polyfit1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Att anpassa kurvor till data\n",
    "\n",
    "## Komandot polyfit\n",
    "\n",
    "Ändras: nytt kommando Polynomial.fit!\n",
    "\n",
    "Kommandot `polyfit()` i numpy kan direkt användas för att bestämma koefficienter i $y=kx+m$ och i $y=ax^2+bx+c$. Först skapar vi lite data med statistiskt brus. Vi gör det genom att generera en rät linje och lägger till lite slumpmässiga variationer i y-värdena. Delen av programmet där data genereras är inget som behövs i en realistisk situation. I 'teoretiska' situationer kan detta läggas i en def."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.00612383 8.23706351]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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CPgv8W4AktwP3Au8A7gZ+M8nIyoeRJA1CXyFfVd/tWX0zUM3yHuDhqnq1qr4BnAHu6KcvSdLq9X2ffJIHgH8J/F/gZ5vmbcAXe3Z7uWlb7v37gf0AO3bs6LccSVKPN7yST/JkkmeX+dkDUFX3V9WtwEPAR5fetsyhapk2qupwVU1U1cTY2Ni1/ndIkpbxhlfyVfWeqzzWp4HPAb/K4pX7rT3btgNzq67uKjlhhyQtr9+7a3b1rH4AeKFZPg7cm+SGJLcBu4Av99PXSpYm7JidX6D4wYQdx07NDqI7SdpQ+h2TfzDJOPB94C+AXwaoqueSPAJ8FXgN+EhVXVz5MNfuShN2eDUv6XrXV8hX1S9cYdsDwAP9HP9qOGGHJK1sw//FqxN2SNLKNnzIO2GHJK1swz9P3gk7JGllGz7kwQk7JGklG364RpK0MkNekjrMkJekDjPkJanDDHlJ6rBULftwyKFIcp7FxyNcq5uAv2ypnDZZ1+pY1+pY1+p0sa6/W1XLPsZ3XYV8v5JMV9XEsOu4nHWtjnWtjnWtzvVWl8M1ktRhhrwkdVjXQv7wsAtYgXWtjnWtjnWtznVVV6fG5CVJl+ralbwkqYchL0kdtuFDPslUkheSPJPk0SSbe7YdSnImyUySyTWu654kzyX5fpKJnvadSRaSPN38/NZ6qKvZNrTzdVkdv5ZktuccvW9YtTT13N2ckzNJDg6zll5JXkpyujlH00Ou5VNJziV5tqftxiRPJHmxeX3rOqlrqJ+vJLcm+aMkzzf/Fj/WtA/mfFXVhv4Bfg74kWb5N4DfaJZvB/4MuAG4DfgaMLKGdf04MA78MTDR074TeHaI52uluoZ6vi6r8deAfz3sz1ZTy0hzLt4OvKk5R7cPu66mtpeAm4ZdR1PLPwZ+uvezDfw74GCzfHDp3+Y6qGuony9gC/DTzfJbgD9v/v0N5Hxt+Cv5qnq8ql5rVr8IbG+W9wAPV9WrVfUN4AxwxxrW9XxVzaxVf1frCnUN9XytY3cAZ6rq61X1N8DDLJ4r9aiqLwB/dVnzHuBIs3wE2LumRbFiXUNVVWer6k+b5e8BzwPbGND52vAhf5lfAv6wWd4GfKtn28tN23pwW5JTSf53kn807GIa6+18fbQZgvvUMP43v8d6Oy+9Cng8yVNJ9g+7mGXcUlVnYTHYgJuHXE+vdfH5SrIT2A18iQGdrw0xM1SSJ4G3LbPp/qp6rNnnfuA14KGlty2zf6v3i15NXcs4C+yoqm8n+QfAsSTvqKrvDrmugZ+vSzq7Qo3AfwE+0fT/CeDfs/gLfBjW9Lys0p1VNZfkZuCJJC80V666snXx+Uryo8DvA79SVd9Nlvuo9W9DhHxVvedK25PsA94P3FXNgBaLV1y39uy2HZhby7pWeM+rwKvN8lNJvgb8GNDaF2fXUhdrcL56XW2NSf4r8NlB1XEV1vS8rEZVzTWv55I8yuLQ0noK+VeSbKmqs0m2AOeGXRBAVb2ytDysz1eSTSwG/ENVdbRpHsj52vDDNUnuBj4OfKCq/rpn03Hg3iQ3JLkN2AV8eRg19koylmSkWX47i3V9fbhVAevofDUf8CUfBJ5dad818BVgV5LbkrwJuJfFczVUSd6c5C1LyyzegDDM87Sc48C+ZnkfsNL/Ra6pYX++snjJ/jvA81X1yZ5Ngzlfw/qGucVvqs+wOGb6dPPzWz3b7mfxzogZ4OfXuK4PsngV+CrwCnCiaf8F4DkW79L4U+CfrYe6hn2+LqvxfwCngWeaD/6WIX/G3sfiHRBfY3HIa2i19NT09uYz9GfN52modQG/x+JQ5IXm83Uf8HeAk8CLzeuN66SuoX6+gH/I4lDRMz259b5BnS8fayBJHbbhh2skSSsz5CWpwwx5SeowQ16SOsyQl6QOM+QlqcMMeUnqsP8PQ53bMmT+ryAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import random as r\n",
    "import numpy as np\n",
    "\n",
    "#Vi låser till 10 element\n",
    "x=np.linspace(-20,20,10)\n",
    "\n",
    "#Vi måste arbeta med listor\n",
    "x=list(x)\n",
    "noise=[]\n",
    "y=[]\n",
    "\n",
    "#Vi delar upp det i två\n",
    "for i in range(0,10):\n",
    "    noise.append(r.random())\n",
    "for i in range(0,10):\n",
    "    y.append(2*x[i]+5+5*noise[i])\n",
    "    \n",
    "plt.plot(x,y,'o')\n",
    "\n",
    "#Nu kommer anpassningen\n",
    "pk=np.polyfit(x,y,1)\n",
    "print(pk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np.polyfit(x,y,1)` skickar listan x och listan y till anpassnings-modulen polyfit. Vi ber också om att polynomet ska ha gradtalet 1, dvs en anpassning till $y=kx+m$.\n",
    "\n",
