Maximising area of 34 sided pollygone.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.optim as optim\n",
    "from torch.autograd import Variable\n",
    "import matplotlib.pyplot as plt\n",
    "from torch import sqrt\n",
    "import numpy as np\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Define the number of variables\n",
    "#n = 34\n",
    "\n",
    "# Create a list of Variables for x and y\n",
    "#x_variables = [torch.randn(1, requires_grad=True) for _ in range(n)]\n",
    "#y_variables = [torch.randn(1, requires_grad=True) for _ in range(n)]\n",
    "\n",
    "# Example: printing the variables\n",
    "#for i in range(n):\n",
    "    #print(f\"x{i+1}:\", x_variables[i].item())\n",
    "\n",
    "#for i in range(n):\n",
    "    #print(f\"y{i+1}:\", y_variables[i].item())\n",
    "\n",
    "# Plot each set of data\n",
    "#for i in range(n):\n",
    "    #plt.plot(x_variables[i].detach().numpy(), y_variables[i].detach().numpy(), 'x', color='red', label=f'Set {i+1}')\n",
    "\n",
    "    \n",
    "\n",
    "#plt.xlabel('X')\n",
    "#plt.ylabel('Y')\n",
    "#plt.title('Plot of 34 sets of data')\n",
    "#plt.show()\n",
    "\n",
    "x1 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y1 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x2 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y2 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x3 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y3 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x4 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y4 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y5 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x5 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x6 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x7 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x8 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x9 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x10 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x11 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x12 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x13 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x14 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x15 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x16 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x17 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x18 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x19 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x20 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x21 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x22 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x23 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x24 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x25 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x26 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x27 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x28 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x29 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x30 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x31 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x32 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x33 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "x34 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y6 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y7 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y8 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y9 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y10 