MeetupOutubro2019/CMS-Open-Data-Tutorial-R-tidyverse.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Física de partículas ...  com R  e tidyverse\n",
    "\n",
    "Esse tutorial utiliza os dados abertos do experimento CMS do LHC [CMS Open Data](http://opendata.cern.ch/about/cms) Disponíveis no site [CERN Open Data portal](http://opendata.cern.ch).\n",
    "\n",
    "Para rodar esse tutorial offline, vide o arquivo [README](https://github.com/cms-opendata-education/cms-rmaterial-multiple-languages/blob/master/README.md), con instruções em inglés. Eu estou rodando o  notebook na minha instalação local de R. \n",
    "\n",
    "Também é possível copiar as linhas de código e colar na consola de comandos do RStudio, ou num script e logo rodá-lo.\n",
    "\n",
    "\n",
    "**Créditos:**\n",
    "   * Adaptado do original de [Edith Villegas Garcia](https://github.com/edithvillegas),  [Andrew John Lowe](https://github.com/andrewjohnlowe) e [Achintya Rao](https://github.com/RaoOfPhysics). \n",
    "\n",
    "   * Traduzido ao português e adicionado o ajuste por [Clemencia Mora Herrera](https://github.com/clemencia).\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Os dados:\n",
    "\n",
    "Este tutorial, introduce análise de dados com  R usando dados divulgados ao público no portal **CMS Open Data**. \n",
    "\n",
    "A origem desses dados colisões de prótons do LHC no ano 2011 (Energia do centro-de-massa de 7 TeV). \n",
    "Estes dados contém medições de partículas do estado final, dois ***múons*** (uma versão um pouco mais pesada do elétron, comúm em raios cósmicos). \n",
    "\n",
    "A primeira imagem mostra um desenho esquemático do LHC e seus 4 principais experimentos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure>\n",
    "    <img src=\"https://github.com/cms-opendata-education/zboson-exercise/blob/master/images/LHC.png?raw=true\" alt=\"image missing\" style=\"height: 350px\" />\n",
    "   <figcaption> Imagem 1: O LHC e seus 4 principais experimentos. &copy; \n",
    "       <a href=\"https://cds.cern.ch/record/1708847\">CERN</a> \n",
    "    </figcaption>\n",
    "</figure>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No LHC prótons são acelerados a altíssimas velocidades e feitos colidir em pontos determinados (os 4 da figura acima), onde cada experimento com seus detectores registra e salva a informação dos produtos da colisão. A energia da colisão pode ser convertida em massa de novas partículas ($E=mc^2$) que podem decair em outras mais leves, deixando sinais nos instrumentos de medição em cada detector. Os sinais são traduzidos em momentum ($p=mv$), carga da partícula, energia e a sua direção de saida do ponto de interação.\n",
    "\n",
    "\n",
    "\n",
    "O seguinte é um vídeo que mostra como acontecem as colisões e medições no acelerador LHC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/pQhbhpU9Wrg\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(IRdisplay)\n",
    "display_html('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/pQhbhpU9Wrg\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se combinarmos a informação da energia e momentum dos dois múons para cada observação (_evento_), podemos observar que em certos valores de  ***massa invariante*** (a energia de uma partícula de massa $m$ em reposo é $E=m c^2$ --> relatividade restrita isto é sempre válido no sistema de referência dela própia, então essa massa própria é constante para sistemas de referência diferentes) a frequência de observações é maior: isto quer dizer que existe uma partícula subatómica que decaiu em um par de múons e chamamos isso de uma \"ressonância\". Podemos inferir a presença dessas partículas indiretamente observando seus produtos de decaimento, os múons, e a sua frequência.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure>\n",
    "    <img src=\"http://github.com/cms-opendata-education/zboson-exercise/blob/master/images/eventdisplay.png?raw=true\" alt=\"image missing\" style=\"height: 350px\" />\n",
    "    <figcaption> Imagem 2: Visualização da detecção de dois múons em uma colisão no CMS. </figcaption>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure>\n",
    "    <img src=\"http://github.com/cms-opendata-education/zboson-exercise/blob/master/images/CMS.jpg?raw=true\" alt=\"image missing\" style=\"height: 350px\" />\n",
    "    <figcaption> Imagem 3: Estrutura do experimento CMS, aberto. &copy; \n",
    "        <a href=\"https://cds.cern.ch/record/1433717\">CERN</a> \n",
    "     </figcaption>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure>\n",
    "    <img src=\"http://github.com/cms-opendata-education/zboson-exercise/blob/master/images/CMS2.gif?raw=true\" alt=\"image missing\" style=\"height: 350px\" /> \n",
    "    <figcaption>Imagem 4: Seção transversal do CMS, e como as partículas são detectadas nele. &copy; \n",
    "        <a href=\\\"https://cms-docdb.cern.ch/cgi-bin/PublicDocDB/ShowDocument?docid=4172\\\">CERN</a> \n",
    "    </figcaption>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nesse tutorial podemos criar um gráfico de frequências onde é possível perceber os picos correspondentes a algumas dessas partículas que tem preferência pelo decaimento em dois múons."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Breve introdução a R\n",
    "\n",
    "R é uma linguagem de programação usada amplamente em estatística e ciência de dados. \n",
    "\n",
    "\n",
    "_\"R é a língua franca da estatística\"_ (W. Zeviani, UFPR)\n",
    "\n",
    "[ http://leg.ufpr.br/~walmes/cursoR/data-vis/slides/01-tidyverse.pdf ] \n",
    "\n",
    "\n",
    "\n",
    " \n",
    "### Os tipos de dados em R\n",
    "\n",
    "Os tipos básicos de dados em R são:\n",
    "- Logical -- lógicos ou booleanos: TRUE ou FALSE)\n",
    "- Numeric -- números em geral, números reais\n",
    "- Integer -- inteiros\n",
    "- Complex -- complexos\n",
    "- Character -- carateres ou sequências deles: letras, números como carater, símbolos e frases\n",
    "\n",
    "Em geral, sem ter que especificar, R assigna automátiamente um tipo às variáveis declaradas.\n",
    "Qualquer número é tipo ```numeric```, mas para especificar ```integer``` temos que adicionar um aletra \"L\" no final do valor.\n",
    "\n",
    "A linha abaixo declara a variável ```a``` com valor $5$ de tipo inteiro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a <- 5L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para declarar variáveis complexas a sintaxe é a seguinte:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "b <- 5 + 3i\n",
    "d <- 8 + 0i"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As variáveis lógicas podem tomar o valor ```TRUE``` ou ```FALSE```, mas també pode ser assignado o valor resultante de uma expressão condicional, p.ex.:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "c <- 3 > 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As variáveis de carateres podem ser letras, frases ou outros carateres incluindo números entre aspas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "cr <- \"3!\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para saber o valor de cada variável eu simplesmente chamo o nome:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "5"
      ],
      "text/latex": [
       "5"
      ],
      "text/markdown": [
       "5"
      ],
      "text/plain": [
       "[1] 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "5+3i"
      ],
      "text/latex": [
       "5+3i"
      ],
      "text/markdown": [
       "5+3i"
      ],
      "text/plain": [
       "[1] 5+3i"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "8+0i"
      ],
      "text/latex": [
       "8+0i"
      ],
      "text/markdown": [
       "8+0i"
      ],
      "text/plain": [
       "[1] 8+0i"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "'3!'"
      ],
      "text/latex": [
       "'3!'"
      ],
      "text/markdown": [
       "'3!'"
