readme: update for changes to ex-1, ex-2

README.md

@@ -27,15 +27,28 @@ The programs used to solve the exercise are written in standard C99 (with the
 only exception of the `#pragma once` clause) and require the following
 libraries to build:
 
-- [GMP](https://gmplib.org/)
+- [GMP] (≥ 6.2)
 
-- [GSL](https://www.gnu.org/software/gsl/)
+- [GSL] (≥ 2.6)
 
-* [pkg-config](https://www.freedesktop.org/wiki/Software/pkg-config/)
-  (build-time only)
+* [pkg-config] (≥ 0.29, build-time only)
 
-Additionally, Python (version 3) with `numpy` and `matplotlib` is required to
-generate plots.
+To generate plots, Python (version 3) with
+
+- [numpy] (≥ 1.18)
+
+- [matplotlib] (≥ 2.2)
+
+- [scipy] (≥ 1.4, optional)
+
+is required to generate plots.
+
+[GMP]: https://gmplib.org/
+[GSL]: https://www.gnu.org/software/gsl/
+[pkg-config]: https://www.freedesktop.org/wiki/Software/pkg-config/
+[numpy]: https://numpy.org/
+[scipy]: https://www.scipy.org/scipylib/index.html
+[matplotlib]: https://matplotlib.org/
 
 For convenience, a `shell.nix` file is provided to set up the build environment.
 See this [guide](https://nixos.org/nix/manual/#chap-quick-start) if you have
@@ -54,7 +67,6 @@ To clean up the build results run:
 
     $ make clean
 
-
 ## Running the programs
 
 Notes:
@@ -76,6 +88,11 @@ comparing the sample mode, FWHM and median, in this order.
 `ex-1/bin.pdf` prints a list of x-y points of the Landau PDF to the `stdout`.
 The output can be redirected to `ex-1/pdf-plot.py` to generate a plot.
 
+(optional) `ex-1/plots/kde.py` makes the example plot (shown in exercises.pdf,
+fig. 4) of the kernel density estimation used to compute a non-parametric FWHM
+from a sample of random points. To run this program you must additionally
+install [scipy].
+
 
 ### Exercise 2
 
@@ -95,6 +112,10 @@ take therefore the required number of decimal places as their only argument.
 The exact γ digits (used in comparison) are limited to 50 and 500 places,
 respectively.
 
+`ex-2/bin/fast` is a highly optimized version of `ex-2/bin/fancier`, meant to
+compute a very large number of digits and therefore doesn't come with a
+verified, fixed, approximation of γ.
+
 
 ### Exercise 3
 
@@ -133,12 +154,12 @@ and `-b`.
 
 ### Exercise 5
 
-`ex-5/main` compute estimations of the integral of exp(1) between 0 and 1
+`ex-5/main` compute estimations of the integral of exp(x) between 0 and 1
 with the methods plain MC, MISER and VEGAS with different number of points.
 It takes no arguments in input.  
 It prints out eight columns:
 
-1. the number of sorted points;
+1. the number of points;
 
 2. the integral estimation with plain MC;
 
@@ -158,6 +179,7 @@ To plot the results do:
 
     $ ex-5/main | ex-5/plot.py
 
+
 ### Exercise 6
 
 `ex-6/bin/main` simulates a Fraunhöfer diffraction experiment. The program
@@ -166,8 +188,8 @@ diffraction angle. To plot a histogram do:
 
     $ ex-6/bin/main | ex-6/plot.py
 
-The program convolves the original signal with a Gaussian kernel (`-s` to
-change the kernel σ), optionally adds a Gaussian noise (`-n` to change the
+The program convolves the original signal with a gaussian kernel (`-s` to
+change the kernel σ), optionally adds a gaussian noise (`-n` to change the
 noise σ) and performs either a naive deconvolution by a FFT (`-m fft` mode)
 or applying the Richardson-Lucy deconvolution algorithm (`-m rl` mode).
 
@@ -176,27 +198,33 @@ deconvolved histogram counts should be printed to `stdout`. For more options
 run the program with `-h` to see the usage screen.
 
 `ex-6/bin/test` simulates a customizable number of experiments and prints
-to `stdout` the histograms of the distribution of the EMD of the convolved
-signal together with the deconvolved signal EMD histograms with both FFT and
-Richardson-Lucy procedures. It also prints to `stderr` the average, standard
-deviation and skewness of the histograms. To plot the results, do:
+to `stdout` the histograms of the distribution of the EMD from the original
+signal to:
+
+1. the result of the FFT deconvolution
+2. the result of the Richardson-Lucy deconvolution
+3. the convolved signal (with noise if `-n` has been given)
+
+It also prints to `stderr` the average, standard deviation and skewness of
+each distribution. To plot the histograms, do:
 
     $ ex-6/bin/test | ex-6/dist-plot.py
 
 The program accepts some parameters to control the histogram and number of
 events, run it with `-h` to see their usage.
 
-`ex-6/plots/emd.py` plots the content of the files `ex-6/plots/emd-noisy.txt`
-and `ex-6/plots/emd-noiseless.txt` depending on the argument passed to it from
-stdin. Do:
+(optional) `ex-6/plots/emd.py` makes the plots of the EMD statistics of the RL
+deconvolution (shown in excercies.pdf, section 6.6) as a function of the number
+of rounds. The programs sources its data from two files in the same directory,
+these were obtained by running `ex-6/bin/test`. Do:
 
-    $ ex-6/plots/emd.py 'noisy'
+    $ ex-6/plots/emd.py noisy
 
-to plot the content of the first file and do:
+for the plots of the experiment with gaussian noise, and
 
-    $ ex-6/plots/emd.py 'noiseless'
+    $ ex-6/plots/emd.py noiseless
 
-to plot the content of the second file.
+for the experiment without noise.
 
 
 ### Exercise 7

ex-1/plots/kde.py

@@ -89,7 +89,7 @@ plt.plot(x, moyal.pdf(x, loc=4), c='xkcd:gray', label='true PDF')
 plt.plot(x, f, '#92182b', label='empirical PDF')
 plt.plot(sample, np.zeros_like(sample),
          '|', c='xkcd:navy')
-#plt.axvline(x=m.mean(), c='r')
+plt.axvline(x=m.mean(), c='r')
 plt.axvline(x=M.mean(), c='xkcd:camel', label='mode')
 plt.legend()
 plt.show()

notes/todo

@@ -1,7 +1,6 @@
 - riscrivere il 2
-- riscrivere il readme del 1
-- riscrivere il readme del 2
 - riscrivere il readme del 6
 - riscrivere il readme del 7
+- incolonnare bene ex-5
 
-On the lambert W function, formula 4.19 Corless
+On the Lambert W function, formula 4.19 Corless