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y11 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y12 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y13 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y14 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y15 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y16 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y17 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y18 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y19 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y20 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y21 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y22 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y23 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y24 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y25 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y26 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y27 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y28 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y29 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y30 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y31 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y32 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y33 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "y34 = Variable(torch.randn(1)*1, requires_grad=True)\n",
    "\n",
    "plt.plot(x1.detach().numpy(), y1.detach().numpy(), 'x',color='red',label='Starting locations')\n",
    "plt.plot(x2.detach().numpy(), y2.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x3.detach().numpy(), y3.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x4.detach().numpy(), y4.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x5.detach().numpy(), y5.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x6.detach().numpy(), y6.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x7.detach().numpy(), y7.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x8.detach().numpy(), y8.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x9.detach().numpy(), y9.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x10.detach().numpy(), y10.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x11.detach().numpy(), y11.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x12.detach().numpy(), y12.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x13.detach().numpy(), y13.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x14.detach().numpy(), y14.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x15.detach().numpy(), y15.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x16.detach().numpy(), y16.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x17.detach().numpy(), y17.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x18.detach().numpy(), y18.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x19.detach().numpy(), y19.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x20.detach().numpy(), y20.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x21.detach().numpy(), y21.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x22.detach().numpy(), y22.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x23.detach().numpy(), y23.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x24.detach().numpy(), y24.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x25.detach().numpy(), y25.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x26.detach().numpy(), y26.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x27.detach().numpy(), y27.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x28.detach().numpy(), y28.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x29.detach().numpy(), y29.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x30.detach().numpy(), y30.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x31.detach().numpy(), y31.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x32.detach().numpy(), y32.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x33.detach().numpy(), y33.detach().numpy(), 'x',color='red')\n",