      ],
      "text/plain": [
       "[1] \"3!\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a\n",
    "b\n",
    "c\n",
    "d\n",
    "cr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vetores\n",
    "\n",
    "É possível agrupar valores em variáveis vetoriais dessa forma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "a <- c(2, 3, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Os vetores podem ser de qualquer tipo. Também podemos aplicar condições aos vetores para criar um vetor lógico:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "a <- c(2, 5, 8, 3, 9)\n",
    "b <- a > 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O vetor ```b``` é o resultado da avaliação da condição ```x>3``` para cada elemento ```x``` do vetor ```a```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>TRUE</li>\n",
       "\t<li>FALSE</li>\n",
       "\t<li>TRUE</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. FALSE\n",
       "2. TRUE\n",
       "3. TRUE\n",
       "4. FALSE\n",
       "5. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] FALSE  TRUE  TRUE FALSE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para acessar algum elemento do vetor, podemos chamar o nome da variável vetor com o índice do elemento desejado. O contador começa de 1 (outras linguagens utilizam 0).\n",
    "\n",
    "Entáo o primeiro elemento de ```a``` será acessado assim:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2"
      ],
      "text/latex": [
       "2"
      ],
      "text/markdown": [
       "2"
      ],
      "text/plain": [
       "[1] 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Também é possível acessar os elementos que satisfazem uma condição. A linha seguinte entrega o subconjunto (sub-vetor) dos elementos de ```a``` que tem valor maior que $3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>5</li>\n",
       "\t<li>8</li>\n",
       "\t<li>9</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 5\n",
       "\\item 8\n",
       "\\item 9\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 5\n",
       "2. 8\n",
       "3. 9\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 5 8 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c<-a[a>3]\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Matrices\n",
    "\n",
    "Em R podemos criar uma matriz a partir de vetores. As matrices são estruturas de dados em 2 dimensões. \n",
    "\n",
    "Podemos criar a matriz especificando os valores nela, o numero de linhas e colunas e se o preenchimento sera por filas ou por colunas.\n",
    "\n",
    "Neste exemplo começamos por um vetor do 1 ao 9:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>7</li>\n",
       "\t<li>8</li>\n",
       "\t<li>9</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\item 7\n",
       "\\item 8\n",
       "\\item 9\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "4. 4\n",
       "5. 5\n",
       "6. 6\n",
       "7. 7\n",
       "8. 8\n",
       "9. 9\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 2 3 4 5 6 7 8 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a <- c(1:9)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logo declaramos ```A``` uma matriz de 3x3 componentes, preenchidas por linha, com os 9 elementos de ```a```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 3 × 3 of type int</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>2</td><td>3</td></tr>\n",
       "\t<tr><td>4</td><td>5</td><td>6</td></tr>\n",
       "\t<tr><td>7</td><td>8</td><td>9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 3 of type int\n",
       "\\begin{tabular}{lll}\n",
       "\t 1 & 2 & 3\\\\\n",
       "\t 4 & 5 & 6\\\\\n",
       "\t 7 & 8 & 9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 3 of type int\n",
       "\n",
       "| 1 | 2 | 3 |\n",
       "| 4 | 5 | 6 |\n",
       "| 7 | 8 | 9 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1    2    3   \n",
       "[2,] 4    5    6   \n",
       "[3,] 7    8    9   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A <- matrix(a, nrow=3, ncol=3, byrow=TRUE)\n",
    "\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para accessar os elementos da matriz, usamos colchetes com o numero de linha e coluna. Por exemplo para acessar o elemento na segunda linha, terceira coluna de ```A``` fazemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6"
      ],
      "text/latex": [
       "6"
      ],
      "text/markdown": [
       "6"
      ],
      "text/plain": [
       "[1] 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A[2,3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos acessar uma linha completa se especificamos só o primeiro número e deixamos em branco o índice das colunas, e viceversa. Por exemplo a chamada ```A[2,]``` retorna os valores da segunda linha de ```A```.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4</li>\n",
       "\t<li>5</li>\n",
       "\t<li>6</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4\n",
       "2. 5\n",
       "3. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4 5 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A[2,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As matrices podem ser acessadas com condições, como foi no caso dos vetores. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1] 16 21 17 22 13 18 23 14 19 24 15 20 25\n"
     ]
    }
   ],
   "source": [
    "# Criar um vetor de valores 1 a 25\n",
    "a <- c(1:25)\n",
    "\n",
    "# Criar a matriz a partir desse vetor com  5 linhas e  5 colunas, preenchendo linha por linha.\n",
    "A <- matrix(a, nrow=5, ncol=5, byrow=TRUE)\n",
    "\n",
    "\n",
    "\n",
    "# Acessar os elementos de A que sejam maiores que 12\n",
    "# ao colocar a condição \"A>12\" nos colchetes\n",
    "# a variável nova é um vetor.\n",
    "C<-A[A>12]\n",
    "\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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       "13"
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      "text/latex": [
       "13"
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      "text/markdown": [
       "13"
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      "text/plain": [
       "[1] 13"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(C)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Arrays (Arranjos)\n",
    "\n",
    "Arrays são similares às matrices, mas podem ter mais de duas dimensões. \n",
    "\n",
    "Podem ser criadas, como as matrices, a partir de um vetor e especificando as dimensões escolhidas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ", , 1\n",
      "\n",
      "     [,1] [,2] [,3]\n",
      "[1,]    1    4    7\n",
      "[2,]    2    5    8\n",
      "[3,]    3    6    9\n",
      "\n",
      ", , 2\n",
      "\n",
      "     [,1] [,2] [,3]\n",
      "[1,]   10   13   16\n",
      "[2,]   11   14   17\n",
      "[3,]   12   15   18\n",
      "\n",
      ", , 3\n",
      "\n",
      "     [,1] [,2] [,3]\n",
      "[1,]   19   22   25\n",
      "[2,]   20   23   26\n",
      "[3,]   21   24   27\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Criar um vetor com valores 1 a 27\n",
    "a <- c(1:27)\n",
    "\n",
    "# Criar um array a partir do vetor a\n",
    "# que contem 3 matrices de 3 linhas e 3 colunas .\n",
    "A <- array(a, dim=c(3,3,3))\n",
    "\n",
    "# Imprimir o array.\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Listas\n",
    "\n",
    "As listas são como  vetores, mas podem conter diferentes tipos de dados concomitantemente, e também vetores, entre seus elementos. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol>\n",
       "\t<li><ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n",
       "</li>\n",
       "\t<li>'a'</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1+5i</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate}\n",
       "\\item \\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\item 'a'\n",
       "\\item 1\n",
       "\\item 1+5i\n",
       "\\end{enumerate}\n"
      ],
      "text/markdown": [
       "1. 1. 1\n",
       "2. 2\n",
       "3. 3\n",
       "\n",
       "\n",
       "\n",
       "2. 'a'\n",
       "3. 1\n",
       "4. 1+5i\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[[1]]\n",
       "[1] 1 2 3\n",
       "\n",
       "[[2]]\n",
       "[1] \"a\"\n",
       "\n",
       "[[3]]\n",
       "[1] 1\n",
       "\n",
       "[[4]]\n",
       "[1] 1+5i\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l <- list(c(1,2,3),'a', 1, 1+5i)\n",
