Vector_Plotting.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Vector_Plotting.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "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/ak-ghoul/Deep-Learning/blob/master/Vector_Plotting.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "metadata": {
        "id": "3bnqQkE3m-GA",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Vector Plotting\n",
        "\n",
        "NUmpy will be used for mathematical things & matplotlib to plot the graph."
      ]
    },
    {
      "metadata": {
        "id": "tMeaaowCnKVr",
        "colab_type": "code",
        "outputId": "e00dcc30-b677-4416-b2de-fed278040ec2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        }
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as mp\n",
        "mp.quiver(0,0,5,6)\n",
        "mp.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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bfjK3Cr/fq2j0Qrq3YRozTB4zTB4zTF4mznC4FymuPtMOBoPat2+fJKm1tVVz5sxJWJ8x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\ngg==\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "FIwp9vJunjvg",
        "colab_type": "code",
        "outputId": "802f16b1-9cc9-4217-bb3a-185e16425c0a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        }
      },
      "cell_type": "code",
      "source": [
        "mp.quiver(0,0,3,4, scale_units = 'xy', angles = 'xy', scale = 1, color = 'r')\n",
        "mp.quiver(0,0,3,-4, scale_units = 'xy', angles = 'xy', scale = 1, color = 'm')\n",
        "mp.xlim(-5,10)\n",
        "mp.ylim(-5,10)\n",
        "mp.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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oFID2jEIGLlVdnRIful9R72w2R/6ICFUtekkNd42yMBiA9oxCBi6BUe5W0oRcRewqMGe+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\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "iW5-S0goonC1",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def plot(a):\n",
        "  colors = ['r','m','g','b','y']\n",
        "  j=0\n",
        "  for i in a:\n",
        "    mp.quiver(i[0],i[1],i[2],i[3],scale_units = 'xy', scale = 1, angles = 'xy',color = colors[j])\n",
        "    mp.xlim(-20,20)\n",
        "    mp.ylim(-20,20)\n",
        "    j=j+1\n",
        "    if j == 4:\n",
        "      j=0"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "h0mNg68atPOO",
        "colab_type": "code",
        "outputId": "58660cb5-9743-4c12-943d-568107f1ba9c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        }
      },
      "cell_type": "code",
      "source": [
        "a=[(2,3,4,5),(6,4,8,9),(1,6,3,5),(1,6,-4,3)]\n",
        "plot(a)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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p0iTde++9+vzzz43cNQAAAcnidDqdl/qirKwsZWVludVuueUWdezYUYMHD9ae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\nNQAAJvb/AfUkuHH7YYcKAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "AyTS1qZcta_F",
        "colab_type": "code",
        "outputId": "48712a36-30f3-4b56-f4a8-3006800d5cee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        }
      },
      "cell_type": "code",
      "source": [
        "a=[np.asarray((-10,-10,4,5)),np.asarray((6,7,8,9)),np.asarray((0,0,3,5)),np.asarray((0,0,-4,3))]  # for vector addition list has to be converted into arrays because '+' will concatenate in case of lists & tuples.\n",
        "plot(a)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8PLX85SjZyss95aprf6Zj7/5J7tSOPmwOAPwLo2+Yq7JSsZMnKDIny6tcft8D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\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "CNe0PBCYTjnv",
        "colab_type": "code",
        "outputId": "81920126-8eef-406c-9136-f81c5d046632",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        }
      },
      "cell_type": "code",
      "source": [
        "  plot([a[0],a[1],a[2],a[3],a[1]+a[3],a[2]+a[3]]) # converted into arrays using numpy for vector addition\n",
        "  "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lmTYI7rJjCIKACdtT8dXJreLrHaI64u1/rYFerfdSj4joajGoifxIQoKARYvK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\nQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "GAZhIRrl8Ypf",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#Projection of Vectors\n",
        "\n",
        "Dot product and projection of one vector over another.<br />\n",
        "Numpy is used"
      ]
    },
    {
      "metadata": {
        "id": "-QKuVdgCVDfj",
        "colab_type": "code",
        "outputId": "b062df56-99e2-4ed6-a435-a199c2151b9f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        }
      },
      "cell_type": "code",
      "source": [
        "b = [(0,0,3,4),(0,0,4,-1)]\n",
        "def nigga(b):\n",
        "  col = ['r','b','g']\n",
        "  j=0\n",
        "  for i in b:\n",
        "    mp.quiver(i[0],i[1],i[2],i[3], scale_units = 'xy', scale = 1,angles = 'xy', color = col[j])\n",
        "    mp.xlim(-5,10)\n",
        "    mp.ylim(-5,10)\n",
        "    j=j+1\n",
        "nigga(b)    "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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WDQ1Kf/A+Jbz7dnDJiotT7YKXdeL2MTYOBqAzI8hAG7iqKpUxIV9xW0uDa4HUNNW8vlzN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\nGQAAAxBkAAAMQJABADAAQQYAwAD/H+34zxEHEjSAAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "8oKnAd2QtDrz",
        "colab_type": "code",
        "outputId": "b53a63b4-e4d3-4fec-b950-404bbb8896b4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "f= (np.dot(b[0],b[1])/(np.linalg.norm(b[1])**2))*np.asarray(b[1])\n",
        "print(f)\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 0.          0.          1.88235294 -0.47058824]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "k-fxOQXWxiSz",
        "colab_type": "code",
        "outputId": "7861238d-463c-4a9e-bf78-6585b4676bd1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        }
      },
      "cell_type": "code",
      "source": [
        "nigga([(0,0,3,4),(0,0,4,-1),(0., 0., 1.88235294, -0.47058824)])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ABiDIAAAYwBEIBAJWDwEAgN1xhgwAgAEIMgAABiDIAAAYgCADAGAAggwAgAEI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\nABiAIAMAYID/DxjoTPc5vXZ4AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "MZUnAZYk0GAk",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import math\n",
        "v = np.dot(b[0],b[1])/(np.linalg.norm(b[0])*np.linalg.norm(b[1]))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "4ywBYQou1U_J",
        "colab_type": "code",
        "outputId": "64546076-511c-4d00-b3bb-8193fa09d856",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "u = math.acos(v)\n",
        "math.degrees(b)  # angle between the two vectors in list"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "67.16634582208245"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "metadata": {
        "id": "pcH6Lf0f1dMv",
        "colab_type": "code",
        "outputId": "8f756446-a55b-4791-f7eb-25cf187e4544",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "f= (np.dot(b[0],b[1])/(np.linalg.norm(b[0])**2))*np.asarray(b[0])\n",
        "print(f)\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.   0.   0.96 1.28]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "S1Dr69y86ADp",
        "colab_type": "code",
        "outputId": "e2841bbf-9c9a-4355-ce13-97dc250cb56b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        }
      },
      "cell_type": "code",
      "source": [
        "nigga([(0,0,3,4),(0,0,4,-1),(0., 0., 0.96, 1.28)])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6y18o7t23A0v+mBhVzntFp4aPtHAwAC0ZQQYugqOsVGnjchSztTCw5ktOUcXiZaof8D0L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\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "-LnUo7IX7FHV",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import math\n",
        "l = np.dot((0., 0., 0.96, 1.28),b[0])/(np.linalg.norm((0., 0., 0.96, 1.28))*np.linalg.norm(b[0]))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "58yoYhr27-cN",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "o = math.acos(l)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "my3UoXCu8EM-",
        "colab_type": "code",
        "outputId": "8d350bb6-a407-45d8-f30d-ebf1b7c7451d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "math.degrees(o)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 85
        }
      ]
    }
  ]
}