Assignment 2 KMR.ipynb

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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
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   "source": [
    "import numpy as np # Since we will define the equation variables and coefficients in array form\n",
    "from numdifftools.nd_algopy import Jacobian # For use of grad operator and finding jacobian of a matrix with ease\n",
    "import math # for using mathematical funcs\n",
    "from matplotlib.pyplot import * #for plotting the links for animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ct = 0\n",
    "# Given data [taken as per Student's wish as Instructed]\n",
    "r1 = 60\n",
    "o2 = math.radians(0) #varries\n",
    "r2 = 40\n",
    "r6 = 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining Func Eqns in Python \n",
    "#r3,r4,r5,o3 = 87.17,130.75,51.96,math.radians(66.58) for theta = 30 degrees\n",
    "eqn = []\n",
    "eq1 = lambda x : 40*np.sin(o2)-x[0]*np.sin(x[3])+60\n",
    "eqn.append(eq1)\n",
    "eq2 = lambda x : 40*np.cos(o2)-x[0]*np.cos(x[3])\n",
    "eqn.append(eq2)\n",
    "eq3 = lambda x : 60-x[1]*np.sin(x[3])+60\n",
    "eqn.append(eq3)\n",
    "eq4 = lambda x : x[2]-x[1]*np.cos(x[3])\n",
    "eqn.append(eq4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Jacobians Defined\n",
    "jacob1 = Jacobian(eq1)\n",
    "jacob2 = Jacobian(eq2)\n",
    "jacob3 = Jacobian(eq3)\n",
    "jacob4 = Jacobian(eq4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plot\n",
    "def ploter(ct):\n",
    "    #Naming file\n",
    "    if ct<10 :\n",
    "        filename = 'QuickReturn00'+str(ct)+'.jpg'\n",
    "    elif ct<100 :\n",
    "        filename = 'QuickReturn0'+str(ct)+'.jpg'\n",
    "    else :\n",
    "        filename = 'QuickReturn'+str(ct)+'.jpg'  \n",
    "    \n",
    "    #Plotting\n",
    "    figure()\n",
    "    xlim(-200, 200)\n",
    "    ylim(0, 125)\n",
    "    plot((s0[0],s3[0]),(s0[1],s3[1]),linewidth='4')\n",
    "    plot((s1[0],s2[0]),(s1[1],s2[1]),linewidth='4')\n",
    "    plot((-200,200),(120,120),linestyle='dashed')\n",
    "    plot((0,0),(0,120),linestyle='dashed')\n",
    "    savefig(filename)\n",
    "    ct=ct+1 \n",
    "    return ct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Newton Raphson Method for Multivariable systems of Non-Linear equation to be implemented\n",
    "\n",
    "def root_finder():\n",
    "    i = 0\n",
    "    er = 100\n",
    "    tol = 0.000001\n",
    "    maxiter = 100\n",
    "    M = 4\n",
    "    N = 4\n",
    "    x0 = np.array([1,1,1,1],dtype=float).reshape(N,1)\n",
    "    while np.any(abs(er)>tol) and i< maxiter:\n",
    "        func_eval = np.array([eq1(x0),eq2(x0),eq3(x0),eq4(x0)]).reshape(M,1)\n",
    "        flat_x0 = x0.flatten()\n",
    "        jac = np.array([jacob1(flat_x0),jacob2(flat_x0),jacob3(flat_x0),jacob4(flat_x0)])\n",
    "        jac = jac.reshape(N,M)\n",
    "        x_new = x0 - np.linalg.inv(jac)@func_eval\n",
    "        er = x_new - x0\n",
    "        x0 = x_new\n",
    "        i+=1\n",
    "    return x_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-5-e7567b2c9fca>:12: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n",
      "  figure()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 87.17797887]\n",
      " [130.76696831]\n",
      " [ 51.96152423]\n",
      " [ 13.72852909]]\n"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Itering through theta to find all solutions\n",
    "for i in range(360):\n",
    "    o2 = np.radians(i)\n",
    "    x_new = root_finder()\n",
    "    #co-ordinates\n",
    "    o3 = x_new[3][0]\n",
    "    r4 = x_new[1][0]\n",
    "    s0 = [0,0]\n",
    "    s1 = [0,r1]\n",
    "    s2 = [s1[0]+r2*math.cos(o2),s1[1]+r2*math.sin(o2)]\n",
    "    s3 = [r4*math.cos(o3),r4*math.sin(o3)]\n",
    "    if i ==30 :\n",
    "        print(x_new)\n",
    "    clf()\n",
    "    ct = ploter(ct)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}