{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "hide_input": false,
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.7.4"
    },
    "name": "elemzes.ipynb",
    "colab": {
      "name": "kl_py_okt_06.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "Zr3vCXeJsK-r"
      ],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/klajosw/python/blob/master/kl_py_okt_06.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bHCSTNEYsK9p",
        "colab_type": "text"
      },
      "source": [
        "<p align=\"left\"> \n",
        "    <img src=\"https://raw.githubusercontent.com/klajosw/python/master/kl_mie_python_logo_250.jpg\" \n",
        "         align=\"left\" width=\"251\" height=\"251\">\n",
        "    \n",
        "</p>\n",
        "\n",
        "\n",
        "<p> </p>\n",
        "\n",
        "\n",
        "\n",
        "# Python alapok 6\n",
        "\n",
        "<https://klajosw.blogspot.com/>\n",
        "\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gHYLQIgmsK9r",
        "colab_type": "text"
      },
      "source": [
        "# Adatok elemzése\n",
        "\n",
        "Az alábbi példasorban két, gyakran előforduló adatelemzési problémát fogunk megvizsgálni. Az első a függvényillesztés, a második pedig a periodikus jelek (például hangminták) Fourier-analízise. Amint már azt megszokhattuk, először is töltsünk be néhány hasznos modult és függvényt!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FCAdh7ErsK9s",
        "colab_type": "code",
        "colab": {},
        "outputId": "8d6ed05d-23d2-4e74-8795-246a9790a004"
      },
      "source": [
        "%pylab inline\n",
        "from scipy.optimize import curve_fit # Az illesztéshez használt függvény\n",
        "from numpy.fft import *              # Fourier-analízishez használt rutinok"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aPEDgIVPsK9v",
        "colab_type": "text"
      },
      "source": [
        "## Függvényillesztés\n",
        "\n",
        "\n",
        "\n",
        "Sokszor előfordul, hogy egy kísérlet eredményeit valamilyen elméleti becsléssel szeretnénk összevetni, illetve, hogy az elméletben szereplő paramétereket egy kísérlethez szeretnénk igazítani. Az egyik legelterjedtebb eljárás ennek a problémának a megoldására az úgynevezett legkisebb négyzetek módszere.\n",
        "\n",
        "Tegyük fel, hogy a kísérleti adataink $(x_i,y_i)$ számpárokként állnak rendelkezésünkre, és van $N$ db mintapontunk, azaz $i=1\\dots N$ ! Erre az adatsorra szeretnénk illeszteni egy $y=f(x,a,b,c,d,\\dots)$ függvényt! A feladat az hogy olyan $a,b,c,d,\\dots$ paramétereket találjunk, amik a legjobban közelítik az adatpontjainkat. Ezt a feladatot az $$S(a,b,c,d,\\dots)=\\sum_{i=1}^N (y_i-f(x_i,a,b,c,d,\\dots))^2$$ függvény minimalizálásával oldhatjuk meg. Ez a legkisebb négyzetek módszerének lényege. Természetesen van Python-csomag, amely a legkisebb négyzetek módszerét használja, az alábbiakban ezzel fogunk megismerkedni néhány példán keresztül."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "UIOYqBQqsK9w",
        "colab_type": "text"
      },
      "source": [
        "Generáljunk először egy adathalmazt, amit később vizsgálhatunk! Legyen ez egy zajos $\\sin$ függvény!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DYnN-AlasK9x",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "t1 = linspace(0,10,100) # mintavételezés\n",
        "zaj=0.3*randn(len(t1))  # normál eloszlású zaj\n",
        "x1=1.5*sin(t1+2)+zaj     # egy zajos sin függvény\n",
        "hiba=2*abs(zaj)        # ez a \"mérés\" hibája"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w-RF2NdTsK9z",
        "colab_type": "text"
      },
      "source": [
        "Most nézzük is meg!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pz8B0O_zsK91",
        "colab_type": "code",
        "colab": {},
        "outputId": "3f676e55-7a15-4b13-a0b7-676e479de023"
      },
      "source": [
        "errorbar(t1,x1,hiba,marker='o',linestyle='')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Container object of 3 artists>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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hd9nO1doO0zvontK1a6/pe3fgw2LPuh0ZPQYv7Nkn0UXvDrZvj79WNm7cHXu9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\n4zBTAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd141ea5630>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hiYLh-I3sK93",
        "colab_type": "text"
      },
      "source": [
