Gradient_Descent_on_higher_order_polynomial_function.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Gradient_Descent_on_higher_order_polynomial_function.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "80y5jIJsR5Va"
      },
      "source": [
        "import numpy as np \n",
        "import sympy as sym\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Uu8KjbXTV4G8"
      },
      "source": [
        "from matplotlib import cycler\n",
        "colors = cycler('color',\n",
        "                ['#EE6666', '#3388BB', '#9988DD',\n",
        "                 '#EECC55', '#88BB44', '#FFBBBB'])\n",
        "plt.rc('axes', facecolor='#E6E6E6', edgecolor='none',\n",
        "       axisbelow=True, grid=True, prop_cycle=colors)\n",
        "plt.rc('grid', color='w', linestyle='solid')\n",
        "plt.rc('xtick', direction='out', color='gray')\n",
        "plt.rc('ytick', direction='out', color='gray')\n",
        "plt.rc('patch', edgecolor='#E6E6E6')\n",
        "plt.rc('lines', linewidth=2)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2fO9Qq_xV4Dj"
      },
      "source": [
        "X = sym.Symbol(\"x\")"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LkMuWnRRV4A_"
      },
      "source": [
        "Y=+0.1*X**8-0.2*X**7+0.3*X**6-X**5+X**4-15*X+9*X**3-X**2-10"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sY5BGxdTV3-H"
      },
      "source": [
        "dY = sym.diff(Y)\n",
        "\n",
        "d2Y = sym.diff(Y)\n",
        "polyRoots = sym.solveset(Y, X)\n",
        "dRoots = sym.solveset(dY, X)\n",
        "\n",
        "d2Roots = sym.solveset(d2Y, X)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mjVbzOEzV37e"
      },
      "source": [
        "dRoots = sym.solveset(sym.diff(Y), X)\n",
        "\n",
        "dRoots = [root for root in dRoots if root.is_real]"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "veBCebhIV347"
      },
      "source": [
        "minima = np.array([root for root in dRoots if sym.diff(sym.diff(Y)).evalf(subs={\"x\": root}) > 0 ])"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5cMwklGTV32P",
        "outputId": "c4470e0f-2433-4c29-fabc-ebc9443b21e4"
      },
      "source": [
        "minima"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.11591693222185, 0.773510942505233], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U6Ln0WxkV3zc"
      },
      "source": [
        "temp = np.array([(root, Y.evalf(subs={\"x\":root})) for root in minima])\n",
        "\n",
        "globalminima = [t[0] for t in temp if t[1] is min(temp[:,1])]"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CC7gdyoeWjIS"
      },
      "source": [
        "plotting the function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6s_gqx6fV3w_"
      },
      "source": [
        "x = np.linspace(-2, 2, 1000)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "lntHtXc6V3uQ",
        "outputId": "89a38c76-883f-4682-bfa8-8707dd2d644c"
      },
      "source": [
        "plt.plot(x, eval(str(Y)))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f86346ea590>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "Iv1gNS_JV3rZ",
        "outputId": "c26c1f25-f117-4ef3-a94c-3b7a566d567c"
      },
      "source": [
        "plt.plot(x, eval(str(sym.diff(Y))))"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f86341e6210>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z27OKxjaV3od"
      },
      "source": [
        "def gradientDescentSym(Y,point=0, mingrad=0.1, learning_rate=0.1, trace=False, max_iterations=1000):\n",
        "\n",
        "  if trace:\n",
        "    tracegrad = []\n",
        "    tracepoint = [point]\n",
        "  grad = mingrad\n",
        "\n",
        "  iteration=0\n",
        "  while np.abs(grad) >= mingrad and iteration < max_iterations :\n",
        "    iteration+=1\n",
        "    grad = sym.diff(Y).evalf(subs={\"x\":point})\n",
        "    point -= learning_rate*grad*point\n",
        "    print(point, grad)\n",
        "    if trace:\n",
        "      tracegrad.append(grad)\n",
        "      tracepoint.append(point)\n",
        "    \n",
        "  if trace:\n",
        "    return tracegrad, tracepoint\n",
