{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Created on Mon Sep 16 09:47:15 2019\n",
    "@author: daniel\n",
    "\"\"\"\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def fractal_dimension(array, max_box_size=None, min_box_size=1, n_samples=20, n_offsets=0, plot=False):\n",
    "    \"\"\"Calculates the fractal dimension of a 3D numpy array.\n",
    "\n",
    "    Args:\n",
    "        array (np.ndarray): The array to calculate the fractal dimension of.\n",
    "        max_box_size (int): The largest box size, given as the power of 2 so that\n",
    "                            2**max_box_size gives the sidelength of the largest box.\n",
    "        min_box_size (int): The smallest box size, given as the power of 2 so that\n",
    "                            2**min_box_size gives the sidelength of the smallest box.\n",
    "                            Default value 1.\n",
    "        n_samples (int): number of scales to measure over.\n",
    "        n_offsets (int): number of offsets to search over to find the smallest set N(s) to\n",
    "                       cover  all voxels>0.\n",
    "        plot (bool): set to true to see the analytical plot of a calculation.\n",
    "\n",
    "\n",
    "    \"\"\"\n",
    "    # determine the scales to measure on\n",
    "    if max_box_size == None:\n",
    "        # default max size is the largest power of 2 that fits in the smallest dimension of the array:\n",
    "        max_box_size = int(np.floor(np.log2(np.min(array.shape))))\n",
    "    scales = np.floor(np.logspace(max_box_size, min_box_size, num=n_samples, base=2))\n",
    "    scales = np.unique(scales)  # remove duplicates that could occur as a result of the floor\n",
    "\n",
    "    # get the locations of all non-zero pixels\n",
    "    locs = np.where(array > 0)\n",
    "    voxels = np.array([(x, y, z) for x, y, z in zip(*locs)])\n",
    "\n",
    "    # count the minimum amount of boxes touched\n",
    "    Ns = []\n",
    "    # loop over all scales\n",
    "    for scale in scales:\n",
    "        touched = []\n",
    "        if n_offsets == 0:\n",
    "            offsets = [0]\n",
    "        else:\n",
    "            offsets = np.linspace(0, scale, n_offsets)\n",
    "        # search over all offsets\n",
    "        for offset in offsets:\n",
    "            bin_edges = [np.arange(0, i, scale) for i in array.shape]\n",
    "            bin_edges = [np.hstack([0 - offset, x + offset]) for x in bin_edges]\n",
    "            H1, e = np.histogramdd(voxels, bins=bin_edges)\n",
    "            touched.append(np.sum(H1 > 0))\n",
    "        Ns.append(touched)\n",
    "    Ns = np.array(Ns)\n",
    "\n",
    "    # From all sets N found, keep the smallest one at each scale\n",
    "    Ns = Ns.min(axis=1)\n",
    "\n",
    "    # Only keep scales at which Ns changed\n",
    "    scales = np.array([np.min(scales[Ns == x]) for x in np.unique(Ns)])\n",
    "\n",
    "    Ns = np.unique(Ns)\n",
    "    Ns = Ns[Ns > 0]\n",
    "    scales = scales[:len(Ns)]\n",
    "    # perform fit\n",
    "    coeffs = np.polyfit(np.log(1 / scales), np.log(Ns), 1)\n",
    "\n",
    "    # make plot\n",
    "    if plot:\n",
    "        fig, ax = plt.subplots(figsize=(8, 6))\n",
    "        ax.scatter(np.log(1 / scales), np.log(np.unique(Ns)), c=\"teal\", label=\"Measured ratios\")\n",
    "        ax.set_ylabel(\"$\\log N(\\epsilon)$\")\n",
    "        ax.set_xlabel(\"$\\log 1/ \\epsilon$\")\n",
    "        fitted_y_vals = np.polyval(coeffs, np.log(1 / scales))\n",
    "        ax.plot(np.log(1 / scales), fitted_y_vals, \"k--\", label=f\"Fit: {np.round(coeffs[0], 3)}X+{coeffs[1]}\")\n",
    "        ax.legend();\n",
    "    return (coeffs[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lib.lib import read_xy_alt, read_load\n",
    "\n",
    "full_data = read_load(\"/Users/joshuacoles/Developer/checkouts/jc3091/CompB DLA/data-analysis/data/rust-3d\", read_xy_alt)\n",
    "df = full_data[full_data.run == '1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "max_actual_radius = max(df.x.abs().max(), df.y.abs().max(), df.z.abs().max())\n",
    "max_radius = int(np.exp2(np.floor(np.log2(max_actual_radius)) + 1))\n",
    "data = np.zeros((max_radius * 2, max_radius * 2, max_radius * 2))\n",
    "data[df.x + max_radius, df.y + max_radius, df.z + max_radius] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(128, 128, 128)"
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "5000.0"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(5000, 8)"
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfs = []\n",
    "for _, df in full_data.groupby('run'):\n",
    "    max_actual_radius = max(df.x.abs().max(), df.y.abs().max(), df.z.abs().max())\n",
    "    max_radius = int(np.exp2(np.floor(np.log2(max_actual_radius)) + 1))\n",
    "    data = np.zeros((max_radius * 2, max_radius * 2, max_radius * 2))\n",
    "    data[df.x + max_radius, df.y + max_radius, df.z + max_radius] = 1\n",
    "    dfs.append(fractal_dimension(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "0.1543448984741014"
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.array(dfs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(run1.x, run1.y, run1.z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(10, 10))\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.scatter(run1.x, run1.y,run1.z, c=run1.N)\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "run1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'mpld3'",
     "output_type": "error",
     "traceback": [
      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[0;31mModuleNotFoundError\u001B[0m                       Traceback (most recent call last)",
      "Cell \u001B[0;32mIn[24], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m \u001B[38;5;28;01mimport\u001B[39;00m \u001B[38;5;21;01mmatplotlib\u001B[39;00m\u001B[38;5;21;01m.\u001B[39;00m\u001B[38;5;21;01mpyplot\u001B[39;00m \u001B[38;5;28;01mas\u001B[39;00m \u001B[38;5;21;01mplt\u001B[39;00m\u001B[38;5;241m,\u001B[39m \u001B[38;5;21;01mmpld3\u001B[39;00m\n",
      "\u001B[0;31mModuleNotFoundError\u001B[0m: No module named 'mpld3'"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt, mpld3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
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