crmccreary/circle_packing_polygonal_room2_basin_hopping.ipynb

## circle_packing_polygonal_room2_basin_hopping.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np, matplotlib.pyplot as plt\n",
    "from IPython import display\n",
    "from shapely.geometry import Point\n",
    "from shapely.geometry.polygon import Polygon\n",
    "from shapely.geometry.polygon import LinearRing\n",
    "from shapely.geometry import box\n",
    "from scipy.optimize import minimize\n",
    "from scipy.optimize import basinhopping\n",
    "from itertools import cycle\n",
    "from itertools import islice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 22 # number of circles\n",
    "R_max = 3\n",
    "\n",
    "vertices = [(0, 0), \n",
    "            (29.3, 0), \n",
    "            (29.3, 4), \n",
    "            (34.3, 4), \n",
    "            (34.3,22), \n",
    "            (4.3,22), \n",
    "            (4.3,18), \n",
    "            (0,18)]\n",
    "\n",
    "polygon = Polygon(vertices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_line = LinearRing(polygon.exterior.coords)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_line_offset = poly_line.parallel_offset(2.0, side=\"left\", join_style=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "offset_polygon = Polygon(poly_line_offset.coords)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6.3, 6.0, 32.3, 20.0)\n"
     ]
    }
   ],
   "source": [
    "coords = list(poly_line_offset.coords[:-1])\n",
    "#print(coords)\n",
    "num_vert = len(coords)\n",
    "positions = cycle(coords)\n",
    "rectangles = []\n",
    "for i in range(num_vert):\n",
    "    #print('vertex: {}'.format(i))\n",
    "    start = islice(positions, i, None)\n",
    "    v1 = coords[i]\n",
    "    for i in range(num_vert):\n",
    "        _ = next(start)\n",
    "        v2 = next(start)\n",
    "        #print(v1,v2)\n",
    "        if v1[0] != v2[0] and v1[1] != v2[1]:\n",
    "            rectangles.append(box(v1[0], v1[1], v2[0], v2[1]))\n",
    "            \n",
    "rectangles = [r for r in rectangles if offset_polygon.contains(r)]\n",
    "rectangles.sort(key=lambda x: x.area, reverse=True)\n",
    "rectangle = rectangles[0]\n",
    "rectangle_bounds = rectangle.bounds\n",
    "print(rectangle_bounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_line(ax, ob, color):\n",
    "    x, y = ob.xy\n",
    "    ax.plot(x, y, color=color, alpha=0.7, linewidth=3, \n",
    "            solid_capstyle='round', zorder=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "plot_line(ax, poly_line, \"blue\")\n",
    "plot_line(ax, poly_line_offset, \"green\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "def boundary_cons(centers):\n",
    "    sum = 0\n",
    "    for center_x,center_y in zip(centers[0::2],centers[1::2]):\n",
    "        point = Point(center_x,center_y)\n",
    "        if not offset_polygon.contains(point):\n",
    "            sum = sum - 100\n",
    "        else:\n",
    "            sum = sum + 1\n",
    "    return sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "def boundary_cons_T_F(centers):\n",
    "    for center_x,center_y in zip(centers[0::2],centers[1::2]):\n",
    "        point = Point(center_x,center_y)\n",
    "        if not offset_polygon.contains(point):\n",
    "            return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "def potential_energy_outside(centers):\n",
    "    U = 0\n",
    "    for center_x,center_y in zip(centers[0::2],centers[1::2]):\n",
    "        point = Point(center_x,center_y)\n",
    "        if not offset_polygon.contains(point):\n",
    "            U = U + offset_polygon.exterior.distance(point)**2\n",
    "    return U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getPairs(N):\n",
    "    '''Generate all (2-way) unique pairings of N objects'''\n",
    "    result=[]\n",
    "    for i in range(0,N):\n",
    "        for j in range(0,i):\n",
    "            result.append([i,j])\n",
    "    return(np.array(result))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "cpairs=getPairs(N)\n",
    "A=cpairs[:,0]\n",
    "B=cpairs[:,1]\n",
    "ind=range(0,2*N)\n",
    "a,b=list(ind[0:2*N:2]),list(ind[1:2*N:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "def genGuess(N):\n",
    "    '''Generate sensible initial guess vector (random circle coordinates)'''\n",
    "    z=np.zeros(2*N)\n",
    "    bounds = offset_polygon.convex_hull.bounds\n",
    "    x = np.random.uniform(low=bounds[0]+R_max,high=bounds[2]-R_max,size=N)\n",
    "    y = np.random.uniform(low=bounds[1]+R_max,high=bounds[3]-R_max,size=N)\n",
    "    z[0::2] = x\n",
    "    z[1::2] = y\n",
    "    return(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.776261317841449\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "rect_area = rectangle.area/(2*np.sqrt(3))\n",
    "print(rect_area/N)\n",
    "#R_init = np.sqrt((rect_area/N)/np.pi)\n",
    "R_init = R_max\n",
    "print(R_init)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = genGuess(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "plot_line(ax, poly_line, \"blue\")\n",