    "\n",
    "l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Data Frames\n",
    "\n",
    "\n",
    "Data  frames  são como listas de vetores com o mesmo comprimento. São usados para armazenar dados em forma de tabela. \n",
    "\n",
    "Para criar um data frame podemos fazer, por exemplo:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 2 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Nome</th><th scope=col>Genero</th><th scope=col>Idade</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Thereza</td><td>F</td><td>20</td></tr>\n",
       "\t<tr><td>Diana  </td><td>F</td><td>23</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 2 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       " Nome & Genero & Idade\\\\\n",
       " <fct> & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Thereza & F & 20\\\\\n",
       "\t Diana   & F & 23\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 2 × 3\n",
       "\n",
       "| Nome &lt;fct&gt; | Genero &lt;fct&gt; | Idade &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| Thereza | F | 20 |\n",
       "| Diana   | F | 23 |\n",
       "\n"
      ],
      "text/plain": [
       "  Nome    Genero Idade\n",
       "1 Thereza F      20   \n",
       "2 Diana   F      23   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data <- data.frame(\n",
    "    Nome = c(\"Thereza\", \"Diana\"),\n",
    "    Genero = c('F','F'),\n",
    "    Idade = c(20, 23)\n",
    ")\n",
    "\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Para mim, aqui reside a beleza do R  ... essa simplicidade!)\n",
    "\n",
    "Para acessar uma coluna em particular, é simplesmente usar o ```$``` e o nome da coluna. \n",
    "Por exemplo para ver os nomes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>Thereza</li>\n",
       "\t<li>Diana</li>\n",
       "</ol>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'Diana'</li>\n",
       "\t\t<li>'Thereza'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item Thereza\n",
       "\\item Diana\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item 'Diana'\n",
       "\\item 'Thereza'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. Thereza\n",
       "2. Diana\n",
       "\n",
       "\n",
       "\n",
       "**Levels**: 1. 'Diana'\n",
       "2. 'Thereza'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] Thereza Diana  \n",
       "Levels: Diana Thereza"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data$Nome"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se queremos ver só uma linha (instância ou observação do seu experimento, medição) chamamos o número da linha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Nome</th><th scope=col>Genero</th><th scope=col>Idade</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Thereza</td><td>F</td><td>20</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       " Nome & Genero & Idade\\\\\n",
       " <fct> & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Thereza & F & 20\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 3\n",
       "\n",
       "| Nome &lt;fct&gt; | Genero &lt;fct&gt; | Idade &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| Thereza | F | 20 |\n",
       "\n"
      ],
      "text/plain": [
       "  Nome    Genero Idade\n",
       "1 Thereza F      20   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[1,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E R tem várias funções para importar arquivos (em formato texto, csv, até xls!) direto para data frames. \n",
    "\n",
    "Como não amar?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explorando o CMS Open Data\n",
    "\n",
    "\n",
    "Agora vamos à tarefa em mãos: analisar dados do CMS.\n",
    "\n",
    "---\n",
    "\n",
    "### Importar dados dos arquivos CSV \n",
    "\n",
    "No portal do [CERN Open Data](http://opendata.cern.ch) tem vários conjuntos de dados disponíveis. Nós vamos usar dados que já foram reduzidos ao formato CSV (comma-separated values), importá-los em R e analizar seu conteúdo. \n",
    "\n",
    "Os dados desse tutorial vêm do seguinte registro: [http://opendata.cern.ch/record/545](http://opendata.cern.ch/record/545)\n",
    "\n",
    "Para importar usamos o seguinte comando:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "mumu <- read.csv(\"http://opendata.cern.ch/record/545/files/Dimuon_DoubleMu.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O comando anterior carregou os dados do arquivo  `Dimuon_DoubleMu.csv` numa variável chamada `mumu`, que é um data frame. \n",
    "\n",
    "Para olhar o conteúdo das primeiras 6 linhas podemos chamar a função `head` e para saber o número de observações usamos a função `nrow`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "100000"
      ],
      "text/latex": [
       "100000"
      ],
      "text/markdown": [
       "100000"
      ],
      "text/plain": [
       "[1] 100000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 21</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Run</th><th scope=col>Event</th><th scope=col>type1</th><th scope=col>E1</th><th scope=col>px1</th><th scope=col>py1</th><th scope=col>pz1</th><th scope=col>pt1</th><th scope=col>eta1</th><th scope=col>phi1</th><th scope=col>⋯</th><th scope=col>type2</th><th scope=col>E2</th><th scope=col>px2</th><th scope=col>py2</th><th scope=col>pz2</th><th scope=col>pt2</th><th scope=col>eta2</th><th scope=col>phi2</th><th scope=col>Q2</th><th scope=col>M</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>⋯</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>165617</td><td>74601703</td><td>G</td><td> 9.6987</td><td>-9.5104</td><td>  0.3662</td><td> 1.8633</td><td> 9.5175</td><td> 0.1945</td><td> 3.1031</td><td>⋯</td><td>G</td><td>9.7633</td><td> 7.3277</td><td>-1.1524</td><td> 6.3473</td><td>7.4178</td><td> 0.7756</td><td>-0.1560</td><td>1</td><td>17.4922</td></tr>\n",
       "\t<tr><td>165617</td><td>75100943</td><td>G</td><td> 6.2039</td><td>-4.2666</td><td>  0.4565</td><td>-4.4793</td><td> 4.2910</td><td>-0.9121</td><td> 3.0350</td><td>⋯</td><td>G</td><td>9.6690</td><td> 7.2740</td><td>-2.8211</td><td>-5.7104</td><td>7.8019</td><td>-0.6786</td><td>-0.3700</td><td>1</td><td>11.5534</td></tr>\n",
       "\t<tr><td>165617</td><td>75587682</td><td>G</td><td>19.2892</td><td>-4.2121</td><td> -0.6516</td><td>18.8121</td><td> 4.2622</td><td> 2.1905</td><td>-2.9881</td><td>⋯</td><td>G</td><td>9.8244</td><td> 4.3439</td><td>-0.4735</td><td> 8.7985</td><td>4.3697</td><td> 1.4497</td><td>-0.1086</td><td>1</td><td> 9.1636</td></tr>\n",
       "\t<tr><td>165617</td><td>75660978</td><td>G</td><td> 7.0427</td><td>-6.3268</td><td> -0.2685</td><td> 3.0802</td><td> 6.3325</td><td> 0.4690</td><td>-3.0992</td><td>⋯</td><td>G</td><td>5.5857</td><td> 4.4748</td><td> 0.8489</td><td>-3.2319</td><td>4.5546</td><td>-0.6605</td><td> 0.1875</td><td>1</td><td>12.4774</td></tr>\n",
       "\t<tr><td>165617</td><td>75947690</td><td>G</td><td> 7.2751</td><td> 0.1030</td><td> -5.5331</td><td>-4.7212</td><td> 5.5340</td><td>-0.7736</td><td>-1.5522</td><td>⋯</td><td>G</td><td>7.3181</td><td>-0.3988</td><td> 6.9408</td><td> 2.2825</td><td>6.9523</td><td> 0.3227</td><td> 1.6282</td><td>1</td><td>14.3159</td></tr>\n",
       "\t<tr><td>165617</td><td>74570517</td><td>G</td><td>14.9422</td><td>-9.1744</td><td>-10.3203</td><td>-5.7079</td><td>13.8087</td><td>-0.4024</td><td>-2.2975</td><td>⋯</td><td>T</td><td>2.9879</td><td>-0.9862</td><td> 0.3541</td><td>-2.7962</td><td>1.0479</td><td>-1.7080</td><td> 2.7969</td><td>1</td><td> 6.8270</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 21\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       " Run & Event & type1 & E1 & px1 & py1 & pz1 & pt1 & eta1 & phi1 & Q1 & type2 & E2 & px2 & py2 & pz2 & pt2 & eta2 & phi2 & Q2 & M\\\\\n",
       " <int> & <int> & <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <int> & <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 165617 & 74601703 & G &  9.6987 & -9.5104 &   0.3662 &  1.8633 &  9.5175 &  0.1945 &  3.1031 & -1 & G & 9.7633 &  7.3277 & -1.1524 &  6.3473 & 7.4178 &  0.7756 & -0.1560 & 1 & 17.4922\\\\\n",
       "\t 165617 & 75100943 & G &  6.2039 & -4.2666 &   0.4565 & -4.4793 &  4.2910 & -0.9121 &  3.0350 & -1 & G & 9.6690 &  7.2740 & -2.8211 & -5.7104 & 7.8019 & -0.6786 & -0.3700 & 1 & 11.5534\\\\\n",
