3.1 Gràfics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gràfics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## La llibreria matplotlib\n",
    "\n",
    "La llibreria *matplotlib* ens dona una potent eina per fer gràfiques de top tipus.\n",
    "\n",
    "Començarem carregant aquesta llibreria, juntament amb *numpy*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podeu trobar molta més informació sobre aquesta llibreria a la guía d'usuari de *matplotlob* a https://matplotlib.org/users/index.html o a l'excel·lent tutorial de J.R. Johansson disponible a https://github.com/jrjohansson/scientific-python-lectures\n",
    "\n",
    "Amb *matplotlib* podem modificar moltíssim paràmetres de la nostre gràfica\n",
    "\n",
    "![](https://matplotlib.org/_images/anatomy.png)\n",
    "\n",
    "Veiem un exemple. Fixeu-vos que podem incloure més d'una funció a la mateixa gràfica:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gràfiques de funcions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x = np.linspace(0, 2, 100)\n",
    "\n",
    "plt.plot(x, x, label='linear')  # Plot some data on the (implicit) axes.\n",
    "plt.plot(x, x**2, label='quadratic')  # etc.\n",
    "plt.plot(x, x**3, label='cubic')\n",
    "plt.xlabel('x label')\n",
    "plt.ylabel('y label')\n",
    "plt.title(\"Simple Plot\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analitzem el codi anterior\n",
    "\n",
    "Amb\n",
    "\n",
    "`x = np.linspace(0, 2, 100)`\n",
    "\n",
    "hem generat un conjunt de 100 valors de x entre 0 i 2\n",
    "\n",
    "Ara afegirem els diferents valors de les funcions:\n",
    "\n",
    "`plt.plot(x, x, label='linear')  # Plot some data on the (implicit) axes.`   \n",
    "`plt.plot(x, x**2, label='quadratic')  # etc.`   \n",
    "`plt.plot(x, x**3, label='cubic')`   \n",
    "\n",
    "Podem afegir els títols pel eixos i la gràfica:\n",
    "\n",
    "`plt.xlabel('x label')`  \n",
    "`plt.ylabel('y label')`    \n",
    "`plt.title(\"Simple Plot\")`   \n",
    "\n",
    "Finalment afegirem una llegenda per identificar cada funció amb el `label` corresponent:\n",
    "\n",
    "`plt.legend();`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utilitzan escales logarítmiques\n",
    "\n",
    "Només hem de fer servir `plt.xscale('log')` o semblants (més informació a https://matplotlib.org/tutorials/introductory/pyplot.html#sphx-glr-tutorials-introductory-pyplot-py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Tpk07Yh7y6upqEhMT8fDw4Pnnn6etra1jP3//+9+59tprKSkp4eOPP+a73z3+fFe1tbXExcXR0tLCiy++SEJCAgDBwcHU1tYes/2oUaM4dOgQGzZsYOrUqdTW1uLv769zlw9gtbbajpDYXLKZHWU7aG6zRlseGjyUMxPOZGL0RCZGT2RE2Ai9V0J1i54R+snkyZO58sorOeOMM0hOTuass84C4Gc/+xlXXHEFL7zwAvPmzevY/uabb+bSSy/ltdde4+yzz+6oSSxevJg1a9Ywfvx4Ro4cyZw5c054zPvvv5/p06eTnJzM+PHjO8LiqquuYunSpTzxxBNHhJWPjw+vvPIKt956K42Njfj7+/PRRx8RFKR35w4UFU0VbCrexKbiTWwu3kxmZSbtph1P8WRMxBguH3k5k2MnMylmElH+Uc4urhqgdFh1J7n33nsJCgriZz/7mbOLclpc7ec5WJU2lLKxeCMbizaysXgjudW5gDVEx8ToiUyOnczk2MlMiJowKIcJVz2jw6or5YbKGsvYULSh45FXkwdAoHcgk2ImcdHwi5gSO4WxkWPx9vR2bmGV23Kr4BhI7r33XmcXQQ0A1c3VbCzayFdFX7GhaAM5VTmAFRRTYqdwadqlTB0ylVERo/RqJ9Vv9DdNKRfS3NbMlpItfHnwS7489CW7K3bTbtrx9/JncsxkFg1bxLQh0xgTOUaDQjmN/uYp5UTtpp3symw+P/g5Xxz8gs0lm2lua8ZLvJgQPYEbJtzAjLgZjI8ar01PymVocCjVz8oby/n84OcdYXH4PooRYSO4fOTlzIyfSUZshnZmK5elwaGUg7W2t7KtdBufFn7Kp4WfsrtiNwDhvuHMjJ/JrPhZzIibQWxgrJNLqlT3uHxwiMh3gG8DMcBTxpgPnFwkh/vkk0945JFHePvtt49574ILLuDf//43YWE60qgrK28s57ODn7G+YD2fHfyMWlstnuLJxOiJ3DrpVs5MOJMxEWN0ilM1IDklOERkObAIKDHGjOuyfiHwOOAJPGOMedAY8xbwloiEA48Abh8cJ/Puu+86uwjqOIwxZFZmsvbAWtYVrGN72XYMhij/KOYlzeNbCd9iZvxMQnx0/C818DmrxrECeBL45+EVIuIJPAUsAAqADSKy0hizy77JXfb3B6x//vOfPPLII4gIEyZMwNPT84hRaoOCgqirqwOgpqaGxYsXk5mZyezZs/nLX/6Ch4cHKSkpbNy4kaioqGP298ILLzjz6w06tjYbG4o28PGBj1lbsJai+iIEYVzUOG464yZmJ87WWoVynJYmqCuGuhKoK+pcnvlj8HPsGGNOCQ5jzDoRSTlq9TQgxxiTCyAiLwMXi8hu4EHgPWPM5hPtU0SWAcsAkpKSTnr8h75+iD0Ve067/MczOmI0v5z2yxO+v3PnTh544AE+//xzoqKiqKio4Kc//ekJt//666/ZtWsXycnJLFy4kDfffPOIYdCPtz/leLW2WtYVrGNN/ho+O/gZ9S31+Hv5MzNuJjdPvJmzEs/SoTzU6TMGmmugttgKg47nw8FQ3Lmuqfo4OxAYe4l7BscJJAAHurwuAKYDtwLzgVARGWGM+dvxPmyMeRp4GiAjI8PlxlFZs2YNl19+OVFR1kklIiLipNtPmzaNYcOGAbBkyRI+/fTTI4Kjp/tTp6+ssYw1+WtYnb+ar4u+prW9lUi/SBamLOScpHOYNmQafl7dG71YDWLNtVYA1B7q8lzc+fpwQLQ0HPtZLz8IioXgIRA9ClJnQ3Cste7wI3gIBESBp+NP664UHMdljHkCeKI723Z3IqeT1Qz6U9ch1dvb27HZbB3vHT0xjk6U07+K6ov4aP9HfLj/Q7aUbMFgSApO4pox13BO0jlMiJ6gTVDK0tZqrwkcgpqD9iA4BDWHoPagFQY1h8B27IjUeAdaJ/zgIRA/CYLjOkOg67NfKLjQOcCVgqMQGNrldaJ9nVs455xzWLx4MT/96U+JjIykoqKiY0j1K664gpUrV9LS0tKx/ddff82+fftITk7mlVdeYdmyZafcn9Y6eqeovogP8j7g/f3vs610G2DdW3HTxJuYlzyPtLA0DfDBpqXRCoOOR2FnQBwOibpisE981cHD2x4IcRAzBoafYy2HxNvDwB4WvsEuFQjd5UrBsQFIE5FUrMC4Cjj+RBMn4MqDHI4dO5bf/OY3zJkzB09PTyZNmsRDDz3ExRdfzLRp05g3b94RkzDNnDmTO++8k+3btzN79mwWL158yv2tWLGin7/VwFfWWMb7ee/zv33/Y2vpVsDqr7pt0m3MT55Pamiqk0uoHKa12QqC6kL7c0FnONQUWssN5cd+zi8UguMhJA5i0zuXuz4HRIKH+9ZInTKsuoi8BMwFooBi4B5jzLMicgHwGNbluMuNMb/r4X4HzLDqA91A/nlWN1fz0f6PeG/fe2wo3kC7aWdk+EgWpizk3JRzSQ5JdnYRVW+1t0N9qRUG1QfsoVDYuVxdYL1/NP9wCEmwagYhCRCaYAVBaIL1OjgOfN13fhqXHlbdGLPkBOvfBU77RgVXrnEo57K12VhbsJZ3ct9hXcE6WtpbSApOYun4pZyfej7Dw4Y7u4iqJ1ptUFMAVflWCFQdDoT8zmBosx35Ge9ACE20QmDIeAhJ7AyE0EQrLHwCj388dQRXaqpSqk8ZY9hSsoVVuat4P+99am21RPlHceWoK1k0bBHpkenaZ+GqWpvtgbDfCocjHgesvgW6tpaI1WcQOhTizoAxF1rLoYn2UEiwahP6790n3Co4TnVVlTFGTxR9wNVnjTxYd5CVe1eycu9KDtQewN/Ln3lJ87hw2IVMj5uu82q7gvY2q+mocj9U5nUGROV+a7m2iCOCQTytAAhLguFnW6EQNrTzOSQRvHyc9W0GHbcKjpM1Vfn5+VFeXk5kZKSGRy8YYygvL8fPz7XuW2hua2b1/tX8J+c/fHXoKwyGaUOmcePEG5mfNF9HmnWGphqo3GcFQ4X9uSMkDkB751WEiIdVKwhLtq5ACkuyP5Kt5+C4frk/QXWPW/1LnKzGkZiYSEFBAaWlx+kQUz3i5+dHYmKis4sBQFZlFm9kvcHbuW9TY6shISiBm864iYuGX0RCUIKzi+fejLE6mCty7Y99VlBU5FoBcfQVSf7hEJ4KcRNhzEUQkWoFQ3iyVXPQ+UYGDKdcVeVoGRkZZuPGjc4uhnKQxtZG/rfvf7ye9Trbyrbh7eHN/KT5XDLyEqYNmaY35vWlw+FQvhcq9tqfuwRF15vaxMNqTgpPtUIhPOXIZQcPg6F6z6WvqlLqdORW5/Jq5quszFlJbUstw0KH8Yupv+DCYRcS5qfDzPdKUzWU51jBUJ7TZXnvkeHg4WXVEiKGQdJMiBxuLYenWk1K2s8wKLhVcHR3yBE1cLS2t7L2wFpeynyJrw59hZeHFwuSF3DFyCuYEjtF+6t6or3N6l8oy4ayLOu5PMd6ri/p3E48rKajyBEwdBpEDO8MiLBk7WtQ2lSlXFN1czVvZL/By3te5lD9IYYEDuGKkVdwSdolRPpHOrt4rs3WAOXZUJoFZZlHhkTXexsCIiEyzQqIqBGdyxGp4OXrvPIrp9GmKjUg7avex792/YuVe1fS1NbE1CFT+eXUXzJn6By8PPTX9QjNdVYwlOyB0j1Qmmk9V+XTcSmreFjNSNGjIG2BFQ5RIyEqDQJ0bDN1evR/onI6YwwbizeyYucK1hWsw8fDh28P+zZXj7maURGjnF0852tptEKhZDeU7LLCoWSPdZf0YZ6+VhgkZsAZV0P0SIgaZTUxae1B9TENDuU0be1trM5fzXM7nmNH+Q4i/CK4eeLNXDHqisHZHNXeZl3GWrzTepTstMKiIrdz9FVPH6vGMHQaTPk+RI+xRl/VvgfVj9zqN007xwcGW5uNVXtXsXzHcvJr80kOSeb/ZvwfFw2/aPBMiNRUbYVD0Q4otj9KdndO4nO4iSk2HcZdZoVDTLrVQa0BoZxMO8dVv2lsbeT1rNdZsWMFJY0lpEem86PxP+Kcoee47zAgxljDcxdtg6LtcOgb67lqf+c2/uEQO84aeC8mHWLHQvRo8NG73VX/0s5x5TIaWhp4NfNVntv5HBVNFWTEZnD/mfczM36me11Oa4x15/Shb458dNxBLVaNIX4STP4+DJkAQ8ZZw2m4089BuT0NDuUwja2NvJr5Kst3LKeiqYKZcTO5YeINTImd4uyi9Z4x1tVLB7d0Pg5ttZqgwJoBLmY0jDofhkyEuAlWTcI32LnlVqoPaHCoPmdrs/Fa1mv8Y9s/KG8qZ1b8LG6aeBNnxJzh7KKdvvoyKNwMhZusx8HNnTUJD28rFMYutob0jj/DanLSq5mUm3Kr4NDOcedqa29jVe4q/rr1rxysP8jUIVP54xl/HHg1jFab1Q9RsMF6FG60rnYCq9M6ejSMPB8SJkH8ZCs0NCTUIKKd46rXjDGsL1zPoxsfZW/1XtIj07l98u3MjBsgfRi1xXDgK+tRsAEOboW2Zuu9kARImGLdH5EwxapRuPHUoWpw085x1S92lu/kjxv/yIaiDSQFJ/HInEc4N/lc1w2M9nbrbuv8LyD/S+tx+AonT1+r43r6MkicZoVFSLxzy6uUC9LgUKelpKGExzc/zsq9Kwn3DedX037F5aMux9vDxeZUaGuFom9g/+fWI/8LaKy03guMgaTpMG0ZDJ1uzROho7sqdUoaHKpHmtuaeX7n8zyz/Rla21v5wbgfsHT8UoJ9XORqobZW6wqnvPWw/zOrRmGrs96LGA6jvw1JsyBphnVprKvWjJRyYRocqtvWFazjwa8f5EDtAeYlzeOOKXcwNGSocwvV3m7ddb1vLexbB/u/6Jw/Ino0TLwKkmdB8pkQPMS5ZVXKTWhwqFM6WHeQP3z9Bz458AkpISn8fcHfmRU/y3kFqtwPuR9D7idWWBy+LDZyBEy4HFLOsh5B0c4ro1JuzOWDQ0SGAb8BQo0xlzm7PINJS3sL/9r1L/76zV8B+MmUn3DNmGvw7u+5oW31sG897F0NOautKUzBuuM67VxInQOpsyFU5xhXqj84JThEZDmwCCgxxozrsn4h8DjgCTxjjHnQGJMLXC8irzujrIPVjrId3PP5PWRVZjF36Fx+Pe3XxAXF9c/BjbEmHsr+AHI+tDq122zg5Q8p34KpP4Lh51hzTGgfhVL9zlk1jhXAk8A/D68QEU/gKWABUABsEJGVxphdTinhINXU2sRftv6F53c9T5RfFI+d/RjzkuY5/sCtNtj/KWS9D1n/67zhLnq0ddXTiPnWHNfeg2T0XKW6aG83NLa0Ud/cSl1zKw02a7nB1ka9rZX65lbqm9tosLVyzYwUQgMc2yrglOAwxqwTkZSjVk8Dcuw1DETkZeBioFvBISLLgGUASUlJfVbWwWRryVbu+uwu9tfs59K0S7kj4w7HXi3VWAnZH8Ked6wmKFstePlZTU+zbrWaocL031INPMaYjpN7bXNrxwm/vrmty/Lh9dYJv2Od/XOHlxvsz921cNwQ9wyOE0gADnR5XQBMF5FI4HfAJBH5lTHmD8f7sDHmaeBpsO4cd3Rh3YmtzcaTW5/k+Z3PExcYxzPnPsP0uOmOOVjNIdjztvXI+xTaWyEoFsZdAqMusPoqdDhx5SQtbe3UNVkn8Zqmlo7luuZWag8vd1lX19RKva3zvfrD79ta6e6gHIE+ngT6ehHk60WgrxcBPp4MCfEjwNer473ALstBvl74+3gesf3h9wN8vPDx8nDsDwnXCo7jMsaUAzd2Z1sdq6rnMisyuXP9neRU5XBp2qX8fOrPCfQO7NuDVBfCrv9ajwNfAca6AmrmLTB6kTWUh4fjf9mV+zLG0NzaTk1jCzVNrdQ2tVDb1Gp/tHQ813RZ1zUMrOcWmlraT3ksD4Eg+wk8yM96DvbzIj7Mj0Af62Qe7OfVccIPPnzi9/Uk2NebQN/Ok76/tyceHgOvn86VgqMQ6HpTQKJ9nXIAYwz/3vNvHt34KCG+ITw17ylmJ87uuwPUFsHOt2Dnm/awwJqs6Oxfw5iLrCHHlbI73LRT09RCTaP11351Q4v9tXXi7/re4eXOMGihpe3kf+KLQJCPdVIP9vMmyM+LyCAfUqKb1EaWAAAgAElEQVQCO07+wV1O+sF+3l2WOwMgwMfTdYfU6SeuFBwbgDQRScUKjKuA7/ZkB8aYVcCqjIyMpQ4on9uoaKrgrk/vYn3heuYkzuG+M+8jwi+i9ztuqoZdK2H7a9ad26YdYsbCOXdB+mKI0pqgOzt88q9qtE76VY02ahpbqGpoobrx2EdNU6tVQ7C/bm0/+Ynf39uTEH/rhB7S5aQf4udFiL91kg/xO/I5uOPZi0AfrwH5170rctbluC8Bc4EoESkA7jHGPCsitwDvY12Ou9wYs7OH+9WmqlPYXLyZn6/7OVVNVfx6+q+5atRVvfvrqa0F9q6Bb16CPe9ao8qGp8JZP4Pxl1mXzKoBxRhDXXMrVQ3WSb+ywUZVYwtVDbaOdVWNNns4WOur7QFxspO/p4cQ6u9NqL83IfbnpIgAQvy8OtaF+Hl3bBPcZX2wnxfentqc6Sp0WPVBot208/zO53l88+MkBCXwx7l/ZHREL5qLSvbA1n/BNy9DfSn4R1hBMeFKq89ikFflXYUxhtrmVirrbZTX26ist1FRbwVARYP1urLBRmWDFQAV9S1UN9pO2uwT5Gud0MMC7A9/H0IOv7af9MMCvAn197FCIMBaF6hNPC5Ph1VXHepb6vnNp79hdf5qFiQv4Lezfnt6l9k211l9FpuetyY38vCCkQvhjO/CiAU6smw/aG83VDW2UF7XTHm9jfI6GxX11nLFUeFwePlEtQBvTyEswIfwAG/CAnxIjQpkSrLPEevC/L0JD7Reh/r7EBbgrX/5K/cKDm2qOlZedR63f3w7+2v28/OMn3NN+jU9/6uvaAdsfBa2vWbdaxE1Cs59ACZcpeNB9YHm1jbK6myU1TZTVnf4YaOsrpnyLs/l9c1U1Ns4UWtQqL83kYE+RAT6MDQigDOGhhER6EN4gLUuItA68UcG+hIe6E2Qr5fWANRp0aYqN7a+YD2/WPcLvD28eWTOI0yLm9b9D7faYPdK2PCMNYeFl581p/aU66y5K/SEc1Lt7YaKBhslNc2U1jVTUtNEaV0zpbVdHnXNlNU2U9PUetx9BPl6ERXkQ2SQLxGBPkQF+RIVZAVAZJAvUYE+RNhfhwf4aE1A9dqgbKrSGkenF3e/yMMbHmZk+EgeP/tx4oO6OZNdfRlsfM4KjLoiq6P73AfgjKshoA+uvBrgjDFUNrRQVN1EcW0TxdVNFNc0U1Lb+VxSY9UajtdEFOzrRVSwL9FBvowZEkLUCB+ig33toeBLVLAVDlFBvvh5ezrhGyp1alrjcDOt7a089PVDvJz5MnOHzuWhsx4iwLsbd2KXZcMXT8LWl6wro4bPg+k3WmNEDZKb89raDSW1TRyqbqKo+vBzY8frohorFGxtx94kFhHoQ0ywLzEhfsQE+xIb4ktMsLUcHWwtRwf74u+jYaBc16CscQx2ja2N/GLtL/ik4BOuTb+Wn0z5CZ4epzhRHdgAn/4JMt8FTx84YwnMuNntLqM1xlDd2EJhVSOFlY0crGrkYHUTB6usYDhU1UhxbTNtR9US/Lw9iAv1JzbEl4zkcGJD/RgS4kdsx8MKBl8vDQQ1eLhVcAzmpqqqpipuWXML20q3cdf0u7hy9JUn3tgYa8a89X+0JkLyD4fZP7dGoR2gnd2Hm5AKKhsoqGzs8mwtF1Y2HjNQnI+XB/GhfsSH+TNjeCTxof7EhfkRF+pHXKg/caF+hPp7aweyUkfRpio3UFRfxA0f3kBBbQEPzX6I+cnzj7+hMdaseZ88CAe+hKAhMOsWmPID8A3q1zKfDltrOwWVDeRX2B/lncsHKhqOCYYQPy8SwgNIDPcnIcyfxHB/4sOs5fgwfyIDffROYqW60KaqQeJAzQGu/+B6am21/G3B35g6ZOrxN9z/Oay+H/I/h+B4uOARmHSNy81vYWtt50BlA/tK68krtz/KGsgrr+dgVeMRl6L6enmQFBFAUkQAM4ZFMjTCCgnrEUCofz/PVKjUIKHBMYDlVuey9P2l2NptLD9vOWMixxy7UdEOWH0fZL9v1TDO//9g8vedGhjGGMrrbewtqWNvaT17S+vILa1jX1k9Byobj+hnCPX3JiUygMlJ4VwyKYGkyECSIwNIjgggOthXm5GUcgINjgEqqzKLpR8sRRCWn7ectPC0IzeoOQRr7oet/wa/EJh/L0y7oV/nujDGUFLbTFZxLVnFdeSU