    "plot_line(ax, poly_line_offset, \"green\")\n",
    "for center_x,center_y in zip(x0[0::2],x0[1::2]):\n",
    "    ax.add_patch(plt.Circle((center_x,center_y), R_init, fill=False, lw=1, ec='black'))\n",
    "\n",
    "ax.set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R: 3.0\n",
      "basinhopping step 0: f 0.0778683\n",
      "basinhopping step 1: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 2: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 3: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 4: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 5: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 6: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 7: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 8: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 9: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 10: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 11: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 12: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 13: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 14: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 15: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 16: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 17: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 18: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 19: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 20: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 21: f 0.0778683 trial_f 0.07814 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 22: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 23: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 24: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 25: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 26: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 27: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 28: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 29: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 30: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 31: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 32: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 33: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 34: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 35: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 36: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 37: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 38: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 39: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 40: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 41: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 42: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 43: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 44: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 45: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 46: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 47: f 0.0778683 trial_f 0.0443486 accepted 0  lowest_f 0.0778683\n",
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      "adaptive stepsize: acceptance rate 0.000000 target 0.500000 new stepsize 0.19371 old stepsize 0.215234\n",
      "basinhopping step 450: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 451: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 452: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 453: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 454: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 455: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 456: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 457: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 458: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 459: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 460: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 461: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 462: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 463: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 464: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 465: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 466: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 467: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 468: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 469: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 470: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 471: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 472: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 473: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 474: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 475: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 476: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 477: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 478: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 479: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 480: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 