        "  return point"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JgYo49yCXGNI"
      },
      "source": [
        "Learning rate = 0.1, mingrad=0.1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SDD5D0U5V3k3",
        "outputId": "d7b7a57d-20d7-4e6b-a760-e7b701d91882"
      },
      "source": [
        "grads, points = gradientDescentSym(Y, point=1, trace=True)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-0.0200000000000000 10.2000000000000\n",
            "-0.0498984656117013 -14.9492328058506\n",
            "-0.123915381868282 -14.8335054693994\n",
            "-0.301689734900029 -14.3464314398607\n",
            "-0.666618503709096 -12.0961612740981\n",
            "-0.949757965847410 -4.24739878300578\n",
            "-0.875384691712773 0.783076076316756\n",
            "-0.879659115954654 -0.0488290951663491\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "HdBMdbuCV3h3",
        "outputId": "719f163e-005a-49c5-baa6-579110a00d09"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(Y)))\n",
        "pointsY= [Y.evalf(subs={\"x\":point}) for point in points]\n",
        "ax.scatter(points, pointsY)\n",
        "\n",
        "for i, txt in enumerate(points):\n",
        "    ax.annotate(i, (points[i], pointsY[i]-10))"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "XRYLjXVyW5fU",
        "outputId": "b2c00bfd-f6aa-4f1a-8fab-f4d9b4b36c63"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(sym.diff(Y))))\n",
        "gradsY= [Y.evalf(subs={\"x\":grad}) for grad in grads]\n",
        "ax.scatter(points[:-1], grads)\n",
        "\n",
        "for i, txt in enumerate(grads):\n",
        "    ax.annotate(i, (points[:-1][i], grads[i]+10))"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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yRx7BfeMNvOHD8YYN839GjMAbPvy4U+9z3ZXUlZdeeokVK1awatUqmpubaWxs5IYbbjhmyGpXwuEwK1eupL6+nmuvvZYNGzZwyimnAHD48GEWLlzITTfdxH/913/l+m3kV2Mjoa1bCW/dSmjr1mNa9+BfYiF58sm406fjxWIai9/HFKr4jwPaHwnaCZzTcSFr7SJgEfhfrTu2uHorEokU5UlE2czleR7u9u0k1q0juWEDXm3t8QsNGUIoGsWJRnEqK3EGD8YZNAhn4EC/SDsOhEKEw2Ga7r4b2o2/7o7juoQ3bDh+RiiEE40SqqrCGT0ar6mJ5EsvQTLpv66+nvLHHqN8yBDKPvjBHreTyf76yU9+wk9+8hMAnnvuOe644w7uu+++lNYRjUa58MILWbNmDeeddx7xeJyrr76az33uc1x66aXcfffdRfV3lur+cg8exN2yhWTw0/FvyBk6lNDJJxM+5RTCp5xCqLIyL7nypdRyFfUBX2PMYmAxQG1trZfuV8Vi/ZqZlVyNjUTWriX06quEDh5sm+yVleGeeCLuhAl4sRhuLAZB33VvcrXU1BzT5w/+sLzO2nbu4MEk5s/Hee89/+fgQZy6Opz33oN9+0ju29f1xuJxji5dyqGWFryRI/1vC+Fwl7my8e/Y0NBAPB7v1brq6uqIRCJUVlZy5MgRnnjiCa6//nr279/PjTfeyOTJk/nKV77CK6+8QjKZLKq/s273l+vi7N9PaMcO/+ftt48bjulFIriTJ+NOmYI7ZYo/Br+1dZ9IgP4/5kUmubq7Umqhiv8uYEK75+ODadJLzp49RP70J0KvveafLAN4Q4aQnDkT9+STcSdMyOhqh+6sWcThmC4ad9o0wn/727EfCGVlJGpq/KsrdhSP4xw4gLN/P05dHZGnn+70wyN09CjlS5b46wuF/C6jkSPxRo7EDX57I0em/V46+vCHP8yHP/zhXi27Z88ebrzxRlzXxXVdLr30Uj7+8Y+zZs0ali1bxqmnnkpVVRWHDh3CdV1mz57N17/+da688sqs5c2Y6/ofyLt2vd8NWFt7XDegV1GBO2EC7qRJuBMn4o0bpytm9mOF+pd9CZhmrT0Rv+gvBIrof0vxcg4eJPLMM4RefRUHvzWePPVUkmed5R9oy+KY6dYDdMdMmzix9332ZWV4VVVtZ22GX36505N9vPJy3AkTCO3fj1Nfj7N/P+zff9xyTSecQFm7D4bWDwdOOKHL953pMYYZM2bw1FNPHTf9nHPOabsefVG1GI8exdm7l9DevTQ3NlL29tuEamtxOhmG6lVW4o4f/36xHz1aY+5LSEGKvzEmYa29AXgSf6jnb4wx6Z8pVAricSLPPUf4z3/GSSbxQiESs2eT/NCH8EaMyFuMzj4Qeisxd+7xXUllZcQvueT9gtzS4ncZ7d/vfxi0/tTV+WeLNjTA9u3HrNcrK8OLRv1vDK0HnCsrcfbuJfLcc22jUlIZnVSoA9O9kkj4H5IHDvg/Bw/6+2vvXpyGhvcXw//PBf63QnfsWNxx4/DGjvW7AXWFzJLmeMHNEYpdbW1t2kGLqmXWTm9zhbZtI/LYY4QOHMDDL1yJOXP8/vEC5kpH2kXVdRkeClH/1lttHwhtHw69PDDdtqqKCpIXXYQ3ZIj/M3SofzwkONbQ8RwH8D9gkmec0XaOA44DnodXWcmABQtomDIlpQzdvU8OHcJpbPR/Ghr8UTaNjX7BP3jQ/93F/1svHMYbNQpv9GgGTJ7M4cGD/UJfRHe56uv/H/Mtwz7/LodgqUOvmCWTRJ55hsiLLwLgjhpF/JOf9G9k0Uel/c0hFCIUjeICtLuoHABNTW0HmNv/tL8m/DGram4m9Nhjx033KirwBg70C25wHKVVx3McCIqvU19Pyz33ED7rLLzJkzu8Wddvpcfj/gHS9o+bm489z+LIEf/50aNdDrNt2zRBl00wnNYbMcL/5jN6tN8gCLpuTohGaSzCYibFQcW/WDU0UL5sGaEdO/Ach+RHP0ri7/5OB+A6M2gQ3qBBx30olt9xR+fHGCoqSJ56Ks6hQ20/HD6M09zcad94qy6LcjJJ2Zo1sGZNBm+iXb7Bg/GGDn3/54QTIPjdei6F/g4kU/oLKkJObS3l996L09iIN3QoLZ/+9PGtSulRl8cYPvGJ47uaXLetNV72m98QSuESEOC3xt3gxK82jgORCF5ZmV+sIxH/IHgkAsG3DAYOxBswwP89cCAMGKCDrpIXKv5FJrRpE2UPPIATj+NOnEjLZz6jA3Np6my4apfHGEKhtgKcuOiiXp/j0Da/spL4woXZfgsiOaPiX0RC69dTtmwZjueRPP104gsW6Ot9htI5xtDbcxza6OqU0gepshSJ0OuvU/bggzieR+K880hceKGulVJAPZ3j0HG0z9FsjfYRyRMV/yIQWr/+/cL/0Y+SmDNHhb