1JJTUkd2SR1VDS0d2/l6eZAaFUh6fAiLJsSTGhVIanQgqZGBhAfq3ehKuRq3Co7B0jm+t2ovSz9YipeHF8+e+ywpoSmdb9oa4PM/w2ePWZMkzboFzrrD6gB3oLrmVvYcqmF3US2ZRTVkFdWRWVxLdWNnQIQFeDMyJpjzx8UxIiaIETFBDIsKJCHMX/salBpATtg5LiKXnOyDxpg3HVKiPuDOneP5Nflc97/rAHhu4XMkhyRbbxhjXVL73p1QnQ/pF8P830JEap8e3xhDcU0zOw9Ws/NgDbsO1rDrUA35FQ0d2wT7ejFqSDAjhwQzKjaYtNgg0mKCiQry0aYlpVxYX3SOX3iS9wzgssHhrgrrCrn+g+tpbW89MjQqcuG9X0L2BxCTDte9Cyln9skxS2qa+Kagmu0FVWwrrGZHYQ1ldc0d76dGBTI+IZQrMhIZExfC6LgQ4kP9NCCUcmMnDA5jzA/6syDq5Moby1n2wTLqW+pZft5yhocNh7ZW+PIp+PgP1ki15/0Bpi0Fz9O7mqippY3thdVsya9k64EqtuRXcai6CbCmy0yLCWbOyGjGJYQwLiGUMXEhBPm6VWunUqobTvm/XkRigd8D8caY80UkHZhpjHnW4aVTADS0NHDL6lsoaSjhH+f+w5pHo2gH/PfHcGgrjLoAvv1HCOnmeFR25XXNbMirYENeJZv2V7LzYHXHPAxDI/zJSIngjKFhTEgMZWx8CAE+GhJKqe51jq8AngN+Y3+dBbwCuFxwuGPneEt7Cz9b+zN2VezisbmPcUbUeFj/KHz8e/APg8tXQPp3ujVabWltM1/mlnc89pbWA9ZVTRMTw7j+W8OYkhzOpKQwooJ8HfzNlFIDVXeCI8oY86qI/ArAGNMqIm2n+pAzuNuc48YYHvjyAdYXrufumXdzdlAKPHeBddd3+sWw6LGTjljbYGvlq9wK1meX8VlOGZnFtYA1XHdGSjiXTRnKtNRwxiWE6lhLSqlu605w1ItIJFaHOCIyA6h2aKkUAP/a/S/ezH6TZROWcbnNE/52FogHLH4aJlxxTC3DGMPe0no+3lPC2qxSvt5Xga2tHR8vD6alRHDxpHhmDY9iXHwIXjp3g1LqNHUnOH4KrASGi8hnQDRwmUNLpfis8DMe2fgI84eezY8L9sKmuyBxKly2HMKSOrZrazdsyKvgw13FrN5dTF65dVnsyNggrp2VzJyRMWSkhOvcDkqpPnPK4DDGbBaROcAoQIBMY0zLKT6meiGvOo+fr/05I4KT+V3WZjyKtsOs22De3eDpTWtbO1/klvPu9iI+3FVEWZ0NH08PZg6P5PpvpXLOmFgSwvyd/TWUUm6qO1dV+QE3A9/Caq5aLyJ/M8Y0Obpwg1F9Sz23fXwb3sCf9+4koMUGS17BjDyPzfmV/HfrQd7dfoiyOhuBPp6cPTqGheOGMHdUjF4aq5TqF9050/wTqAX+bH/9XeAF4HJHFWqwMsZw/5f3s786j38UlRIfkEDJpc/xWp4/r69ay76yeny9PJg/JpYLJ8Yxd1SMNkEppfpdd4JjlDFmYpfXH4vIN44q0NFEJBD4C2ADPjHGvNhfx+5v/8l6g3dy3+HHlVUMD5vKrT4/4Z2n82k3MD01gpvmDueC8XFas1BKOVV3zkBbRGSGMeZLABGZDnzWm4OKyHJgEVBijBnXZf1C4HHAE3jGGPMgcAnwujFmlYi8ArhlcGSV7uT3X97HjMZGYmqnM63o+4QHtXHT3OFcmZFEUmT/jWqrlFInc8LgEJHtWH0a3sD3RSTf/joZ2N3L464AnsRqBjt8PE/gKWABUABsEJGVQCKw3b6ZS94/0lv5JYXcvupqgmkl8eCZvBS3jMcvTuXc9CH4eOlls0op13KyGsciRx3UGLNORFKOWj0NyDHG5AKIyMvAxVghkghsBU54FhWRZcAygKSkpBNt5lKKqptYvmY7ZQeWURDaxpVN81i09H7uGRrm7KIppdQJnWyQw/1dX4tIDODIaeMSgANdXhcA04EngCdF5NvAqhN92BjzNPA0WMOqO7CcvVbd2MJfPsnh1c92c0fA73gpoZXvhE7mrmv/fOoPK6WUk3XnctyLgD8C8UAJnU1VYx1bNIsxph7o1ki9rj5WVUtbOy98sZ8n1mTT0ljLq+GP8NOIBpJ8Y/jVt//q7OIppVS3dKdz/H5gBvCRMWaSiJwNLHFAWQqBoV1eJ9rXuYXN+ZX8+s3t7CmqZc7wUJ6SP/NoUxGHvIN5/pzHCPDWzm+l1MDQnZ7XFmNMOeAhIh7GmI+BMxxQlg1AmoikiogPcBXWUCfdZoxZZYxZFhoa6oDinZ765lbuems7l/71c6oaWvjb1ZNYEf4ce8q+4rXgIK4dey2TYiY5u5hKKdVt3alxVIlIELAOeFFESoDW3hxURF4C5gJRIlIA3GOMeVZEbgHex7ocd7kxZmcP9+tSTVXfHKji9pe3sL+igetmpXDHgpEEffx/tOx4nd+NnEC8TwA3n3Gzs4uplFI9csI5xzs2sG7Aa8Iap+pqIBR40V4LcUnOnnO8vd3w9PpcHnk/k5hgX/505RlMHxYJG56Bd+5gxfjz+GPdbp44+wnOTjrbaeVUSqmu+mLOcaCjc/qw53tVqkGg0dbGT1/dyns7irhg/BD+sHgCoQHesP9zeO+XFI04h7805TEncY6GhlJqQDrZDYC12OfgOPotwBhjQhxWqtPk7Kaqkpomlv5zI9sKq7nr22O4/lupiAhUF8Kr34ewZB6OS6T90AHunHanU8qolFK9dcLOcWNMsDEm5DiPYFcMDXBu53hOSR3feeozskvqePqaDH501jArNFqb4ZXvQUsjGxb8hg8LPuFH439EYnBiv5dRKaX6gluNluesGsf+8nqufuZL2trh1RtmMi6hS3CtuR8ObsZc8QKP5b5CTEAM1429rl/Lp5RSfcmtBkJyRo2jsKqR7/7jK2yt7bz4o+lHhsa+9fD5k5DxQ9YEBrKtbBs3T7wZPy9H3oCvlFKO5VbB0d9Kapu4+h9fUtPUwgvXT2fUkODON5uq4a2bICKV1vn38viWx0kNTeXiERc7rbxKKdUXThkcInKriIT3R2F6S0QuFJGnq6urHX6s1rZ2bv33Foprmlnxg2lH1jQA3vsl1ByES/7BygOr2Ve9j9sm3YaXh1u1DiqlBqHu1DhisYY4f1VEFoqIOLpQp6s/m6qeWJ3NV/sqeOA745iSfFSuZv4PvnkJZv+MpiHjeGrrU0yImsC8pHkOL5dSSjnaKYPDGHMXkAY8C1wHZIvI70VkuIPL5rI+zS7jzx/ncNmURC6dctTVUS1N8L9fQtQomP1z/pvzX0oaSrht8m24cOYqpVS3dauPw1i3lxfZH61AOPC6iDzswLK5pJLaJv7fK1sZER3EfRcfZ4DgL5+Cyjw4/0FaRVixcwUToiYwbci0fi+rUko5Qnf6OG4XkU3Aw1hTxo43xtwETAEudXD5XM4f3t1DbVMLT109mQCfo/orqgth3SMwehEMP4eP8j+ioK6AH4z7gdY2lFJuozs9tRHAJUdP7GSMaRcRh80SeDocfR/HnqIa3tpayA2zhzMyNvjYDT68G0w7nPd7jDEs376clJAUzh6qQ4sopdxHd/o47jk6NLq819u5x/uUozvHH3k/kyBfL26ac5zunfyvYMfrcObtEJ7Ml4e+ZHfFbq4bex2eHp4OKY9SSjmD3sfRTRvzKvhodwk3zhluDVp4tLUPQmA0nPn/AHhux3NE+UexaLhLVcqUUqrXNDi6wRjDw+9nEhXkyw/OTDl2g8JNsHcNzPwx+ASQWZHJF4e+4Htjvoevp2+/l1cppRxJg6Mb1maV8vW+Cm6bN+LYDnGA9Y+CXyhkXA/Aa1mv4evpy2UjL+vnkiqllOO5VXA46s7xF7/KJzbEl6umJh37ZvEu2PM2TL8R/EJobG3kndx3ODf5XEJ9XWcKW6WU6ituFRyO6BxvtLWxPruUhWOH4ON1nB/Xp4+Cd6AVHMAHeR9Q11LHJWmX9FkZlFLKlbhVcDjCpzllNLW0syB9yLFvlu+FHW/A1B9CQAQAb2a/SUpIClNip/RzSZVSqn9ocJzCh7uKCPbzYvqwiGPf3LgcxBNm3gJAblUum0s2c0naJXrDn1LKbWlwnERbu2H17hLOHhWDt+dRP6q2Ftj2Cow8D4Kt2sib2W/iJV5cOPxCJ5RWKaX6hwbHSWzOr6S83saC9Nhj38xZDfWlcMbVALS0tbBy70rmDp1LlH9UP5dUKaX6jwbHSXy4qxhvT2HuqOhj3/zm3xAQBWkLAFhbsJbK5krtFFdKuT2XDw4RGSYiz4rI6/15XGMMH+4qZubwKIL9jrpTvKECMt+DCVeAp/Xeh/s/JNw3nJnxM/uzmEop1e8cGhwislxESkRkx1HrF4pIpojkiMidJ9uHMSbXGHO9I8t5PHtL69hXVn/8Zqodb0CbDSYuAcDWZmNdwTrOTjpbZ/hTSrk9R5/lVgBPAv88vEJEPIGngAVAAdbsgisBT+APR33+h8aYEgeX8bg+2FUMwIIxxwmOrf+G2HEQNwGArw59RV1Lnc7wp5QaFBwaHMaYdSKSctTqaUCOMSYXQEReBi42xvwBOO0RAUVkGbAMICnpOHd491BWUS2J4f4MCfU78o3STDi4Gc77fceq1fmrCfQOZEbcjF4fVymlXJ0z+jgSgANdXhfY1x2XiESKyN+ASSLyqxNtZ4x52hiTYYzJiI4+Tmd2DxnAy+M492Jsfx3EA8ZfDkBbextr8tcwO3E2Pp4+vT6uUkq5OpdvkDfGlAM3dmdbR0/kBEDux5AwBYJiANhcspnK5krmJ8133DGVUsqFOKPGUQgM7fI60b6u1xw9kRNN1dYQ6sPmdqxanb8aX09fvpXwLcccUymlXIwzgmMDkCYiqSLiA1wFrOyLHTtqdNwOeZ9ZU8MOmwtYl+x+tP8jZsXPIsA7wDHHVEopF+Poy3FfAr4ARolIgYhcb4xpBW4B3gd2A68aY3Y6shx9JvcT8PKHxKkA7CzfSXFDMfOTtZlKKTV4OPqqqiUnWP8u8K4DjrcKWJWRkbG0r/cNWMGRPAu8rFn91hWsQxDmJM5xyOGUUsoVufyd4y6j5hCUZR7Rv7GxeCOjI0brhE1KqUHFrYLDoX0c+9Zaz8Os2kVzWzPflHxDxpCMvj+WUkq5MLcKDodeVZX7CfhHQOx4ALaVbsPWbmNq7NS+P5ZSSrkwtwoOh9U4jIHctVZtw8P6kW0s3oggTI6d3LfHUkopF+dWweGwGkdZNtQehNTOTvCNRRsZFTFK+zeUUoOOWwWHw+R+Yj0PmwtYo+F+U/oNGbHav6GUGnzcKjgc1lR1cDMEx0FEKgDby7bT3NasHeNKqUHJrYLDcU1VWRA1suPlxiKrf0NrHEqpwcitgsMhjLH6OLoEx4biDYwMH6n9G0qpQUmD41TqSqC5BqLSAGhpa9H7N5RSg5oGx6mUZVnP9uDYUb6DprYmvX9DKTVouVVwOKRzvDzbeo60gmNT8SYAvX9DKTVouVVwOKRzvCwbvAMgxJqkMLMik4SgBML9wvvuGEopNYC4VXA4RFkWRI7ouGM8uzKbtLA0JxdKKaWcR4PjVMqyO/o3bG028mrySAvX4FBKDV4aHCfhY5qhKr/jUtx91ftoM22MDB95ik8qpZT7cqvg6OvO8QRzCDBWUxWQVWldYaU1DqXUYOZWwdHXneNJ7YXWgr3GkV2ZjbeHN0khSX2yf6WUGojcKjj6WlJ7gbUQORyArKoshoUOw9vD24mlUkop59LgOImk9oMQOhR8AgH7FVXaTKWUGuQ0OE4iyRR0XFFV3VxNSUOJBodSatDT4DgRYxjaXthxx3h2pXUHud7DoZQa7DQ4TiC0tYwAmjpqHNlV9uDQGodSapBz+eAQke+IyD9E5L8icm5/HTfWlm8tRHXWOEJ8QogNiO2vIiillEtyaHCIyHIRKRGRHUetXygimSKSIyJ3nmwfxpi3jDFLgeuAKx1Y3CPE2A5YC10uxU0LT0NE+qsISinlkhxd41gBLOy6QkQ8gaeA84F0YImIpIvIeBF5+6hHTJeP3mX/XL+IseXTgB8Ex2GMIacqR/s3lFIK8HLkzo0x60Qk5ajV04AcY0wugIi8DFxsjPkDsOjofYj1J/6DwHvGmM0nOpaILAOWASQl9f4GvcC2GioljAARDtUdpK6lTvs3lFIK5/RxJAAHurwusK87kVuB+cBlInLjiTYyxjxtjMkwxmRER0f3SUENVrPU4SuqdIwqpZRycI2jLxhjngCe6M62InIhcOGIESP6tAyHx6gaEda3+1VKqYHIGTWOQmBol9eJ9nW95pCJnIADtQeI9o8myCeoT/erlFIDkTOCYwOQJiKpIuIDXAWs7IsdO2TqWKCksUQvw1VKKTtHX477EvAFMEpECkTkemNMK3AL8D6wG3jVGLPTkeU4LaZzsaShhOiAvuk3UUqpgc7RV1UtOcH6d4F3HXC8VcCqjIyMpX2539KGUibHTO7LXSql1IDl8neOO1tzWzNVzVXEBMScemOllBoE3Co4HNHHUdpQCkC0vzZVKaUUuFlwOOKqqtJGKzi0xqGUUha3Cg5H1DiKG4oBDQ6llDrMrYLDITWOBq1xKKVUV24VHI5Q0lCCr6cvIT4hzi6KUkq5BLcKDkc0VZU0lBDtH63DqSullJ1bBYejOse1mUoppTq5VXA4QklDiQaHUkp1ocFxEgYdbkQppY6mwXESDQKNrY06wKFSSnXhVsHR153j5faRvPSucaWU6uRWwdHXnePlntaVVNpUpZRSndwqOPpauaf1rE1VSinVSYPjJCq8rBpHlH+Uk0uilFKuQ4PjJMo8Idg7mADvAGcXRSmlXIZbBUdfd45XeIrew6GUUkdxq+Do+85x7RhXSqmjuVVw9LVyL61xKKXU0TQ4TqAdQ4WnDqeulFJH0+A4gVppo01Eb/5TSqmjaHCcQJVHK6D3cCil1NE0OE6g0h4c2jmulFJHcvngEJExIvI3EXldRG7qr+MernFoH4dSSh3JocEhIstFpEREdhy1fqGIZIpIjojcebJ9GGN2G2NuBK4AMhxZ3q6qPFsRY4j0j+yvQyql1IDg6BrHCmBh1xUi4gk8BZwPpANLRCRdRMaLyNtHPWLsn7kI+BRY7eDydqjyaCOsHbw9vPvrkEopNSB4OXLnxph1IpJy1OppQI4xJhdARF4GLjbG/AFYdIL9rARWisg7wL+Pt42ILAOWASQlJfW67M2049fe690opZTbcWhwnEACcKDL6wJg+ok2FpG5wCWAL/DuibYzxjwNPA2QkZFh+qKgSimljuWM4OgRY8wnwCfd2VZELgQuHDFihCOLpJRSg5ozrqoqBIZ2eZ1oX9drfT1WlVJKqWM5Izg2AGkikioiPsBVwMq+2HFfj46rlFLqWI6+HPcl4AtglIgUiMj1xphW4BbgfWA38KoxZqcjy6GUUqrvOPqqqiUnWP8uJ+no7sXxVgGrMjIylvb1vpVSSllc/s5xpZRSrsWtgkP7OJRSyvHcKjj0qiqllHI8McZ97pU7fB8HcCWQfZq7iQLK+qxQA4N+58FBv7P76+33TTbGnHJIcLcKjr4gIhuNMf02mKIr0O88OOh3dn/99X3dqqlKKaWU42lwKKWU6hENjmM97ewCOIF+58FBv7P765fvq30cSimlekRrHEoppXpEg0MppVSPaHB00ZO50Ac6ERkqIh+LyC4R2Skitzu7TP1FRDxFZIuIvO3ssvQHEQkTkddFZI+I7BaRmc4uk6OJyE/sv9c7ROQlEfFzdpn6mogsF5ESEdnRZV2EiHwoItn253BHHFuDw+5Ec6E7t1QO1QrcYYxJB2YAP3bz79vV7VgjMw8WjwP/M8aMBibi5t9dRBKA24AMY8w4wBNr+gZ3swJYeNS6O4HVxpg0YLX9dZ/T4OjUMRe6McYGvAxc7OQyOYwx5pAxZrN9uRbrZJLg3FI5nogkAt8GnnF2WfqDiIQCs4FnAYwxNmNMlXNL1S+8AH8R8QICgINOLk+fM8asAyqOWn0x8Lx9+XngO444tgZHp+PNhe72J1IAEUkBJgFfObck/eIx4BdAu7ML0k9SgVLgOXvz3DMiEujsQjmSMaYQeATIBw4B1caYD5xbqn4Ta4w5ZF8uAmIdcRANjkFORIKAN4D/Z4ypcXZ5HElEFgElxphNzi5LP/ICJgN/NcZMAupxUPOFq7C361+MFZrxQKCIfM+5pep/xrrXwiH3W2hwdHLYXOiuSkS8sULjRWPMm84uTz84E7hIRPKwmiLPEZF/ObdIDlcAFBhjDtcmX8cKEnc2H9hnjCk1xrQAbwKznFym/lIsInEA9ucSRxxEg6OTw+ZCd0UiIljt3ruNMY86uzz9wRjzK2NMojEmBevfd40xxq3/EjXGFAEHRGSUfdU8YJcTi9Qf8oEZIhJg/z2fh5tfENDFSuBa+/K1wH8dcRCHTh07kBhjWkXk8FzonsByN58L/UzgGmC7iGy1r/u1fVpf5V5uBV60/0GUC/zAyeVxKGPMVyLyOrAZ6+rBLbjh0CMi8hIwF4gSkQLgHuBB4FURuR7YD1zhkGPrkCNKKaV6QpuqlFJK9YgGh1JKqR7R4FBKKdUjGhxKKaV6RINDKaVUj2hwKOUAIlJ3ivdTuo5q2s19rhCRy3pXMqV6T4NDKaVUj2hwKNUDIjJVRLaJiJ+IBNrnfBh3ku2D5P9v7w5ebArjMEnbZ7EAAAGgSURBVI5/n5hCUxKzUmNlxW7YSbGxtFGKovwfNhLN0tJGlLGapQXJYsqUBRo0NVYWlnai5C5+Fu+5uYmrN9IM38/qdO97Tueunt5zus8veZzkRZLXSSYbl7cnuTNcbznJruGchSQrSZ4neTiukJA2C/8AKHVKchXYAeyk9UBd/8Gaj1U1O671rqoPSfYBT4GDwAHgLXCsqlaT3KJVgdwAVoDTVfU+yVngVFVdSnIbuF9Vy3/jd0o/Y+WI1O8KrdvsM21g0DQBriU5Tqty38+3qut3VbU6HN8drvUAOAw8ajVLbKNVg0ubhsEh9dsLzAIztJ3HpylrzwNzwEJVjYZm3vEY0++3+0ULmvWq+ufHu2rr8h2H1O8mcBlYAhZ/sXY3bQbIKMkJ2iOqsfmJ+d/ngCfAG2Bu/HmSmSSH/ujdS7/J4JA6JLkAjKrqHq2J9GiSk1NOWQKOJHlG231sTHy3AVxM8grYQxu29AU4AywmeQms8f/MktAW4ctxSVIXdxySpC4GhySpi8EhSepicEiSuhgckqQuBockqYvBIUnq8hUbbQdYZg6eawAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "x = np.linspace(0, 10, 100)\n",
    "plt.plot(x, x, label='linear')  # Plot some data on the (implicit) axes.\n",
    "plt.plot(x, x**2, label='quadratic')  # etc.\n",
    "plt.plot(x, x**3, label='cubic')\n",
    "plt.xlabel('x label')\n",
    "plt.ylabel('y label')\n",
    "plt.title(\"Simple Plot\")\n",
    "plt.legend();\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gràfiques de dades experimentals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podem posar directamen a `plt.plot` el conjunt de dades i indicar com representar cada punt. En aquest cas l'opcio `'ro'` farà punts rodons (*o*) de color vermell (*r*) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot([1, 2, 3, 4], [1, 4, 9, 16], 'ro')\n",
    "plt.axis([0, 6, 0, 20])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podríem haver escollit un altre color o forma dels punts:\n",
    "\n",
    "   **Colors suportats**:\n",
    "    \n",
    "    =============    ===============================\n",
    "    character        color\n",
    "    =============    ===============================\n",
    "    ``'b'``          blue\n",
    "    ``'g'``          green\n",
    "    ``'r'``          red\n",
    "    ``'c'``          cyan\n",
    "    ``'m'``          magenta\n",
    "    ``'y'``          yellow\n",
    "    ``'k'``          black\n",
    "    ``'w'``          white\n",
    "    =============    ===============================\n",
