SkillboxMSEsubsgradient.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "SkillboxMSEsubsgradient.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyO1D78FvfFddHA4SiTiSv48",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mcrewcow/ChaginLab/blob/main/SkillboxMSEsubsgradient.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Khj9Zb0RhEDr"
      },
      "source": [
        "import numpy as np"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aJ7EdAzGhLJi",
        "outputId": "13d66081-5d2a-4995-d589-fcfb82f3b44c"
      },
      "source": [
        "a = np.array([2,5,0,6,8,10,6,7,5,7])\n",
        "a\n",
        "print(*a)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2 5 0 6 8 10 6 7 5 7\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fIV0hAOShahN"
      },
      "source": [
        "b = np.array([8,6,7,9,6,6,2,3,2,3])\n",
        "c = 3 * a * 2 * b"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vN4E4U0Mhu5B",
        "outputId": "bf05cb7b-d170-4e95-b9a3-7662fbbb2d88"
      },
      "source": [
        "print(*c)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "96 180 0 324 288 360 72 126 60 126\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UM1e1CqDhvyX",
        "outputId": "809ac37e-d9b2-4006-9a92-fb9fc9e718b9"
      },
      "source": [
        "a = np.array([9,6,7,7,0,1,6,8,1,2])\n",
        "b = np.array([0,2,2,6,7,8,8,3,1,8])\n",
        "c = 6 * a * 5 * b\n",
        "print(*c)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0 360 420 1260 0 240 1440 720 30 480\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rsoyt_50iDif",
        "outputId": "3cf5a459-df62-4064-9b2f-98c08b24aeac"
      },
      "source": [
        "a = np.array([2,5,0,6,8,10,6,7,5,7])\n",
        "b = np.array([8,6,7,9,6,6,2,3,2,3])\n",
        "print(*(a * b))"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "16 30 0 54 48 60 12 21 10 21\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5-ToOK3iiTfE",
        "outputId": "f73e1bfe-4275-4d81-a4f2-d28ed1282186"
      },
      "source": [
        "print(*(np.array([9,6,7,7,0,1,6,8,1,2]) * np.array([0,2,2,6,7,8,8,3,1,8])))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0 12 14 42 0 8 48 24 1 16\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gN1T30IBijL1",
        "outputId": "e85dff72-67c6-421b-8353-0c1a81b83377"
      },
      "source": [
        "m1 = np.array([[2,1,7,4],[5,6,7,3],[9,8,2,12],[11,14,15,15]])\n",
        "m1"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2,  1,  7,  4],\n",
              "       [ 5,  6,  7,  3],\n",
              "       [ 9,  8,  2, 12],\n",
              "       [11, 14, 15, 15]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nqOWCO3Ai5sU",
        "outputId": "abfe3c71-a69d-4ee5-d17b-d649fcb35154"
      },
      "source": [
        "print(*(m1.transpose()),sep = '\\n')"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 2  5  9 11]\n",
            "[ 1  6  8 14]\n",
            "[ 7  7  2 15]\n",
            "[ 4  3 12 15]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xkMoF1jwjDEY",
        "outputId": "738fd229-a70b-4f79-ac42-a441a7a5df06"
      },
      "source": [
        "m2 = np.array([[3,7,8,3,6],[2,5,9,4,13]])\n",
        "print(*(m2.transpose()),sep = '\\n')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3 2]\n",
            "[7 5]\n",
            "[8 9]\n",
            "[3 4]\n",
            "[ 6 13]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ugDVNi8rjV3u"
      },
      "source": [
        "from sympy import *\n",
        "from sympy.plotting import plot\n",
        "init_printing(use_unicode=False, wrap_line=False, no_global=True)\n",
        "a1,a2 = symbols('a1,a2')\n",
        "MSE = 1/4*((1*a1 + 2*a2 - 5)**2 + (5*a1 + 3*a2 - 6)**2 + (2*a1 + 4*a2 - 10)**2 + (3*a1 + 7*a2 - 8)**2)"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "U8wJgxrljppg",
        "outputId": "1c96cdc5-4c12-45a5-8b65-fa1ad43a364d"
      },
      "source": [
        "MSE"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 0.25 \\left(a_{1} + 2 a_{2} - 5\\right)^{2} + 0.25 \\left(2 a_{1} + 4 a_{2} - 10\\right)^{2} + 0.25 \\left(3 a_{1} + 7 a_{2} - 8\\right)^{2} + 0.25 \\left(5 a_{1} + 3 a_{2} - 6\\right)^{2}$",