481: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 482: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "basinhopping step 483: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 484: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 485: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 486: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 487: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 488: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 489: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 490: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 491: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 492: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 493: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 494: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 495: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 496: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 497: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 498: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "basinhopping step 499: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "adaptive stepsize: acceptance rate 0.000000 target 0.500000 new stepsize 0.174339 old stepsize 0.19371\n",
      "basinhopping step 500: f 0.0778683 trial_f 0.0778683 accepted 0  lowest_f 0.0778683\n",
      "                        fun: 0.07786832752499848\n",
      " lowest_optimization_result:       fun: 0.07786832752499848\n",
      " hess_inv: array([[ 5.22254597e-01, -1.29050283e-02,  8.13780870e-03, ...,\n",
      "        -3.72144167e-02, -2.43879725e-01, -3.51665415e-02],\n",
      "       [-1.29050283e-02,  8.94968180e-01, -3.90914801e-02, ...,\n",
      "        -6.78434186e-02, -4.69237677e-01,  1.78550412e-02],\n",
      "       [ 8.13780870e-03, -3.90914801e-02,  4.34111978e-01, ...,\n",
      "         2.31749572e-02,  1.42792894e-01,  5.22209578e-02],\n",
      "       ...,\n",
      "       [-3.72144167e-02, -6.78434186e-02,  2.31749572e-02, ...,\n",
      "         5.54351200e-01,  4.51135860e-01, -7.22153341e-03],\n",
      "       [-2.43879725e-01, -4.69237677e-01,  1.42792894e-01, ...,\n",
      "         4.51135860e-01,  9.28347320e+00,  1.23461104e+00],\n",
      "       [-3.51665415e-02,  1.78550412e-02,  5.22209578e-02, ...,\n",
      "        -7.22153341e-03,  1.23461104e+00,  1.00696912e+00]])\n",
      "      jac: array([ 1.97440386e-07, -4.54485416e-07, -1.53388828e-06,  1.49104744e-06,\n",
      "        1.17532909e-06,  4.91738319e-07,  2.53319740e-07, -1.34110451e-06,\n",
      "        7.66478479e-07, -1.68569386e-06,  0.00000000e+00,  0.00000000e+00,\n",
      "        0.00000000e+00,  0.00000000e+00,  4.83915210e-06,  2.09175050e-06,\n",
      "        1.68289989e-06,  1.72760338e-06, -2.01910734e-06,  2.49966979e-06,\n",
      "        8.55885446e-07, -1.38767064e-07,  1.18464231e-06, -2.11503357e-06,\n",
      "       -3.34344804e-07,  5.53205609e-07, -4.88664955e-06, -3.13017517e-06,\n",
      "        3.44496220e-06,  2.74740160e-07, -1.95018947e-06, -3.44589353e-08,\n",
      "       -2.14949250e-06,  1.59256160e-06, -1.22934580e-06,  1.90269202e-06,\n",
      "       -4.39584255e-07, -4.88385558e-06,  0.00000000e+00,  0.00000000e+00,\n",
      "       -5.58793545e-08, -1.90641731e-06,  5.92321157e-07, -3.27732414e-06])\n",
      "  message: 'Optimization terminated successfully.'\n",
      "     nfev: 7774\n",
      "      nit: 138\n",
      "     njev: 169\n",
      "   status: 0\n",
      "  success: True\n",
      "        x: array([ 1.95428421,  7.91416969, 32.34786739, 17.86317204, 12.07463287,\n",
      "       13.18656755,  1.98052838,  1.95709283, 13.95355995,  1.98198308,\n",
      "       20.99815544,  2.25017301,  6.91912223, 19.93071232, 21.39504609,\n",
      "       10.4421514 , 17.67783541, 15.07919317, 32.36526511,  5.95786973,\n",
      "        1.9514788 , 16.04555505, 26.80284085, 20.0221211 ,  6.27720512,\n",
      "       11.98429207, 10.21845164,  7.49347782, 16.19320619,  7.52734249,\n",
      "       20.84870736, 20.07227561, 26.17538251, 14.05961536, 26.78212883,\n",
      "        7.9642328 , 27.30057605,  1.99336064, 13.55875539, 19.63911027,\n",
      "        7.96085439,  1.96973856, 31.77248474, 11.9089529 ])\n",
      "                    message: ['requested number of basinhopping iterations completed successfully']\n",
      "      minimization_failures: 0\n",
      "                       nfev: 1651814\n",
      "                        nit: 500\n",
      "                       njev: 35909\n",
      "                          x: array([ 1.95428421,  7.91416969, 32.34786739, 17.86317204, 12.07463287,\n",
      "       13.18656755,  1.98052838,  1.95709283, 13.95355995,  1.98198308,\n",
      "       20.99815544,  2.25017301,  6.91912223, 19.93071232, 21.39504609,\n",
      "       10.4421514 , 17.67783541, 15.07919317, 32.36526511,  5.95786973,\n",
      "        1.9514788 , 16.04555505, 26.80284085, 20.0221211 ,  6.27720512,\n",
      "       11.98429207, 10.21845164,  7.49347782, 16.19320619,  7.52734249,\n",
