colab-notebooks/03_Vector.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "03_Vector.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/satyajitghana/PadhAI-Course/blob/master/03_Vector.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "udhY69A6NYXh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "sns.set()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4x5NM5WKV8qY",
        "colab_type": "text"
      },
      "source": [
        "# Vector Plotting"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VOh6jrjFNjec",
        "colab_type": "code",
        "outputId": "b577ef30-2b94-4416-a9ce-043e2711d9b6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        }
      },
      "source": [
        "plt.quiver(0, 0, 3, 4)\n",
        "plt.plot()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0SpUd07tNm2P",
        "colab_type": "code",
        "outputId": "9fd61366-6a4f-4daa-918d-0651e56d1862",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        }
      },
      "source": [
        "plt.quiver(0, 0, 3, 4, scale_units='xy', angles='xy', scale=1)\n",
        "plt.plot()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7Oc7b1Hxx5oYWR7O7OC4iTe/o0SOMHj2SQ4cOAtCjRyRZWbmEhNxocTLxBXpWlYif+eyz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PwAdcRAkN45O",
        "colab_type": "code",
        "outputId": "99501a2f-d606-4782-f3a7-8de8af1ae615",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        }
      },
      "source": [
        "plt.quiver(0, 0, 3, 4, scale_units='xy', angles='xy', scale=1)\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.plot()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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r4eXlhdDQUOzdu1fueESK+P777zFz5gv45z//PwBg3Ljx2LZtB/r109o5GZE4sheKwWCA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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f9wULQsJOM9L",
        "colab_type": "code",
        "outputId": "9abce632-0d02-4e03-c134-f993b5561966",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        }
      },
      "source": [
        "plt.quiver(0, 0, 3, 4, scale_units='xy', angles='xy', scale=1, color='r')\n",
        "plt.quiver(0, 0, -3, 4, scale_units='xy', angles='xy', scale=1, color='g')\n",
        "plt.xlim(-10, 10)\n",
        "plt.ylim(-10, 10)\n",
        "plt.plot()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BhhMbcbT0uJ2TNc/Vrw6jaM1fYa7+7wSP4f+/foJHjeOfDyLHxDPedFdTqVSYfG8ovJw9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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "try9smhbORxe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot_vectors(vecs):\n",
        "    colors = ['r', 'b', 'g', 'y']\n",
        "    i = 0\n",
        "    for vec in vecs:\n",
        "        plt.quiver(vec[0], vec[1], vec[2], vec[3], scale_units='xy', angles='xy', scale=1, color=colors[i%len(colors)])\n",
        "        i += 1\n",
        "    plt.xlim(-10, 10)\n",
        "    plt.ylim(-10, 10)\n",
        "    plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wBbjghIBOsN7",
        "colab_type": "code",
        "outputId": "1958bec4-0dfa-4858-cf6f-77fbdea334c4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "plot_vectors([(0, 0, 3, 4), (0, 0, -3, 4), (0, 0, -3, -2), (0, 0, 4, -1)])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RY4IAAJfqmvCXbT/gm1OOcWZh5dEjyF/3vzDVXJ7gMeI/mid4VKnsnIxuVzziTbc1hUKB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\n1DpdAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xKVCKe6zPMLx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "vecs = [(0, 0, 3, 4), (0, 0, -3, 4), (0, 0, -3, -2), (0, 0, 4, -1)]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wBqgLDsQOx8d",
        "colab_type": "code",
        "outputId": "4ce26b58-96a7-40bd-b3eb-4f17ee8ad3e2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "plot_vectors([vecs[0], vecs[3]])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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iRbttv7a2FnV1dTh27JjduI0bN+KDDz5AWFgYAGDIkCFYtmyZS7NlZmZi//79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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kITrDEmmPRqB",
        "colab_type": "code",
        "outputId": "27c9da8e-ae76-40f0-e2cd-779cb56c88dc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "vecs[0] + vecs[1]"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0, 0, 3, 4, 0, 0, -3, 4)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4PuSq9f3PV3T",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "vecs = [np.asarray([0, 0, 3, 4]), np.asarray([0, 0, -3, 4]), np.asarray([0, 0, -3, -2]), np.asarray([0, 0, 4, -1])]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QvP5Iq1hP62Z",
        "colab_type": "code",
        "outputId": "52e6542b-8652-4f22-ab1a-30b538c82dbb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 86
        }
      },
      "source": [
        "vecs"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[array([0, 0, 3, 4]),\n",