    "plt.plot(x34.detach().numpy(), y34.detach().numpy(), 'x',color='red')\n",
    "\n",
    "print(x1.detach().numpy(), y1.detach().numpy(), 'x')\n",
    "print(x2.detach().numpy(), y2.detach().numpy(), 'x')\n",
    "print(x3.detach().numpy(), y3.detach().numpy(), 'x')\n",
    "print(x4.detach().numpy(), y4.detach().numpy(), 'x')\n",
    "print(x5.detach().numpy(), y5.detach().numpy(), 'x')\n",
    "print(x6.detach().numpy(), y6.detach().numpy(), 'x')\n",
    "print(x7.detach().numpy(), y7.detach().numpy(), 'x')\n",
    "print(x8.detach().numpy(), y8.detach().numpy(), 'x')\n",
    "print(x9.detach().numpy(), y9.detach().numpy(), 'x')\n",
    "print(x10.detach().numpy(), y10.detach().numpy(), 'x')\n",
    "print(x11.detach().numpy(), y11.detach().numpy(), 'x')\n",
    "print(x12.detach().numpy(), y12.detach().numpy(), 'x')\n",
    "print(x13.detach().numpy(), y13.detach().numpy(), 'x')\n",
    "print(x14.detach().numpy(), y14.detach().numpy(), 'x')\n",
    "print(x15.detach().numpy(), y15.detach().numpy(), 'x')\n",
    "print(x16.detach().numpy(), y16.detach().numpy(), 'x')\n",
    "print(x17.detach().numpy(), y17.detach().numpy(), 'x')\n",
    "print(x18.detach().numpy(), y18.detach().numpy(), 'x')\n",
    "print(x19.detach().numpy(), y19.detach().numpy(), 'x')\n",
    "print(x20.detach().numpy(), y20.detach().numpy(), 'x')\n",
    "print(x21.detach().numpy(), y21.detach().numpy(), 'x')\n",
    "print(x22.detach().numpy(), y22.detach().numpy(), 'x')\n",
    "print(x23.detach().numpy(), y23.detach().numpy(), 'x')\n",
    "print(x24.detach().numpy(), y24.detach().numpy(), 'x')\n",
    "print(x25.detach().numpy(), y25.detach().numpy(), 'x')\n",
    "print(x26.detach().numpy(), y26.detach().numpy(), 'x')\n",
    "print(x27.detach().numpy(), y27.detach().numpy(), 'x')\n",
    "print(x28.detach().numpy(), y28.detach().numpy(), 'x')\n",
    "print(x29.detach().numpy(), y29.detach().numpy(), 'x')\n",
    "print(x30.detach().numpy(), y30.detach().numpy(), 'x')\n",
    "print(x31.detach().numpy(), y31.detach().numpy(), 'x')\n",
    "print(x32.detach().numpy(), y32.detach().numpy(), 'x')\n",
    "print(x33.detach().numpy(), y33.detach().numpy(), 'x')\n",
    "print(x34.detach().numpy(), y34.detach().numpy(), 'x')\n",
    "\n",
    "\n",
    "\n",
    "def compute_area(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6,  x7, y7, x8, y8, x9, y9, x10, y10, x11, y11, x12, y12, x13, y13, x14, y14, x15, y15, x16, y16, x17, y17, x18, y18, x19, y19, x20, y20, x21, y21, x22, y22, x23, y23, x24, y24, x25, y25, x26, y26, x27, y27, x28, y28, x29, y29, x30, y30, x31, y31, x32, y32, x33, y33, x34, y34):\n",
    "\n",
    "\n",
    "   #  area = 0.5 * |x1*y2 -x1*y4 -x3*y2 + x3*y4 -y1*x2 +y1*x4 +y3*x2 -y3*x4|\n",
    "\n",
    "        return 0.5 * torch.abs((x1*y2 - y1*x2)+(x2*y3 - y2*x3)+(x3*y4 -y3*x4)+(x4*y5-y4*x5)+(x5*y6-y5*x6)+(x6*y7-y6*x7)+(x7*y8-y7*x8)+(x8*y9-y8*x9)+(x9*y10-y9*x10)+(x10*y11-y10*x11)+(x11*y12-y11*x12)+(x12*y13-y12*x13)+(x13*y14-y13*x14)+(x14*y15-y14*x15)+(x15*y16-y15*x16)+(x16*y17-y16*x17)+(x17*y18-y17*x18)+(x18*y19-y18*x19)+(x19*y20-y19*x20)+(x20*y21-y20*x21)+(x21*y22-y21*x22)+(x22*y23-y22*x23)+(x23*y24-y23*x24)+(x24*y25-y24*x25)+(x25*y26-y25*x26)+(x26*y27-y26*x27)+(x27*y28-y27*x28)+(x28*y29-y28*x29)+(x29*y30-y29*x30)+(x30*y31-y30*x31)+(x31*y32-y31*x32)+(x32*y33-y32*x33)+(x33*y34-y33*x34)+(x34*y1-y34*x1))\n",
