table.\n",
    "df.rename(columns=lambda x: x.strip(), inplace=True) # Strip whitespace from headers\n",
    "df  # display the dataframe to see that it read in properly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e8ee8da0-6e80-4fb5-bcf9-f51a6d900b51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0         0.00130\n",
       "1         0.00184\n",
       "2         0.00241\n",
       "3         0.00255\n",
       "4         0.00267\n",
       "           ...   \n",
       "331307    0.11864\n",
       "331308    0.11880\n",
       "331309    0.11890\n",
       "331310    0.11907\n",
       "331311    0.11931\n",
       "Name: Dist50, Length: 331312, dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sort the dataframe by distance (50th percentile, kpc)\n",
    "# Note that the data selection for GCNS is < 0.1 kpc in the 1st percentile distance, \n",
    "# so at 50th percentile we'll see more than 0.1 kpc.\n",
    "df.sort_values(by=['Dist50'], inplace=True, \n",
    "               ignore_index=True) # Forget the old index values.\n",
    "df['Dist50'] # prints index, Dist50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "538ae1e7-8dd9-48a8-87aa-246973ac327e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Illustrate the selection effect described in the previous cell.\n",
    "plt.figure()\n",
    "df['Dist50'].plot(xlabel='Data Frame Row Index (from 0)', ylabel='Distance (kpc), 50th percentile',\n",
    "                  title='GCNS selection anomaly at large Dist50')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d72ea70b-e5f0-4340-9382-0e7c400312b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "trimming  30745  rows.\n",
      "0         0.00130\n",
      "1         0.00184\n",
      "2         0.00241\n",
      "3         0.00255\n",
      "4         0.00267\n",
      "           ...   \n",
      "300562    0.10000\n",
      "300563    0.10000\n",
      "300564    0.10000\n",
      "300565    0.10000\n",
      "300566    0.10000\n",
      "Name: Dist50, Length: 300567, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Downselect to Dist50 ≤ 0.1 kpc.\n",
    "R = 0.1       # GCNS radius limit in kpc\n",
    "R_pc = 1000*R # GCNS radius in pc\n",
    "for j in range(1, 100000):\n",
    "    if df['Dist50'].iloc[-j] <= R:\n",
    "        break\n",
    "print('trimming ', j-1, ' rows.')\n",
    "df = df.drop(index=df.index[(1-j):])\n",
    "print(df['Dist50'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fbdeca0c-16d6-49eb-911a-9e2341b0f356",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dist_pc = 1e3 * df['Dist50'].to_numpy()\n",
    "Nstars = len(dist_pc)\n",
    "cum_distro = (0.5+np.arange(Nstars))/Nstars\n",
    "model_cum = (dist_pc/R_pc)**3  # Null hypothesis cum dist evaluated at dist_pc\n",
    "plt.figure()\n",
    "plt.loglog(dist_pc, cum_distro, label='GCNS')\n",
    "plt.plot(dist_pc, model_cum,'--', label='cubic')\n",
    "plt.xlabel('distance (pc)')\n",
    "plt.ylabel('cumulative distribution (normalized)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
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    "## Kolmogorov-Smirnov (KS) Test\n",
    "\n",
    "The KS test [(e.g., _Numerical Recipes_, 2ed, §14.3)](https://numerical.recipes) asks: ___Do two distributions differ?___ The KS statistic, $D$, is defined as the maximum absolute difference between two CDFs:\n",
    "$$\n",
    "    D = \\max_x \\left| C(x) - C'(x) \\right|,\n",
    "$$\n",
    "where $C_1(x)$ is evaluated for $N$ discrete samples, $x \\in x_1, x_2,... x_N$. \n",
    "- In the __one-sample test__, $C'(x)$ is a proposed analytic CDF. The effective sample size is $N_e=N$.\n",
    "- In the __two-sample test__, $C'(x)$ is evaluated for $M$ discrete samples, $x \\in x'_1, x'_2,... x'_{M'}$. The effective sample size is $$ N_e = \\frac{N N'}{N+N'}.$$\n",
    "\n",
    "__Note__: [Many authors](https://ocw.mit.edu/courses/18-443-statistics-for-applications-fall-2006/resources/lecture14/) include a factor of $\\sqrt{N_e}$ in the definition of $D$. I have instead followed the _NR_ approach, in which $D \\in (0,1)$ is useful measure of the _degree_ of discrepancy, independent of sample size. This convention is similar to how we define correlation coefficients (Pearson's $r$, Spearman's $r_s$, Kendall's $\\tau$). See the \"What does it mean?\" heading below.\n",
    "\n",
    "The $p$-value is \n",
    "$$\n",
    "\\Pr(D \\ge \\text{observed}) = Q_{\\mathrm{KS}}(\\lambda) \\equiv \\sum_{i=1}^{\\infty}{(-1)^{j-1}e^{-2j^2\\lambda^2}}, \n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\lambda \\equiv D \\left( \\sqrt{N_e} + 0.12 + \\frac{0.11}{\\sqrt{N_e}} \\right).\n",
    "$$\n",
    "\n",
    "__Critical $p$-values do not depend on the form of the distributions $C,C'$__. The terms after $\\sqrt{N_e}$ in the $\\lambda$ formula are intended to correct for small $N_e$. Using these terms, _NR_ (see references therein) reports that the $p$-values are accurate for $N_e \\ge 4$. _I have verified this_. Moreover, as we shall see, the sum for $Q_{\\mathrm{KS}}(\\lambda)$ converges extremely rapidly for $\\lambda > 1$. Even the first term ($j=1$) is sufficient for all practical purposes. Note that the 98% confidence level (confidence refers to $1-p$) is at about $\\lambda = 1.5$, and 90% at about $\\lambda = 1.2$, so $\\lambda < 1$ _never_ results in rejection of the null hypothesis."