        "A függvényillesztéshez a `curve_fit` függvényt fogjuk használni, ennek az első bemenete az a függvény, amelyet illeszteni szeretnénk. Definiáljuk tehát az illesztendő függvényt! Legyen ez $$f(t)=A\\sin(\\omega t+\\varphi)$$ alakú!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2Es3QtHFsK94",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def fun(t,A,omega,phi):\n",
        "    return A*sin(omega*t+phi)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MDQjZpA0sK96",
        "colab_type": "text"
      },
      "source": [
        "A `curve_fit` függvény az illesztendő függvény első változóját tekinti futó változónak, és a függvény többi paraméterét pedig meghatározandó paraméternek. Alapvetően két tömbbel tér vissza. Az első tömb tartalmazza a meghatározott illesztési paramétereket, a másik pedig az úgy nevezett kovarianciamátrixot. A kovarianciamátrix diagonális elemei határozzák meg az illesztett paraméterek pontosságát."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zsyiEi-VsK97",
        "colab_type": "code",
        "colab": {},
        "outputId": "08ed5b08-b3f9-4597-bcd3-0161ffc11dc4"
      },
      "source": [
        "popt,pcov=curve_fit(fun,t1,x1) # az illesztés elvégzése\n",
        "perr = sqrt(diag(pcov))      # az illesztési paraméterek hibáinak meghatározása\n",
        "print (['A','omega','phi'])\n",
        "print (popt)\n",
        "print (perr)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['A', 'omega', 'phi']\n",
            "[ 1.53582722  1.00691135  1.97696955]\n",
            "[ 0.03986391  0.00910056  0.04989062]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ItV8JY6sK99",
        "colab_type": "text"
      },
      "source": [
        "A `popt` array első eleme az $A$ paraméter, a második az $\\omega$, a harmadik pedig a $\\varphi$.\n",
        "Amint látszik, ez egy viszonylag jól sikerült illesztés, a paraméterek illesztési hibái az illesztett paraméterértékekhez képest kicsik! Mivel a mintaadatsort mi generáltuk 'kézzel', ezért ha összevetjük az illesztett értékeket az adatsor generálása során használt $A=1.5,\\,\\omega=1.0,\\,\\varphi=2.0$ értékkekkel, akkor ezen értékekhez is viszonylag közeli számokat kapunk! Az illesztett paraméterek ismeretében már ki tudjuk értékelni az illesztett függvényt. Tegyük ezt meg!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qrj_RrU5sK9-",
        "colab_type": "code",
        "colab": {},
        "outputId": "8dce537e-c8c4-4299-e075-bd641a22da1a"
      },
      "source": [
        "errorbar(t1,x1,hiba,marker='o',linestyle='') # az adatok ábrázolása\n",
        "plot(t1,fun(t1,popt[0],popt[1],popt[2]),color='red',linewidth=3) # az illesztett függvény ábrázolása"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd1400ef9e8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GZ4GgM0B+r4SUCOl+Xsncq8g6HXxwPQ89dCfr11cAc4Bp7M12ljGYfVkLwD84\ng3N4HNgaFQo7Xh0K6VkmQ074sbv9kesau4gczpsiRUVhrfG227ytWA6Q7L1xawN1s7ZmzDqNHRs6\n4RvaSje+jOHxkr9rl+YSXtwr+3MOeyedwrO2h3YuZ8Y0panG7kyueMUUDP/hCLjyynDUuunTYeRI\nOOigpPIrJL9da52NcY77sXp1I3YvFYD2rFnT6Hg/zuIxmD8/lPpCRvFVIBJnGI24mUvYn3PYw+l5\nTuVvnM+vuAeAu1lEp9m3w/77Z6mmzZRE3wTJ/sgDjR3Ev3TewQeHtY6I5fQyXSev8aIe8fJwq7GH\n8lizRtYRXuZOxo0TSHAWsUfX1VzwXmO3R0jtwJfyefGe4Wd6/PEiu3erxu4SHTx1ICXBLiKydKls\no3WoYT7Y65iUPS5ypbGmW7C7dUEEEWlsFDnllLAA6NlTZMMGgcJbuzSX8OJeRT/n5dKhwyiBK6Ss\nrFxWP/oPEWPCz/a221Swu0QFuwMpC3YRuZRrQ41yF0VyJC+n5COdK4013YJdxJ1XDIjI3Xdb1XpZ\nM//huMJchYE3eHWvnF6+wfGYxUeHZw/vbNFafsh/XdWhuT5Lp36TjGBXrxiH84qMj5ep5jgWA1BD\nX4bxOqPL5saNQ+J1nbzGi3okEo7XaUHpX5d+zMdtDw2Fft04cRI/+vfecRcVV08Kb/D6XjlGRd2x\nA4YPhw8/BOB9hnFIw3+gVSt9lhHE8ybr168PomueeiPYjfHRk1/yEUPZi40APMB4bj+kD++9l/ha\nqMnWyesB2EwLdqcO/17rIziU9wFYymBuOXcM8x69ilhB3ILB4+Jdf3MUBsmSMcEO8N//wo9+BA2B\nxTiuuAJuukkFewROQfHKyuZQWVmesGBv9l4xVsEZXCfTTxFf0Jlf8xceDYS+mcCDvFFzGKWl/lgn\nicb+Tga33iiJELzGrHnqzJgREuq0akXZjko6r32cWN400Gh5JkreMWgQzJ4Nl13m37/5ZjjxROCE\nrFYr14jnTZYMzV6wOwm0ioqJ9O/v4++rKjiFcYznIQBu3PgpB1f/k2q65G1go6Cg9OpFEY/gYhrQ\nyNixRdx8ykD2vfnmcIIbb2TpZUMp6/EkboK4KcnhpMBk5IU+ZQq88AK8+KJ/f/x4OvMR1dVdoiY9\nVVXNI9hWMqE45QrxguIlg5pi4uRRU+MXShs+38bdb95Jr11bAVjMTziOReymocnY317Xycs8IvNz\na/Zxb4rohI2rAAAbFklEQVSpp3//sN2wM/UsazGY7rs3+xOMHAkvvIBpUWRbvjBoY+zUyceAAZM5\n+eTeMevhdF1KZok3lhJ6XmvX8vW+Q+nKNwD8i9GMaXzKfzLRbcXNjOVCwmsbu3rFuMxj/IBJspMW\noVH+8sBsu0MOcRf7OxPeKInmkaxngtt6gNXXuVGe4dTQ/fuaLiKrV9vySyWgV3P1pMgF3HpJnczP\nbV5QctddljwSn7Gcj8Sbwa1eMU2W5b12fMIJFRz5yi5mcT0AjRhO4BcsblHEQQf1p7R0Imec0Tsp\njdJrTTkebtd19WJwyxgf4B9ovoTbuI3LQv87hed4Xk6JmV8y16kae/aId+8jNdHb+A2X8Gf/P1u3\nhiVLYNgwW1uxUlrqY9GixJ0V8gGn+2YMVFWFZUJFRRYWs3ZdUJ4L9traek464Xb+UvNuyAXyS7px\nMB/xDe3dBbpK0JMk2Tzc5p9+we5fuu5QPuZNjqQVOwF47odHctqKNxzroYI9v0hkCcTWbGcJwxnG\nUn+CAQPgnXcwHW8lmWUOreRbCI94gt3eHzQImIikz+xRU1Mnvz1zqnxjWoW+F1/gRDHsbvKz0b35\nIrn/uSWzppg6Gdbnt7KSfqH79WHrblLz8adx65HMdaopJnvEu/exlkAcwCfyPeE+JOecI1Dr6aIp\n+dAenOoY3R8SN8Woy0EC9O3bmz89PoebhpwdOnYSL3E1fyAV16TCpRevDVzJAdQAsK24FZ1e+Ad9\nDxyQ5XopmSLs7RFmJT24gFHhA3//OxfwIgsXTqasbA7go6xsTrMZOE0Hzd7dMRnWDBnIDR9N5Sr+\nCMB1zOQthtI1hmtSpLtfply4nD5LM1nWNObQ/qWXQunaPjyfXb17M3ZsBdDI0KFFlJZOZMSI3jb3\nO6VwmDVrIkuW+KK8PR5d9UceuaAzzJ0LwO1cQpvvXmf+fB+VlbZgn82bRYuSOy9RFT/ZHwVgigny\n8MN10mWvy6SKY0Kfk+tMG3nq9tds6eIFxHIaHU+HKcbJ7JFoWa5jwIiIVFfLLsKx7W/h0sQChCVI\nPnx6FypuvWKiYgBt3SoydGjYJNOrl8g3/lWXUl3/NB/aQ5OmmKefFoGkTDEq2JPMo6amTn5z5lT5\nplWHUMNcscd+MvHca0KCKuEQtk2Um03BnpBQXr1apFu30EXX9zxKjvvJDhkyJPH7kcw1KpklmfGj\n4Pbnr1TJ5pbhSKpbjzpaWrAz5bVs86E9xBXsK1aI7LGHCnYrmRDsQV7yPSY7LJrp35ggbVpfLmee\nWScdO0YPHIF9Ud/IsnJVsLt9SbVmm8jw4eFE++wj8r//iUjsgbSm7kcy16hklmQFe1BZOJV/2hrE\nDZSlPJCaD+3BqY4dWS8ycGDofiQj2HXwNILa2vqADdjH2LEV1NbWx03/wGfLuJwbQ/vn8wAXNHSj\nbdt5bNwYPXCUyjThbOIqloUIc7kA3noLgF20gEcfhR49gNgDafl6P5TUmTFjHqtWVfAcZ1OOL3R8\nOpUcumoo4fbWnlWrKgJjVe4pL/f/SkrC2+kOoZEyu3dTSRl8+ql/v23b5PJJ9E2Q7I880Njdmhus\n+LXQRnmQ8JqduyiS3w39hTitBBTPppzXGvvNN9s0r4u5w5ZHMmMObu2q+aChFRLJPK/Itmf9gjPs\nts1M3kobOYz/xP2yi0e8dp5qW0uVuGamq6+2f84++mjmTTHA2cAyYDdwaBNp03Sbokm2qGQWYg6e\n05pt8iaHh07c0rK1/IDliQ04NlH3nLaxP/ecfcWc888XaIzKN1XbqZVsd1AlMSLbXmR/68h6+ZgB\noTb0Jd2kJ/Wu+mFTZblJlwni9qN58+xC/corA3XMvGA/EBgALCoEwe7WBmzl4YfrpFMn/4Pqxpfy\nOT1CJ66kv8jXXzdZp3wQ7CJxhPK774q0bx++YcccI9LQkFMdSsk+TjZ2q5A7rtd5so7weqkfMFQ6\n8KX07PkrGT16mgwbNlOGDCmXKVPq4r7Mc1WwOymPfzh+vEhxcfjgySeL7NoVqGOGBXsoE6gqBMGe\njMYuEhZ4paUz5eqTL5TdbduGMxg+XGTz5qwL9mTWEHXlkllba/OAqaOXyFdfpe1alPwlVjuP1S6P\npVoaW7YMtanX9+oje+/xW9sLwK9M1SVUVlPpMkG08lgng7hINhK+3g8YKrJxo6WOKthFgleVBMnY\n2GPyxBN2s8TJJ0sxO+LWN1GTTSI42frddozIffAL+NlXrJP6tgeGrnNHh710XUvFkXjtPEoQ33ef\nVfrJg5wbCN3hb89wrcC4qL6SC4ugxzMR2pXHOtmXC6WOnqHr/LJFB+nBmxHXkgbBDiwEPrL8lgb+\njrKkcSXYfT5f6FeVRkNoKg/LMxvwXXfZGub9TBBpjLY5++sb/4WSuk9v5JeIc8cIn+O8DyK1y5bL\nJ13CDbKxVSuRxYtzVlNSsk+8dh5LcXj1J9fY+tAtXCpQKxA7DyfFLBEFxvtrtu9b69iZK2QZPwhd\n3/d0kIN5Q2CCTJlyiXTqdKTAVc1bY/d6IM2Ll8Msy8xUAZHLLosp3J1iUQ8ZUi7Dh4dt+Ml+RYD1\n868uqmN06jQ1ymYZT7C34WN5vW0v27Vd3O20mB3UuU6uq68UCPFirgeFua3/zmyU1addYGtnV3Gc\nY1/p2jV2/lAep07u65+qJ1CQmpo6+dX/XSnvsneoojsolpNYENidGaHZJy7YvYwVk1hYSY/JldCc\n9vjTM9mXifySB/3/vPVWNm7azG+37sfqNRJaNxVi+4h36dIYWCqsgmifXns403ghS/3LywWX3YrO\nb/36Cr79dg6vvuqzxIB2uMDt23mSUzlq2+ehQ5dwG3/66kSePe5yYHAoJg70jn+zlILH2i47dmxk\n40bnuRDRa9sa2H03nx/1Bb3eWgDAH1hEA3/hFqba8ujSpZGlS/3bkflDoyexk5zWH66udl5HOBZ9\nu3Zh7up/A98BsJsixjKfF/kpweUgY88bSYBE3wTWH3A68AWwDfgSWBAnrftXYw6QbHUjB2BbsFMe\nY7RN67iJSwQaLZ+K0+JoMol76kRr29ZPVOf84mnbICINDSKjRtlOvJIbYn4FZPsTWMk94jknxG0P\n27fL1qOOjtHuIvNwZ3J0+1UZD6fzYvUbq5b/++nfS23vEbZrmcTdUf0mVY09JcGeUEF51pOTrW4s\nl8lidsjjFluaX7hPCwl3uDSO7TFxT51g3a22+TFjLpXRo6cJnOGqc0Vefzs2i5x0ku0aZlIe2Ezv\nJ7BSGMRzTmiyPWzaJHLssbb2dy3XReRhzb9O4LImy8qEYA+yN+tEDjvMdg3rZvpCHnXWwV77vVLB\n7hleaezBRtWSa2VxlwOtB2Ue46WYHQIz43gLJO6pE90wrNrAa1HHgz7Cjp4E69bZJl8JyN17DRfY\nFNi9JuplFrQVen1/lfzGjVeMI5s3i5SW2hrZ0wcdLTWf1YTyCOefnALjloQF+5o1spRBtrpP46a4\neaTVK8arX3MR7PFG5k8qvVae4DTbw32B46UDV0WVG1vbducVA84vGCiPyrtXrykx6ysiIl98IfLD\nH9rq7MMnUybXypAh5dKx40z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MB14WkQOBRcBVTWWSbo19OLBSROpFZCfwKDAmzWXmJCKy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\n1gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd1400f9550>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_i8W2AQYsK-A",
        "colab_type": "text"
      },
      "source": [
        "A `curve_fit` parancs segítségével figyelembe tudjuk venni az eredeti adatoknak a mérési hibáit (amit a `hiba` válltozóban tároltunk el )! Ez azt jelenti, hogy az illesztés során azok a pontok, amelyek nagy mérési hibával rendelkeznek, kisebb súlyal vannak figyelembe véve, mint azok a pontok, ahol a mérési hiba kicsi. \n",
        "A mérési hibák figyelembe vétele a `sigma` kulcsszóval történik meg. Nézzük meg, mi történik, ha megadjuk a hibákat!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1n-c6GnGsK-B",
        "colab_type": "code",
        "colab": {},
        "outputId": "db43c6f1-4989-4106-8aa5-8978c510a8ad"
      },
      "source": [
        "popt_hibaval,pcov_hibaval=curve_fit(fun,t1,x1,sigma=hiba)\n",
        "perr_hibaval = sqrt(diag(pcov_hibaval))\n",
        "print (['A','omega','phi'])\n",
        "print (popt_hibaval)\n",
        "print (perr_hibaval)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['A', 'omega', 'phi']\n",
            "[ 1.48184745  0.99871729  2.0061375 ]\n",