    "    \n",
    "\n",
    "\n",
    "def compute_perimeter(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6,  x7, y7, x8, y8, x9, y9, x10, y10, x11, y11, x12, y12, x13, y13, x14, y14, x15, y15, x16, y16, x17, y17, x18, y18, x19, y19, x20, y20, x21, y21, x22, y22, x23, y23, x24, y24, x25, y25, x26, y26, x27, y27, x28, y28, x29, y29, x30, y30, x31, y31, x32, y32, x33, y33, x34, y34):\n",
    "   \n",
    "    s1 = torch.sqrt((x2 - x1)**2 + (y2 - y1)**2)\n",
    "    s2 = torch.sqrt((x3 - x2)**2 + (y3 - y2)**2)\n",
    "    s3 = torch.sqrt((x4 - x3)**2 + (y4 - y3)**2)\n",
    "    s4 = torch.sqrt((x5 - x4)**2 + (y5 - y4)**2)\n",
    "    s5 = torch.sqrt((x6 - x5)**2 + (y6 - y5)**2)\n",
    "    s6 = torch.sqrt((x7 - x6)**2 + (y7 - y6)**2)\n",
    "    s7 = torch.sqrt((x8 - x7)**2 + (y8 - y7)**2)\n",
    "    s8 = torch.sqrt((x9 - x8)**2 + (y9- y8)**2)\n",
    "    s9 = torch.sqrt((x10 - x9)**2 + (y10 - y9)**2)\n",
    "    s10 = torch.sqrt((x11 - x10)**2 + (y11 - y10)**2)\n",
    "    s11 = torch.sqrt((x12 - x11)**2 + (y12 - y11)**2)\n",
    "    s12= torch.sqrt((x13 - x12)**2 + (y13 - y12)**2)\n",
    "    s13= torch.sqrt((x14 - x13)**2 + (y14 - y13)**2)\n",
    "    s14= torch.sqrt((x15 - x14)**2 + (y15 - y14)**2)\n",
    "    s15= torch.sqrt((x16 - x15)**2 + (y16 - y15)**2)\n",
    "    s16= torch.sqrt((x17 - x16)**2 + (y17- y16)**2)\n",
    "    s17= torch.sqrt((x18 - x17)**2 + (y18- y17)**2)\n",
    "    s18= torch.sqrt((x19 - x18)**2 + (y19- y18)**2)\n",
    "    s19= torch.sqrt((x20 - x19)**2 + (y20- y19)**2)\n",
    "    s20= torch.sqrt((x21 - x20)**2 + (y21 - y20)**2)\n",
    "    s21= torch.sqrt((x22 - x21)**2 + (y22 - y21)**2)\n",
    "    s22= torch.sqrt((x23 - x22)**2 + (y23 - y22)**2)\n",
    "    s23= torch.sqrt((x24 - x23)**2 + (y24 - y23)**2)\n",
    "    s24= torch.sqrt((x25 - x24)**2 + (y25 - y24)**2)\n",
    "    s25= torch.sqrt((x26 - x25)**2 + (y26 - y25)**2)\n",
    "    s26= torch.sqrt((x27 - x26)**2 + (y27- y26)**2)\n",
    "    s27= torch.sqrt((x28 - x27)**2 + (y28- y27)**2)\n",
    "    s28= torch.sqrt((x29- x28)**2 + (y29- y28)**2)\n",
    "    s29= torch.sqrt((x30- x29)**2 + (y30 - y29)**2)\n",
    "    s30= torch.sqrt((x31 - x30)**2 + (y31 - y30)**2)\n",
    "    s31= torch.sqrt((x32 - x31)**2 + (y32 - y31)**2)\n",
    "    s32= torch.sqrt((x33 - x32)**2 + (y33 - y32)**2)\n",
    "    s33= torch.sqrt((x34 - x33)**2 + (y34 - y33)**2)\n",
    "    s34= torch.sqrt((x1 - x34)**2 + (y1 - y34)**2)\n",
    " \n",
    "    return s1 + s2 + s3 + s4 + s5 + s6 + s7 + s8 + s9 + s10 + s11 + s12 + s13 + s14 + s15 + s16 + s17 + s18 + s19 + s20 + s21 + s22 + s23 + s24 + s25 + s26 + s27 + s28 + s29 + s30 +s31 + s32 + s33 + s34 \n",
    "\n",
    "\n",
    "\n",
    "optimizer = optim.RMSprop([x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6, x7, y7, x8, y8, x9, y9, x10, y10, x11, y11, x12, y12, x13, y13, x14, y14, x15, y15, x16, y16, x17, y17, x18, y18, x19, y19, x20, y20, x21, y21, x22, y22, x23, y23, x24, y24, x25, y25, x26, y26, x27, y27, x28, y28, x29, y29, x30, y30, x31, y31, x32, y32, x33, y33, x34, y34], lr=.008)\n",
    "#, momentum=0\n",
    "steps = 500000\n",
    "\n",
    "max_perimeter = 100\n",
    "\n",
    "loss_history = []\n",
    "\n",
    "# Optimization loop\n",
    "for step in range(steps):\n",
    "    # Compute area\n",