       "\t 165617 & 75587682 & G & 19.2892 & -4.2121 &  -0.6516 & 18.8121 &  4.2622 &  2.1905 & -2.9881 & -1 & G & 9.8244 &  4.3439 & -0.4735 &  8.7985 & 4.3697 &  1.4497 & -0.1086 & 1 &  9.1636\\\\\n",
       "\t 165617 & 75660978 & G &  7.0427 & -6.3268 &  -0.2685 &  3.0802 &  6.3325 &  0.4690 & -3.0992 & -1 & G & 5.5857 &  4.4748 &  0.8489 & -3.2319 & 4.5546 & -0.6605 &  0.1875 & 1 & 12.4774\\\\\n",
       "\t 165617 & 75947690 & G &  7.2751 &  0.1030 &  -5.5331 & -4.7212 &  5.5340 & -0.7736 & -1.5522 & -1 & G & 7.3181 & -0.3988 &  6.9408 &  2.2825 & 6.9523 &  0.3227 &  1.6282 & 1 & 14.3159\\\\\n",
       "\t 165617 & 74570517 & G & 14.9422 & -9.1744 & -10.3203 & -5.7079 & 13.8087 & -0.4024 & -2.2975 & -1 & T & 2.9879 & -0.9862 &  0.3541 & -2.7962 & 1.0479 & -1.7080 &  2.7969 & 1 &  6.8270\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 21\n",
       "\n",
       "| Run &lt;int&gt; | Event &lt;int&gt; | type1 &lt;fct&gt; | E1 &lt;dbl&gt; | px1 &lt;dbl&gt; | py1 &lt;dbl&gt; | pz1 &lt;dbl&gt; | pt1 &lt;dbl&gt; | eta1 &lt;dbl&gt; | phi1 &lt;dbl&gt; | ⋯ ⋯ | type2 &lt;fct&gt; | E2 &lt;dbl&gt; | px2 &lt;dbl&gt; | py2 &lt;dbl&gt; | pz2 &lt;dbl&gt; | pt2 &lt;dbl&gt; | eta2 &lt;dbl&gt; | phi2 &lt;dbl&gt; | Q2 &lt;int&gt; | M &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 165617 | 74601703 | G |  9.6987 | -9.5104 |   0.3662 |  1.8633 |  9.5175 |  0.1945 |  3.1031 | ⋯ | G | 9.7633 |  7.3277 | -1.1524 |  6.3473 | 7.4178 |  0.7756 | -0.1560 | 1 | 17.4922 |\n",
       "| 165617 | 75100943 | G |  6.2039 | -4.2666 |   0.4565 | -4.4793 |  4.2910 | -0.9121 |  3.0350 | ⋯ | G | 9.6690 |  7.2740 | -2.8211 | -5.7104 | 7.8019 | -0.6786 | -0.3700 | 1 | 11.5534 |\n",
       "| 165617 | 75587682 | G | 19.2892 | -4.2121 |  -0.6516 | 18.8121 |  4.2622 |  2.1905 | -2.9881 | ⋯ | G | 9.8244 |  4.3439 | -0.4735 |  8.7985 | 4.3697 |  1.4497 | -0.1086 | 1 |  9.1636 |\n",
       "| 165617 | 75660978 | G |  7.0427 | -6.3268 |  -0.2685 |  3.0802 |  6.3325 |  0.4690 | -3.0992 | ⋯ | G | 5.5857 |  4.4748 |  0.8489 | -3.2319 | 4.5546 | -0.6605 |  0.1875 | 1 | 12.4774 |\n",
       "| 165617 | 75947690 | G |  7.2751 |  0.1030 |  -5.5331 | -4.7212 |  5.5340 | -0.7736 | -1.5522 | ⋯ | G | 7.3181 | -0.3988 |  6.9408 |  2.2825 | 6.9523 |  0.3227 |  1.6282 | 1 | 14.3159 |\n",
       "| 165617 | 74570517 | G | 14.9422 | -9.1744 | -10.3203 | -5.7079 | 13.8087 | -0.4024 | -2.2975 | ⋯ | T | 2.9879 | -0.9862 |  0.3541 | -2.7962 | 1.0479 | -1.7080 |  2.7969 | 1 |  6.8270 |\n",
       "\n"
      ],
      "text/plain": [
       "  Run    Event    type1 E1      px1     py1      pz1     pt1     eta1   \n",
       "1 165617 74601703 G      9.6987 -9.5104   0.3662  1.8633  9.5175  0.1945\n",
       "2 165617 75100943 G      6.2039 -4.2666   0.4565 -4.4793  4.2910 -0.9121\n",
       "3 165617 75587682 G     19.2892 -4.2121  -0.6516 18.8121  4.2622  2.1905\n",
       "4 165617 75660978 G      7.0427 -6.3268  -0.2685  3.0802  6.3325  0.4690\n",
       "5 165617 75947690 G      7.2751  0.1030  -5.5331 -4.7212  5.5340 -0.7736\n",
       "6 165617 74570517 G     14.9422 -9.1744 -10.3203 -5.7079 13.8087 -0.4024\n",
       "  phi1    <U+22EF>   type2 E2     px2     py2     pz2     pt2    eta2    phi2   \n",
       "1  3.1031 <U+22EF> G     9.7633  7.3277 -1.1524  6.3473 7.4178  0.7756 -0.1560\n",
       "2  3.0350 <U+22EF> G     9.6690  7.2740 -2.8211 -5.7104 7.8019 -0.6786 -0.3700\n",
       "3 -2.9881 <U+22EF> G     9.8244  4.3439 -0.4735  8.7985 4.3697  1.4497 -0.1086\n",
       "4 -3.0992 <U+22EF> G     5.5857  4.4748  0.8489 -3.2319 4.5546 -0.6605  0.1875\n",
       "5 -1.5522 <U+22EF> G     7.3181 -0.3988  6.9408  2.2825 6.9523  0.3227  1.6282\n",
       "6 -2.2975 <U+22EF> T     2.9879 -0.9862  0.3541 -2.7962 1.0479 -1.7080  2.7969\n",
       "  Q2 M      \n",
       "1 1  17.4922\n",
       "2 1  11.5534\n",
       "3 1   9.1636\n",
       "4 1  12.4774\n",
       "5 1  14.3159\n",
       "6 1   6.8270"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nrow(mumu)\n",
    "head(mumu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O nosso conjunto de dados tem 100 mil linhas (cada linha é um evento de colisão) e 21 colunas (cada coluna é uma variável da descrição ou das medições dos produtos finais do evento).\n",
    "\n",
    "\n",
    "Nesse ponto já podemos chamar o *tidyverse*. Para ter uma visualização mais \"agradável\" dos dados podemos mudar de data frame para *tibble*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: tidyverse\n",
      "Warning message in as.POSIXlt.POSIXct(Sys.time()):\n",
      "\"unknown timezone 'zone/tz/2019b.1.0/zoneinfo/America/Sao_Paulo'\"-- \u001b[1mAttaching packages\u001b[22m --------------------------------------- tidyverse 1.2.1 --\n",
      "\u001b[32mv\u001b[39m \u001b[34mggplot2\u001b[39m 3.2.1     \u001b[32mv\u001b[39m \u001b[34mpurrr  \u001b[39m 0.3.3\n",
      "\u001b[32mv\u001b[39m \u001b[34mtibble \u001b[39m 2.1.3     \u001b[32mv\u001b[39m \u001b[34mdplyr  \u001b[39m 0.8.3\n",
      "\u001b[32mv\u001b[39m \u001b[34mtidyr  \u001b[39m 1.0.0     \u001b[32mv\u001b[39m \u001b[34mstringr\u001b[39m 1.4.0\n",
      "\u001b[32mv\u001b[39m \u001b[34mreadr  \u001b[39m 1.1.1     \u001b[32mv\u001b[39m \u001b[34mforcats\u001b[39m 0.4.0\n",
      "-- \u001b[1mConflicts\u001b[22m ------------------------------------------ tidyverse_conflicts() --\n",
      "\u001b[31mx\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31mx\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n"
     ]
    }
   ],
   "source": [
    "require(tidyverse)\n",
    "tbmumu<- mumu %>% as_tibble()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O tidyverse inclui o pacote `magrittr`,  que introduz o operador *pipe* (como tubulação, mas também \"ce ci n'est pas une pipe\") com símbolo `%>%` o que entrega o objeto da esquerda como argumento à função da direita. E com esses encanamentos é possível fazer várias operações sucessivas de forma concisa.\n",
    "\n",
    "Então o código acima aplica a função `as_tibble` ao data frame `mumu` e o resultado (que é um *tibble*) é armazenado na variável `tbmumu`.\n",
    "\n",
    "Logo ao imprimir as primeiras 6 linhas da nossa tabela tipo *tibble* temos uma visualização que: \n",
    "\n",
    "   * cabe na tela\n",
    "   * dá informações sobre aquilo que não coube\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[38;5;246m# A tibble: 6 x 21\u001b[39m\n",
      "     Run  Event type1    E1    px1     py1   pz1   pt1   eta1  phi1    Q1 type2\n",
      "   \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<fct>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m   \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<fct>\u001b[39m\u001b[23m\n",
      "\u001b[38;5;250m1\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.46\u001b[38;5;246me\u001b[39m7 G      9.70 -\u001b[31m9\u001b[39m\u001b[31m.\u001b[39m\u001b[31m51\u001b[39m    0.366  1.86  9.52  0.194  3.10    -\u001b[31m1\u001b[39m G    \n",
      "\u001b[38;5;250m2\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.51\u001b[38;5;246me\u001b[39m7 G      6.20 -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m27\u001b[39m    0.456 -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m48\u001b[39m  4.29 -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m912\u001b[39m  3.04    -\u001b[31m1\u001b[39m G    \n",
      "\u001b[38;5;250m3\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.56\u001b[38;5;246me\u001b[39m7 G     19.3  -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m21\u001b[39m   -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m652\u001b[39m 18.8   4.26  2.19  -\u001b[31m2\u001b[39m\u001b[31m.\u001b[39m\u001b[31m99\u001b[39m    -\u001b[31m1\u001b[39m G    \n",
      "\u001b[38;5;250m4\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.57\u001b[38;5;246me\u001b[39m7 G      7.04 -\u001b[31m6\u001b[39m\u001b[31m.\u001b[39m\u001b[31m33\u001b[39m   -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m268\u001b[39m  3.08  6.33  0.469 -\u001b[31m3\u001b[39m\u001b[31m.\u001b[39m\u001b[31m10\u001b[39m    -\u001b[31m1\u001b[39m G    \n",
      "\u001b[38;5;250m5\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.59\u001b[38;5;246me\u001b[39m7 G      7.28  0.103  -\u001b[31m5\u001b[39m\u001b[31m.\u001b[39m\u001b[31m53\u001b[39m  -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m72\u001b[39m  5.53 -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m774\u001b[39m -\u001b[31m1\u001b[39m\u001b[31m.\u001b[39m\u001b[31m55\u001b[39m    -\u001b[31m1\u001b[39m G    \n",