    "\n",
    "     \n",
    "    **Tipus de punts**\n",
    "    \n",
    "    =============    ===============================\n",
    "    character        description\n",
    "    =============    ===============================\n",
    "    ``'.'``          point marker\n",
    "    ``','``          pixel marker\n",
    "    ``'o'``          circle marker\n",
    "    ``'v'``          triangle_down marker\n",
    "    ``'^'``          triangle_up marker\n",
    "    ``'<'``          triangle_left marker\n",
    "    ``'>'``          triangle_right marker\n",
    "    ``'1'``          tri_down marker\n",
    "    ``'2'``          tri_up marker\n",
    "    ``'3'``          tri_left marker\n",
    "    ``'4'``          tri_right marker\n",
    "    ``'s'``          square marker\n",
    "    ``'p'``          pentagon marker\n",
    "    ``'*'``          star marker\n",
    "    ``'h'``          hexagon1 marker\n",
    "    ``'H'``          hexagon2 marker\n",
    "    ``'+'``          plus marker\n",
    "    ``'x'``          x marker\n",
    "    ``'D'``          diamond marker\n",
    "    ``'d'``          thin_diamond marker\n",
    "    ``'|'``          vline marker\n",
    "    ``'_'``          hline marker\n",
    "    =============    ===============================\n",
    "    \n",
    "    Recordeu que tota aquesta informació i més la podeu obtenir amb:\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function plot in module matplotlib.pyplot:\n",
      "\n",
      "plot(*args, scalex=True, scaley=True, data=None, **kwargs)\n",
      "    Plot y versus x as lines and/or markers.\n",
      "    \n",
      "    Call signatures::\n",
      "    \n",
      "        plot([x], y, [fmt], data=None, **kwargs)\n",
      "        plot([x], y, [fmt], [x2], y2, [fmt2], ..., **kwargs)\n",
      "    \n",
      "    The coordinates of the points or line nodes are given by *x*, *y*.\n",
      "    \n",
      "    The optional parameter *fmt* is a convenient way for defining basic\n",
      "    formatting like color, marker and linestyle. It's a shortcut string\n",
      "    notation described in the *Notes* section below.\n",
      "    \n",
      "    >>> plot(x, y)        # plot x and y using default line style and color\n",
      "    >>> plot(x, y, 'bo')  # plot x and y using blue circle markers\n",
      "    >>> plot(y)           # plot y using x as index array 0..N-1\n",
      "    >>> plot(y, 'r+')     # ditto, but with red plusses\n",
      "    \n",
      "    You can use `.Line2D` properties as keyword arguments for more\n",
      "    control on the appearance. Line properties and *fmt* can be mixed.\n",
      "    The following two calls yield identical results:\n",
      "    \n",
      "    >>> plot(x, y, 'go--', linewidth=2, markersize=12)\n",
      "    >>> plot(x, y, color='green', marker='o', linestyle='dashed',\n",
      "    ...      linewidth=2, markersize=12)\n",
      "    \n",
      "    When conflicting with *fmt*, keyword arguments take precedence.\n",
      "    \n",
      "    **Plotting labelled data**\n",
      "    \n",
      "    There's a convenient way for plotting objects with labelled data (i.e.\n",
      "    data that can be accessed by index ``obj['y']``). Instead of giving\n",
      "    the data in *x* and *y*, you can provide the object in the *data*\n",
      "    parameter and just give the labels for *x* and *y*::\n",
      "    \n",
      "    >>> plot('xlabel', 'ylabel', data=obj)\n",
      "    \n",
      "    All indexable objects are supported. This could e.g. be a `dict`, a\n",
      "    `pandas.DataFame` or a structured numpy array.\n",
      "    \n",
      "    \n",
      "    **Plotting multiple sets of data**\n",
      "    \n",
      "    There are various ways to plot multiple sets of data.\n",
      "    \n",
      "    - The most straight forward way is just to call `plot` multiple times.\n",
      "      Example:\n",
      "    \n",
      "      >>> plot(x1, y1, 'bo')\n",
      "      >>> plot(x2, y2, 'go')\n",
      "    \n",
      "    - Alternatively, if your data is already a 2d array, you can pass it\n",
      "      directly to *x*, *y*. A separate data set will be drawn for every\n",
      "      column.\n",
      "    \n",
      "      Example: an array ``a`` where the first column represents the *x*\n",
      "      values and the other columns are the *y* columns::\n",
      "    \n",
      "      >>> plot(a[0], a[1:])\n",
      "    \n",
      "    - The third way is to specify multiple sets of *[x]*, *y*, *[fmt]*\n",
      "      groups::\n",
      "    \n",
      "      >>> plot(x1, y1, 'g^', x2, y2, 'g-')\n",
      "    \n",
      "      In this case, any additional keyword argument applies to all\n",
      "      datasets. Also this syntax cannot be combined with the *data*\n",
      "      parameter.\n",
      "    \n",
      "    By default, each line is assigned a different style specified by a\n",
      "    'style cycle'. The *fmt* and line property parameters are only\n",
      "    necessary if you want explicit deviations from these defaults.\n",
      "    Alternatively, you can also change the style cycle using the\n",
      "    'axes.prop_cycle' rcParam.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    x, y : array-like or scalar\n",
      "        The horizontal / vertical coordinates of the data points.\n",