            "text/plain": [
              "                    2                          2                         2                         2\n",
              "0.25*(a1 + 2*a2 - 5)  + 0.25*(2*a1 + 4*a2 - 10)  + 0.25*(3*a1 + 7*a2 - 8)  + 0.25*(5*a1 + 3*a2 - 6) "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "At2mD6E4jyWN"
      },
      "source": [
        "MSE.subs({a1:0.395, a2:0.62})\n",
        "MSEar = np.array([0.395,0.62])"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "UykOtxRGkAdt",
        "outputId": "4b568a72-a9ea-4856-a26c-3130b140d910"
      },
      "source": [
        "msef2 = diff(MSE,a2)\n",
        "msef2"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAAWCAYAAAAy0SvmAAAABHNCSVQICAgIfAhkiAAABnRJREFUeJztmnmMFEUUxn8iHlEQEFYWw4oLBsEQQaN4BGSRSKIGRTQRjcoikpCIighBjUQkUfEIgojxiIpEEqJ4IFFABVEBRZBdhCBZFWcBuS8FReRY//iqs21P9Ux177Czy/aXTHqm6tWrV9/Uq+O9hgQJEtQ5tATuAT4EfgEOAH8Ai4EhQCNLm2eABcBGI78bKAMeN/qioi3wJrAZOAikgElAixi66jLi8HYCMBRYBuwH/gJWAMOw/zfZ0FC49tAHze2taLybgfnAdQG5OH6QDZG5HgZUmQYzgKeNgr2mfBaaEH78C3xn5CYAU4DlRv53oCiCwR2AbabtR0bfQvN7HfGcu64iDm8zTP024HVgMrDWlE2P2H9D4hrgWTS2jcBrwFOIw5Wmzo84fpAJsbi+GuhHuucXAhtM45sDdaeGGPCkkX85gtHzTZv7AuUTTfkrEXTVBkqRXSUx2kbl7SZTvh5o5Ss/GZhj6gZE6L++cV0TDEVjmob4CuKkwO84fpAJOef6UdNwiqN8VyP/uaN8ByP/G+kkNKX6WHa6pe3taAWrAPYBe9AuM9ix77goJb4zhiGMt+mm/F5Lm26mbqFjH/WR67g4BdgOVGJ3xKiI6geRuHY9/x4yz8OO8v3M80dH+d7m+RlwNFC3D1gCnAZcHqhriiZqe+Ab4CXgA6AYHS3GOPZfVxDGW6F5rre08cp64jbhGhLX1wAFyM6jwPXIzgeAK2Loi+oHkbhu7KCwMXCX+T4vRGYU0ARoBlwC9EATaoKj0eebZ0VI/c9AX6AjCnx4qEKX460B+ceMrsEoWFJX4crbTvMstuhob56Nzfd1WfpsSFxfap7/oABZl0D918AtwA4HXS5+EEQkrl2ccQIaxKfo/GvDKKC17/c8dIxzGSRoMoKiVjZ45c0D5fvNJ4gt6AJ+pmP/+YIrb58AtwEjgZko+gq67zzhk3OJhDYkrs8yz9Eo2NUTKEeL2vPIEd7D7arh4gdBROI62zH1fuAhtNremUGuEEWYClEgoT1aiS7Obm+N0AIYiyKTe4AjaAWvQqvNJp/sVcDHKFpZhSa9K1I+vd7nLVP3paVumqNeV95mognQAU2qV1E0tRxNsA1GLngUyiWicP0Iukv+iRaWOaTvSjakSOcy0+edLPq8+X0YuAGlJ/YDq1FQbBPQi+xHVlc/qBEy7YzDqQ6f96F6Nc6EbSg/sxJtzdNx+xO8FaJZSL1XvtdXdiE6i7cGvkcTdhcivhgdKVb55JsAa4xNUVMBk0jfKboBNwJvo0nkR3lE/dl4O4LukyOBO4BB6Oi1CEX2Zhm57Q591QbXJSgivBwtNuOBL4ALyDyPfkXjcsXmLPXeGMpI/4/+RgvcEKA78G2Ijjh+4CEO12kYgVae1VRv9VFRZnS0yiaIkqxVaMW3wQsP9/GVrUJ/XIlFfjzh0UfQ6ljqYFcmlJL7aCpE4w2UJjmI+5WgtrkGLYTeglKbuBvZNjek/jlT/3BIfU39IA7X/8MYI1CG+4SwwUt0utxjoobbi4y87SLdHCV3q0iPCHqoy84YhTe/HS86ytc21wBtjEwPRxtzhXbo6F6J/Uo2F9l1q6UuF35QkzQSY03jFWS/kHfEvv02ojp5vSTEwE6kJ1ujJEcLTFlFQE9Ln55DhCfX8+mMcXk7w1LWDe2Iu4GzLfV1gWuAd9GkPjGDzLHCbGTjg4HyvshR95D+f0TxAw815tr/Ws8gFHg4gpKatghQiurgxAj0qtBi5Pm70J2iFwpEbEXb71qLjnborpEKDGYpOg7MBn4CLkO5mgrgStOHhwXobYkydB9pA1yLAioD0P2wq2UMIGccjnugxYZSFMTpje5urojL2zL0nuQalKPqjPJmB9Dx7ytLXynyz/VEYCDaFW150mONtmisRWgcZYiP/sgZBgLv++Sj+oG/LBdcAzCO7NGrRT75LijxW47yYIeN4cuNrrAVJWV0nWupK0ITfAt6f7OS8BdqC1CgYweanEtRIOEio/+NkP4hvztjXN5GAz+gy/5BNLGnoskWhhT55foFo79TBhtrAwXIsSrRWHeigFl3i+w4ovmBhxS54brBIRfOmCAzJqNdvnO+DakvcEn6Hy9oApxnvjcCzkF3rt1U5+kS5AZTUT6uP7qTea/zhb04kKCBoQT7kWNa/kw6bhF2vBuXR5sSJEiQIEGCBAkSJEiQIEGCeov/AGnwl7yZplp9AAAAAElFTkSuQmCC\n",
            "text/latex": "$\\displaystyle 23.0 a_{1} + 39.0 a_{2} - 62.0$",
            "text/plain": [
              "23.0*a1 + 39.0*a2 - 62.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "rSdBl3nGkOmD",
        "outputId": "1d7d5456-36e5-4b30-c17d-463693686fb5"
      },
      "source": [
        "msef1 = diff(MSE,a1)\n",
        "msef1"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 19.5 a_{1} + 23.0 a_{2} - 39.5$",
            "text/plain": [
              "19.5*a1 + 23.0*a2 - 39.5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-sTQgEREkbap"
      },
      "source": [
        "msearr = np.array([msef1,msef2])"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 162
        },
        "id": "g6au76q7lRgo",
        "outputId": "50b5c6d9-36aa-4344-c7dc-4ca483207677"
      },
      "source": [
        ""
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "error",
          "ename": "AttributeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-37-8998c5caf13a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmsearr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0.395\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.62\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'array'"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 162