    "När vi skriver ut det som skickats med `return()` till oss från polyfit funktionen så är första elementet i 'listan' koefficienten framför $x^1$ och andra elementet står framför $x^0$: $y=pk[0]x+pk[1]$.\n",
    "\n",
    "Men vi vill rita det anpassade polynomet också. Vi låter x vara oförändrat, `x_fit=x`, och beräknar y från det anpassade polynomet, `y_fit=pk[0]x_fit+pk[1]`, men vi kan inte skriva så(!) utan måste loopa igenom alla värdena, `x_fit[i]`, och använda append: `    y_fit.append(pk[0]*x_fit[i]+pk[1])`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.90877087 14.4771657 ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fcf20641970>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import random as r\n",
    "import numpy as np\n",
    "\n",
    "x=np.linspace(-20,20,10)\n",
    "#Vi måste arbeta med listor\n",
    "x=list(x)\n",
    "noise=[]\n",
    "y=[]\n",
    "#delar upp det i två omgångar\n",
    "for i in range(0,10):\n",
    "    noise.append(r.random())\n",
    "for i in range(0,10):\n",
    "    y.append(2*x[i]+5+20*noise[i])\n",
    "    \n",
    "\n",
    "#Nu kommer anpassningen\n",
    "pk=np.polyfit(x,y,1)\n",
    "print(pk)\n",
    "#x_fit är samma som x, y_fit beräknas ur y=kx+m\n",
    "x_fit=x\n",
    "y_fit=[]\n",
    "for i in range(0,10):\n",
    "    y_fit.append(pk[0]*x_fit[i]+pk[1])\n",
    "\n",
    "plt.plot(x,y,'o')\n",
    "plt.plot(x_fit,y_fit,'--')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Liknande procedur gäller för att anpassa ett kvadratiskt polynom.\n",
    "På samma sätt som tidigare så skapar vi data med brus och anpassar sedan och plottar därefter. Denna gång använder vi dock fler punkter för att rita den anpassade kurvan."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.52478884  1.14039337 10.29472774]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fcf207fd670>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import random as r\n",
    "import numpy as np\n",
    "\n",
    "x=np.linspace(-4,4,10)\n",
    "#Vi måste arbeta med listor\n",
    "x=list(x)\n",
    "noise=[]\n",
    "y=[]\n",
    "#delar upp det i två omgångar\n",
    "for i in range(0,10):\n",
    "    noise.append(r.random())\n",
    "for i in range(0,10):\n",
    "    y.append(2*x[i]**2+5+20*noise[i])\n",
    "    \n",
    "\n",
    "#Nu kommer anpassningen\n",
    "pk=np.polyfit(x,y,2)\n",
    "print(pk)\n",
    "#x_fit innehåller fler punkter för att få en jämnare graf\n",
    "x_fit=list(np.linspace(-4,4,30))\n",
    "y_fit=[]\n",
    "for i in range(0,30):\n",
    "    y_fit.append(pk[0]*(x_fit[i])**2+pk[1]*x_fit[i]+pk[2])\n",
    "\n",
    "plt.plot(x,y,'o')\n",
    "plt.plot(x_fit,y_fit,'--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prova med att sänka bruset till 0 och se om anpassningen ger samma funktion som vi använt. Sätt koefficienten framför noise till 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kanske tycker man att det borde vara möjligt för en lista att multiplicera alla element i listan med ett tal! När man multiplicerar en lista med ett tal, tex. 3, så är det en konkatenering. Säg att vi har L=[1,2] och skriver `M=3*L`, då erhåller vi `M=[1,2,1,2,1,2]`. Men säg att vi vill att `3*L=[3*1,3*2]` då måste vi använda något som heter array() som lägger grunden för vektorer och matriser."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Uppgifter\n",
    "\n",
    "**Uppgift 1**\n",
    "\n",
    "Läs in data från filen [data1v2.csv](./uppg/data1v2.csv) och anpassa ett andragradspolynom.\n",
    "\n",
    "<!--[Lösningsförslag](./uppg/polyfitUppg1.ipynb)-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}