   ]
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   "source": [
    "### !!! KS Implementation Note !!!\n",
    "To calculate $D$ correctly, we must exercise care in thinking about the cumulative distribution of a discrete set of points $x_1,x_2,...x_N$. The sample CDF jumps by $1/N$ at each point, starting at $0$ for $x < x_1$, and ending at $1$ for $x > x_N$. Because of the jumps, the sample CDF is technically undefined at the data points. Practically, we may consider the values on the data points as double-valued:\n",
    "$$\n",
    "    C(x_i) =  \\frac{i - \\frac{1}{2}  \\pm \\frac{1}{2}}{N}\n",
    "$$\n",
    "Consequently, for the one-sample test,\n",
    "$$\n",
    "    D = \\max_x \\left| C(x) - C'(x) \\right| \n",
    "        = \\max_i \\left| \\frac{i - \\frac{1}{2}}{N} - C'(x_i) \\right| + \\frac{1}{2}.\n",
    "$$\n",
    "If the above prescription is not adhered to, the $p$-values implied by $Q_{\\mathrm{KS}}$ will be incorrect!\n",
    "\n",
    "![Plot showing implementation of $C(x)$ and $D$ in relation to the $x_i$ and $C'(x)$ for the one-sample test.](./KS-sketch.svg)\n",
    "\n",
    "___Above:__ Implementation of $C(x)$ and $D$ in relation to data $x_i$ and analytic distribution $C'(x)$ for the one-sample KS test._\n",
    "\n",
    "The two-sample test is more complicated since generally $N \\ne M$. There are then two stairstep distributions, which must be compared at every $x_i$ _and_ at every $x'_j$.\n",
    "\n",
    "In Python, we index from $0$, so the implementation is something like this:\n",
    "```\n",
    "# Let x be the data array, with N elements; \n",
    "\n",
    "def Cp(x):\n",
    "    \"\"\"\n",
    "    Analytic CDF evaluated at x.\n",
    "    \"\"\"\n",
    "    cdf = ...\n",
    "    return cdf\n",
    "    \n",
    "C = (np.arange(N) + 0.5) / N         # Sample CDF, center of range for each x.\n",
    "D = np.amax(abs(C - Cp(x))) + 0.5/N  # KS statistic (NR style)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a6eb545c-a286-42b5-be5d-054be2ca228c",
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   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def Q_KS(jmax, lam, progress=False):\n",
    "    \"\"\"\n",
    "    Q_KS(lambda) defined in Numerical Recipes (2 ed.) for calculating\n",
    "    p-values for the\n",
    "\n",
    "    jmax: maximum index for the infinite sum.\n",
    "    lam: lambda, the Ne-dependent version of the KS-statistic.\n",
    "    progress: if true, display a progress bar while calculating the sum.\n",
    "    \"\"\"\n",
    "    result = 0\n",
    "    if progress:    \n",
    "        for j in tqdm(range(1,jmax+1)):\n",
    "            result += (-1.0)**(j-1) * np.exp( -2.0 * (j*lam)**2 )\n",
    "    else:\n",
    "        for j in range(1,jmax+1):\n",
    "            result += (-1.0)**(j-1) * np.exp( -2.0 * (j*lam)**2 )        \n",
    "    return 2*result\n",
    "\n",
    "\n",
    "lam_arr = np.linspace(0.01,3, num=1000)\n",
    "plt.figure()\n",
    "plt.loglog(lam_arr, Q_KS(1,lam_arr),'--', label=r'$j_{\\mathrm{max}}=1$ (adequate)')\n",
    "plt.plot(lam_arr, Q_KS(2,lam_arr), label=r'$j_{\\mathrm{max}}=2$')\n",
    "plt.plot(lam_arr, Q_KS(5,lam_arr), '--', label=r'$j_{\\mathrm{max}}=3$')\n",
    "plt.plot(lam_arr, Q_KS(10,lam_arr), label=r'$j_{\\mathrm{max}}=10$')\n",
    "plt.plot(lam_arr, Q_KS(11,lam_arr), '--', label=r'$j_{\\mathrm{max}}=11$')\n",
    "plt.plot(lam_arr, Q_KS(1000,lam_arr), 'k', label=r'$j_{\\mathrm{max}}=1000$')\n",
    "plt.xlabel(r'$\\lambda$')\n",
    "plt.ylabel(r'$Q_{\\mathrm{KS}}(\\lambda)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76db2f5b-2590-4f69-87e1-58a1a8cff1de",
   "metadata": {},
   "source": [
    "## Applying KS to the distribution of star distances\n",