            "[ 0.01214574  0.00169755  0.00561813]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mf7SnqTIsK-D",
        "colab_type": "text"
      },
      "source": [
        "Ha összehasonlítjuk a hibák figyelembevételével történt illesztést és a hiba nélküli illesztést, azt tapasztaljuk, hogy az illesztett paraméterek kicsit megválltoztak, **de** illesztési hiba jóval kisebb! Hasonlítsuk össze a két illesztési módszerrel kapott paraméterezést! Az alábbi példában az előzőhöz képest egy kicsit kompaktabb írásmódot alkamazunk a paramétervektor [kicsomagolásával](http://django.arek.uni-obuda.hu/python3-doc/html/tutorial/controlflow.html#argumentumlista-kicsomagolasa)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sP-ufgN-sK-E",
        "colab_type": "code",
        "colab": {},
        "outputId": "ce10c879-c3bf-4458-8403-42c7356c8fd7"
      },
      "source": [
        "errorbar(t1,x1,hiba,marker='o',label='adatok',linestyle='') \n",
        "plot(t1,fun(t1,*popt),color='red',label='illesztes',linewidth=4)  # itt használtuk az argumentumok kicsomagolását                  \n",
        "plot(t1,fun(t1,*popt_hibaval),color='black',label='illesztes hibaval',linewidth=3)  # itt is.\n",
        "legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fd1339efeb8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BijJERO655x7Jy8uT5s2bS48ePeTVV18VEZGqqiqZMmWKtGrVSvLy8uTBBx/0WFVp3rx5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\nAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd1400a0d30>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WZxJOHNfsK-G",
        "colab_type": "text"
      },
      "source": [
        "Az illesztési allgoritmusok, amik a `curve_fit` parancs mélyén elvégzik az illesztési feladatokat, nem mindig találják meg a megfelelő paramétereket. Ha egy illeszési feladatban sok meghatározandó paraméter van, akkor ez a probléma sokkal súlyosabb lehet. Vizsgáljunk meg erre egy másik adatsort. A  `data/ket_gauss_plus_hiba` file egy zajos adatsort tartalmaz, ami két Gauss-görbe összege. Próbáljunk meg erre illeszteni egy olyan függvényt, ami két Gauss-görbe összege! Először olvassuk be a file-t és jelenítsük meg!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZO6nUbAssK-G",
        "colab_type": "code",
        "colab": {},
        "outputId": "d8578cb4-f6a7-40e2-8567-cf80e146960f"
      },
      "source": [
        "t2,x2=loadtxt('data/ket_gauss_plus_hiba',unpack=True) # beolvasas\n",
        "plot(t2,x2)                        # megjelenites"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd133966a90>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jl24S+LOf+U3sK5eKs1HWjdjBk/p993mZ5swz4eCDfXVpXbz0ko/yjzoqjWBF\nJFYDB8Kuu3pptbgYfvtbL8V27uzrVQ49FC6/3NucG0Pl0XqpJ57w+x+/+abvg9MYPv/c27qnTPGv\nl1+OqRRjZv2AwfgngBEhhL9U8Zo6J/b166FNG//Ic9RR8OGHvghJRPLD8uXQtavfnnLoUC/RPP20\nf6L/6isYPRquuspvUL/11tFf//bbfa5v1KiKx4uLfR1NQQEcf3w015o40X+BLVzoX+Dzjj17+tex\nx8aQ2M2sCfAe0BdYDEwDzgghzK/0unptKfDzn8P48T5rPmJEWiGKSA4aORJOOcX3kxk+HL7znYrP\nH3ecd9ZdcEG015061c/9xhs+31fZI4946/WECdFcr29f34W2f3/fGmW77SrufBnL5KmZ9QRuCiEc\nU/L9dUCoPGqvb2KfPNkXGE2b5r8hRST/lP77r2qL33HjfORcn8VDU6fCZ595W3Xbtt5sUb6ksmyZ\nX2/IEBgwoOpzbNgAe+zhib1z53r972xmxQpo377iPleVxTV52hb4pNz3i0qOpaVnTy/FKKmL5K+D\nDqp+3/ajj/ZEXLrQsTZPP+3lkwce8InQbt18r6nhwz1Zb9rke1CdfXb1SR38TlCXXOLJP13PPedr\nbqpL6g2V0d6RgoKC/z1OpVKkauhfNPM/OBGRqjRt6gl62DBft1KT0aM9GY8f76vcS02Z4qtfb73V\nE33TpvCHP9R+7Ysvho4d4ZZbytbgNMTo0ZuvpC8qKqKo/I6GDRBVKaYghNCv5PtISjEiIrVZssQT\n7EcfQatWfuzVV2HGDL9LU8eO8M47cNFFXrr54Q+rPs9rr3nd/C9/8Qnaujj7bF+sdM01tb923Trv\ndil/m85vvvEdLj/4oOZrxlVjbwoswCdPPwPeBM4MIcyr9DoldhGJ3Gmn+TqXn/7U78Hw+ONeclmw\nwPeOWr/ey7rdu0d73WnT4NRTvbe9pnUzCxb43aOWLIH588s6/J591rtvXnml5uvEtvK0pN3xHsra\nHW+t4jVK7CISuYkTvSTTvLkv+7///ooj4OLixus579ULrr7au3eq8vDD/vzNN/tcQLNmvkYH/FNE\np07wy1/WfI1EbCkgIlIfIfhk54kn+j2QM3mT7Jde8kWUf/iDt2iXXvvDD2HQIHj3XV/U1LUrfPml\nJ/LRo70k1KaNd/9Vt7FhKSV2EZEMW7DA6+2tW/sk7AMP+NYHV17p9ffyC6geeQTuuss3F7v8cpg5\ns/bzJ2JSixFEAAAEeklEQVSvGBGRXNKhA0ya5Fuf9O7to/Z587zbpvKq2J/8xGvs555bc0tlujRi\nFxHJoAULvDRTeoOh2qgUIyKSA5Yt850s60KJXUQkYVRjFxERJXYRkaRRYhcRSRgldhGRhFFiFxFJ\nGCV2EZGEUWIXEUkYJXYRkYRRYhcRSRgldhGRhFFiFxFJGCV2EZGEUWIXEUkYJXYRkYRRYhcRSRgl\ndhGRhFFiFxFJmLQSu5ndZmbzzOwdMxtpZi2jCkxERBom3RH7i0DnEEI34H1gUPohJV9RUVHcIWQN\n/SzK6GdRRj+L9KSV2EMIE0IIxSXfTgHapR9S8ukvbRn9LMroZ1FGP4v0RFljvwAYH+H5RESkAZrV\n9gIzewnYufwhIAA3hBDGlrzmBmBjCOGxRolSRETqzEII6Z3A7DzgIuCIEML6Gl6X3oVERPJUCMHq\n8/paR+w1MbN+wLXAYTUl9YYEJiIiDZPWiN3M3ge2BL4oOTQlhHBpFIGJiEjDpF2KERGR7NLoK0/N\nrJ+ZzTez98zsN419vWxlZu3MrNDM5pjZLDO7Mu6Y4mZmTcxsupmNiTuWOJlZKzN7smSx3xwz6xF3\nTHExs1+a2Wwzm2lmj5rZlnHHlElmNsLMlprZzHLHtjezF81sgZm9YGatajtPoyZ2M2sC/BU4GugM\nnGlm+zbmNbPYJuDqEEJn4GDgsjz+WZS6CpgbdxBZ4B5gXAihI7AfMC/meGJhZm2AK4ADQghd8TnA\nM+KNKuMexPNledcBE0IIHYBC6rAQtLFH7N2B90MIH4cQNgL/AgY08jWzUghhSQjhnZLHa/B/vG3j\njSo+ZtYO6A/8X9yxxKlkG47eIYQHAUIIm0IIq2MOK05Nga3NrBnQAlgcczwZFUJ4Hfiy0uEBwEMl\njx8CTqjtPI2d2NsCn5T7fhF5nMxKmVl7oBswNd5IYnU33lGV75M83wOWm9mDJWWp4WbWPO6g4hBC\nWAzcCSwEPgVWhhAmxBtVVtgphLAUfIAI7FTbG7S7Y4aZ2TbAU8BVJSP3vGNmxwJLSz7BWMlXvmoG\nHADcF0I4AFiLf/TOO2a2HT463QNoA2xjZgPjjSor1ToYauzE/imwe7nv25Ucy0slHy+fAh4OIYyO\nO54YHQIcb2b/BR4H+pjZP2OOKS6LgE9CCG+VfP8Unujz0ZHAf0MIK0II3wKjgF4xx5QNlprZzgBm\ntguwrLY3NHZinwbsZWZ7lMxunwHkcwfEA8DcEMI9cQcSpxDC9SGE3UMIe+J/JwpDCOfEHVccSj5i\nf2Jm+5Qc6kv+TigvBHqa2VZmZvjPIh8nkit/ih0DnFfy+Fyg1kFhWitPaxNC+NbMLse3920CjAgh\n5OMfFGZ2CPATYJaZzcA/Tl0fQng+3sgkC1wJPGpmWwD/Bc6POZ5YhBDeNLOngBnAxpL/Do83qswy\ns8eAFLCDmS0EbgJuBZ40swuAj4HTaj2PFiiJiCSLJk9FRBJGiV1EJGGU2EVEEkaJXUQkYZTYRUQS\nRoldRCRhlNhFRBJGiV1EJGH+H/cI5EbfzhXcAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd13399a550>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q_PHaty1sK-I",
        "colab_type": "text"
      },
      "source": [
        "Az alábbiakban definiáljuk az illesztendő függvényt!\n",
        "$$f_2(t)=A_1\\mathrm{e}^{-(t-e_1)^2/s_1^2}+A_2\\mathrm{e}^{-(t-e_2)^2/s_2^2}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pOcRnFblsK-J",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def func2(t,A1,e1,s1,A2,e2,s2):\n",
        "    'Ket Gauss-gorbe osszege'\n",
        "    return A1*exp(-((t-e1)/s1)**2)+A2*exp(-((t-e2)/s2)**2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KgbDWMlLsK-L",
        "colab_type": "text"
      },
      "source": [
        "Próbáljuk ezzel elvégezni az illesztést!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0JbvUgVHsK-M",
        "colab_type": "code",
        "colab": {},
        "outputId": "218f78d4-2f1b-4c6e-f024-18aacbe98a4e"
      },
      "source": [
        "popt,pcov=curve_fit(func2,t2,x2)\n",
        "perr = sqrt(diag(pcov))\n",
        "print (['A1','e1','s1','A2','e2','s2'])\n",
        "print (popt)\n",
        "print (perr)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "error",
          "ename": "RuntimeError",
          "evalue": "Optimal parameters not found: Number of calls to function has reached maxfev = 1400.",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[1;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
            "\u001b[1;32m<ipython-input-11-704f7492e125>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mpopt\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mpcov\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mcurve_fit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mt2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mperr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdiag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpcov\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'A1'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'e1'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m's1'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'A2'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'e2'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m's2'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mpopt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mperr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
            "\u001b[1;32m/opt/conda/lib/python3.5/site-packages/scipy/optimize/minpack.py\u001b[0m in \u001b[0;36mcurve_fit\u001b[1;34m(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, **kwargs)\u001b[0m\n\u001b[0;32m    653\u001b[0m         \u001b[0mcost\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minfodict\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'fvec'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m**\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    654\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mier\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32min\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 655\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Optimal parameters not found: \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0merrmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    656\u001b[0m     \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    657\u001b[0m         res = least_squares(func, p0, args=args, bounds=bounds, method=method,\n",
            "\u001b[1;31mRuntimeError\u001b[0m: Optimal parameters not found: Number of calls to function has reached maxfev = 1400."
