assignment2.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# **Histogram Transformation**"
      ],
      "metadata": {
        "id": "RWNY2TbWXDse"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![qus1.jpg](data:image/jpeg;base64,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)\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "90M2dM_0TRgn"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0CJBKO9yK4e5",
        "outputId": "77352d8d-2be5-41a3-8a50-f3c3e641b1fc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.37454012 0.95071431 0.73199394 ... 0.67445341 0.49944724 0.38990849]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "\n",
        "# Set the seed for reproducibility (optional)\n",
        "np.random.seed(42)\n",
        "\n",
        "#Generate uniform values\n",
        "uniform_values = np.random.uniform(low=0.0, high=1.0, size=100000)\n",
        "\n",
        "#Print the values\n",
        "print(uniform_values)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Mwh5QZa1K4fC",
        "outputId": "6fbef6cb-2cb5-42d9-c6bb-760c415b2009"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.20913978, 0.77799619, 0.48230698, ..., 1.5705669 , 1.70749753,\n",
              "       1.78108355])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "# Uniform to traingle\n",
        "y = 1- np.sqrt(1 - uniform_values)\n",
        "np.append(y,1+ np.sqrt(1 - uniform_values))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        },
        "id": "SmTo2qHPK4fE",
        "outputId": "c5525ba4-c3f5-4fc0-b9ce-50f10cbdf29e"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.hist(y,bins=150)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "obB0Tpk4K4fG",
        "outputId": "5dbe85b0-f364-4a75-a2ed-1344855b9a80"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.61199683,  0.9750458 ,  0.85556645, ..., -0.82125112,\n",
              "       -0.70671582, -0.62442653])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "z = np.sqrt(2*y - y**2)\n",
        "np.append(z,-np.sqrt(2*y - y**2))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "5I_DCfIzK4fH",
        "outputId": "42d97bbf-e7a2-421a-a236-d902da97a049"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.hist(z,bins=150)\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "base",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.11.4"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}