    "    area = compute_area(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6,  x7, y7, x8, y8, x9, y9, x10, y10, x11, y11, x12, y12, x13, y13, x14, y14, x15, y15, x16, y16, x17, y17, x18, y18, x19, y19, x20, y20, x21, y21, x22, y22, x23, y23, x24, y24, x25, y25, x26, y26, x27, y27, x28, y28, x29, y29, x30, y30, x31, y31, x32, y32, x33, y33, x34, y34)\n",
    "    \n",
    "    # Compute perimeter\n",
    "    perimeter = compute_perimeter(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6,  x7, y7, x8, y8, x9, y9, x10, y10, x11, y11, x12, y12, x13, y13, x14, y14, x15, y15, x16, y16, x17, y17, x18, y18, x19, y19, x20, y20, x21, y21, x22, y22, x23, y23, x24, y24, x25, y25, x26, y26, x27, y27, x28, y28, x29, y29, x30, y30, x31, y31, x32, y32, x33, y33, x34, y34)\n",
    "    \n",
    "    # apply a penalty if peremter of 100 units is exceeded (not really confindent in this step and the next step)\n",
    "    perimeter_penalty = (torch.max(torch.tensor(0.), ((perimeter)**2 - (max_perimeter)**2))) #hmmmm\n",
    "    \n",
    "    # loss function\n",
    "    loss = -area + perimeter_penalty**1\n",
    "    #(torch.log(1/area) + perimeter_penalty**1)\n",
    "    #-area + perimeter_penalty**1\n",
    "    #(torch.log((1/area) + 1*perimeter_penalty**2))\n",
    "    #(torch.log(1/area) + perimeter_penalty**1)  # hmmmm\n",
    "    #loss = -area + perimeter_penalty**1\n",
    "    # 2*perimeter_penalty - area\n",
    "    \n",
    "    \n",
    "    # Zero gradients\n",
    "    optimizer.zero_grad()\n",
    "    \n",
    "    # Compute gradients\n",
    "    loss.backward()\n",
    "    \n",
    "    # Update parameters\n",
    "    optimizer.step()\n",
    "\n",
    "    loss_history.append(loss.item())\n",
    "\n",
    "    if step % 100 == 0:\n",
    "        print(f'Step {step}: loss_history = {loss.item()}') # Prints a value for loss function once every hundred iterations\n",
    "\n",
    "optimized_x1 = x1.item()\n",
    "optimized_y1 = y1.item()\n",
    "optimized_x2 = x2.item()\n",
    "optimized_y2 = y2.item()\n",
    "optimized_x3 = x3.item()\n",
    "optimized_y3 = y3.item()\n",
    "optimized_x4 = x4.item()\n",
    "optimized_y4 = y4.item()\n",
    "optimized_x5 = x5.item()\n",
    "optimized_y5 = y5.item()\n",
    "\n",
    "optimized_x6 = x6.item()\n",
    "optimized_x7 = x7.item()\n",
    "optimized_x8 = x8.item()\n",
    "optimized_x9 = x9.item()\n",
    "optimized_x10 = x10.item()\n",
    "optimized_x11 = x11.item()\n",
    "optimized_x12 = x12.item()\n",
    "optimized_x13 = x13.item()\n",
    "optimized_x14 = x14.item()\n",
    "optimized_x15 = x15.item()\n",
    "optimized_x16 = x16.item()\n",
    "optimized_x17 = x17.item()\n",
    "optimized_x18 = x18.item()\n",
    "optimized_x19 = x19.item()\n",
    "optimized_x20 = x20.item()\n",
    "optimized_x21 = x21.item()\n",
    "optimized_x22 = x22.item()\n",
    "optimized_x23 = x23.item()\n",
    "optimized_x24 = x24.item()\n",
    "optimized_x25 = x25.item()\n",
    "optimized_x26 = x26.item()\n",
    "optimized_x27 = x27.item()\n",
    "optimized_x28 = x28.item()\n",
    "optimized_x29 = x29.item()\n",
    "optimized_x30 = x30.item()\n",
    "optimized_x31 = x31.item()\n",
    "optimized_x32 = x32.item()\n",
    "optimized_x33 = x33.item()\n",
    "optimized_x34 = x34.item()\n",
    "\n",
    "optimized_y6 = y6.item()\n",
    "optimized_y7 = y7.item()\n",
    "optimized_y8 = y8.item()\n",
    "optimized_y9 = y9.item()\n",
    "optimized_y10 = y10.item()\n",
    "optimized_y11 = y11.item()\n",
    "optimized_y12 = y12.item()\n",
    "optimized_y13 = y13.item()\n",