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5LAmMXm8sK-O",
        "colab_type": "text"
      },
      "source": [
        "Úgy tűnik, az illesztés nem sikerült! Ez az adatsor és a meghatározandó függvény tehát jól illusztrálja a fent említett problémát!\n",
        "\n",
        "Az illesztés nagyobb valószínűséggel sikeres lehet, ha a megillesztendő paramétereket az illesztés előtt valamilyen módon meg tudjuk becsülni. A fenti adatsorban például van egy nagy csúcs 6 körül, aminek a szélessége nagyjából 1, és magassága 10, továbbá egy viszonylag széles váll a csúcstól balra, ami egy szélesebb és laposabb csúcsból származhat, mondjuk 4 körül egy 4 magasségú és 3 szélességű csúcsból. Ábrázoljuk az eredeti függvényt, és ezt a két becsült függvényt!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aO85TgLisK-P",
        "colab_type": "code",
        "colab": {},
        "outputId": "4760d6b2-22e0-43f1-f1cb-70d64ebdff0c"
      },
      "source": [
        "plot(t2,x2,label='adatok') # az adatok\n",
        "plot(t2,10*exp(-((t2-6)/1)**2),label='egyik csucs') # a magasabb és vékonyabb csúcs\n",
        "plot(t2,4*exp(-((t2-4)/3)**2),label='masik csucs')  # a szélesebb de alacsonyabb csúcs\n",
        "legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fd133907e48>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3d9WJSgWEJnbl8bZsSXuoY0Z2ndxF0UJFqVm6plNjymt9+8K50K7M36GJvSDQ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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd1400e1fd0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "enDsPdDpsK-R",
        "colab_type": "text"
      },
      "source": [
        "A `curve_fit` függvénynek megadhatjuk ezeket a becsült értékeket mint az illesztési procedúra kezdő értékeit. Ezt a `p0` kulcsszón kerresztül tehetjük meg."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rYfjnWmUsK-S",
        "colab_type": "code",
        "colab": {},
        "outputId": "dd0693f2-ee49-43bf-fce4-81ed0682f783"
      },
      "source": [
        "A1=10;e1=6;s1=1\n",
        "A2=4;e2=4;s2=3\n",
        "popt,pcov=curve_fit(func2,t2,x2,p0=[A1,e1,s1,A2,e2,s2]) # A p0-ba egyszeruen felsoroljuk a becsult ertekeket\n",
        "perr = sqrt(diag(pcov))\n",
        "print (['A1','e1','s1','A2','e2','s2'])\n",
        "print (popt)\n",
        "print (perr)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['A1', 'e1', 's1', 'A2', 'e2', 's2']\n",
            "[ 8.21260636  5.99414772  1.0291653   3.83303602  3.88151827  2.48802627]\n",
            "[ 0.32159323  0.0130322   0.03320234  0.11389945  0.13779395  0.12601698]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c3rOlMyCsK-U",
        "colab_type": "text"
      },
      "source": [
        "A becslés tehát segített az illesztés elvégzésében! Ábrázoljuk végül az illesztett függvényt, az eredeti adatokat, illetve az eredetileg  becsült görbéket!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jZz6fjiNsK-V",
        "colab_type": "code",
        "colab": {},
        "outputId": "0bd1422f-3ef5-499a-97b1-b98e8d819973"
      },
      "source": [
        "plot(t2,x2,label='adatok') # a beolvasott adatok\n",
        "plot(t2,10*exp(-((t2-6)/1)**2),label='egyik csucs') # a két becsült Gauss\n",
        "plot(t2,4*exp(-((t2-4)/3)**2),label='masik csucs')\n",
        "plot(t2,func2(t2,*popt),label='illesztes',color='black',linewidth=2) # az illesztéssel meghatározott gorbe\n",
        "legend(loc='upper left')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fd1338898d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Le7gdT09PAgIC2LBhQ4Yx3C+5l5aWxpw5c+jXrx8REREmOsLi6cyZM5w5sxNb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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd1338df240>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NJqgSO6asK-X",
        "colab_type": "text"
      },
      "source": [
        "A korábbi feladatok között már szerepelt Felix Baumgartner ugrásának adatsora. Most újra vizsgáljunk meg ehhez kapcsolódóan egy életszerű illesztési problémát! \n",
        "\n",
        "Az ugrás első fázisában ($t=0\\dots 40$ s) a mozgás jó közelítéssel szabadeséssel írható le: mielőtt az ejtőernyő kinyílna, a légellenállás kiegyensúlyozza a gravitációs erőt, és az esés sebessége közelítőleg állandó (kb $t=210\\dots 260$ s  intervallumban).\n",
        "\n",
        "Határozzuk meg a nehézségi gyorsulás értékét a pálya elején szereplő pontokból, illetve határozzuk meg\n",
        "Felix Baumgartner légellenállását a pálya végén szereplő pontokból!\n",
        "Kezdjük a feladatot a felhasznált fizikai jelenségek [összefoglalásával](http://www.livescience.com/23710-physics-supersonic-skydive.html)!\n",
        "\n",
        "**Szabadesés az ugrás elején**\n",
        "\n",
        "Mivel a szabadesés egyenletesen gyorsuló mozgásnak felel meg, ezért a magasság--idő függvényt a $$h(t)=h_0+v_0t-\\frac{g}{2}t^2,$$ alakban kereshetjük! A nehézségi gyorsulás tehát meghatározható a pálya elejére illesztett parabola együtthatóiból hiszen a négyzetes tag együtthatójának a kétszerese épen $g$!\n",
        "\n",
        "**Egyenletes sebesség az ugrás végén**\n",
        "\n",
        "Mivel nincs gyorsulás, ezért ezen a ponton a közegellenállás és a gravitációs erő kiegyenlítik egymást!\n",
        "Azaz $$mg=\\alpha v^2 $$, amiből a közegellenállás  $\\alpha=\\frac{mg}{v^2}$. \n",
        "Baumgartner [súlya](http://www.livescience.com/23710-physics-supersonic-skydive.html) a szkafanderrel együtt kb 110 kg. Az illesztésből pedig meg tudjuk határozni $v$-t."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ziu4vhRGsK-X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tB,h=loadtxt('data/h_vs_t',unpack=True) # adatok beolvasása\n",
        "# ido az elso oszlop\n",
        "# magassag a masodik"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QLFf3KKSsK-a",
        "colab_type": "text"
      },
      "source": [
        "Definiáljuk most az illesztendő függvényeket. Egy lineáris függvényt és egy másodfokú polinomot!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qlbaRyGDsK-c",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def linearis(x,a,b):\n",
        "    'Linearis fuggveny: a*x+b'\n",
        "    return a*x+b\n",
        "\n",
        "def masodfok(x,a,b,c):\n",
        "    'Masodfoku fuggveny: a*x^2+b*x+c '\n",
        "    return a*x**2+b*x+c"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "coSuuNxlsK-f",
        "colab_type": "text"
      },
      "source": [
        "Először illeszünk egy másodfokú polinomot az adatsor elejére. Az adatsor megfelelő részét az array-ek már ismert szeletelésével tudjuk megoldani. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q5FhDXg9sK-f",