    "I could use [`scipy.stats.kstest`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html), but that would require me to write a separate routine to evaluate the analytic CDF. Since KS is very simple, and I have done all of the steps myself anyway to generate the plots above, using [`scipy.stats`](https://docs.scipy.org/doc/scipy/reference/stats.html) would only make more work."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0a469b7a-70b3-4b57-a1a0-57f73d34beff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Back to our star sample....\n",
    "plt.figure()\n",
    "plt.semilogx(dist_pc, cum_distro - model_cum)\n",
    "plt.xlabel('distance (pc)')\n",
    "plt.ylabel('CDF discrepancy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b3ff08cc-6e39-4aed-be81-c98a4b5decd3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size, Ne  =  300567\n",
      "KS statistic D   =  0.012503124751393419\n",
      "Lambda           =  6.8562148843975175\n",
      "p = Q_KS(Lambda) =  2.9558046389820403e-41\n"
     ]
    }
   ],
   "source": [
    "# Kolmogorov-Smirnov (K-S) test\n",
    "\n",
    "Ne = len(dist_pc)  # For testing data against an analytic CDF, effective N is just N.\n",
    "D = np.amax(np.abs(cum_distro - model_cum)) + 0.5/Ne # KS D-statistic\n",
    "Lambda = D * ( np.sqrt(Ne) + 0.12 + 0.11/np.sqrt(Ne) )\n",
    "\n",
    "print(\"Sample size, Ne  = \", Ne)\n",
    "print(\"KS statistic D   = \", D)\n",
    "print(\"Lambda           = \", Lambda)\n",
    "print(\"p = Q_KS(Lambda) = \", Q_KS(1000,Lambda))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59151403-b0a2-427b-9605-9d0dcc574f92",
   "metadata": {},
   "source": [
    "### What does this mean?\n",
    "\n",
    "Parameter           |            |  Interpretation\n",
    "--------------------|------------|--------------------------------------\n",
    "Small $D$           | $\\implies$ | Star distribution is nearly uniform!\n",
    "$p\\rightarrow 0$    | $\\implies$ | Star distribution is NOT uniform!\n",
    "\n",
    "___Is there a contradiction? Discuss.___\n",
    "\n",
    "The low $p$-value says we can reject the _null hypothesis_, which was that the distribution is uniform. The small value of $D=0.0125$ tells us that the distribution deviates by only 1.25% from uniform. The $p$-value is telling us that this small deviation is _statistically significant._\n",
    "\n",
    "#### Aside: Anderson-Darling\n",
    "\n",
    "The KS test is robust and quite useful, but there is a more powerful test called [Anderson-Darling](https://asaip.psu.edu/Articles/beware-the-kolmogorov-smirnov-test/). Unfortunately, the $p$-values for AD depend on the form of the expected distribution, $C'(x)$. The current implementation [`scipy.stats.anderson`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html) is limited to comparison with a short list of distributions, and even that with only a handful of critical values tabulated. Consequently, if you want to use the AD test, be prepared to generate your own $p$-values by MonteCarlo."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a671487-903f-4bfa-87f7-390e8a9bc4da",
   "metadata": {},
   "source": [
    "## Are the $p$-values given by $Q_{\\mathrm{KS}}$ correct?\n",
    "__MonteCarlo test__\n",
    "\n",
    "If you have time, it is worth running the code a few times. Suggested parameters:\n",
    "\n",
    "$\\mathtt{Ntrials}$   | $\\mathtt{Nstarsmc}$ \n",
    "--------------------:|------------------------:\n",
    "  $\\mathtt{1000000}$ |     $\\mathtt{10}$\n",
    "  $\\mathtt{1000000}$ |    $\\mathtt{100}$\n",
    "  $\\mathtt{1000000}$ |   $\\mathtt{1000}$\n",
    "  $\\mathtt{10000}$   |     $\\mathtt{Ne}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b693a2b9-e6f6-4c9c-9020-1a25efb2e8e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████| 1000000/1000000 [00:11<00:00, 89761.50it/s]\n"
