From 3fd547ec8ebd4572507e7c056da936760d501a35 Mon Sep 17 00:00:00 2001 From: ae44f8007c63991902a8055ff9736871 Date: Mon, 13 May 2024 11:35:15 +0000 Subject: [PATCH] Update toy_document_en.Rmd --- module2/exo1/toy_document_en.Rmd | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/module2/exo1/toy_document_en.Rmd b/module2/exo1/toy_document_en.Rmd index a96387b..b9a24c0 100644 --- a/module2/exo1/toy_document_en.Rmd +++ b/module2/exo1/toy_document_en.Rmd @@ -5,7 +5,6 @@ date: "25 juin 2018" output: html_document --- - ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) ``` @@ -29,7 +28,7 @@ theta = pi/2*runif(N) ``` ## Using a surface fraction argument -A method that is easier to understand and does not make use of the $\sin$ function is based on the fact that if $X\sim U(0,1)$ and $Y\sim U(0,1)$, then $P[X^2+Y^2\leq 1] = \pi/4$ (see [“Monte Carlo method” on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach: +A method that is easier to understand and does not make use of the $\sin$ function is based on the fact that if $X\sim U(0,1)$ and $Y\sim U(0,1)$, then $P[X^2+Y^2\leq 1] = \pi/4$ (see ["Monte Carlo method" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach: ```{r} set.seed(42) @@ -38,9 +37,12 @@ df = data.frame(X = runif(N), Y = runif(N)) df$Accept = (df$X**2 + df$Y**2 <=1) library(ggplot2) ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw() + ``` -It is then straightforward to obtain a (not really good) approximation to $\pi$ by counting how many times, on average, $X^2+Y^2$ is smaller than 1 : +It is then straightforward to obtain a (not really good) approximation to $\pi$ by counting how many times, on average, $X^2+Y^2$ is smaller than 1: + ```{r} 4*mean(df$Accept) -``` \ No newline at end of file +``` + -- 2.18.1