      "\u001b[38;5;250m6\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.46\u001b[38;5;246me\u001b[39m7 G     14.9  -\u001b[31m9\u001b[39m\u001b[31m.\u001b[39m\u001b[31m17\u001b[39m  -\u001b[31m10\u001b[39m\u001b[31m.\u001b[39m\u001b[31m3\u001b[39m   -\u001b[31m5\u001b[39m\u001b[31m.\u001b[39m\u001b[31m71\u001b[39m 13.8  -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m402\u001b[39m -\u001b[31m2\u001b[39m\u001b[31m.\u001b[39m\u001b[31m30\u001b[39m    -\u001b[31m1\u001b[39m T    \n",
      "\u001b[38;5;246m# ... with 9 more variables: E2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, px2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, py2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, pz2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m,\n",
      "#   pt2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, eta2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, phi2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, Q2 \u001b[3m\u001b[38;5;246m<int>\u001b[38;5;246m\u001b[23m, M \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "print(head(tbmumu))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do output acima podemos ver as primeiras 12 colunas, com seus tipos, com cores para valores negativos, e temos a informação adicional de 9 variáveis não mostradas. Podemos acessar as colunas e linhas da mesma forma do data frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]  9.6987  6.2039 19.2892  7.0427  7.2751 14.9422\n"
     ]
    }
   ],
   "source": [
    "# imprime os primeiros 6 elementos da coluna chamada E1\n",
    "# o que é retornado com esse operador é um vetor\n",
    "print(head(tbmumu$E1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[38;5;246m# A tibble: 1 x 21\u001b[39m\n",
      "     Run  Event type1    E1   px1   py1   pz1   pt1  eta1  phi1    Q1 type2\n",
      "   \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<fct>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<fct>\u001b[39m\u001b[23m\n",
      "\u001b[38;5;250m1\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.46\u001b[38;5;246me\u001b[39m7 G      9.70 -\u001b[31m9\u001b[39m\u001b[31m.\u001b[39m\u001b[31m51\u001b[39m 0.366  1.86  9.52 0.194  3.10    -\u001b[31m1\u001b[39m G    \n",
      "\u001b[38;5;246m# ... with 9 more variables: E2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, px2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, py2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, pz2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m,\n",
      "#   pt2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, eta2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, phi2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, Q2 \u001b[3m\u001b[38;5;246m<int>\u001b[38;5;246m\u001b[23m, M \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# imprime a primeira linha de dados\n",
    "# retora um novo tibble que é sub-conjunto do original\n",
    "print(tbmumu[1,])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[38;5;246m# A tibble: 10 x 21\u001b[39m\n",
      "      Run  Event type1    E1    px1     py1    pz1   pt1   eta1  phi1    Q1\n",
      "    \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<fct>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m   \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m\n",
      "\u001b[38;5;250m 1\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.46\u001b[38;5;246me\u001b[39m7 G      9.70 -\u001b[31m9\u001b[39m\u001b[31m.\u001b[39m\u001b[31m51\u001b[39m    0.366   1.86  9.52  0.194  3.10    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m 2\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.51\u001b[38;5;246me\u001b[39m7 G      6.20 -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m27\u001b[39m    0.456  -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m48\u001b[39m  4.29 -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m912\u001b[39m  3.04    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m 3\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.56\u001b[38;5;246me\u001b[39m7 G     19.3  -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m21\u001b[39m   -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m652\u001b[39m  18.8   4.26  2.19  -\u001b[31m2\u001b[39m\u001b[31m.\u001b[39m\u001b[31m99\u001b[39m    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m 4\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.57\u001b[38;5;246me\u001b[39m7 G      7.04 -\u001b[31m6\u001b[39m\u001b[31m.\u001b[39m\u001b[31m33\u001b[39m   -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m268\u001b[39m   3.08  6.33  0.469 -\u001b[31m3\u001b[39m\u001b[31m.\u001b[39m\u001b[31m10\u001b[39m    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m 5\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.59\u001b[38;5;246me\u001b[39m7 G      7.28  0.103  -\u001b[31m5\u001b[39m\u001b[31m.\u001b[39m\u001b[31m53\u001b[39m   -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m72\u001b[39m  5.53 -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m774\u001b[39m -\u001b[31m1\u001b[39m\u001b[31m.\u001b[39m\u001b[31m55\u001b[39m    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m 6\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.46\u001b[38;5;246me\u001b[39m7 G     14.9  -\u001b[31m9\u001b[39m\u001b[31m.\u001b[39m\u001b[31m17\u001b[39m  -\u001b[31m10\u001b[39m\u001b[31m.\u001b[39m\u001b[31m3\u001b[39m    -\u001b[31m5\u001b[39m\u001b[31m.\u001b[39m\u001b[31m71\u001b[39m 13.8  -\u001b[31m0\u001b[39m\u001b[31m.\u001b[39m\u001b[31m402\u001b[39m -\u001b[31m2\u001b[39m\u001b[31m.\u001b[39m\u001b[31m30\u001b[39m    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m 7\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.47\u001b[38;5;246me\u001b[39m7 G     42.0  -\u001b[31m1\u001b[39m\u001b[31m.\u001b[39m\u001b[31m48\u001b[39m  -\u001b[31m12\u001b[39m\u001b[31m.\u001b[39m\u001b[31m5\u001b[39m    40.0  12.6   1.88  -\u001b[31m1\u001b[39m\u001b[31m.\u001b[39m\u001b[31m69\u001b[39m    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m 8\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.47\u001b[38;5;246me\u001b[39m7 G     14.4  -\u001b[31m4\u001b[39m\u001b[31m.\u001b[39m\u001b[31m34\u001b[39m   -\u001b[31m6\u001b[39m\u001b[31m.\u001b[39m\u001b[31m0\u001b[39m\u001b[31m7\u001b[39m  -\u001b[31m12\u001b[39m\u001b[31m.\u001b[39m\u001b[31m3\u001b[39m   7.46 -\u001b[31m1\u001b[39m\u001b[31m.\u001b[39m\u001b[31m28\u001b[39m  -\u001b[31m2\u001b[39m\u001b[31m.\u001b[39m\u001b[31m19\u001b[39m     1\n",
      "\u001b[38;5;250m 9\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.52\u001b[38;5;246me\u001b[39m7 G      9.76  2.39   -\u001b[31m3\u001b[39m\u001b[31m.\u001b[39m\u001b[31m78\u001b[39m    8.67  4.47  1.42  -\u001b[31m1\u001b[39m\u001b[31m.\u001b[39m\u001b[31m0\u001b[39m\u001b[31m1\u001b[39m    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;250m10\u001b[39m \u001b[4m1\u001b[24m\u001b[4m6\u001b[24m\u001b[4m5\u001b[24m617 7.52\u001b[38;5;246me\u001b[39m7 G     10.2   0.476  -\u001b[31m8\u001b[39m\u001b[31m.\u001b[39m\u001b[31m52\u001b[39m    5.52  8.53  0.609 -\u001b[31m1\u001b[39m\u001b[31m.\u001b[39m\u001b[31m51\u001b[39m    -\u001b[31m1\u001b[39m\n",
      "\u001b[38;5;246m# ... with 10 more variables: type2 \u001b[3m\u001b[38;5;246m<fct>\u001b[38;5;246m\u001b[23m, E2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, px2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, py2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m,\n",
      "#   pz2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, pt2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, eta2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, phi2 \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m, Q2 \u001b[3m\u001b[38;5;246m<int>\u001b[38;5;246m\u001b[23m, M \u001b[3m\u001b[38;5;246m<dbl>\u001b[38;5;246m\u001b[23m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# Este outro exemplo retorna o subconjunto das 10 primeiras linhas\n",
    "print(tbmumu[1:10,])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calcular a Massa invariante\n",
    "\n",
    "Nossa tabela tem observações de colisões com 2 *múons* no estado final.\n",
    "\n",
    "Como vimos na tabela, temos valores para energia (E), o momentum linear (px, py, pz), a *pseudo-rapidez* (eta ou η, que tem relação com o ángulo polar) e o ángulo azimutal (phi ou φ). \n",
    "\n",
    "Podemos calcular a massa invariante, ou seja a energia equivalente em repouso que produziu esses múons, com a seguinte equação: \n",