        "colab_type": "code",
        "colab": {},
        "outputId": "9903fd9a-6d41-4ba2-dea7-3ef20242ff6b"
      },
      "source": [
        "p_eleje,pcov =curve_fit(masodfok,tB[tB<40],h[tB<40]) # illesztes azon pontokra ahol az ido kissebb mint 40\n",
        "err_eleje = sqrt(diag(pcov))\n",
        "# az illesztett parameterek ertekei es a hibak\n",
        "print('a=',p_eleje[0],'±',err_eleje[0]) \n",
        "print('b=',p_eleje[1],'±',err_eleje[1])\n",
        "print('c=',p_eleje[2],'±',err_eleje[2])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "a= -4.74047528359 ± 0.0285659683743\n",
            "b= 45.2385570965 ± 1.16034897662\n",
            "c= 38893.934827 ± 9.87019931891\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iL8APPi-sK-h",
        "colab_type": "text"
      },
      "source": [
        "A gravitációs gyorsulás tehát az illesztett $a$ paraméter kétszerese!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bTzvpv3wsK-h",
        "colab_type": "code",
        "colab": {},
        "outputId": "fbc53111-7680-472a-c47a-d090426de78b"
      },
      "source": [
        "g=abs(p_eleje[0]*2)\n",
        "g"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9.4809505671794199"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cNP9VFwRsK-j",
        "colab_type": "text"
      },
      "source": [
        "Végezzük el az illesztést most a lineáris szakaszra is! Most is célszerű a már megismert indexelési trükkökkel megszorítani az illesztendő ttartományt. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XV4tmqPCsK-k",
        "colab_type": "code",
        "colab": {},
        "outputId": "8905a101-33d0-4181-d81e-50c1e92f28ac"
      },
      "source": [
        "p_vege,pcov =curve_fit(linearis,tB[(tB>210)*(tB<260)],h[(tB>210)*(tB<260)]) # illesztes azon pontokra ahol az ido 210 es 260 kozott van\n",
        "err_vege = sqrt(diag(pcov))\n",
        "# az illesztett parameterek ertekei es a hibak\n",
        "print('a=',p_vege[0],'±',err_vege[0]) \n",
        "print('b=',p_vege[1],'±',err_vege[1])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "a= -60.1648024714 ± 0.145934354195\n",
            "b= 18299.0046872 ± 34.3553394487\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aDxoyXGIsK-l",
        "colab_type": "text"
      },
      "source": [
        "A keresett sebességérték tehát ismét az első illesztett paraméter értékéből határozható meg. Míg $\\alpha $ az $\\alpha=mg/v^2$ kifejezésből adódik:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0KZvPRDasK-m",
        "colab_type": "code",
        "colab": {},
        "outputId": "09b1a77e-6c53-4f37-a27a-d0fae265bb4a"
      },
      "source": [
        "v=p_vege[0]\n",
        "m=110\n",
        "alpha= m*g/v**2\n",
        "alpha"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.28811082561386603"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hQkH6yXGsK-n",
        "colab_type": "text"
      },
      "source": [
        "Foglaljuk össze eredményeinket egy ábrában!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mZcTX94_sK-o",
        "colab_type": "code",
        "colab": {},
        "outputId": "e247e84b-4f2f-4b90-c310-787e90f5104f"
      },
      "source": [
        "figsize(8,4*3/2)\n",
        "plot(tB,h,label='meres',linewidth=7,color='lightgreen')\n",
        "plot(tB,masodfok(tB,*p_eleje),label='parabola az elejen',linewidth=3,color='red')\n",
        "plot(tB,linearis(tB,*p_vege),label='linearis a vegen',linestyle='dashed',linewidth=3,color='blue')\n",
        "ylim(0,40000)\n",
        "legend(fontsize=20)\n",
        "xlabel(r'$t[s]$',fontsize=20)\n",
        "ylabel(r'$h[m]$',fontsize=20)\n",
        "text(150,20000,r'$g=$'+str(g)+r' $m/s^2$',fontsize=20)\n",
        "text(150,15000,r'$\\alpha=$'+str(alpha)+r' $kg/m$',fontsize=20)\n",
        "grid()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ChWRmZlK1alUaN27M+PHjadq0KWC8nHbGjBmEhoaaVvqsUKECDRo0YObMmTz99NOFeVuE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3gkryQ8wYtNL7KhcQMHEgcAOPR2BUPf35Dy+HU/nsrJs/YyetrbAFRaZdt0SbFF8cp7kezTmoss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\nISIiImn1/+6iFNUWH1GnAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd133853d68>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_IDkVVYusK-q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "figsize(6,4) #Ez csak vissza állítja az ábraméreteket az alapértelmezettre "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zr3vCXeJsK-r",
        "colab_type": "text"
      },
      "source": [
        "## Periodikus jelek vizsgálata és a Fourier-transzformáció\n",
        "![winamp](http://winampheritage.com/plugin/222660/EZ_Spectrum_Analyzer.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GVTgAWy9sK-s",
        "colab_type": "text"
      },
      "source": [
        "Számtalan fizikai rendszerben előfordul az, hogy bizonyos jelenségek periodikus viselkedést mutatnak. A hétköznapból talán a legismertebb példa erre a zene. Sok zenelejátszó (amint azt a fenti ábra is bizonyítja) rendelkezik \"spektrumanalizátorral\". Ezek a spektrumanalizátorok azt mutatják, hogy egy bizonyos hang minta milyen frekveniájú hangokat tartalmaz. A módszer, ami egy adott hangmintából a frekvenciaspektrumot előállítja, a [Fourier-transzformáció](https://hu.wikipedia.org/wiki/Fourier-transzform%C3%A1ci%C3%B3).\n",
        "Egy függvény Fourier-transzformáltját az alábbi matematikai kifejezés definiálja:\n",
        "$$ \\mathcal{F}[f](\\nu)=\\int^{\\infty}_{-\\infty} \\mathrm{e}^{\\mathrm{i 2\\pi\\nu t}}f(t)$$\n",
        "A Fourier-transzformáció elvégzésére létezik egy gyors [allgoritmus](http://itl7.elte.hu/jelfel/node32.htm), ami igen sok alkalmazásban felbukkan. A Python-nyelvben a `numpy.fft` almodulban van implementálva a gyors Fourier transzformáció, az alábbi néhány példában ezzel fogunk megismerkedni. Ezt az almodult már a notebook elején betöltöttük!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iLn8iJvssK-s",
        "colab_type": "text"
      },
      "source": [
        "Először generáljunk egy meghatározott $\\nu$ frekvenciájú, azaz $\\omega=2\\pi\\nu$ körfrekvenciájú jelet! Ezt például a \n",
        "\n",
        "$$f(t)=\\sin(\\omega t)$$ függvény. (Vajon melyik függvény ennek a Fourier-transzformáltja?)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g4peAN_lsK-t",
        "colab_type": "code",
        "colab": {},
        "outputId": "a7c530ba-3f42-4bc6-a523-ea0fb89b440e"
      },
      "source": [
        "t3 = linspace(0,10,1000) # mintavetelezesi pontok\n",