              " array([ 0,  0, -3,  4]),\n",
              " array([ 0,  0, -3, -2]),\n",
              " array([ 0,  0,  4, -1])]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v8flqxxtQKdL",
        "colab_type": "code",
        "outputId": "3cad5fc9-b5f6-48ef-eef4-6d2c9799656f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "plot_vectors([vecs[0], vecs[3]])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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iRbttv7a2FnV1dTh27JjduI0bN+KDDz5AWFgYAGDIkCFYtmyZS7NlZmZi//79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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w997ellOQP2u",
        "colab_type": "code",
        "outputId": "009378d3-83e3-4aa6-a21a-d83721a528fb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "vecs[0] + vecs[3]"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 7, 3])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g0TgwNtDQUXR",
        "colab_type": "code",
        "outputId": "5eb32462-51de-4c0a-c610-ae31c2bcef40",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "plot_vectors([vecs[0], vecs[3], vecs[0] + vecs[3]])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CZrehpLa0/cJC63GcqTsLGa4XG+v8whCvi8MwXRziwgYhQNM3rty/3rFQiLyErbERljfW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\nRERC/H9kQ/aO/OvjUwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pvO3QpB8QYkB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "37tQesUsV10R",
        "colab_type": "text"
      },
      "source": [
        "# Vector Dot Product"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PvemQGXkV3d5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "vecs = [np.asarray([0, 0, 3, 4]), np.asarray([0, 0, -3, 4]), np.asarray([0, 0, -3, -2]), np.asarray([0, 0, 4, -1])]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rbzfI-fbV5Bj",
        "colab_type": "code",
        "outputId": "b3eed4ab-e33f-4227-9513-e722ae94a7f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "plot_vectors(vecs)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RY4IAAJfqmvCXbT/gm1OOcWZh5dEjyF/3vzDVXJ7gMeI/mid4VKnsnIxuVzziTbc1hUKB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\n1DpdAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zlTdQ4aAYSSS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a = np.asarray([3, 4])\n",
        "b = np.asarray([4, -1])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EdGpKpPgYbne",
        "colab_type": "text"
      },
      "source": [
        "$\\vec{a}\\cdot\\vec{b} = |\\vec{a}||\\vec{b}|\\cos{\\theta} = a_xb_x+a_yb_y$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OmM0uT7iYaVK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a_dot_b = np.dot(a, b)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pBF2vL4AYwDX",
        "colab_type": "code",
        "outputId": "1a5955a7-d527-45df-d875-285f83089676",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "a_dot_b"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jLZRzhE-Y4t8",
        "colab_type": "text"
      },
      "source": [
        "$a_b = |\\vec{a}|\\cos{\\theta} = |\\vec{a}|\\frac{\\vec{a}\\cdot\\vec{b}}{|\\vec{a}||\\vec{b}|} = \\frac{\\vec{a}\\cdot\\vec{b}}{|\\vec{b}|}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4cEmEpsrYxAa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "a_b = np.dot(a, b)/np.linalg.norm(b)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5n-OFucyZjFu",
        "colab_type": "code",
        "outputId": "d386a7bd-0be1-424e-f184-a6b47d36537d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "a_b"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.9402850002906638"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ftjeKtDMZpIC",
        "colab_type": "text"
      },
      "source": [
        "$\\vec{a_b} = a_b \\hat{b} = a_b \\frac{\\vec{b}}{|\\vec{b}|}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zkocku-bZj5q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "vec_a_b = (a_b/np.linalg.norm(b)) * b"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YTYGWffyZ3N_",
        "colab_type": "code",
        "outputId": "6d9ebb1d-545e-4f19-b934-e20513ceaea0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "vec_a_b"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.88235294, -0.47058824])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1-bXQp1yZ4Ah",
        "colab_type": "code",
        "outputId": "0d8a6d5a-756c-4ec0-b8c5-45ec9f1c57ef",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "plot_vectors([np.asarray([0, 0, 3, 4]), np.asarray([0, 0, 4, -1]), np.asarray([0, 0, 1.88235294, -0.47058824])])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ZM0exnMuWLcORI0eg1WoREBCA9PR0DBkyxGncjh07sHLlSsdMDdHR0di0aZNb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\ngoVCRERCsFCIiEiI/wUPMCI37QlvewAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZDoIkPagaMZR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}