    "\n",
    "$M = \\sqrt{(\\sum{E})^2 - ||\\sum{p}||^2}$\n",
    "\n",
    "onde $M$ é a massa invariante,  $\\sum{E}$ é o total da soma das energias (cinética relativística) das partículas finais, e $\\sum{p}$ é o total da soma dos momentos lineares. \n",
    "\n",
    "No nosso código, vamos calcular a massa invariante usando os valores de  `px`, `py` e `pz` e a energia dos dois múons. Primeiramente precisamos calcular a soma vetorial do  momentum. \n",
    "\n",
    "A função `mutate` do **tidyverse** faz o cálculo especificado para cada observação e _adiciona novas variáveis_, nesse casso `ptotal`, `E` e `mass`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in sqrt(E^2 - ptotal^2):\n",
      "\"NaNs produced\""
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Run</th><th scope=col>Event</th><th scope=col>ptotal</th><th scope=col>E</th><th scope=col>mass</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>165617</td><td>74601703</td><td> 8.532071</td><td>19.4620</td><td>17.492090</td></tr>\n",
       "\t<tr><td>165617</td><td>75100943</td><td>10.884198</td><td>15.8729</td><td>11.553492</td></tr>\n",
       "\t<tr><td>165617</td><td>75587682</td><td>27.633828</td><td>29.1136</td><td> 9.163692</td></tr>\n",
       "\t<tr><td>165617</td><td>75660978</td><td> 1.946736</td><td>12.6284</td><td>12.477448</td></tr>\n",
       "\t<tr><td>165617</td><td>75947690</td><td> 2.831320</td><td>14.5932</td><td>14.315904</td></tr>\n",
       "\t<tr><td>165617</td><td>74570517</td><td>16.579585</td><td>17.9301</td><td> 6.826847</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       " Run & Event & ptotal & E & mass\\\\\n",
       " <int> & <int> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 165617 & 74601703 &  8.532071 & 19.4620 & 17.492090\\\\\n",
       "\t 165617 & 75100943 & 10.884198 & 15.8729 & 11.553492\\\\\n",
       "\t 165617 & 75587682 & 27.633828 & 29.1136 &  9.163692\\\\\n",
       "\t 165617 & 75660978 &  1.946736 & 12.6284 & 12.477448\\\\\n",
       "\t 165617 & 75947690 &  2.831320 & 14.5932 & 14.315904\\\\\n",
       "\t 165617 & 74570517 & 16.579585 & 17.9301 &  6.826847\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 6 × 5\n",
       "\n",
       "| Run &lt;int&gt; | Event &lt;int&gt; | ptotal &lt;dbl&gt; | E &lt;dbl&gt; | mass &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 165617 | 74601703 |  8.532071 | 19.4620 | 17.492090 |\n",
       "| 165617 | 75100943 | 10.884198 | 15.8729 | 11.553492 |\n",
       "| 165617 | 75587682 | 27.633828 | 29.1136 |  9.163692 |\n",
       "| 165617 | 75660978 |  1.946736 | 12.6284 | 12.477448 |\n",
       "| 165617 | 75947690 |  2.831320 | 14.5932 | 14.315904 |\n",
       "| 165617 | 74570517 | 16.579585 | 17.9301 |  6.826847 |\n",
       "\n"
      ],
      "text/plain": [
       "  Run    Event    ptotal    E       mass     \n",
       "1 165617 74601703  8.532071 19.4620 17.492090\n",
       "2 165617 75100943 10.884198 15.8729 11.553492\n",
       "3 165617 75587682 27.633828 29.1136  9.163692\n",
       "4 165617 75660978  1.946736 12.6284 12.477448\n",
       "5 165617 75947690  2.831320 14.5932 14.315904\n",
       "6 165617 74570517 16.579585 17.9301  6.826847"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tbmumu<-tbmumu%>%mutate(ptotal = sqrt((px1+px2)^2 + (py1+py2)^2 + (pz1+pz2)^2), \n",
    "         E = E1+E2, \n",
    "         mass = sqrt(E^2 - ptotal^2))\n",
    "tbmumu%>% select(Run, Event, ptotal,E, mass)%>%head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "É possível também definir uma função para fazer nosso cálculo:\n",
    "\n",
    "```\n",
    "myfunctionname = function(arg1, arg2...)\n",
    "{\n",
    "statements\n",
    "return(a) \n",
    "}\n",
    "```\n",
    "\n",
    "Por exemplo podemos definir uma função para a  magnitude soma vetorial de dois vetores de 3 componentes,  e outra função que entrega o resultado para a massa invariante a partir de `ptotal` e `E`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "sumvecmag = function(x1,x2,y1,y2,z1,z2){\n",
    "    x = x1+x2\n",
    "    y = y1+y2\n",
    "    z = z1+z2\n",
    "    tot = sqrt(x^2+y^2+z^2)\n",
    "    return(tot)\n",
    "}\n",
    "\n",
    "invmass = function(ptot, E) {\n",
    "    m = sqrt(E^2 - ptot^2)\n",
    "    return(m)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora podemos adicionar uma nova coluna calculada chamando as funções definidas :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in sqrt(E^2 - ptot^2):\n",
      "\"NaNs produced\""
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[38;5;246m# A tibble: 6 x 5\u001b[39m\n",
      "  ptotal ptotal_f     E  mass mass_f\n",
      "   \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m    \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m  \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m\n",
      "\u001b[38;5;250m1\u001b[39m   8.53     8.53  19.5 17.5   17.5 \n",
      "\u001b[38;5;250m2\u001b[39m  10.9     10.9   15.9 11.6   11.6 \n",
      "\u001b[38;5;250m3\u001b[39m  27.6     27.6   29.1  9.16   9.16\n",
      "\u001b[38;5;250m4\u001b[39m   1.95     1.95  12.6 12.5   12.5 \n",
      "\u001b[38;5;250m5\u001b[39m   2.83     2.83  14.6 14.3   14.3 \n",
      "\u001b[38;5;250m6\u001b[39m  16.6     16.6   17.9  6.83   6.83\n"
     ]
    }
   ],
   "source": [
    "tbmumu<- tbmumu %>% mutate( \n",
    "    ptotal_f = sumvecmag( px1, px2, py1, py2 , pz1, pz2),\n",
    "    E = E1 + E2,\n",
    "    mass_f=invmass(ptotal_f,E)) \n",
    "\n",
    "# Visualizar as primeiras 6 linhas do tibble, selecionando só as colunas do meu interesse\n",
    "print(head(tbmumu%>% select(ptotal,ptotal_f, E, mass, mass_f)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fazer um Histograma\n",
    "\n",
    "Em física de partículas trabalhamos com distribuições de frequências, quer dizer histogramas.\n",
    "\n",
    "Nesse caso, quero olhar só uma porção dos dados, onde a variável massa esta entre 1.1 e 5 (GeV). Para isto posso utilizar a função `filter` do tidyverse, com operadores `%>%`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "tbsel <- tbmumu%>% filter(mass>1.1 & mass < 5) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A visualização do gráfico do histograma pode ser feita com a função própria básica do R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/C'"
      ],
      "text/latex": [
       "'en\\_US.UTF-8/en\\_US.UTF-8/en\\_US.UTF-8/C/en\\_US.UTF-8/C'"
      ],
      "text/markdown": [
       "'en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/C'"
      ],
      "text/plain": [
       "[1] \"en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/C\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Sys.setlocale(locale = \"en_US.UTF-8\") #Para ter carateres de acentos\n",
    "library(repr)\n",
    "options(repr.plot.width=6,repr.plot.height=4 ) #Para  ter gráficos de tamanho que caiba na tela"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MzKyvrDH/7Qs2fPhg0bGo3GoKCgfv36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\nTkSuQmCC",
      "text/plain": [
       "Plot with title “Histograma da Massa Invariante”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(tbsel$mass, breaks = 200, xlim=c(1,5),\n",
    "     main=\"Histograma da Massa Invariante\",\n",
    "     xlab = \"Massa (GeV)\",ylab=\"Frequência \", \n",
    "     lty=\"blank\", \n",
    "     col=\"purple\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observamos um pico maior perto do valor de $3.1$ GeV  e outro pequeno perto de $3.7$ GeV.\n",
    "Esses valores correspondem às massas de duas partículas que decaem em dois múons ou mais específicamente, um múon e um anti-múon (múon carregado positivamente). \n",
    "\n",
    "Olhando na base de dados do  [Particle Data Group](http://pdg.lbl.gov/), podemos ver que essas partículas são os **mésons** (partículas **hadrônicas** compostas de um quark e um anti-quark)  ***J/ψ(1S)*** e ***ψ(2S)***, respectivamente. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graficando com o tidyverse\n",
    "\n",
    "Podemos condensar o processo de importar, manipular as variáveis e graficar o histograma com um código muito enxuto:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in sqrt(E^2 - ptotal^2):\n",
      "“NaNs produced”Warning message:\n",
      "“Transformation introduced infinite values in continuous y-axis”Warning message:\n",
      "“Removed 3 rows containing missing values (geom_bar).”"