8IdfUtYmg0mvalDkQKRcW/wJzt2yl76CG/8J9/vl/4RURyTMMKCsh9913K77sPJ5kk8cEPkrjggkJHEpESoZZ/oRw+zNG77sJpbiZ5yikk5s9XV4+I5I1a/oXgupQ9+CDewYO448YR//SnNbZbRPJKFacAIk8/TXjrVhgyxB/HX1ZW6EgiUmJU/PMstGkTkRdfxHMcBnzhC5Dm3ZBERDKh4p9Phw9Ttnw54F96IDx9eoEDiUipUvHPF8/zLxlw+DDJyZNJ9vJOUiIiuaDinyfhV14hvGEDXkUF8csu0wFeESkoVaB8aGwk8sQTAMTnz4dhwwocSERKXc7G+VtrbwW+BOwLJt1sjPl9MO/bwLVAEviqMebJXOUoBmUrVvjj+adOxT3jjELHERHJ+Uledxhj/nf7CdbaGfg3bD8NGAustNZON8Ykc5ylIEJbthB+7TW8SITEJz6hE7lEpCgUottnAbDEGNNsjNkGbAbOLkCO3IvHiTz+OACJ88/P2T13RURSleuW/w3W2quBtcDXjTEHgXHA6nbL7AymHcdauwhYBFBTU0N1dXVaISKRCNFoNK3XZqJl5UriBw7gjBlD5SWX4HS4Nn+hcvVEuVKjXKlRrtTkKldGxd9auxIY08msW4BfAj/AvwnSD4CfAF9MZf3GmMXAYoDa2lov3TvYR6NR0n1t2g4fpuKJJ3CA5gsv5Egn95ItSK5eUK7UKFdqlCs1meSKxWJdzsuo+BtjLuzNctbaXwP/L3i6C2h/p+3xwbR+JfL88/5B3pNOwp06tdBxRESOkbM+f2tt+4+cy4HXg8ePAguttRXW2hOBacBfcpWjEJy6OsIvvYTnOCQuuqjQcUREjpPLPv8fWWvPxO/22Q78E4AxZr21dinwBpAAru9vI30iTz+N47okPvABvKqqQscRETlOzoq/MeaqbubdBtyWq20XkrN3L6H16/HCYd2cRUSKls7wzbLI88/jAMnqal2xU0SKlop/Fjl79xJ6/XW8UIjERz5S6DgiIl1S8c8itfpFpK9Q8c8Sp65OrX4R6TNU/LMkvGaN3+qfNUtX7RSRoqfinw1HjhBetw6A5Ic+VOAwIiI9U/HPgvDatTjxOMmTTtK4fhHpE1T8M5VIEPmLf4KyWv0i0leo+GcotH49TmMj7qhRuCedVOg4IiK9ouKfochLLwGQPPdc3ahFRPoMFf8MOHv2ENq5E6+iguTppxc6johIr6n4ZyC8di0QDO8sLy9wGhGR3lPxT1dLC+FXXwUgedZZBQ4jIpIaFf80hV9/Hae5GXf8eA3vFJE+R8U/TeGXXwYgoVa/iPRBKv5pcPbuJbRrF15FBe6MGYWOIyKSMhX/NLT19Z92mg70ikiflNGdvKy1/wDcCpwKnG2MWdtu3reBa4Ek8FVjzJPB9HnAz4EwcJcx5vZMMuSd675f/GfNKnAYEZH0ZNryfx34FPB8+4nW2hnAQuA0YB7w79basLU2DPwCmA/MAK4Ilu0zQm+/jdPQgFdZiTdxYqHjiIikJaOWvzHmTQBrbcdZC4AlxphmYJu1djNwdjBvszFma/C6JcGyb2SSI59Cf/sbAMkzzoCQes1EpG/K1Q3cxwGr2z3fGUwDeKfD9HO6Wom1dhGwCKCmpobq6uq0wkQiEaLRaFqvbc9raaHpzTcBGHr++YQyXGe2cmWbcqVGuVKjXKnJVa4ei7+1diUwppNZtxhjlmc9UTvGmMXAYoDa2lqvrq4urfVEo1HSfW17oddeo7y5GXfcOA6Gw5DhOrOVK9uUKzXKlRrlSk0muWKxWJfzeiz+xpgL09jmLmBCu+fjg2l0M73ohdevB9B1fESkz8tVt8+jwL3W2p8CY4FpwF8AB5hmrT0Rv+gvBK7MUYbsam4mtHkzAMlTTy1wGBGRzGR0xNJae7m1difwIeBxa+2TAMaY9cBS/AO5TwDXG2OSxpgEcAPwJPAmsDRYtuiF3noLJ5HAnTABKisLHUdEJCOO53mFztArtbW1aQfNRl9e2dKlhN94g3hNTdbu2NUf+xhzSblSo1yp6Y+5YrFYlzcZ0VjF3mhpIbRpEwBJXc5BRPoBFf9eaOvyGT9eXT4i0i+o+PdC+A3/HDS1+kWkv1Dx70kiQeittwBwNcpHRPoJFf8ehLZvx2lpwa2qwhs+vNBxRESyQsW/B60Het3p0wucREQke1T8u+N574/yUfEXkX5Exb8bzt69hN57D2/wYLxx43p+gYhIH6Hi3422Vv+0abp8s4j0K6po3Qhv3AiAe/LJBU4iIpJdKv5dOXQIZ+dOvHAYd8qUQqcREckqFf8uhLZswQHcyZOhoqLQcUREskrFvwvhLVsAcKdOLXASEZHsU/HvjOcRai3+J51U4DAiItmn4t8JZ88enMOH8YYOxRs1qtBxRESyTsW/E62t/uRJJ4HT5eWwRUT6LBX/TqjLR0T6OxX/juJxQm+/DaAhniLSb2V0A3dr7T8AtwKnAmcbY9YG0yfj36N3Y7DoamPMdcG82cBvgYHA74EbjTFFcy/J0Ntv4ySTuLEYDB5c6DgiIjmRUfEHXgc+Bfyqk3lbjDFndjL9l8CXgDX4xX8e8IcMc2RNW5ePWv0i0o9l1O1jjHnTGLOx5yV91toYcIIxZnXQ2r8buCyTDNkW2rYNUH+/iPRvmbb8u3OitXYd0AB8xxjzAjAO2NlumZ3BtE5ZaxcBiwBqamqorq5OK0gkEiEajfa4nNfURNOePRCJMOyMM3DKy9PaXrZz5ZtypUa5UqNcqclVrh6Lv7V2JTCmk1m3GGOWd/GyWmCiMaYu6ON/xFp7WqrhjDGLgcUAtbW1Xl1dXaqrACAajdKb14Y2bKDc83DHjuVAY2Na28pFrnxTrtQoV2qUKzWZ5IrFYl3O67H4G2MuTHWDxphmoDl4/LK1dgswHdgFjG+36PhgWlEIbd8OBNfzERHpx3Iy1NNaO8paGw4eTwGmAVuNMbVAg7X2XGutA1wNdPXtIe9U/EWkVGRU/K21l1trdwIfAh631j4ZzPoo8Kq19hVgGXCdMeZAMO+fgbuAzcAWimWkz5EjOLt3+5dwHj++5+VFRPqwjA74GmMeBh7uZPqDwINdvGYtMDOT7eZCaMcO/xLO48ZBjg/0iogUms7wDajLR0RKiYp/QMVfREqJij/A0aN+f38opP5+ESkJKv5A6J13cDwPT/39IlIiVPzxiz+AO2FCgZOIiOSHij/gqPiLSIlR8U8mCe30Lzek4i8ipaLki7+zZw9OPI47YgQMGVLoOCIieVHyxb+1v99Tq19ESoiKv/r7RaQEqfir+ItICSrt4l9fj1Nfj1dRgTdqVKHTiIjkTUkX/7ZRPuPHQ6ikd4WIlJiSrnjq8hGRUlXaxX+XfxMxT9fzEZESU7rFP5nEqa0FwB07tsBhRETyq2SLv7N3L04igTt8OAwaVOg4IiJ5ldGdvKy1PwYuBVrwb8n4BWPMe8G8bwPXAkngq8aYJ4Pp84CfA2HgLmPM7ZlkSFfo3XcB/Ct5ioiUmExb/k8BM40xs4BNwLcBrLUzgIXAacA84N+tteHgpu6/AOYDM4ArgmXzzgn6+10VfxEpQZnew3dFu6ergb8PHi8AlhhjmoFt1trNwNnBvM3GmK0A1tolwbJvZJIjHa0He9XfLyKlKKPi38EXgfuDx+PwPwxa7QymAbzTYTuZULYAAAn7SURBVPo5Xa3QWrsIWARQU1NDdXV1WsEikQjRaLTtudfSQtO+fRAKMfy003AqKtJab6Y65ioWypUa5UqNcqUmV7l6LP7W2pXAmE5m3WKMWR4scwuQAO7JZjhjzGJgMUBtba1XV1eX1nqi0SjtX+vs2EGF6+JWVXHg0CE4dCgreTPNVSyUKzXKlRrlSk0muWKxWJfzeiz+xpgLu5tvrb0GuASYa4zxgsm7gPZnTo0PptHN9LxRl4+IlLpMR/vMA74FnG+MaWo361HgXmvtT4GxwDTgL4ADTLPWnohf9BcCV2aSIR0a6SMipS7T0T53AkOBp6y1r1hr/wPAGLMeWIp/IPcJ4HpjTNIYkwBuAJ4E3gSWBsvmlUb6iEipy3S0z9Ru5t0G3NbJ9N8Dv89kuxk5coTQgQN44TDe6NEFiyEiUkgld4ZvaPduALyqKgiHC5xGRKQwSq74O0Hxd7s5Ci4i0t+VXPEPBRdz88Z0NnpVRKQ0lFzxV8tfRKTUin88jrNvH57j6GCviJS0