        "nu=2;                   # frekvencia\n",
        "omega=2*pi*nu           # korfrekvencia\n",
        "jel=sin(omega*t3)        # maga a jel\n",
        "plot(t3,jel)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd1325a45f8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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JlxPJr11bi8G5D/eKCi5GLgVfqR/lAMTxI4e0z9KSbWV0NS2H4Ut4RR/Gxy2B+nwMo8ZY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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd132ddfcf8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m-7qHJm_sK-v",
        "colab_type": "text"
      },
      "source": [
        "Maga a Fourier-transzformáció egyszerűen az `fft` függvény meghívásával történik."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "cF9Ur119sK-w",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Fjel=fft(jel)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AVMLWfnUsK-x",
        "colab_type": "text"
      },
      "source": [
        "Most már az `Fjel` változó tartalmazza a jel Fourier-transzformáltját! Ahogy azt a definició is mutatja, a Fourier- transzformált általában egy komplex kifejezés. A legtöbb alkalmazás szempontjából elegendő a Fourier-transzformált abszolút értékének vizsgálata.\n",
        "Ahhoz hogy a Fourier-transzformált jelet ábrázolni tudjuk a frekvencia függvényében, először le kell gyártanunk egy megfelelő frekvencia-mintavételezést. Ennek a mintavételezésnek illenie kell az eredeti idő-mintavételezéshez. A frekvencia-mintavételezést az `fftfreq` függvény végzi el. Ennek két bemenő paramétere van. Az első paraméter az eredeti idősor hossza, a második paraméter pedig az idősor felbontása (lépésköze). "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "0boyBNDGsK-y",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "freq = fftfreq(len(t3),t3[1]-t3[0])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3q43f2cUsK-z",
        "colab_type": "text"
      },
      "source": [
        "Most már meg tudjuk jeleníteni a Fourier-transzformált abszolút értékét!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "schOutWJsK-0",
        "colab_type": "code",
        "colab": {},
        "outputId": "e6baed3c-0d46-4ea9-d3f8-c3a72c3c1ea8"
      },
      "source": [
        "plot(freq,abs(Fjel))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd133560748>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd1338bae10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RljLbOD_sK-1",
        "colab_type": "text"
      },
      "source": [
        "A Fourier-transzformált pozitív és negatív frekvenciaértékekre is definiálva van, azonban időfüggő jelek elemzése során elegendő pozitív frekvenciákra szorítkoznunk. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "co4wc8CLsK-2",
        "colab_type": "code",
        "colab": {},
        "outputId": "36147963-e154-4ab8-dbe0-5d17906fe535"
      },
      "source": [
        "plot(freq,abs(Fjel))\n",
        "xlim(0,10);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Soe/ALRAktWToO3BGL6klQ9+BoZfUkqHvwL1uJLVk6DtwRi+pJUPfgaGX1JKh78C9biS1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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd1337ade10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eejO_5lQsK-3",
        "colab_type": "text"
      },
      "source": [
        "Tehát egy 2 frekvenciával oszcilláló jel Fourier-transzformáltja egy éles csúcs pontosan 2-nél (talán nem túl meglepő módon)!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zGe-3HXZsK-4",
        "colab_type": "text"
      },
      "source": [
        "Vizsgáljuk meg utolsó példaképpen a napfoltadatok számának ingadozását! Vajon látszani fog benne a 11 éves periódusidő ?\n",
        "A napfoltadatok ismét az `data/SN_m_tot_V2.0.txt` file-ban vannak. Olvassuk őket be!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "WiaEIWP2sK-4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "napfolt=loadtxt('data/SN_m_tot_V2.0.txt');"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "HjwX3n4msK-6",
        "colab_type": "text"
      },
      "source": [
        "A harmadik oszlop tartalmazza az időt években, a negyedik oszlop pedig a napfoltok számát tartalmazza. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "collapsed": true,
        "id": "BrsWYtUzsK-7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "tN=napfolt[:,2]\n",
        "N=napfolt[:,3]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8fLVOEzzsK-9",
        "colab_type": "text"
      },
      "source": [
        "Gyártsuk le a frekvencia-mintavételezést, és végezzük el a Fourier-transzformáltat!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6JlfCYWtsK--",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "freqN = fftfreq(len(tN),tN[1]-tN[0])\n",
        "FN=fft(N)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8-8dqXCbsK-_",
        "colab_type": "text"
      },
      "source": [
        "Végül ábrázoljuk a kapott Fourier-spektrumot!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HMDkZLjGsK-_",
        "colab_type": "code",
        "colab": {},
        "outputId": "1f039810-9915-4146-b4bc-ab9c89f2bbf8"
      },
      "source": [
        "plot(freqN,abs(FN)) # A spektrum ábrázolása\n",
        "xlim(0,0.5)\n",
        "ylim(0,80000)\n",
        "# A maximum hely megtalálása\n",
        "maxN=max(abs(FN)[(freqN>0.03)*(freqN<0.2)])\n",
        "maxf=freqN[(abs(FN)==maxN)*(freqN>0)]\n",
        "plot(maxf,maxN,'o',color='red') # Egy kis piros pont a csúcson\n",
        "xlabel(r'$\\nu [1/\\mathrm{ev}]$',fontsize=20)\n",
        "ylabel(r'$\\mathcal{F}(N_{\\mathrm{Napfolt}})$',fontsize=20)\n",
        "text(0.3,60000,'T='+str(1/maxf[0])+' ev',fontsize=20)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.text.Text at 0x7fd1335118d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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j4FO/9uu9snxgnV/5Oq/c12at19dBEdkuInVUtcjKt0wSKLOgjLLEJ598wn//+9+A+Znl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\ncA9eX3LXZFhQp54Kn33m3pc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zZkV/rVjZsUP1xhtVGzRQPfJI1Vat3P2Ihby8wuz/U6e6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\nyc4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd1334d7b00>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "1CV4fC1TsK_C",
        "colab_type": "text"
      },
      "source": [
        "Tehát a Fourier-transzformált egy éles maximumot mutat 10.8 évnél! Azaz a megfigyelések Fourier-transzformáltja alapján is nagyjábol 11 éves periódussal változik a naptevékenységek intenzitása!"
      ]
    }
  ]
}