{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ex_chi2.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PE1KLXUn95Bk",
        "colab_type": "text"
      },
      "source": [
        "# **תרגיל על התאמות באמצעות פייתון**\n",
        "**עדיף לצפות בתסריט \"קצר\" בשם**\\\n",
        "**simple_script_for_chi2_regression**\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "46MwS9Zq-Zhg",
        "colab_type": "text"
      },
      "source": [
        "## **נתון לכם את התוצאות הבאות**\n",
        "X =  -3.00,-2.50,-2.00,-1.50,-1.00,-0.50,0.00,0.50,1.00,1.50,2.00,2.50,3.00,3.50,4.00,4.50,5.00,5.50,6.00,6.50\n",
        "\n",
        "\n",
        "y = -0.22,0.06,0.28,0.23,0.31,0.01,-0.36,-0.17,0.12,0.25,0.14,-0.01,-0.24,-0.32,-1.13,-0.96,-0.34,0.10,0.71,1.01\n",
        "\n",
        "\n",
        "y_err = 0.23,0.16,0.19,0.06,0.27,0.09,0.28,0.21,0.10,0.21,0.06,0.22,0.22,0.22,0.28,0.20,0.05,0.11,0.12,0.13\n",
        "\n",
        "## **בצעו התאמה של \"כאי בריבוע\" עבור שתי הפונקציות**:\n",
        "\n",
        "**פולינום מסדר 5**\n",
        "f(x) = a* x^5 + b* x^4 + c* x^3 + d* x^2 + e* x + f \n",
        "\n",
        "**פונקציה**\n",
        "f(x) = a* x* sin(b*x)\n",
        "\n",
        "\n",
        "ותקבעו לפי התוצאות איזה פונקציה מבין שתיהן מתאימה יותר לתוצאות\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "inglKyHcA8qJ",
        "colab_type": "text"
      },
      "source": [
        "____________________________________________________________________________________________________________________"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wNwjDt__Brl1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import warnings\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hapCNj3KSS3g",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mulhgyQdDosf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "warnings.simplefilter(\"ignore\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7IDUSHEcA5WM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip install -q matplotlib-venn probfit"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2puo44PtA66y",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from probfit import Chi2Regression "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ksBF1naEA5e6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip install -q matplotlib-venn iminuit"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vd4E0iwCBkVY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from iminuit import Minuit"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4figJlcQHK92",
        "colab_type": "text"
      },
      "source": [
        "### **numpy שימו את הנתונים בתוך מערכים באמצעות**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5Kv1GQ0L-wHH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = np.array([ -3.00,-2.50,-2.00,-1.50,-1.00,-0.50,0.00,0.50,1.00,1.50,2.00,2.50,3.00,3.50,4.00,4.50,5.00,5.50,6.00,6.50])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j-wUkqY6Cd7L",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y = np.array(...)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z-ZP-Ue9CiIg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_err = ..."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FSrRuBkYIVJ3",
        "colab_type": "text"
      },
      "source": [
        "**תגדירות את פונק' הפולינום 5**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fHo2-BZKIk0L",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pol_5_fun = lambda X,a,b,c,d,e,f: a * X ** 5 + b * X ** 4 +...\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OdHdDqqSJIbH",
        "colab_type": "text"
      },
      "source": [
        "**ביעצו ההתאמה לפי הקוד הבא**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w2gwdnWICm2n",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#regression\n",
        "reg = Chi2Regression(pol_5_fun,X,y, error=y_err)\n",
        "\n",
        "#optimization\n",
        "opt = Minuit(reg)\n",
        "opt.migrad()\n",
        "\n",
        "#plot\n",
        "plt.rc(\"font\", size=16, family=\"Times New Roman\")\n",
        "fig = plt.figure(figsize=(10, 6))\n",
        "ax = fig.add_axes([0,0,1,1])\n",
        "ax.set_xlabel(\"X_data\", fontdict={\"size\": 20, \"weight\":\"bold\"})\n",
        "ax.set_ylabel(\"y_data\", fontdict={\"size\": 20, \"weight\":\"bold\"})\n",
        "ax.errorbar(x=X, y=y,yerr=y_err, xerr=X_err, capsize=4, elinewidth=3, fmt='none', ecolor=\"blue\")\n",
        "ax.scatter(X,y, c='blue', s=30)\n",
        "reg.show(opt)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0z7PA63hJUnG",
        "colab_type": "text"
      },
      "source": [
        "**תגדירות את הפונק' עם סינוס**\\\n",
        "np לא לשכוח שלפני סינוס צריך לכתוב\\\n",
        "np.sin()"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bO9ISpcnKBK3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pol_sin = lambda X,a,b:...\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6KeR4gu1KMkI",
        "colab_type": "text"
      },
      "source": [
        "בצעו התאמה לפונקיה\\\n",
        "נסו לשנות לאתחל את הפרמטרים מאחד כדי לקבל תוצאות יותר טובות\\\n",
        "opt = Minuit(reg, a=1, b=1)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZdGwH3tfDUSA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "......"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kc7MIPVxGvCL",
        "colab_type": "text"
      },
      "source": [
        "### **אזת איזה פונקציה מתאימה יותר?**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H63So-GEG4N6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}