diff --git a/module2/exo1/figure_pi_mc1.png b/module2/exo1/figure_pi_mc1.png new file mode 100644 index 0000000000000000000000000000000000000000..d4f36f4c13035c065e9a1acb40309873c770b243 Binary files /dev/null and b/module2/exo1/figure_pi_mc1.png differ diff --git a/module2/exo1/figure_pi_mc2.png b/module2/exo1/figure_pi_mc2.png new file mode 100644 index 0000000000000000000000000000000000000000..16a3756e3a9bdb9c7b3c73503dd23710b4c92183 Binary files /dev/null and b/module2/exo1/figure_pi_mc2.png differ diff --git a/module2/exo1/toy_document_orgmode_R_en.org b/module2/exo1/toy_document_orgmode_R_en.org index 0febcfe34f204f56d08923d6106792bf2520606a..1caa19b43721209d2d384ebdd945befbee630aac 100644 --- a/module2/exo1/toy_document_orgmode_R_en.org +++ b/module2/exo1/toy_document_orgmode_R_en.org @@ -8,7 +8,7 @@ #+HTML_HEAD: #+HTML_HEAD: -#+PROPERTY: header-args :session :exports both +#+PROPERTY: header-args :session :exports both * Asking the maths library My computer tells me that $\pi$ is /approximatively/ @@ -35,7 +35,7 @@ theta = pi/2*runif(N) : [1] 3.14327 * 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 $X\simU(0,1)$ and $Y\simU(0,1)$, then $P[X^2+Y^2\leq 1] = \pi/4$ (see [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on Wikipedia]]). 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 [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on Wikipedia]]). The following code uses this approach: #+begin_src R :results output graphics :file figure_pi_mc1.png :exports both :width 600 :height 400 :session *R* set.seed(42) @@ -50,6 +50,7 @@ ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + t [[file:figure_pi_mc1.png]] 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: + #+begin_src R :results output :session *R* :exports both 4*mean(df$Accept) #+end_src diff --git a/module2/exo1/toy_document_orgmode_python_en.org b/module2/exo1/toy_document_orgmode_python_en.org index b23a4b867d3472c8299eb5445cf36aae3d9e5b3b..f6a5f09fc50d9cfe989afa9ac0ad015416d3b6fa 100644 --- a/module2/exo1/toy_document_orgmode_python_en.org +++ b/module2/exo1/toy_document_orgmode_python_en.org @@ -1,8 +1,5 @@ -#+TITLE: Your title -#+AUTHOR: Your name -#+DATE: Today's date +#+TITLE: On the computation of pi #+LANGUAGE: en -# #+PROPERTY: header-args :eval never-export #+HTML_HEAD: #+HTML_HEAD: @@ -11,84 +8,65 @@ #+HTML_HEAD: #+HTML_HEAD: -* Some explanations +#+PROPERTY: header-args :session :exports both -This is an org-mode document with code examples in R. Once opened in -Emacs, this document can easily be exported to HTML, PDF, and Office -formats. For more information on org-mode, see -https://orgmode.org/guide/. +* Asking the maths library +My computer tells me that $\pi$ is /approximatively/ -When you type the shortcut =C-c C-e h o=, this document will be -exported as HTML. All the code in it will be re-executed, and the -results will be retrieved and included into the exported document. If -you do not want to re-execute all code each time, you can delete the # -and the space before ~#+PROPERTY:~ in the header of this document. - -Like we showed in the video, Python code is included as follows (and -is exxecuted by typing ~C-c C-c~): +#+begin_src python :results value :session *python* :exports both +from math import * +pi +#+end_src -#+begin_src python :results output :exports both -print("Hello world!") +#+RESULTS: +: 3.141592653589793 + +* Buffon's needle +Applying the method of [[https://en.wikipedia.org/wiki/Buffon%2527s_needle_problem][Buffon's needle]], we get the *approximation* + +#+begin_src python :results value :session *python* :exports both +import numpy as np +np.random.seed(seed=42) +N = 1000 +x = np.random.uniform(size=N, low=0, high=1) +theta = np.random.uniform(size=N, low=0, high=pi/2) +2/(sum((x+np.sin(theta))>1)/N) #+end_src #+RESULTS: -: Hello world! +: 3.144654088050314 + +* 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 $X\simU(0,1)$ and $Y\simU(0,1)$, then $P[X^2+Y^2 \le1]=\pi/4$ (see [[https://en.wikipedia.org/wiki/Monte_Carlo_method]["Monte Carlo method" on Wikipedia]]). The following code uses this approach: + +#+begin_src python :results output :session *python* :var matplot_lib_filename="figure_pi_mc2.png" :exports both +import matplotlib.pyplot as plt -And now the same but in an Python session. With a session, Python's -state, i.e. the values of all the variables, remains persistent from -one code block to the next. The code is still executed using ~C-c -C-c~. +np.random.seed(seed=42) +N = 1000 +x = np.random.uniform(size=N, low=0, high=1) +y = np.random.uniform(size=N, low=0, high=1) -#+begin_src python :results output :session :exports both -import numpy -x=numpy.linspace(-15,15) -print(x) +accept = (x*x+y*y) <= 1 +reject = np.logical_not(accept) + +fig, ax = plt.subplots(1) +ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None) +ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None) +ax.set_aspect('equal') + +plt.savefig(matplot_lib_filename) +print(matplot_lib_filename) #+end_src #+RESULTS: -#+begin_example -[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041 - -11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592 - -8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143 - -5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694 - -2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245 - 0.30612245 0.91836735 1.53061224 2.14285714 2.75510204 - 3.36734694 3.97959184 4.59183673 5.20408163 5.81632653 - 6.42857143 7.04081633 7.65306122 8.26530612 8.87755102 - 9.48979592 10.10204082 10.71428571 11.32653061 11.93877551 - 12.55102041 13.16326531 13.7755102 14.3877551 15. ] -#+end_example - -Finally, an example for graphical output: -#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results -import matplotlib.pyplot as plt +: figure_pi_mc2.png -plt.figure(figsize=(6,3)) -plt.plot(x,numpy.cos(x)/x) -plt.tight_layout() +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: -plt.savefig(matplot_lib_filename, bbox_inches='tight') -print(matplot_lib_filename) +#+begin_src python :results value :session *python* :exports both +4*np.mean(accept) #+end_src #+RESULTS: -[[file:./cosxsx.png]] - -Note the parameter ~:exports results~, which indicates that the code -will not appear in the exported document. We recommend that in the -context of this MOOC, you always leave this parameter setting as -~:exports both~, because we want your analyses to be perfectly -transparent and reproducible. - -Watch out: the figure generated by the code block is /not/ stored in -the org document. It's a plain file, here named ~cosxsx.png~. You have -to commit it explicitly if you want your analysis to be legible and -understandable on GitLab. - -Finally, don't forget that we provide in the resource section of this -MOOC a configuration with a few keyboard shortcuts that allow you to -quickly create code blocks in Python by typing ~