      "       20.84870736, 20.07227561, 26.17538251, 14.05961536, 26.78212883,\n",
      "        7.9642328 , 27.30057605,  1.99336064, 13.55875539, 19.63911027,\n",
      "        7.96085439,  1.96973856, 31.77248474, 11.9089529 ])\n",
      "181.06821354785862\n",
      "-988\n",
      "All constraints exactly satisfied: False\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for R in np.linspace(R_max, R_max, num=1, endpoint=True):\n",
    "    \n",
    "    print('R: {}'.format(R))\n",
    "    \n",
    "    r = np.ones(N)*R\n",
    "    \n",
    "    def circle_distances(centers):\n",
    "        z=np.array(centers,dtype=np.float)\n",
    "        x,y=z.take(a,axis=0),z.take(b,axis=0)\n",
    "        '''\n",
    "        Overlapping depth or separation.\n",
    "        If circles overlap, the c5 entry will be positive.\n",
    "        If circles are separated, the c5 entry will be negative.\n",
    "        '''\n",
    "        c5=r.take(A,axis=0) + \\\n",
    "           r.take(B,axis=0) - \\\n",
    "           np.sqrt(np.power(x.take(A,axis=0) - \\\n",
    "                            x.take(B,axis=0),2) + \\\n",
    "                   np.power(y.take(A,axis=0) - \\\n",
    "                            y.take(B,axis=0),2)) # <=0\n",
    "        return c5\n",
    "\n",
    "    def potential_energy(centers):\n",
    "        c5 = circle_distances(centers)\n",
    "        return c5[c5 > 0]**2\n",
    "    \n",
    "    def circle_cons(centers):\n",
    "        c5 = circle_distances(centers)\n",
    "        #print(len(c5),c5)\n",
    "        #print(len(c5[c5 > 0]))\n",
    "        neg_norm = np.linalg.norm(c5[c5 < 0])\n",
    "        pos_norm = np.linalg.norm(c5[c5 > 0])\n",
    "        return neg_norm - pos_norm\n",
    "    \n",
    "    def accept(f_new, x_new, f_old, x_old):\n",
    "        #print(x_new - x_old)\n",
    "        center_to_center_dist = circle_distances(x_new)\n",
    "        if (center_to_center_dist < 0).all() and boundary_cons_T_F(x_new):\n",
    "            print('Accepted')\n",
    "            return True\n",
    "        return False\n",
    "    \n",
    "    def total_potential_energy(centers):\n",
    "        return potential_energy(centers).sum() + potential_energy_outside(centers)\n",
    "    \n",
    "    \n",
    "    opt = basinhopping(total_potential_energy,\n",
    "                       x0,\n",
    "                       accept_test=accept,\n",
    "                       niter=500,\n",
    "                       #T=1000,\n",
    "                       #stepsize=1,\n",
    "                       disp=True,\n",
    "                       minimizer_kwargs={'method':'BFGS'})\n",
    "    #display.clear_output()\n",
    "    print(opt)\n",
    "    print(circle_cons(opt.x))\n",
    "    print(boundary_cons(opt.x))\n",
    "    print('All constraints exactly satisfied: {}'.format(accept(0,opt.x,0,0)))\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    plot_line(ax, poly_line, \"blue\")\n",
    "    for center_x,center_y in zip(opt.x[0::2],opt.x[1::2]):\n",
    "        ax.add_patch(plt.Circle((center_x,center_y), R, fill=False, lw=1, ec='black'))\n",
    "    ax.set_aspect('equal')\n",
    "    plt.show()\n",
    "\n",
    "    if not opt.lowest_optimization_result.success:\n",
    "        centers_opt = x0\n",
    "        break\n",
    "    x0 = opt.x\n",
    "centers_opt = opt.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0\n"
     ]
    }
   ],
   "source": [
    "print(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.95428421 32.34786739 12.07463287  1.98052838 13.95355995 20.99815544\n",
      "  6.91912223 21.39504609 17.67783541 32.36526511  1.9514788  26.80284085\n",
      "  6.27720512 10.21845164 16.19320619 20.84870736 26.17538251 26.78212883\n",
      " 27.30057605 13.55875539  7.96085439 31.77248474]\n",
      "[ 7.91416969 17.86317204 13.18656755  1.95709283  1.98198308  2.25017301\n",
      " 19.93071232 10.4421514  15.07919317  5.95786973 16.04555505 20.0221211\n",
      " 11.98429207  7.49347782  7.52734249 20.07227561 14.05961536  7.9642328\n",
      "  1.99336064 19.63911027  1.96973856 11.9089529 ]\n"
     ]
    }
   ],
   "source": [
    "print(centers_opt[0::2])\n",
    "print(centers_opt[1::2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "181.06821354785862"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circle_cons(centers_opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-988"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boundary_cons(centers_opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "plot_line(ax, poly_line, \"blue\")\n",
    "plot_line(ax, poly_line_offset, \"green\")\n",
    "for center_x,center_y in zip(centers_opt[0::2],centers_opt[1::2]):\n",
    "    ax.add_patch(plt.Circle((center_x,center_y), R, fill=False, lw=1, ec='black'))\n",
    "\n",
    "ax.set_aspect('equal')\n",
    "plt.show()\n",
    "fig.savefig('room1.pdf', dpi=300)\n",
    "fig.savefig('room1.png', dpi=300)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}