kir+zt69OJ6HF41CeXmh44iIFExJFf+2/n51+YhIiSup4t/W36+DvSJS4kqq+KvlLyLiK53i77o4e/b4D9XyF5ESVzLF36mrw0kk8Cordc9eESl5pVP8gy4ftfpFREqo+IeCLh+d2SsiUkLFv62/v6qqwElERAqvZIp/aO9eAJ3ZKyJCiRR/r6kJp6EBLxLBGzGi0HFERAquJIq/2zq+f9QoCJXEWxYR6Vam9/D9MXAp0AJsAb5gjHnPWjsZ/zaNG4NFVxtjrgteMxv4LTAQ/45eN7a78XtOtBV/dfmIiAAZFn/gKeDbxpiEtfbfgG8D/xLM22KMObOT1/wS+BKwBr/4zwP+kGGObrnBDdt1sFdExJfpPXxXtHu6Gvj77pa31saAE4wxq4PndwOXkafir5a/iIgv05Z/e18E7m/3/ERr7TqgAfiOMeYFYByws90yO4NpnbLWLgIWAdTU1FBdXZ1yKM/zOBJ0+1SecgqhysqU15ErkUiEaDRa6BjHUa7UKFdqlCs1ucrVY/G31q4EOjsz6hZjzPJgmVuABHBPMK8WmGiMqQv6+B+x1p6WajhjzGJgMUBtba1XV1eX6iqgoYEBTU14AwdyMB6HdNaRI9FolLTeU44pV2qUKzXKlZpMcsW6uYhlj8XfGHNhd/OttdcAlwBzWw/cGmOagebg8cvW2i3AdGAXML7dy8cH03Km7cze0aPBcXK5KRGRPiOjcY/W2nnAt4BPGmOa2k0fZa0NB4+nANOArcaYWqDBWnuutdYBrgaWZ5KhJ05wcper/n4RkTaZ9vnfCVQAT1lr4f0hnR8Fvm+tjQMucJ0x5kDwmn/m/aGefyDHB3vbzuzVSB8RkTaZjvaZ2sX0B4EHu5i3FpiZyXZT0XZNH7X8RUTa9O/TXV0XZ98+QMM8RUTa69fF3zlwACeZxBk+HAYMKHQcEZGi0a+LP4cP41VWEho7ttBJRESKSjZP8io63qRJNN90E4OHDePwe+8VOo6ISNHo3y3/gBMOFzqCiEhRKYniLyIix1LxFxEpQSr+IiIlSMVfRKQEqfiLiJQgFX8RkRKk4i8iUoo8z+v3P7feeuuiQmdQLuVSLuUqplyl0vJfVOgAXVCu1ChXapQrNSWVq1SKv4iItKPiLyJSgkql+C8udIAuKFdqlCs1ypWaksrleJ6Xi/WKiEgRK5WWv4iItKPiLyJSgvrlzVystT8GLgVagC3AF4wxx93NxVo7D/g5EAbuMsbcnuNc/wDcCpwKnB3czL6z5bYDjUASSBhjziqSXPneXyOA+4HJwHbgM8aYg50slwReC57uMMZ8Mkd5un3/1toK4G5gNlAHfNYYsz0XWVLMdQ3wY2BXMOlOY8xdOc70G+ASYK8xZmYn850g88VAE3CNMeavuczUy1wXAMuBbcGkh4wx389Drgn4fztVgAcsNsb8vMMyWd1n/bXl/xQw0xgzC9gEfLvjAtbaMPALYD4wA7jCWjsjx7leBz4FPN+LZecYY87MdeEP9JirQPvrX4FVxphpwKrgeWeOBPvqzBwW/t68/2uBg8aYqcAdwL/lIksauQDub7ePclr4A78F5nUzfz4wLfhZBPwyD5mg51wAL7TbVzkv/IEE8HVjzAzgXOD6Tv4ds7rP+mXxN8asMMYkgqergfGdLHY2sNkYs9UY0wIsARbkONebxpiNudxGOnqZK+/7K1j/74LHvwMuy/H2utOb998+7zJgbtBaK3SuvDPGPA8c6GaRBcDdxhjPGLMaGGatjRVBroIwxtS2tuKNMY3Am8C4DotldZ/1y26fDr6I33XQ0TjgnXbPdwLn5CVRzzxghbXWA35ljCmGIWiF2F9Vxpja4PFu/K/EnRlgrV2L33q63RjzSA6y9Ob9ty1jjElYa+uBKLA/B3lSyQXwaWvtR/G/Cd9kjHmnk2XyqbPc44DazhfPqw9Za/8GvAt8wxizPp8bt9ZOBj4ArOkwK6v7rM8Wf2vtSmBMJ7NuMcYsD5a5Bb8g3FNMuXrhI8aYXdba0cBT1toNQYul0Lmyrrtc7Z8YY7zgw7Azk4L9NQV42lr7mjFmS7az9mGPAfcZY5qttf+E/+3kYwXOVKz+iv/3dMhaezHwCH43S15Ya4cADwL/0xjTkMtt9dnib4y5sLv5wUGuS4C5xpjOisYuYEK75+N5/4BYznL1ch27gt97rbUP43+1z6j4ZyFX3veXtXaPtTZmjKkNvt7u7WIdrftrq7X2WfxWU7aLf2/ef+syO621EaAS/8BvLvWYyxjTPsNdwI9ynKk3cvL3lKn2BdcY83tr7b9ba0caY3L57Q0Aa20ZfuG/xxjzUCeLZHWf9dni351g9MO3gPONMU1dLPYSMM1aeyL+DlwIXJmniF2y1g4GQsaYxuDxRUC+Djp1pxD761HgH4Hbg9/HfUOx1g4HmoJW7UjgPHJT3Hrz/lvz/hn4e+DpLhoeec3V+gEaPP0kfn9yoT0K3GCtXYLfTVXfLmPBWGvHAHuCb5pn4x8XzfUHeOtInv8E3jTG/LSLxbK6z/rlGb7W2s1ABe//o602xlxnrR2LPxTu4mC5i4Gf4Q+R+40x5rYc57oc+D/AKOA94BVjTE37XEHXxcPBSyLAvcWQK1gu3/srCiwFJgJv4w/1PGCtPQu4zhjzP6y1HwZ+Bbj4/1F/Zoz5zxzlOe79W2u/D6w1xjxqrR0A/F/8bx4HgIXGmK25yJJirv+FX/QTQa4vG2M25DjTfcAFwEhgD2CAMgBjzH8Exe5O/JE3TfjDsTsdYpznXDcAX8bfV0eArxlj/pSHXB8BXsAfsuwGk2/G/9vPyT7rl8VfRES61y+HeoqISPdU/EVESpCKv4hICVLxFxEpQSr+IiIlSMVfRKQEqfiLiJSg/w/qY8d959q2mgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qHsGOgaOW5lJ",
        "outputId": "8884d03c-ec74-44ec-8deb-bcb5703cf8d2"
      },
      "source": [
        "print(f\"Minima point: {points[-1]} after {len(grads)} iterations. Precision (Global): {np.abs(points[-1] - globalminima[0])}. Precision (Local): {min([np.abs(points[-1] - root) for root in minima])}\")"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Minima point: -0.879659115954654 after 8 iterations. Precision (Global): 1.65317005845989. Precision (Local): 0.236257816267192\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M4AZCIbgW5q-",
        "outputId": "808888eb-37b7-4554-f80d-87fd2d5eac4d"
      },
      "source": [
        "grads, points = gradientDescentSym(Y, point=1, learning_rate=0.001, trace=True)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.989800000000000 10.2000000000000\n",
            "0.980208511259567 9.69033010753010\n",
            "0.971175513186634 9.21538424648548\n",
            "0.962656445435422 8.77191366085731\n",
            "0.954611462365171 8.35706560569731\n",
            "0.947004809056514 7.96832387682691\n",
            "0.939804295954462 7.60345991191547\n",
            "0.932980854099880 7.26049230031627\n",
            "0.926508156643536 6.93765303746603\n",