     ]
    },
    {
     "data": {
      "image/png": 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WgBtgLHT3/60+3btw8aNCgUJbUETdOcTmdmZma4Cwmgrq6uuro6MmsLIsgJVsnJ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\ngQMAAChH4AAAAMr9f72Wa++6GClQAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "read_csv(\"http://opendata.cern.ch/record/545/files/Dimuon_DoubleMu.csv\", \n",
    "         col_types = cols()) %>% \n",
    "  mutate(ptotal = sqrt((px1+px2)^2 + (py1+py2)^2 + (pz1+pz2)^2), \n",
    "         E = E1+E2, \n",
    "         mass = sqrt(E^2 - ptotal^2)) %>% \n",
    "  filter(mass >0.1 & mass<120) %>% \n",
    "  ggplot(aes(mass)) + \n",
    "     geom_histogram(bins = 250, fill = \"purple\", alpha = 0.5) + \n",
    "     xlab(\"Massa (GeV)\") + \n",
    "     ylab(\"Frequência\") + \n",
    "     scale_x_continuous(trans = 'log10') +\n",
    "     scale_y_continuous(trans = 'log10') +\n",
    "     ggtitle(\"Espectro de di-múons no CMS\") + \n",
    "     theme_bw() + \n",
    "     theme(plot.title = element_text(hjust = 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora está ficando bom!\n",
    "\n",
    "A cadeia de comandos pode ser lida como uma frase, com uma sucessão de **ações** sobre os dados:\n",
    "\n",
    "\"**Leia** o arquivo, \n",
    "  logo **mude** o conteúdo criando as novas variáveis `ptotal`,`E` e `mass`, \n",
    "  logo **filtre** para ver só as observações no intervalo desejado, \n",
    "  logo **grafique** com os parâmetros apropriados\"\n",
    "\n",
    "O pacote de gráficos do tidyverse é ``ggplot2``, onde as diferentes opções do gráfico estão sequenciadas com símbolo `+`. Neste caso eu escolhi usar uma escala `log-log` que permite ter uma visualização abrangente de várias ordens de grandeza, e assim observar vários picos de ressonância."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As opções do gráfico são:\n",
    "\n",
    "- `ggplot()` a função central do pacote `ggplot2`, que trabalha com o princípio de *camadas*:\n",
    "    1. `aes(mass)` quer dizer que vamos usar a variável `mass` \n",
    "    1. `geom_histogram()` tomar a variável e fazer o histograma\n",
    "    1. `xlab()` e `ylab()` os nomes dos eixos\n",
    "    1. `ggtitle()` título do gráfico\n",
    "    1. `theme_bw()` tema preto-e-branco, \n",
    "    1. `theme()` permite manipular alguns elementos específicos do gráfico"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ajustando uma função ao pico do $J/\\psi$\n",
    "\n",
    "Voltando ao *tibble* onde já habiamos selecionado o intervalo que apresenta o pico do méson $J/\\psi$, podemos chamar a função hist sem graficar para ter só os resultados das frequências nos intervalos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "a<-hist(tbsel$mass,breaks=200,plot=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     x nobs\n",
      "1 1.11  123\n",
      "2 1.13  128\n",
      "3 1.15  112\n",
      "4 1.17  116\n",
      "5 1.19  142\n",
      "6 1.21  113\n"
     ]
    }
   ],
   "source": [
    "mydf<- data.frame(x=a$mids, nobs=a$counts) \n",
    "print(head(mydf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pWXlxNCvLy8fvvtt/79+zs6Ovr4+MTExMTHx3McJAAAAFg2VpfFqujdu/elS5eM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\nAAAAAIf7D6B594+5onJmAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(latex2exp)\n",
    "mydf %>%\n",
    "   ggplot(aes(x,nobs, ymin=nobs-sqrt(nobs),ymax=nobs+sqrt(nobs))) + \n",
    "   geom_point() + \n",
    "   geom_errorbar() + \n",
    "   xlab(\"Massa (GeV)\")+\n",
    "   ylab(\"Frequência\")+\n",
    "   ggtitle(TeX(\"Histograma do pico dos mésons J/$\\\\psi$ e $\\\\psi$\"))+\n",
    "   theme_bw() + theme(plot.title = element_text(hjust = 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A função que descreve os dados\n",
    "\n",
    "Uma possível função para descrever esses dois picos seria a soma de uma gaussiana com média perto de $3.1$, outra com média perto de $3.7$ e uma reta decrescente como \"base\" (nosso *background*)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "my2gausspluslin <- function(x, mean1, sigma1, norm1,mean2,sigma2,norm2,a,b) {\n",
    "    \n",
    "    f <- norm1 * exp(-1*((x-mean1)/sigma1)^2)+ norm2 * exp(-1*((x-mean2)/sigma2)^2) + a*x +b\n",
    "    return(f)\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vou chamar a função `nls` que faz a optimização dos parámetros da função com mínimos quadrados não lineares [documentação](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/nls.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Formula: nobs ~ my2gausspluslin(x, mean1, sigma1, norm1, mean2, sigma2, \n",
       "    norm2, a, b)\n",
       "\n",
       "Parameters:\n",
       "         Estimate Std. Error   t value Pr(>|t|)    \n",
       "mean1   3.093e+00  2.501e-04 12368.436  < 2e-16 ***\n",
       "sigma1  4.189e-02  3.562e-04   117.597  < 2e-16 ***\n",
       "norm1   1.731e+03  1.269e+01   136.445  < 2e-16 ***\n",
       "mean2   3.686e+00  7.868e-03   468.453  < 2e-16 ***\n",
       "sigma2  3.522e-02  1.122e-02     3.140 0.001963 ** \n",
       "norm2   5.044e+01  1.384e+01     3.645 0.000346 ***\n",
       "a      -3.294e+01  1.071e+00   -30.758  < 2e-16 ***\n",
       "b       1.695e+02  3.471e+00    48.844  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 16.74 on 187 degrees of freedom\n",
       "\n",
       "Number of iterations to convergence: 16 \n",
       "Achieved convergence tolerance: 5.399e-06\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res <- nls( nobs ~ my2gausspluslin(x,mean1,sigma1,norm1,mean2,sigma2,norm2,a,b), \n",
    "           data = mydf, \n",
    "           start=list(mean1=3.1, sigma1=0.1, norm1=3000,mean2=3.7,sigma2=0.05,norm2=30,a=-10,b=100))\n",
    "summary(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aqui o resultado foi salvo na variável `res`, e posso aplicar esse resultado com a função `predict`. Vamos adicionar uma coluna do número calculado a partir da função ao data frame e salvar com um novo nome de `nexp` por *expected*, número esperado segundo um modelo de 2 gaussianas mais um fundo linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     x nobs     nexp\n",
      "1 1.11  123 132.9737\n",
      "2 1.13  128 132.3149\n",
      "3 1.15  112 131.6560\n",
      "4 1.17  116 130.9972\n",
      "5 1.19  142 130.3383\n",
      "6 1.21  113 129.6794\n"
     ]
    }
   ],
   "source": [
    "newdf<- mydf%>% mutate(nexp = predict(res,mydf))\n",
    "print(head(newdf))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graficamos a predição"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V7vt771rZdeeimz2K5du6688srDDz/c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\n47xsJAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "newdf%>%\n",
    "ggplot(aes(x,nexp))+\n",
