Mathematics_using_NumPy.ipynb

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        "<a href=\"https://colab.research.google.com/github/UtkKnight10/NumPy/blob/main/Mathematics_using_NumPy.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
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      "metadata": {
        "id": "bUR25biiGhA3"
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      "source": [
        "import numpy as np\n",
        "import sys"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Mathematics using NumPy**"
      ],
      "metadata": {
        "id": "KQv6pm3hGnpp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Arithematic operations"
      ],
      "metadata": {
        "id": "koP7slRGIFED"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array([1,2,3,4])\n",
        "print(a)"
      ],
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        "id": "nfqm9qXuGk_K",
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      "outputs": [
        {
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          "name": "stdout",
          "text": [
            "[1 2 3 4]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "These a element wise operations.\n",
        "That means every element will be changed."
      ],
      "metadata": {
        "id": "2VkfjKIRIgZm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a + 2"
      ],
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        "id": "3NzuLF9VHTh2",
        "outputId": "bde7e155-979e-49da-accd-8cf8270f77b4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 4, 5, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a - 2"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/"
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        "id": "XGCzLanBHW5L",
        "outputId": "7b7a874d-be81-4896-8fd3-26cc2b96a462"
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      "execution_count": null,
      "outputs": [
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          "data": {
            "text/plain": [
              "array([-1,  0,  1,  2])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a * 2"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/"
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        "id": "cgcEvLxXHYgq",
        "outputId": "19926cd0-2ecb-4380-ccf5-f168eb704991"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 4, 6, 8])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a / 2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c8qC1_FwHZ8C",
        "outputId": "285d9227-185a-41c1-c39d-c5c99646c2f4"
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.5, 1. , 1.5, 2. ])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = np.array([1,0,1,0])\n",
        "a + b"
      ],
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          "base_uri": "https://localhost:8080/"
        },
        "id": "NdYG1AElHd8z",
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      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 2, 4, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a ** 2"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/"
        },
        "id": "h8WQp5dpHsCz",
        "outputId": "dc0c590c-c287-479d-b969-a5372fa62b5f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1,  4,  9, 16])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Trignometric operation"
      ],
      "metadata": {
        "id": "wpnDZIZzH8Gk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Take the sine\n",
        "np.sin(a)"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/"
        },
        "id": "dBj3O5ATHwA7",
        "outputId": "d9ae06ad-92f9-43d1-c30d-d78e2e49b0c9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.84147098,  0.90929743,  0.14112001, -0.7568025 ])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Take the cosine\n",
        "np.cos(a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rd_lVQ4AH1Hz",
        "outputId": "95e4cc6c-bbe6-465f-9453-53ef76d01be9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.54030231, -0.41614684, -0.9899925 , -0.65364362])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.tan(a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C6AuAwS2H3Sr",
        "outputId": "46ca660a-5a39-4230-fef9-c6720e743838"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.55740772, -2.18503986, -0.14254654,  1.15782128])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Linear algebra**"
      ],
      "metadata": {
        "id": "5JkLeH6lIV8k"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In linear algebra we are not doing element wise operations"
      ],
      "metadata": {
        "id": "zrU4o5ugI070"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.ones((2,3))\n",
        "print(a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WSATkeI8IKP8",
        "outputId": "2bc1323b-9226-4f39-b3b6-bb1e6b3f3789"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1. 1. 1.]\n",
            " [1. 1. 1.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = np.full((3,2), 2)\n",
        "print(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b_z4NZVFI_j_",
        "outputId": "d0d8136f-d3bd-480e-befb-ea66e5d23ef0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[2 2]\n",
            " [2 2]\n",
            " [2 2]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Matrix multiplication"
      ],
      "metadata": {
        "id": "zISAEdtpJfoL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# a * b -> gives an error as we cant multiply matrix like this\n",
        "# we have to use matmul() to multiply the matrices\n",
        "# The dimensions of the matrix should be compatible.\n",
        "# It means that number of columns in 'a' matrix should be equal to number of rows in 'b' matrix\n",
        "np.matmul(a,b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KIrztJYBJDXM",
        "outputId": "5fc37296-6bc3-4fc6-f3b6-900c970d269c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[6., 6.],\n",
              "       [6., 6.]])"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finding Determinant"
      ],
      "metadata": {
        "id": "tYPsETzJKJrG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "c = np.identity(3)\n",
        "np.linalg.det(c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C_mz2cP0JPek",
        "outputId": "ec3b9868-06e2-4844-8c1c-2944065b7dce"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Reference doc: https://docs.scipy.org/doc/numpy/reference/routines.linalg.html\n",
        "\n",
        "# Determinant\n",
        "# Trace\n",
        "# Singular vector decomposition\n",
        "# Eigenvalues\n",
        "# Matrix Norm\n",
        "# Inverse\n",
        "# Etc..."