      "        *x* values are optional. If not given, they default to\n",
      "        ``[0, ..., N-1]``.\n",
      "    \n",
      "        Commonly, these parameters are arrays of length N. However,\n",
      "        scalars are supported as well (equivalent to an array with\n",
      "        constant value).\n",
      "    \n",
      "        The parameters can also be 2-dimensional. Then, the columns\n",
      "        represent separate data sets.\n",
      "    \n",
      "    fmt : str, optional\n",
      "        A format string, e.g. 'ro' for red circles. See the *Notes*\n",
      "        section for a full description of the format strings.\n",
      "    \n",
      "        Format strings are just an abbreviation for quickly setting\n",
      "        basic line properties. All of these and more can also be\n",
      "        controlled by keyword arguments.\n",
      "    \n",
      "    data : indexable object, optional\n",
      "        An object with labelled data. If given, provide the label names to\n",
      "        plot in *x* and *y*.\n",
      "    \n",
      "        .. note::\n",
      "            Technically there's a slight ambiguity in calls where the\n",
      "            second label is a valid *fmt*. `plot('n', 'o', data=obj)`\n",
      "            could be `plt(x, y)` or `plt(y, fmt)`. In such cases,\n",
      "            the former interpretation is chosen, but a warning is issued.\n",
      "            You may suppress the warning by adding an empty format string\n",
      "            `plot('n', 'o', '', data=obj)`.\n",
      "    \n",
      "    \n",
      "    Other Parameters\n",
      "    ----------------\n",
      "    scalex, scaley : bool, optional, default: True\n",
      "        These parameters determined if the view limits are adapted to\n",
      "        the data limits. The values are passed on to `autoscale_view`.\n",
      "    \n",
      "    **kwargs : `.Line2D` properties, optional\n",
      "        *kwargs* are used to specify properties like a line label (for\n",
      "        auto legends), linewidth, antialiasing, marker face color.\n",
      "        Example::\n",
      "    \n",
      "        >>> plot([1,2,3], [1,2,3], 'go-', label='line 1', linewidth=2)\n",
      "        >>> plot([1,2,3], [1,4,9], 'rs',  label='line 2')\n",
      "    \n",
      "        If you make multiple lines with one plot command, the kwargs\n",
      "        apply to all those lines.\n",
      "    \n",
      "        Here is a list of available `.Line2D` properties:\n",
      "    \n",
      "          agg_filter: a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array \n",
      "      alpha: float\n",
      "      animated: bool\n",
      "      antialiased: bool\n",
      "      clip_box: `.Bbox`\n",
      "      clip_on: bool\n",
      "      clip_path: [(`~matplotlib.path.Path`, `.Transform`) | `.Patch` | None] \n",
      "      color: color\n",
      "      contains: callable\n",
      "      dash_capstyle: {'butt', 'round', 'projecting'}\n",
      "      dash_joinstyle: {'miter', 'round', 'bevel'}\n",
      "      dashes: sequence of floats (on/off ink in points) or (None, None)\n",
      "      drawstyle: {'default', 'steps', 'steps-pre', 'steps-mid', 'steps-post'}\n",
      "      figure: `.Figure`\n",
      "      fillstyle: {'full', 'left', 'right', 'bottom', 'top', 'none'}\n",
      "      gid: str\n",
      "      in_layout: bool\n",
      "      label: object\n",
      "      linestyle: {'-', '--', '-.', ':', '', (offset, on-off-seq), ...}\n",
      "      linewidth: float\n",
      "      marker: unknown\n",
      "      markeredgecolor: color\n",
      "      markeredgewidth: float\n",
      "      markerfacecolor: color\n",
      "      markerfacecoloralt: color\n",
      "      markersize: float\n",
      "      markevery: unknown\n",
      "      path_effects: `.AbstractPathEffect`\n",
      "      picker: float or callable[[Artist, Event], Tuple[bool, dict]]\n",
      "      pickradius: float\n",
      "      rasterized: bool or None\n",
      "      sketch_params: (scale: float, length: float, randomness: float) \n",
      "      snap: bool or None\n",
      "      solid_capstyle: {'butt', 'round', 'projecting'}\n",
      "      solid_joinstyle: {'miter', 'round', 'bevel'}\n",
      "      transform: matplotlib.transforms.Transform\n",
      "      url: str\n",
      "      visible: bool\n",
      "      xdata: 1D array\n",
      "      ydata: 1D array\n",
      "      zorder: float\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    lines\n",
      "        A list of `.Line2D` objects representing the plotted data.\n",
      "    \n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    scatter : XY scatter plot with markers of varying size and/or color (\n",
      "        sometimes also called bubble chart).\n",
      "    \n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    **Format Strings**\n",
      "    \n",
      "    A format string consists of a part for color, marker and line::\n",
      "    \n",
      "        fmt = '[color][marker][line]'\n",
      "    \n",
      "    Each of them is optional. If not provided, the value from the style\n",
      "    cycle is used. Exception: If ``line`` is given, but no ``marker``,\n",
      "    the data will be a line without markers.\n",
      "    \n",
      "    **Colors**\n",