    "optimized_y14 = y14.item()\n",
    "optimized_y15 = y15.item()\n",
    "optimized_y16 = y16.item()\n",
    "optimized_y17 = y17.item()\n",
    "optimized_y18 = y18.item()\n",
    "optimized_y19 = y19.item()\n",
    "optimized_y20 = y20.item()\n",
    "optimized_y21 = y21.item()\n",
    "optimized_y22 = y22.item()\n",
    "optimized_y23 = y23.item()\n",
    "optimized_y24 = y24.item()\n",
    "optimized_y25 = y25.item()\n",
    "optimized_y26 = y26.item()\n",
    "optimized_y27 = y27.item()\n",
    "optimized_y28 = y28.item()\n",
    "optimized_y29 = y29.item()\n",
    "optimized_y30 = y30.item()\n",
    "optimized_y31 = y31.item()\n",
    "optimized_y32 = y32.item()\n",
    "optimized_y33 = y33.item()\n",
    "optimized_y34 = y34.item()\n",
    "\n",
    "# Print the optimized coords, area and perimeter (should be a square)\n",
    "print(\"Optimized Coordinates:\")\n",
    "print(\"Vertex 1: ({}, {})\".format(optimized_x1, optimized_y1))\n",
    "print(\"Vertex 2: ({}, {})\".format(optimized_x2, optimized_y2))\n",
    "print(\"Vertex 3: ({}, {})\".format(optimized_x3, optimized_y3))\n",
    "print(\"Vertex 4: ({}, {})\".format(optimized_x4, optimized_y4))\n",
    "print(\"Vertex 5: ({}, {})\".format(optimized_x5, optimized_y5))\n",
    "print(\"Vertex 6: ({}, {})\".format(optimized_x6, optimized_y6))\n",
    "print(\"Vertex 7: ({}, {})\".format(optimized_x7, optimized_y7))\n",
    "print(\"Vertex 8: ({}, {})\".format(optimized_x8, optimized_y8))\n",
    "print(\"Vertex 9: ({}, {})\".format(optimized_x9, optimized_y9))\n",
    "print(\"Vertex 10: ({}, {})\".format(optimized_x10, optimized_y10))\n",
    "print(\"Vertex 11: ({}, {})\".format(optimized_x11, optimized_y11))\n",
    "print(\"Vertex 12: ({}, {})\".format(optimized_x12, optimized_y12))\n",
    "print(\"Vertex 13: ({}, {})\".format(optimized_x13, optimized_y13))\n",
    "print(\"Vertex 14: ({}, {})\".format(optimized_x14, optimized_y14))\n",
    "print(\"Vertex 15: ({}, {})\".format(optimized_x15, optimized_y15))\n",
    "print(\"Vertex 16: ({}, {})\".format(optimized_x16, optimized_y16))\n",
    "print(\"Vertex 17: ({}, {})\".format(optimized_x17, optimized_y17))\n",
    "print(\"Vertex 18: ({}, {})\".format(optimized_x18, optimized_y18))\n",
    "print(\"Vertex 19: ({}, {})\".format(optimized_x19, optimized_y19))\n",
    "print(\"Vertex 20: ({}, {})\".format(optimized_x20, optimized_y20))\n",
    "print(\"Vertex 21: ({}, {})\".format(optimized_x21, optimized_y21))\n",
    "print(\"Vertex 22: ({}, {})\".format(optimized_x22, optimized_y22))\n",
    "print(\"Vertex 23: ({}, {})\".format(optimized_x23, optimized_y23))\n",
    "print(\"Vertex 24: ({}, {})\".format(optimized_x24, optimized_y24))\n",
    "print(\"Vertex 25: ({}, {})\".format(optimized_x25, optimized_y25))\n",
    "print(\"Vertex 26: ({}, {})\".format(optimized_x26, optimized_y26))\n",
    "print(\"Vertex 27: ({}, {})\".format(optimized_x27, optimized_y27))\n",
    "print(\"Vertex 28: ({}, {})\".format(optimized_x28, optimized_y28))\n",
    "print(\"Vertex 29: ({}, {})\".format(optimized_x29, optimized_y29))\n",
    "print(\"Vertex 30: ({}, {})\".format(optimized_x30, optimized_y30))\n",
    "print(\"Vertex 31: ({}, {})\".format(optimized_x31, optimized_y31))\n",
    "print(\"Vertex 32: ({}, {})\".format(optimized_x32, optimized_y32))\n",
    "print(\"Vertex 33: ({}, {})\".format(optimized_x33, optimized_y33))\n",
    "print(\"Vertex 34: ({}, {})\".format(optimized_x34, optimized_y34))\n",
    "\n",