        },
        "id": "IDX91rQelUUe",
        "outputId": "4d913a99-1ad4-4f38-f4e9-10213543d40c"
      },
      "source": [
        ""
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-38-2a84fbdbc507>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmsef1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.395\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m: 'Add' object is not callable"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "3oVUnuMKln4N",
        "outputId": "89336b5c-719f-41b1-a604-8be921f7dce1"
      },
      "source": [
        "msef1.subs({a1:0.395, a2:0.62})"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle -17.5375$",
            "text/plain": [
              "-17.5375000000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "kmPdqGTrlpqt",
        "outputId": "3744d9cd-11e7-4203-cd9f-0b956b815171"
      },
      "source": [
        "msef2.subs({a1:0.395, a2:0.62})"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle -28.735$",
            "text/plain": [
              "-28.7350000000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kzXj8u74mEUz",
        "outputId": "fe373b67-5a93-4469-c3ce-5ae23998cb74"
      },
      "source": [
        "MSEar2 = np.array([msef1.subs({a1:0.395, a2:0.62}),msef2.subs({a1:0.395, a2:0.62})])\n",
        "MSEar2"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-17.5375000000000, -28.7350000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vNN0O26imRea",
        "outputId": "2151645a-1a34-4271-b555-91aff2fa66b3"
      },
      "source": [
        "MSE2try = MSEar + 0.01 * (-MSEar2)\n",
        "MSE2try"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.570375000000000, 0.907350000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "GAV7W_F_m6i7",
        "outputId": "66d191df-2ae2-4918-bd8d-8320c5eabece"
      },
      "source": [
        "MSE.subs({a1: 0.57, a2: 0.91})"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 8.560825$",
            "text/plain": [
              "8.56082500000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "ko-5rZ-snB-e",
        "outputId": "ec4b8e78-1d07-49d8-8b81-dae461d13f9f"
      },
      "source": [
        "msef1.subs({a1: 0.57, a2: 0.91})"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle -7.455$",
            "text/plain": [
              "-7.45500000000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "GwxKZJvlnO4L",
        "outputId": "505f738b-6f89-4dac-8362-d753bcd7e851"
      },
      "source": [
        "msef2.subs({a1: 0.57, a2: 0.91})"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle -13.4$",
            "text/plain": [
              "-13.4000000000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qQVzZXxenRGA"
      },
      "source": [
        "MSEar3 = np.array([msef1.subs({a1: 0.57, a2: 0.91}),msef2.subs({a1: 0.57, a2: 0.91})])"
      ],
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "exC9zsSQnZHP",
        "outputId": "af11baec-e088-4f36-cef0-57be7e0bf660"
      },
      "source": [
        "MSEar3"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-7.45500000000000, -13.4000000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WklXP_Danai1",
        "outputId": "46b5d4a0-f36b-4a14-ce14-839438339ec9"
      },
      "source": [
        "MSE3try =  MSEar + 0.01 * (-MSEar2) + 0.01 * (-MSEar3)\n",
        "MSE3try"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.644925000000000, 1.04135000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "0G6JLIyDnhr5",
        "outputId": "3c051f2e-9333-4556-cd5e-1837abcb47d4"
      },
      "source": [
        "MSE.subs({a1:0.645, a2:1.04})"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 6.86834375$",
            "text/plain": [
              "6.86834375000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sqX2jv5MnrmI"
      },
      "source": [
        "MSEar4 = np.array([msef1.subs({a1: 0.645, a2: 1.041}),msef2.subs({a1: 0.645, a2: 1.041})])"
      ],