            "0.920362295210222 6.63335923083361\n",
            "0.914521501911932 6.34618924383023\n",
            "0.908965909555957 6.07486247656339\n",
            "0.903677343971582 5.81822214538180\n",
            "0.898639143473449 5.57522054939480\n",
            "0.893836001354623 5.34490641066537\n",
            "0.889253828006263 5.12641395224087\n",
            "0.884879629830377 4.91895343952993\n",
            "0.880701402575500 4.72180295943462\n",
            "0.876708037104156 4.53430125087291\n",
            "0.872889235912391 4.35584143197658\n",
            "0.869235438978890 4.18586549492927\n",
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            "0.782401094178979 0.367162648347552\n",
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            "0.781853490161123 0.344419255545708\n",
            "0.781592669627807 0.333592593238559\n",
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            "0.780629507063836 0.293644583738338\n",
            "0.780407462897009 0.284442446534709\n",
            "0.780192434358769 0.275533677551619\n",
            "0.779984194275578 0.266908616413356\n",
            "0.779782523169238 0.258557939788978\n",
            "0.779587208975424 0.250472648476710\n",
            "0.779398046773771 0.242644055052433\n",
            "0.779214838528965 0.235063772053654\n",
            "0.779037392842317 0.227723700671970\n",
            "0.778865524713332 0.220616019928669\n",
            "0.778699055310817 0.213733176309510\n",
            "0.778537811753076 0.207067873836135\n",
            "0.778381626896790 0.200613064552828\n",
            "0.778230339134186 0.194361939408537\n",
            "0.778083792198120 0.188307919515205\n",
            "0.777941834974721 0.182444647764499\n",
            "0.777804321323268 0.176765980785991\n",
            "0.777671109902971 0.171265981230808\n",
            "0.777542064006371 0.165938910365622\n",
            "0.777417051399054 0.160779220962623\n",
            "0.777295944165424 0.155781550471962\n",
            "0.777178618560262 0.150940714463764\n",
            "0.777064954865839 0.146251700327608\n",
            "0.776954837254341 0.141709661217884\n",
            "0.776848153655381 0.137309910234117\n",
            "0.776744795628401 0.133047914825884\n",
            "0.776644658239740 0.128919291412453\n",
            "0.776547639944201 0.124919800207807\n",
            "0.776453642470909 0.121045340242200\n",
            "0.776362570713314 0.117291944571737\n",
            "0.776274332623140 0.113655775668024\n",
            "0.776188839108151 0.110133120980235\n",
            "0.776106003933566 0.106720388662306\n",
            "0.776025743626981 0.103414103458423\n",
            "0.775947977386663 0.100210902740154\n",
            "0.775872626993083 0.0971075326890089\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "K47ym1JaW5xi",
        "outputId": "8b3bfa4e-ed42-4ba5-9d90-1bbe509f969a"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(Y)))\n",
        "pointsY= [Y.evalf(subs={\"x\":point}) for point in points]\n",
        "ax.scatter(points, pointsY)\n",
        "\n",
        "for i, txt in enumerate(points):\n",
        "    ax.annotate(i, (points[i], pointsY[i]+10))"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "GNC10McMW52_",
        "outputId": "75a68324-6089-40c0-9d4f-be06c4c3585c"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(sym.diff(Y))))\n",
        "gradsY= [Y.evalf(subs={\"x\":grad}) for grad in grads]\n",
        "ax.scatter(points[:-1], grads)\n",
        "\n",
        "for i, txt in enumerate(grads):\n",
        "    ax.annotate(i, (points[:-1][i], grads[i]+10))"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4JtitKV2W58r",
        "outputId": "1a23f62b-f188-4f0b-9f21-c867459804c7"
      },
      "source": [
        "print(f\"Minima point: {points[-1]} after {len(grads)} iterations. Precision (Global): {np.abs(points[-1] - globalminima[0])}. Precision (Local): {min([np.abs(points[-1] - root) for root in minima])}\")"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Minima point: 0.775872626993083 after 134 iterations. Precision (Global): 0.00236168448785057. Precision (Local): 0.00236168448785057\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "67KFfy4DYPjq"