    " geom_path(color=\"purple\")+\n",
    " xlab(\"Massa (GeV)\")+\n",
    " ylab(\"frequência\")+ \n",
    " ggtitle(\"Predição do ajuste da função gaussiana + reta decrescente\")+\n",
    " theme_bw() + theme(plot.title = element_text(hjust = 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resultado \n",
    "\n",
    "Finalmente graficamos os pontos das frequências observadas (com erros de distribuição de *Poisson*, $\\sigma_n =\\sqrt{n}$ )   junto com a linha da predição."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Ignoring unknown aesthetics: y”"
     ]
    },
    {
     "data": {
      "image/png": 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qMJy2OG0Wg0YXnMoPlUzUvzCVW9GroIrUZz8+NXX6Xi/ehWiHBtPtv9bsL16GOt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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(newdf) +\n",
    " geom_path(aes(x,nexp),color=\"purple\")+\n",
    " geom_point(aes(x,nobs))+\n",
    " geom_errorbar(aes(x,nobs, ymin=nobs-sqrt(nobs),ymax=nobs+sqrt(nobs)))+\n",
    " xlab(\"Massa (GeV)\")+\n",
    " ylab(\"frequência\")+ \n",
    " ggtitle(\"Resultado dos dados com a função do ajuste\")+\n",
    " theme_bw() +theme(plot.title = element_text(hjust = 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivação!\n",
    "\n",
    "Agora estou entusiasmada, vamos dar uma olhada no pico de maior massa nesse espectro?\n",
    "É o pico do bóson Z, que é análogo a um fóton, só que com massa alta (para uma partícula subatómica)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o/HZfTvINM0LcuS9Lw5KPn97cbGRvddj84wDMMwCmg0xjIcshBCCF0XsZie/K+9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\nwAEAAKQjcAAAAOkIHAAAQLr/B+IozpUGf2CFAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tbZboson<-tbmumu %>% filter(mass>70 & mass <110)\n",
    "\n",
    "\n",
    "tbZboson %>% \n",
    "ggplot(aes(mass)) + \n",
    "     geom_histogram(bins = 80, fill = \"purple\", alpha = 0.5) + \n",
    "     xlab(\"Massa (GeV)\") + \n",
    "     ylab(\"Frequência\") + \n",
    "     ggtitle(\"Pico do bóson Z\") + \n",
    "     theme_bw() + \n",
    "     theme(plot.title = element_text(hjust = 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pekV5SJIpGIVUejETgKXzW7PfsR6BJ8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\nI3AAAADp/g8+ui4MtG6GiQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tbZboson %>% filter(abs(eta1)<2.4 & abs(eta2)<2.4, pt1>20 & pt2>20, type1==\"G\" & type2==\"G\") %>%\n",
    "ggplot(aes(mass)) + \n",
    "     geom_histogram(bins = 80, fill = \"purple\", alpha = 0.5) + \n",
    "     xlab(\"Massa (GeV)\") + \n",
    "     ylab(\"Frequência\") + \n",
    "     ggtitle(\"Pico do bóson Z\") + \n",
    "     theme_bw() + \n",
    "     theme(plot.title = element_text(hjust = 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      x  n\n",
      "1 70.25 10\n",
      "2 70.75  8\n",
      "3 71.25  8\n",
      "4 71.75 10\n",
      "5 72.25 19\n",
      "6 72.75  9\n"
     ]
    }
   ],
   "source": [
    "zfilt<- tbZboson %>% filter(abs(eta1)<2.4 & abs(eta2)<2.4, pt1>20 & pt2>20, type1==\"G\" & type2==\"G\")  \n",
    "\n",
    "zh<- hist(zfilt$mass,breaks=80,plot=FALSE)\n",
    "\n",
    "zdf<-data.frame(x=zh$mids,n=zh$counts)\n",
    "print(head(zdf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "breitwpluslin  <- function(x,M,gamma,N,a,b){\n",
    "    \n",
    "    b<- a*x +b \n",
    "    s<- N*( (2*sqrt(2)*M*gamma*sqrt(M**2*(M**2+gamma**2)))/(pi*sqrt(M**2+sqrt(M**2*(M**2+gamma**2)))) )/((x**2-M**2)**2+M**2*gamma**2)\n",
    "    return(b+s)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Formula: n ~ breitwpluslin(x, m, g, norm, a, b)\n",
       "\n",
       "Parameters:\n",
       "       Estimate Std. Error  t value Pr(>|t|)    \n",
       "m      90.90515    0.02804 3242.298  < 2e-16 ***\n",
       "g       4.23815    0.09440   44.895  < 2e-16 ***\n",
       "norm 2757.98245   51.43696   53.619  < 2e-16 ***\n",
       "a      -0.28158    0.09698   -2.903  0.00485 ** \n",
       "b      24.11621    8.83846    2.729  0.00792 ** \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 9.925 on 75 degrees of freedom\n",
       "\n",
       "Number of iterations to convergence: 12 \n",
       "Achieved convergence tolerance: 1.49e-08\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(minpack.lm)\n",
    "resz <-nlsLM( n~ breitwpluslin(x,m,g,norm,a,b),\n",
    "           data = zdf, \n",
    "           start=list(m=90, g=3, norm =100,a=-10,b=100))\n",
    "summary(resz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[38;5;246m# A tibble: 80 x 3\u001b[39m\n",
      "       x     n  nexp\n",
      "   \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<int>\u001b[39m\u001b[23m \u001b[3m\u001b[38;5;246m<dbl>\u001b[39m\u001b[23m\n",
      "\u001b[38;5;250m 1\u001b[39m  70.2    10  9.82\n",
      "\u001b[38;5;250m 2\u001b[39m  70.8     8  9.91\n",
      "\u001b[38;5;250m 3\u001b[39m  71.2     8 10.0 \n",
      "\u001b[38;5;250m 4\u001b[39m  71.8    10 10.2 \n",
      "\u001b[38;5;250m 5\u001b[39m  72.2    19 10.3 \n",
      "\u001b[38;5;250m 6\u001b[39m  72.8     9 10.5 \n",
      "\u001b[38;5;250m 7\u001b[39m  73.2    10 10.7 \n",
      "\u001b[38;5;250m 8\u001b[39m  73.8    10 10.9 \n",
      "\u001b[38;5;250m 9\u001b[39m  74.2    13 11.2 \n",
      "\u001b[38;5;250m10\u001b[39m  74.8    14 11.5 \n",
      "\u001b[38;5;246m# … with 70 more rows\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "newz<- zdf %>% mutate(nexp=predict(resz,zdf))\n",
    "print(as_tibble(newz))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Ignoring unknown aesthetics: y”"
     ]
    },
    {
     "data": {
      "image/png": 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tpL2y35p3giqqioYIXFxcWeixYA6gCnPAHAF9U4wKhNZActEVUWCG+/uSI2NpYV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3kGtuzkO2TIkPr162/dulU/58CBA7/55psqrG8t5dic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oimrcuLHhhEGKoh4/fswZ5apUKuVyuYOD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\nDgMOhBBCCFW6/wdA8bHVW5jssQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "newz%>%\n",
    "ggplot(aes(x,nexp))+\n",
    " geom_path(color=\"purple\")+\n",
    "geom_point(aes(x,n))+\n",
    " geom_errorbar(aes(x,n, ymin=n-sqrt(n),ymax=n+sqrt(n)))+\n",
    " xlab(\"Massa (GeV)\")+\n",
    " ylab(\"frequência\")+ \n",
    " ggtitle(\"Predição do ajuste da função Breit-Wigner + reta decrescente\")+\n",
    " theme_bw() + theme(plot.title = element_text(hjust = 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahhh amei! \n",
    "Corações roxinhos 4 ever 💜💜💜"
   ]
  }
 ],
 "metadata": {
  "kernel_info": {
   "name": "ir"
  },
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.3.3"
  },
  "nteract": {
   "version": "0.3.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}