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tmu84z-Bn2We",
        "outputId": "426da97c-8997-4e25-daa3-421210b6fc95"
      },
      "source": [
        "MSEar4"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-2.97950000000000, -6.56600000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gRVazg1pn3jv",
        "outputId": "a79e9adb-ef96-4385-e6c3-c445530fefb9"
      },
      "source": [
        "MSE4try =  MSEar + 0.01 * (-MSEar2) + 0.01 * (-MSEar3) + 0.01 * (-MSEar4)\n",
        "MSE4try"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.674720000000000, 1.10701000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "ScbBuiJJn744",
        "outputId": "d03d9d41-47fe-4e95-ead4-57d1f3c41694"
      },
      "source": [
        "MSE.subs({a1:0.674, a2:1.1})"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 6.503391$",
            "text/plain": [
              "6.50339100000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nUpnGn1JoCcc",
        "outputId": "979f2fbe-6412-477c-a7cb-13e81068d5f3"
      },
      "source": [
        "MSEar5 = np.array([msef1.subs({a1: 0.674, a2: 1.1}),msef2.subs({a1: 0.674, a2: 1.1})])\n",
        "MSEar5"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.05700000000000, -3.59799999999999], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2jmGtVJooKlW",
        "outputId": "54987258-8499-44ea-e8d3-d0d08169199b"
      },
      "source": [
        "MSE5try =  MSEar + 0.01 * (-MSEar2) + 0.01 * (-MSEar3) + 0.01 * (-MSEar4) + 0.01 *(-MSEar5)\n",
        "MSE5try"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.685290000000000, 1.14299000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "DFsscf1ooPJX",
        "outputId": "f03018e8-8a02-4bad-c659-88af75f1e346"
      },
      "source": [
        "MSE.subs({a1:0.685,a2:1.142})"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 6.38685175$",
            "text/plain": [
              "6.38685175000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "slXfWvKwoTiU",
        "outputId": "54b76708-0969-41d6-9ef9-4e0510840b74"
      },
      "source": [
        "MSEar6 = np.array([msef1.subs({a1: 0.685, a2: 1.142}),msef2.subs({a1: 0.685, a2: 1.142})])\n",
        "MSEar6"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.123500000000000, -1.70700000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mM5yMERgob04",
        "outputId": "b67a33c6-ba65-42f9-cfa6-d82ee6b2a77d"
      },
      "source": [
        "MSE6try =  MSEar + 0.01 * (-MSEar2) + 0.01 * (-MSEar3) + 0.01 * (-MSEar4) + 0.01 *(-MSEar5) + 0.01 * (-MSEar6)\n",
        "MSE6try"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.684055000000000, 1.16006000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "3mSZpddxoflp",
        "outputId": "2e8efde9-92f4-4c76-8257-ede203cc212c"
      },
      "source": [
        "MSE.subs({a1:0.684,a2:1.16})"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 6.361916$",
            "text/plain": [
              "6.36191600000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BpBQru4mojSn",
        "outputId": "1f7c3d71-315a-4e12-cb31-64fc5b421b47"
      },
      "source": [
        "MSEar7 = np.array([msef1.subs({a1: 0.684, a2: 1.16}),msef2.subs({a1: 0.684, a2: 1.16})])\n",
        "MSEar7"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.518000000000001, -1.02800000000001], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BbU79a_3orlx",
        "outputId": "0ff4109c-c790-42b8-b873-25c2ee49eea4"
      },
      "source": [
        "MSE7try =  MSEar + 0.01 * (-MSEar2) + 0.01 * (-MSEar3) + 0.01 * (-MSEar4) + 0.01 *(-MSEar5) + 0.01 * (-MSEar6) + 0.01 * (-MSEar7)\n",
        "MSE7try"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.678875000000000, 1.17034000000000], dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "lIcldBG0oyik",
        "outputId": "9da31d0b-0375-4869-e893-8edfdb457396"
      },
      "source": [
        "MSE.subs({a1:0.678,a2:1.17})"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 6.349449$",
            "text/plain": [
              "6.34944900000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rg5iL9pvo21c"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}