      },
      "source": [
        "learning rate=1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Zf82N8BHW6CM",
        "outputId": "b761bf1d-990b-4c69-91aa-3000df8bb68b"
      },
      "source": [
        "grads, points = gradientDescentSym(Y, point=1, learning_rate=1, trace=True, max_iterations=500)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-9.20000000000000 10.2000000000000\n",
            "-50295951.0947348 -5466950.20594944\n",
            "-3.27607776797630e+61 -6.51360138673121e+53\n",
            "-1.06150882089888e+492 -3.24018199834920e+430\n",
            "-1.28967073866245e+3936 -1.21494114158219e+3444\n",
            "-6.12238670062153e+31488 -4.74724789597940e+27552\n",
            "-1.57926875215900e+251910 -2.57949853445009e+220421\n",
            "-3.09555358436117e+2015281 -1.96011830166923e+1763371\n",
            "-6.74522740414946e+16122251 -2.17900521516621e+14106970\n",
            "-3.42817318191466e+128978014 -5.08236857930950e+112855762\n",
            "-1.52613169645628e+1031824116 -4.45173454044678e+902846101\n",
            "-2.35410638881403e+8254592929 -1.54253161393629e+7222768813\n",
            "-7.54568505884009e+66036743434 -3.20532882230590e+57782150505\n",
            "-8.40774215694117e+528293947478 -1.11424504089144e+462257204044\n",
            "-1.99767605289684e+4226351579831 -2.37599585668504e+3698057632352\n",
            "-2.02903947052794e+33810812638650 -1.01569995174424e+29584461058819\n",
            "-2.29833827681854e+270486501109202 -1.13272231033560e+236675688470552\n",
            "-6.22875984070462e+2163892008873618 -2.71011447859048e+1893405507764416\n",
            "-1.81260292926469e+17311136070988950 -2.91005428949023e+15147244062115331\n",
            "-9.32204954930343e+138489088567911601 -5.14290769301859e+121177952496922651\n",
            "-4.56227272370227e+1107912708543292815 -4.89406615956378e+969423619975381213\n",
            "-1.50155045838389e+8863301668346342525 -3.29123344727489e+7755388959803049709\n",
            "-2.06732822543983e+70906413346770740201 -1.37679570732834e+62043111678424397676\n",
            "-2.66910377865545e+567251306774165921610 -1.29108853921229e+496344893427395181409\n",
            "-2.06069476565366e+4538010454193327372883 -7.72054942986042e+3970759147419161451272\n",
            "-2.60135324706385e+36304083633546618983066 -1.26236708629611e+31766073179353291610183\n",
            "-1.67758537678815e+290432669068372951864531 -6.44889493067363e+254128585434826332881464\n",
            "-5.01842041725089e+2323461352546983614916249 -2.99145455527217e+2033028683478610663051718\n",
            "-3.21829846824092e+18587690820375868919329997 -6.41297101609497e+16264229467828885304413747\n",
            "-9.20662672284018e+148701526563006951354639979 -2.86071252051163e+130113835742631082435309982\n",
            "-4.12946956271088e+1189612212504055610837119839 -4.48532311239069e+1040910685941048659482479859\n",
            "-6.76463147618173e+9516897700032444886696958716 -1.63813569114696e+8327285487528389275859838877\n",
            "-3.50786703809018e+76135181600259559093575669734 -5.18559961535434e+66618283900227114206878711017\n",
            "-1.83415052869282e+609081452802076472748605357876 -5.22867745207185e+532946271201816913655029688141\n",
            "-1.02463642273184e+4872651622416611781988842863010 -5.58643582793658e+4263570169614535309240237505133\n",
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            "-8.94286587101143e+65830831285077038953048400049429735556599063789707747320760694775542359383420287930435402250787320082766033015968526118860930163025519208841943778303510354913458098545674329447426058014496303902593274007223544855780476098703833508137279338587469709779687593901888459780477490415019717077362781329221558889281072275197349274005852208371562449326921655298545452369312344777101047010242780724210776506987368788315018535616798488297090967416429658931346 -3.71901881746609e+57601977374442409083917350043251018612024180815994278905665607928599564460492751939130976969438905072420278888972460354003313892647329307736700806015571560549275836227465038266497800762684265914769114756320601748807916586365854319620119421264035996057226644664152402307917804113142252442692433663068864028120938240797680614755120682325117143161056448386227270823148301679963416133962433133684429443613947689775641218664698677259954596489375951564928\n",