      ],
      "metadata": {
        "id": "FpjoBmRbKP0U"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Statistics"
      ],
      "metadata": {
        "id": "8tN2sk3xLLfA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "stats = np.array([[1,2,3], [4,5,6]])\n",
        "stats"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FCNtu7VyKleE",
        "outputId": "0170221b-670e-445d-857b-d9f1b7a79e67"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6]])"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.min(stats)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5-KFefukLWRs",
        "outputId": "8ca86dae-0df8-48f0-e1af-7d1ad0a931ca"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# axis = 1 gives the row wise minimum\n",
        "# axis = 0 gives the column wise minimum\n",
        "np.min(stats, axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DqsjjPr4LgI9",
        "outputId": "a613f527-6847-4801-d54c-194104a5d9d7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.max(stats)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rl5pWlVNLY5t",
        "outputId": "af5be646-6318-448e-ee0a-3f4587ad1e49"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# axis = 1 gives the row wise max\n",
        "# axis = 0 gives the column wise max\n",
        "np.max(stats, axis=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IVJPoDZvLb7F",
        "outputId": "503dadc4-d81a-4e9c-a99d-9ed8ca32586b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 6])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.sum(stats)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lmML_mO9Me0d",
        "outputId": "0f33e683-ef93-422f-da25-a9534f3fcaba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "21"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# axis = 1 gives the row wise sum -> gives sum of of all elements in the row\n",
        "# axis = 0 gives the column wise sum -> gives sum of all elements in the column\n",
        "np.sum(stats, axis=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XXE4jl_sMWwO",
        "outputId": "48ebd3fb-952f-445d-d634-330de4279417"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5, 7, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Reorganizing Arrays**"
      ],
      "metadata": {
        "id": "xqMfUmwXSjkL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "before = np.array([[1,2,3,4], [5,6,7,8]])\n",
        "print(before)\n",
        "\n",
        "# as long as multiplication of dimensions of after array\n",
        "# is equal to total number of elements in before array it is fine\n",
        "after = before.reshape((2,2,2))\n",
        "print(after)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OM285JmHMjmW",
        "outputId": "750b9ee2-1cc8-4664-e4e6-1bf33876a6c0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3 4]\n",
            " [5 6 7 8]]\n",
            "[[[1 2]\n",
            "  [3 4]]\n",
            "\n",
            " [[5 6]\n",
            "  [7 8]]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Vertically stacking vectors\n",
        "# The number of columns in the arrays should be same\n",
        "v1 = np.array([[1,2,3,4], [1,1,1,1]])\n",
        "v2 = np.array([5,6,7,8])\n",
        "\n",
        "np.vstack([v1,v2,v1,v2])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OhrAptviSvZV",
        "outputId": "dbbfc58d-2f90-481c-abc6-9f5b7ec77206"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3, 4],\n",
              "       [1, 1, 1, 1],\n",
              "       [5, 6, 7, 8],\n",
              "       [1, 2, 3, 4],\n",
              "       [1, 1, 1, 1],\n",
              "       [5, 6, 7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Horizontal stacking vectors\n",
        "# The number of rows in the arrays should be same\n",
        "h1 = np.ones((2,4))\n",
        "h2 = np.zeros((2,2))\n",
        "\n",
        "np.hstack((h1,h2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8apl4GqlUk-F",
        "outputId": "11f49d66-e0ef-4aec-ace4-b5447778d0c1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 1., 1., 1., 0., 0.],\n",
              "       [1., 1., 1., 1., 0., 0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Miscellaneous**\n",
        "\n",
        "##### Load Data from file"
      ],
      "metadata": {
        "id": "RRQESkF3V05C"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "file_data = np.genfromtxt('data.txt', delimiter=',')\n",
        "file_data = file_data.astype('int32')\n",
        "print(file_data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w1MdC4tPU2P8",
        "outputId": "86dbe681-cd0a-4435-9139-f73f5ba49e34"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[  1  13  21  11 196  75   4   3  34   6   7   8   0   1   2   3   4   5]\n",
            " [  3  42  12  33 766  75   4  55   6   4   3   4   5   6   7   0  11  12]\n",
            " [  1  22  33  11 999  11   2   1  78   0   1   2   9   8   7   1  76  88]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### Boolean Masking and Advanced Indexing"
      ],
      "metadata": {
        "id": "GlKQ3tv2XL9G"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "file_data[file_data > 50]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Zrox12VMWvPS",
        "outputId": "2e43afa8-9f82-4f77-cb48-d4609bb0423c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([196,  75, 766,  75,  55, 999,  78,  76,  88], dtype=int32)"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# We can index with a list in Numpy\n",
        "a = np.array([1,2,3,4,5,6,7,8,9])\n",
        "a[[1,2,8]] # here [1,2,8] this list acts as the index values to be accessed"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dJUx_rDLXaUm",
        "outputId": "f78837b7-d77f-4f31-8ef4-20b366a8bd1e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 3, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Want to know if any value in the columns is greater than 50\n",
        "# rows put axis = 1\n",
        "np.any(file_data > 50, axis=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fILslOznX5S3",
        "outputId": "5e1dbc76-a1e3-477e-fc0f-1c16c8e2f67f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False, False, False, False,  True,  True, False,  True,  True,\n",
              "       False, False, False, False, False, False, False,  True,  True])"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# want to know if all values in the columns are greater than 50\n",
        "# for rows put axis = 1\n",
        "np.all(file_data > 50, axis=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "x7oxd0inYat2",
        "outputId": "b924ae4d-158a-4bb9-daa0-b867decb6202"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False, False, False, False,  True, False, False, False, False,\n",
              "       False, False, False, False, False, False, False, False, False])"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(~((file_data > 50) & (file_data < 100)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a8e1Wp4zYvNX",
        "outputId": "f995605e-48f7-45b2-dd70-71c143e1b60d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ True,  True,  True,  True,  True, False,  True,  True,  True,\n",
              "         True,  True,  True,  True,  True,  True,  True,  True,  True],\n",
              "       [ True,  True,  True,  True,  True, False,  True, False,  True,\n",
              "         True,  True,  True,  True,  True,  True,  True,  True,  True],\n",
              "       [ True,  True,  True,  True,  True,  True,  True,  True, False,\n",
              "         True,  True,  True,  True,  True,  True,  True, False, False]])"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "J8Y4b6EBZMuo"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}