    "print(\"Optimized Perimeter: {:.4f}\".format(compute_perimeter(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6,  x7, y7, x8, y8, x9, y9, x10, y10, x11, y11, x12, y12, x13, y13, x14, y14, x15, y15, x16, y16, x17, y17, x18, y18, x19, y19, x20, y20, x21, y21, x22, y22, x23, y23, x24, y24, x25, y25, x26, y26, x27, y27, x28, y28, x29, y29, x30, y30, x31, y31, x32, y32, x33, y33, x34, y34).item()))\n",
    "print(\"Optimized Area: {:.4f}\".format(compute_area(x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6,  x7, y7, x8, y8, x9, y9, x10, y10, x11, y11, x12, y12, x13, y13, x14, y14, x15, y15, x16, y16, x17, y17, x18, y18, x19, y19, x20, y20, x21, y21, x22, y22, x23, y23, x24, y24, x25, y25, x26, y26, x27, y27, x28, y28, x29, y29, x30, y30, x31, y31, x32, y32, x33, y33, x34, y34).item()))\n",
    "print(\"Theoretical maximum = (aprox 795)\")\n",
    "\n",
    "\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.plot(x1.item(), y1.item(), 'o',color='black', label='final locations' )\n",
    "plt.plot(x2.item(), y2.item(), 'o' ,color='black')\n",
    "plt.plot(x3.item(), y3.item(), 'o',color='black')\n",
    "plt.plot(x4.item(), y4.item(),'o',color='black')\n",
    "plt.plot(x5.item(), y5.item(),'o',color='black')\n",
    "plt.plot(x6.item(), y6.item(), 'o',color='black')\n",
    "plt.plot(x7.item(), y7.item(), 'o',color='black')\n",
    "plt.plot(x8.item(), y8.item(), 'o',color='black')\n",
    "plt.plot(x9.item(), y9.item(),'o',color='black')\n",
    "plt.plot(x10.item(), y10.item(),'o',color='black')\n",
    "plt.plot(x11.item(), y11.item(), 'o' ,color='black')\n",
    "plt.plot(x12.item(), y12.item(), 'o' ,color='black')\n",
    "plt.plot(x13.item(), y13.item(), 'o',color='black')\n",
    "plt.plot(x14.item(), y14.item(),'o',color='black')\n",
    "plt.plot(x15.item(), y15.item(),'o',color='black')\n",
    "plt.plot(x16.item(), y16.item(), 'o',color='black')\n",
    "plt.plot(x17.item(), y17.item(), 'o',color='black')\n",
    "plt.plot(x18.item(), y18.item(), 'o',color='black')\n",
    "plt.plot(x19.item(), y19.item(),'o',color='black')\n",
    "plt.plot(x20.item(), y20.item(),'o',color='black')\n",
    "plt.plot(x21.item(), y21.item(), 'o' ,color='black')\n",
    "plt.plot(x22.item(), y22.item(), 'o' ,color='black')\n",
    "plt.plot(x23.item(), y23.item(), 'o',color='black')\n",
    "plt.plot(x24.item(), y24.item(),'o',color='black')\n",
    "plt.plot(x25.item(), y25.item(),'o',color='black')\n",
    "plt.plot(x26.item(), y26.item(), 'o',color='black')\n",
    "plt.plot(x27.item(), y27.item(), 'o',color='black')\n",
    "plt.plot(x28.item(), y28.item(), 'o',color='black')\n",
    "plt.plot(x29.item(), y29.item(),'o',color='black')\n",
    "plt.plot(x30.item(), y30.item(),'o',color='black')\n",
    "plt.plot(x31.item(), y31.item(), 'o' ,color='black')\n",
    "plt.plot(x32.item(), y32.item(), 'o' ,color='black')\n",
    "plt.plot(x33.item(), y33.item(), 'o',color='black')\n",
    "plt.plot(x34.item(), y34.item(),'o',color='black')\n",
    "plt.xlim(-30, 30)\n",
    "plt.ylim(-30, 30)\n",
    "plt.title(\"Optimising Area of a 34 Sided Pollygon While Constraining the Perimeter\")\n",
    "plt.xlabel('length units')\n",
    "plt.ylabel('length units')\n",
    "plt.legend()\n",
    "plt.grid(color='gray', linestyle='-', linewidth=0.5)\n",
    "plt.savefig(\"34_inital_and_final_coords_RMSprop_500000its_lr0.0008.pdf\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss_history)\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"loss\")\n",
    "plt.title(\"loss history - 34 Point Optimizer \")\n",
    "plt.savefig(\"loss_history_34_RMSprop_500000its_lr0.0008.pdf\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}