            "-3.27268136455779e+526646650280616311624387200395437884452792510317661978566085558204338875067362303443483218006298560662128264127748208950887441304204153670735550226428082839307664788365394635579408464115970431220746192057788358846243808789630668065098234708699757678237500751215107678243819923320157736618902250633772471114248578201578794192046817666972499594615373242388363618954498758216808376081942245793686212055898950306520148284934387906376727739331437271450775 -3.65954428005712e+460815818995539272671338800346008148896193446527954231245324863428796515683942015513047815755511240579362231111779682832026511141178634461893606448124572484394206689819720306131982406101474127318152918050564813990463332690926834556960955370112287968457813157313219218463342432905138019541539469304550912224967505926381444918040965458600937145288451587089818166585186413439707329071699465069475435548911581518205129749317589418079636771915007612519428\n",
            "-1.05273672822725e+4213173202244930492995097603163503075622340082541295828528684465634711000538898427547865744050388485297026113021985671607099530433633229365884401811424662714461318306923157084635267712927763449765969536462306870769950470317045344520785877669598061425900006009720861425950559386561261892951218005070179768913988625612630353536374541335779996756922985939106908951635990065734467008655537966349489696447191602452161186279475103251013821914651498171606204 -3.21674068128994e+3686526551964314181370710402768065191169547572223633849962598907430372125471536124104382526044089924634897848894237462656212089129429075695148851584996579875153653518557762449055859248811793018545223344404518511923706661527414676455687642960898303747662505258505753747706739463241104156332315754436407297799740047411051559344327723668807497162307612696718545332681491307517658632573595720555803484391292652145641037994540715344637094175320060900155428\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "id": "6PvK5uuFYFcr",
        "outputId": "cd3f5264-e5a3-4e91-c0ba-2a0194b15b07"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(Y)))\n",
        "pointsY= [Y.evalf(subs={\"x\":point}) for point in points]\n",
        "ax.scatter(points, pointsY)\n",
        "\n",
        "for i, txt in enumerate(points):\n",
        "    ax.annotate(i, (points[i], pointsY[i]+10))"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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F9tPD6bSAb2ZmC/h0dQ/LUsyUu6sbJxes5HM+k1LP+TERMVZ9/SBwzAzbPSczbwMmgCsi4vo5SfdM3ZzDvdtUN1/ZBTSB/53NAZ81RZ2Z/wa8YJqHLomITRFxCXBJZl4MvIP2NEcROmWvtrmE9g/n52fYze9ExI7MPBq4MTPvjohunrrPWp9yz4tusnehyHNeqv1ln7oQEa3qP7/pnFCd898AbsrMH0fET/udtTTPmqKOiNVdbvp52ner2beod/CLp17Qvonv1p6DdaFT9sx8M7AWWDXTU6eI2FH9vjMzv0L76dlAS6MPueftxskH8POyv30Ud867UOQ5z8yHMnM4IsYyc5j2i/7T7WPynN+XmVuBl9B+sXoudXMOJ7fZnpkN4HDaLyrOyrOmqPcnM5dGxL3V4vnA3dNsthn4yykvIJ7L/l+4mxPVq8vvA86OiMdn2Oa5wKKI2F19fS6wYQ5jTpepY25qfOPkEs95l0o95/8KvAm4ovr9l54dVP82H4+In2fmkcBZwF/Pacq2bs7h5J/nu7Rfn7lptvPTsHCu+rgiM+/MzDto/4N6F0BmvjQzrwKoXkT8EO2/hB8AGyZfWJxnnwAOo/3U+oeZ+fcAmflrmTl5H8tjgG9n5o+A7wNfi4hvzE/cvTrmjogJ2tNQm4G7gC+WcOPkzPz9zNwO/DbwtczcXK0v+px3k7vUc067oF+VmfcCq6vlZ/wbpX3Z4W3VOb+Z9hz1nL8IOtM5zMwNmTl5JcpngGZm/gR4DzNfxdIV30IuSYVbKCNqSaoti1qSCmdRS1LhLGpJKtyCuDxPknqVmVfTfl/Azog4rYvtX0f7beQt4EcR8YZq/TeAM4FvR8Tabo7tiFqSuvNZ2p//01FmLqX9PoyzIuJFwLunPPwR4I0HcmBH1JLUhYi4JTNPnLouM0+i/Ul6RwGPAxdGxN3AhcCVkx/VGhE7p+xnS2aecyDHdkQtSbO3EXhnRKwA3gt8slq/DFiWmd/JzO9V79SdNYtakmYhMw8FVgJfyswfAp8GhquHG8BS2p8f9HrgHzLzebM9llMfkjQ7i4BHqxuS7Gs7cGtEPAlsy8x7aBf3D2Z7IEnSAapuSLKtugUamTmUmS+uHr6e6tM4qw+QWgbcN9tj+VkfktSFzLyWdvkeCTxE+6OSbwI+RXvKYwlwXURsyMwh4KO0rxJ5Crg8Iq6r9vMt4BTgUNofffrWiNi8v2Nb1JJUOKc+JKlwFrUkFc6ilqTCWdSSVDiLWpIKZ1FLUuEsakkq3P8DgnSqRr8+UXYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "id": "QsH9nbHXYFZg",
        "outputId": "a709a875-c4f0-4a1f-98e3-53016d298f70"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(sym.diff(Y))))\n",
