hw1gradientdescent.ipynb

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      "Starting while\n",
      "1   -3    17    -8   19.0\n",
      "-0.7   -2.2    4.554    -3.0   1.92905\n",
      "-1.1554   -1.9    5.258694    -1.4892   -0.971852\n",
      "-1.681269   -1.75108    5.913576    -0.139621   -4.091548\n",
      "-2.272627   -1.737118    4.169875    1.071018   -7.268541\n",
      "-2.689615   -1.84422    0.110269    1.69079   -8.416211\n",
      "-2.700641   -2.013299    0.291395    1.374685   -8.677581\n",
      "-2.729781   -2.150767    0.139377    1.158027   -8.857984\n",
      "-2.743719   -2.26657    0.160553    0.954297   -8.982385\n",
      "-2.759774   -2.362    0.103971    0.795548   -9.06801\n",
      "-2.770171   -2.441555    0.099942    0.657233   -9.12686\n",
      "-2.780165   -2.507278    0.072407    0.545775   -9.167256\n",
      "-2.787406   -2.561855    0.065049    0.451101   -9.194957\n",
      "-2.793911   -2.606965    0.049638    0.373891   -9.213939\n",
      "-2.798875   -2.644354    0.043198    0.30904   -9.226936\n",
      "-2.803194   -2.675258    0.033892    0.255872   -9.235832\n",
      "-2.806584   -2.700846    0.028989    0.211476   -9.241918\n",
      "-2.809482   -2.721993    0.023122    0.174978   -9.246079\n",
      "-2.811795   -2.739491    0.019572    0.144607   -9.248925\n",
      "-2.813752   -2.753952    0.015775    0.1196   -9.25087\n",
      "-2.815329   -2.765912    0.013264    0.098835   -9.252199\n",
      "-2.816656   -2.775795    0.010765    0.081721   -9.253107\n",
      "-2.817732   -2.783967    0.00901    0.06753   -9.253728\n",
      "-2.818633   -2.79072    0.007348    0.055826   -9.254152\n",
      "-2.819368   -2.796303    0.00613    0.04613   -9.254441\n",
      "-2.819981   -2.800916    0.005016    0.03813   -9.254639\n",
      "-2.820483   -2.804729    0.004175    0.031507   -9.254774\n",
      "-2.8209   -2.80788    0.003425    0.026041   -9.254866\n",
      "-2.821243   -2.810484    0.002846    0.021518   -9.254929\n",
      "-2.821527   -2.812636    0.002339    0.017783   -9.254972\n",
      "-2.821761   -2.814414    0.00194    0.014694   -9.255002\n",
      "-2.821955   -2.815883    0.001597    0.012144   -9.255022\n",
      "-2.822115   -2.817098    0.001324    0.010034   -9.255035\n",
      "-2.822247   -2.818101    0.001091    0.008292   -9.255045\n",
      "-2.822356   -2.81893    0.000903    0.006852   -9.255051\n",
      "-2.822447   -2.819616    0.000745    0.005662   -9.255055\n",
      "-2.822521   -2.820182    0.000616    0.004679   -9.255058\n",
      "-2.822583   -2.82065    0.000509    0.003866   -9.25506\n",
      "-2.822634   -2.821036    0.000421    0.003195   -9.255062\n",
      "-2.822676   -2.821356    0.000347    0.00264   -9.255063\n",
      "-2.82271   -2.82162    0.000287    0.002181   -9.255063\n",
      "-2.822739   -2.821838    0.000237    0.001803   -9.255064\n",
      "-2.822763   -2.822018    0.000196    0.001489   -9.255064\n",
      "-2.822782   -2.822167    0.000162    0.001231   -9.255064\n",
      "-2.822799   -2.82229    0.000134    0.001017   -9.255064\n",
      "-2.822812   -2.822392    0.000111    0.00084   -9.255065\n",
      "the minimum value is: -9.255064587534488\n"
     ]
    }
   ],
   "source": [
    "#func= 4*x**3+9*x**2-4*x-20\n",
    "import numpy as npy\n",
    "#from numpy import linalg as la\n",
    "\n",
    "itr = 0\n",
    "exit = False\n",
    "err_thrshld = 0.001 # need to change this value\n",
    "learning_rate = 0.1 # need to change this value\n",
    "max_itrs = 200 #should change\n",
    "x10=1\n",
    "x20=-3\n",
    "print (\"Starting while\")\n",
    "x1=x10\n",
    "x2=x20\n",
    "while not exit:\n",
    " #   itr=itr+1\n",
    "   # print (itr)\n",
    "  #  print(x1,x2)\n",
    "    fx = 1.5*(x1**2)+(x2**2)-2*(x1*x2)+2*(x1**3)+0.5*(x1**4)\n",
    "    dx1 = 3*x1 -2*x2+6*(x1**2)+2*(x1**3)\n",
    "    dx2 = 2*x2 - 2*x1\n",
    "    print (round(x1,6),\" \", round(x2,6),\"  \", round(dx1,6),\"  \", round(dx2,6), \" \",round(fx,6))\n",
    "    dx = npy.array([dx1,dx2])\n",
    "    if( npy.sqrt(dx1**2+dx2**2) < err_thrshld):\n",
    "        exit = True\n",
    "    if(itr>max_itrs):\n",
    "        print(\"max itrs over\")\n",
    "        exit =True\n",
    "    x1=x1-(learning_rate * dx1)\n",
    "    x2=x2-(learning_rate * dx2)\n",
    "\n",
    "print (\"the minimum value is:\",fx)\n",
    "    \n",
    "\n"
   ]
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