      "    \n",
      "    The following color abbreviations are supported:\n",
      "    \n",
      "    =============    ===============================\n",
      "    character        color\n",
      "    =============    ===============================\n",
      "    ``'b'``          blue\n",
      "    ``'g'``          green\n",
      "    ``'r'``          red\n",
      "    ``'c'``          cyan\n",
      "    ``'m'``          magenta\n",
      "    ``'y'``          yellow\n",
      "    ``'k'``          black\n",
      "    ``'w'``          white\n",
      "    =============    ===============================\n",
      "    \n",
      "    If the color is the only part of the format string, you can\n",
      "    additionally use any  `matplotlib.colors` spec, e.g. full names\n",
      "    (``'green'``) or hex strings (``'#008000'``).\n",
      "    \n",
      "    **Markers**\n",
      "    \n",
      "    =============    ===============================\n",
      "    character        description\n",
      "    =============    ===============================\n",
      "    ``'.'``          point marker\n",
      "    ``','``          pixel marker\n",
      "    ``'o'``          circle marker\n",
      "    ``'v'``          triangle_down marker\n",
      "    ``'^'``          triangle_up marker\n",
      "    ``'<'``          triangle_left marker\n",
      "    ``'>'``          triangle_right marker\n",
      "    ``'1'``          tri_down marker\n",
      "    ``'2'``          tri_up marker\n",
      "    ``'3'``          tri_left marker\n",
      "    ``'4'``          tri_right marker\n",
      "    ``'s'``          square marker\n",
      "    ``'p'``          pentagon marker\n",
      "    ``'*'``          star marker\n",
      "    ``'h'``          hexagon1 marker\n",
      "    ``'H'``          hexagon2 marker\n",
      "    ``'+'``          plus marker\n",
      "    ``'x'``          x marker\n",
      "    ``'D'``          diamond marker\n",
      "    ``'d'``          thin_diamond marker\n",
      "    ``'|'``          vline marker\n",
      "    ``'_'``          hline marker\n",
      "    =============    ===============================\n",
      "    \n",
      "    **Line Styles**\n",
      "    \n",
      "    =============    ===============================\n",
      "    character        description\n",
      "    =============    ===============================\n",
      "    ``'-'``          solid line style\n",
      "    ``'--'``         dashed line style\n",
      "    ``'-.'``         dash-dot line style\n",
      "    ``':'``          dotted line style\n",
      "    =============    ===============================\n",
      "    \n",
      "    Example format strings::\n",
      "    \n",
      "        'b'    # blue markers with default shape\n",
      "        'ro'   # red circles\n",
      "        'g-'   # green solid line\n",
      "        '--'   # dashed line with default color\n",
      "        'k^:'  # black triangle_up markers connected by a dotted line\n",
      "    \n",
      "    .. note::\n",
      "        In addition to the above described arguments, this function can take a\n",
      "        **data** keyword argument. If such a **data** argument is given, the\n",
      "        following arguments are replaced by **data[<arg>]**:\n",
      "    \n",
      "        * All arguments with the following names: 'x', 'y'.\n",
      "    \n",
      "        Objects passed as **data** must support item access (``data[<arg>]``) and\n",
      "        membership test (``<arg> in data``).\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(plt.plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quan tenim molts dades podem fer servir vectors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "U = [0,1,2,3,4,5,6,7,8,9,10]\n",
    "I = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]\n",
    "plt.plot(U, I, 'bx')\n",
    "plt.xlabel('U [V]')\n",
    "plt.ylabel('I [mA]')\n",
    "plt.title(\"Llei d'Ohm\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fent múltiples gràfiques\n",
    "\n",
    "Podem tenir diferents gràfiques simultànies amb *subplot*.\n",
    "\n",
    "Primer anem a preparar les dades. Fixeu-vos com he obtingut **P** calculada com a producte de les dades experimentals **U** i **I**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],\n",
       " [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1],\n",
       " [0,\n",
       "  0.1,\n",
       "  0.4,\n",
       "  0.8999999999999999,\n",
       "  1.6,\n",
       "  2.5,\n",
       "  3.5999999999999996,\n",
       "  4.8999999999999995,\n",
       "  6.4,\n",
       "  8.1,\n",
       "  10])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U = [0,1,2,3,4,5,6,7,8,9,10]\n",
    "I = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]\n",
    "P = []                        #Create empty list\n",
    "for i in range(0, len(U)):\n",
    "     P.append(U[i]*I[i])\n",
    "(U,I,P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primer definirem l'espai utilitzat per la nostra gràfica amb el paràmetre *figsize* de `plt.figure()`   \n",
    "\n",
    "Indicarem la posició de cada gràfica amb `plt.subplot()` abans de generar-la. `plt.subplot()` utilitza un paràmetre de 3 *fci* dígits que indica que la propera gràfica ocuparà la posició *i* d'una graella de *f* files i *c* columnes\n",