        "gradsY= [Y.evalf(subs={\"x\":grad}) for grad in grads]\n",
        "ax.scatter(points[:-1], grads)\n",
        "\n",
        "for i, txt in enumerate(grads):\n",
        "    ax.annotate(i, (points[:-1][i], grads[i]+10))"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TsgjfgPmYFWt",
        "outputId": "a5e0122e-126d-4c4d-c3bb-ea6c0c16e27d"
      },
      "source": [
        "print(f\"Minima point: {repr(points[-1])} after {len(grads)} iterations. Precision (Global): {repr(np.abs(points[-1] - globalminima[0]))}. Precision (Local): {repr(min([np.abs(points[-1] - root) for root in minima]))}\")\n"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Minima point: -1.05273672822725e+4213173202244930492995097603163503075622340082541295828528684465634711000538898427547865744050388485297026113021985671607099530433633229365884401811424662714461318306923157084635267712927763449765969536462306870769950470317045344520785877669598061425900006009720861425950559386561261892951218005070179768913988625612630353536374541335779996756922985939106908951635990065734467008655537966349489696447191602452161186279475103251013821914651498171606204 after 500 iterations. Precision (Global): 1.05273672822725e+4213173202244930492995097603163503075622340082541295828528684465634711000538898427547865744050388485297026113021985671607099530433633229365884401811424662714461318306923157084635267712927763449765969536462306870769950470317045344520785877669598061425900006009720861425950559386561261892951218005070179768913988625612630353536374541335779996756922985939106908951635990065734467008655537966349489696447191602452161186279475103251013821914651498171606204. Precision (Local): 1.05273672822725e+4213173202244930492995097603163503075622340082541295828528684465634711000538898427547865744050388485297026113021985671607099530433633229365884401811424662714461318306923157084635267712927763449765969536462306870769950470317045344520785877669598061425900006009720861425950559386561261892951218005070179768913988625612630353536374541335779996756922985939106908951635990065734467008655537966349489696447191602452161186279475103251013821914651498171606204\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hokSfLLGYFUG",
        "outputId": "61ae3fb8-57fc-4a96-d28e-85e93cdd0ad0"
      },
      "source": [
        "grads, points = gradientDescentSym(Y, point=1,learning_rate=0.05,mingrad=1, trace=True)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.490000000000000 10.2000000000000\n",
            "0.717312237805626 -9.27805052267861\n",
            "0.794790702323636 -2.16024376650897\n",
            "0.760716680455545 0.857433831786729\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "jm9txPXQW6Hr",
        "outputId": "814d4593-de39-4991-d3be-7491405abaf4"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(Y)))\n",
        "pointsY= [Y.evalf(subs={\"x\":point}) for point in points]\n",
        "ax.scatter(points, pointsY)\n",
        "\n",
        "for i, txt in enumerate(points):\n",
        "    ax.annotate(i, (points[i], pointsY[i]+10))"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "EGgxplzeYEyS",
        "outputId": "0ccc4065-d21c-4b16-cfa3-1f9913d7e63e"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(x, eval(str(sym.diff(Y))))\n",
        "gradsY= [Y.evalf(subs={\"x\":grad}) for grad in grads]\n",
        "ax.scatter(points[:-1], grads)\n",
        "\n",
        "for i, txt in enumerate(grads):\n",
        "    ax.annotate(i, (points[:-1][i], grads[i]+10))\n"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "dark"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NSpX1RFuZA5j",
        "outputId": "d6b8e1cd-04b1-469c-e9fe-a8834a4b1ae8"
      },
      "source": [
        "print(f\"Minima point: {points[-1]} after {len(grads)} iterations. Precision (Global): {np.abs(points[-1] - globalminima[0])}. Precision (Local): {min([np.abs(points[-1] - root) for root in minima])}\")"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Minima point: 0.760716680455545 after 4 iterations. Precision (Global): 0.0127942620496879. Precision (Local): 0.0127942620496879\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}