     ]
    }
   ],
   "source": [
    "Ntrials = 1000000\n",
    "Nstarsmc = 100 # Ne to directly replicate above results with GCNS. Smaller for quick test.\n",
    "\n",
    "Ncube = int( 2*(1+6/np.sqrt(Nstarsmc))*Nstarsmc )  # Number of stars in cube (need extras!)\n",
    "cum_distro_mc = (0.5+np.arange(Nstarsmc))/Nstarsmc\n",
    "D_mc = np.empty((Ntrials))\n",
    "\n",
    "for i in tqdm(range(Ntrials)):\n",
    "    # Create a uniformly distributed sample of \"stars\" with 0.1 kpc\n",
    "    x = R_pc * np.random.random((Ncube))\n",
    "    y = R_pc * np.random.random((Ncube))\n",
    "    z = R_pc * np.random.random((Ncube))\n",
    "    r = np.sqrt(x**2 + y**2 + z**2)\n",
    "    r = r[r<R_pc] # Select only stars within the GCNS distance limit.\n",
    "    r = r[:Nstarsmc] # Select the same number of stars as my trimmed GCNS.\n",
    "    r = np.sort(r) # Sorted distances\n",
    "    cum_model_mc = (r/R_pc)**3\n",
    "    D_mc[i] = np.amax(np.abs(cum_model_mc - cum_distro_mc)) + 0.5/Nstarsmc\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f264e9e7-8604-429a-87f8-6cdf9e929d3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gonna use a very large jmax in Q_KS, this could take awhile....\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|████████████████████████████████████| 10000/10000 [00:22<00:00, 435.20it/s]\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D_mc = np.sort(D_mc)\n",
    "lam_mc = D_mc * ( np.sqrt(Nstarsmc) + 0.12 + 0.11/np.sqrt(Nstarsmc) )\n",
    "cum_mc = np.flip((0.5+np.arange(Ntrials))/Ntrials) # Flipped cum distro, as with Q_KS.\n",
    "print('Gonna use a very large jmax in Q_KS, this could take awhile....')\n",
    "QKS_mc = Q_KS(10000, lam_mc, progress=True)\n",
    "\n",
    "plt.figure()\n",
    "plt.semilogy(lam_mc, cum_mc, label='MonteCarlo')\n",
    "plt.plot(lam_mc, QKS_mc, \"--\", label=r'$Q_{\\mathrm{KS}}(\\lambda)$')\n",
    "plt.ylabel('Cumulative Distribution of Trials')\n",
    "plt.xlabel(r'$\\lambda$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6865ed19-8cdf-49da-aec4-a1512f647379",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(lam_mc, (QKS_mc-cum_mc)/cum_mc)\n",
    "plt.ylim((-0.2,0.2))\n",
    "plt.ylabel(r'Fractional Discrepancy in $p$-value')\n",
    "plt.xlabel(r'$\\lambda$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "781ac61a-4f8d-44bf-a7f0-c5987e879b58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D = np.amax(np.abs(cum_mc-QKS_mc)) + 0.5/Ntrials\n",
    "plt.figure()\n",
    "plt.title(r'Testing $Q_{\\mathrm{KS}}$...with Kolmogorov-Smirnov!')\n",
    "plt.plot(lam_mc, cum_mc-QKS_mc)\n",
    "plt.ylabel(r'CDF discrepancy')\n",
    "plt.xlabel(r'$\\lambda$')\n",
    "plt.annotate(r'$D={:.3f}$,  $\\lambda={:.1f}$'.format(D,D*np.sqrt(Ntrials)),(1.5,-D/2))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cba50be-fc7d-44f8-807a-1208187e3aed",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "The Kolmogorov-Smirnov test is a handy, nonparametric test of whether two distributions differ. KS is so straightforward that I did not bother using the [`scipy.stats`](https://docs.scipy.org/doc/scipy/reference/stats.html) implementation. The Anderson-Darling test is more sensitive, especially in the tails of the distribution, but since the results depend on the form of the distribution, you will likely have to calculate your own $p$-values by MonteCarlo.\n",
    "\n",
    "The analytic cumulative distribution, $Q_{\\mathrm{KS}}(\\lambda)$, used to generate $p$-values for the KS test is quite reliable. A careful MonteCarlo test reveals deviations at small $\\lambda$, which are inconsequential."
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