    "\n",
    "Quan hem definit totes les gràfiques les visualitzem amb `plt.show()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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u5hljSZIkCYOxJElq22DQdgcSYDCWJEltO3my7Q4kwGAsSZIkAQZjSZLUhsGgeTxS0myfW/eyCrXIp1JIkqT9NxicD8EJVLXZjQR4xliSJEkCDMaSJKltJ0603YEEGIwlSVLbvK5YB4TBWJIkScJgLEmSJAETBuMktyV5KsmZJPdc4vX3JXkiyZeTfCbJ0vRb7a7hEJaXYWGhWQ6HbXckqeuSXJ/kc+PZ/XiS97bdkyS17bLBOMkh4F7gduAYcFeSYxft9hiwUlV/F3gA+OfTbrSrhkNYXYXNzeZJNZubzbbhWNIeexF4f1UdA24B3n2J2S5Jc2WSM8Y3A2eq6umqegG4Dzi+c4eq+lxVjcabXwCOTrfN7lpbg9Howtpo1NQlaa9U1XNV9cXx+l8CTwLXtduVJLVrkmB8HfDMju2zvPzwfBfwXy/1QpLVJBtJNra3tyfvssO2tnZXl6RpS7IM3AQ8fFHdmS1prkz15rskbwdWgH9xqderar2qVqpq5ciRI9P86Jm1uLi7uiRNU5JXA78O/ExV/cXO15zZkubNJMH4WeD6HdtHx7ULJHkLsAbcUVX/Zzrtdd+pU9DrXVjr9Zq6JO2lJK+gCcXDqvp02/1IUtsmCcaPADcmuSHJNcCdwOmdOyS5Cfi3NKH4+em32V39Pqyvw9JS81XxS0vNdr/fdmeSuixJgI8BT1bVh9vuR5IOgsOX26GqXkxyN/AQcAj4eFU9nuRDwEZVnaa5dOLVwH9uZi1bVXXHHvbdKf2+QVjSvnsT8JPAV5J8aVz7+ap6sMWeJKlVlw3GAONB+eBFtQ/uWH/LlPuSJO2hqvpvQNruQwfYYOBXNWvu+M13kiTp25082XYH0r4zGEuSJEkYjCVJ0jmDQXMneMZX2Zxb95IKzYmJrjGWJElzYOd1xQlUtdmNtO88YyxJkiRhMJYkSZdy4kTbHUj7zmAsSZK+ndcVaw4ZjCVJkiQMxpIkSRJgMJYkSZIAg7EkSZIEGIxf0nAIy8uwsNAsh8O2O5IkSdJe8gs+LmE4hNVVGI2a7c3NZhug32+vL0mSJO0dzxhfwtra+VB8zmjU1CVJaoWPT5P2nMH4Era2dleXJGnPnTzZdgdS5xmML2FxcXd1SZIkzT6D8SWcOgW93oW1Xq+pS5K0bwYDSJofOL/uZRXSnjAYX0K/D+vrsLTUzJ+lpWbbG+8kSftqMICq5gfOrxuMpT3hUyleQr9vEJYkSZonnjGWJGkWnDjRdgdS5xmMJUmaBV4+Ie05g7EkSZKEwViSJEkCDMaSJF0ZL22QOsdgLEnSlfCb6KTOMRhLkiRJGIwlSZqc30QndZpf8CFJ0qQGg/MhODn/jXSSOsEzxpIkSRIGY0lSl+znJQ1+E53UORMF4yS3JXkqyZkk91zi9b+R5D+NX384yfK0G5UkTdflZvtM2s8nRXhdsdQ5lw3GSQ4B9wK3A8eAu5Icu2i3dwHfqKrvA/4l8IvTbnQ4hOVlWFholsPhtD9BkubHhLP96hkeJc2QSc4Y3wycqaqnq+oF4D7g+EX7HAc+OV5/ALg1OXfL7tUbDmF1FTY3m/scNjebbcOxJF2xSWb71duPM7g+KULSlEwSjK8DntmxfXZcu+Q+VfUi8E3gu6fRIMDaGoxGF9ZGo6YuSboik8z22TAYNGdNzj0h4ty6wVjSLu3rzXdJVpNsJNnY3t6e+M9tbe2uLkm6elc6sz2DK2lWTRKMnwWu37F9dFy75D5JDgOvAf704jeqqvWqWqmqlSNHjkzc5OLi7uqSpMu67Gy/0pnd6hlcnxQh6SpMEowfAW5MckOSa4A7gdMX7XMaeMd4/SeAz1ZN76nnp05Br3dhrddr6pKkKzLJbJ89npWWdBUuG4zH1wzfDTwEPAncX1WPJ/lQkjvGu30M+O4kZ4D3AVN97E+/D+vrsLTU/DZuaanZ7ven+SmSND9earZP/YM8gytphmSKJ3Z3ZWVlpTY2Nlr5bEm6GkkeraqVtvvYT85sSbNs0rntN99JkiRJGIwlSZIkwGAsSZIkAQZjSZIkCTAYS5IkSUCLT6VIsg1sXsEfvRb4kym3c1B0+dig28fnsc2uKzm+paraxTdezD5n9iV1+dig28fX5WODbh/flR7bRHO7tWB8pZJsdPUxSV0+Nuj28Xlss6vrx9e2Lv/z7fKxQbePr8vHBt0+vr0+Ni+lkCRJkjAYS5IkScBsBuP1thvYQ10+Nuj28Xlss6vrx9e2Lv/z7fKxQbePr8vHBt0+vj09tpm7xliSJEnaC7N4xliSJEmaupkJxkluS/JUkjNJ7mm7n2lKcn2SzyV5IsnjSd7bdk/TluRQkseS/FbbvUxTktcmeSDJ7yd5MskPtt3TNCX52fG/k19N8qkkr2y7pyuV5ONJnk/y1R2170ryu0n+YLx8XZs9dk1X57Yze7Z1eW53aWZDO3N7JoJxkkPAvcDtwDHgriTH2u1qql4E3l9Vx4BbgHd37PgA3gs82XYTe+BXgN+uqr8N/D06dIxJrgN+GlipqjcAh4A72+3qqnwCuO2i2j3AZ6rqRuAz421NQcfntjN7tnVybndwZkMLc3smgjFwM3Cmqp6uqheA+4DjLfc0NVX1XFV9cbz+lzT/kV7XblfTk+Qo8KPAR9vuZZqSvAb4YeBjAFX1QlX9ebtdTd1h4DuSHAZ6wB+13M8Vq6rfA/7sovJx4JPj9U8CP76vTXVbZ+e2M3t2zcHc7szMhnbm9qwE4+uAZ3Zsn6VDQ2inJMvATcDD7XYyVb8M/Bzw1203MmU3ANvAr45/5fjRJK9qu6lpqapngV8CtoDngG9W1e+029XUvb6qnhuvfx14fZvNdMxczG1n9szp7Nyek5kNezy3ZyUYz4UkrwZ+HfiZqvqLtvuZhiQ/BjxfVY+23cseOAy8EfhIVd0E/BUd+lX8+Lqt4zR/kXwv8Kokb2+3q71TzSN6fEyPJubMnkmdndvzNrNhb+b2rATjZ4Hrd2wfHdc6I8kraAbssKo+3XY/U/Qm4I4kf0jzq9QfSfJr7bY0NWeBs1V17kzRAzQDtyveAnytqrar6lvAp4EfarmnafvjJN8DMF4+33I/XdLpue3MnlldntvzMLNhj+f2rATjR4Abk9yQ5Bqai8lPt9zT1CQJzfVOT1bVh9vuZ5qq6gNVdbSqlmn+d/tsVXXi/8FW1deBZ5L8wLh0K/BEiy1N2xZwS5Le+N/RW+nITSo7nAbeMV5/B/CbLfbSNZ2d287s2dXxuT0PMxv2eG4fnuab7ZWqejHJ3cBDNHdZfryqHm+5rWl6E/CTwFeSfGlc+/mqerDFnjSZ9wDD8V/8TwPvbLmfqamqh5M8AHyR5i78x5jhb1NK8ingzcC1Sc4CJ4BfAO5P8i5gE3hbex12S8fntjN7tnVybndtZkM7c9tvvpMkSZKYnUspJEmSpD1lMJYkSZIwGEuSJEmAwViSJEkCDMaSJEkSYDCWJEmSAIOxJEmSBBiMJUmSJAD+H9d9X4OhgEigAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 4))\n",
    "plt.subplot(121)\n",
    "plt.plot(U, I, 'bo')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(U, P, 'r+')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utilitzant *pandas* per millorar la visualització de les dades experimentals\n",
    "\n",
    "Podem millorar la visualització d'aquestes taules de dades amb la libreria *pandas*. Trobareu molts consells útils a https://nikgrozev.com/2015/12/27/pandas-in-jupyter-quickstart-and-useful-snippets/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>U</th>\n",
       "      <th>I</th>\n",
       "      <th>P</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.4</td>\n",
       "      <td>1.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>0.6</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>0.7</td>\n",
       "      <td>4.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>0.8</td>\n",
       "      <td>6.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>0.9</td>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     U    I     P\n",
       "0    0  0.0   0.0\n",
       "1    1  0.1   0.1\n",
       "2    2  0.2   0.4\n",
       "3    3  0.3   0.9\n",
       "4    4  0.4   1.6\n",
       "5    5  0.5   2.5\n",
       "6    6  0.6   3.6\n",
       "7    7  0.7   4.9\n",
       "8    8  0.8   6.4\n",
       "9    9  0.9   8.1\n",
       "10  10  1.0  10.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas\n",
    "df = pandas.DataFrame({\n",
    "   'U': U,\n",
    "   'I': I,\n",
    "   'P': P\n",
    "})\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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