ex-5: add header to the results table

README.md

@@ -155,27 +155,10 @@ and `-b`.
 ### Exercise 5
 
 `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.
+using several methods: a plain Monte Carlo, the MISER and VEGAS algorithms
-It takes no arguments in input.  
+with different number of samples. The program takes no arguments and prints
-It prints out eight columns:
+a table of the result and its error for each method.
-
+To visualise the results, you can plot the table by doing:
-1. the number of points;
-
-2. the integral estimation with plain MC;
-
-3. its uncertainty;
-
-4. the integral estimation with MISER;
-
-5. its uncertainty;
-
-6. the integral estimation with VEGAS;
-
-7. its uncertainty;
-
-8. its χ².
-
-To plot the results do:
 
     $ ex-5/main | ex-5/plot.py
 
@@ -214,7 +197,7 @@ The program accepts some parameters to control the histogram and number of
 events, run it with `-h` to see their usage.
 
 (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
+deconvolution (shown in exercises.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-5/main.c

@@ -5,7 +5,7 @@
 #include <math.h>
 
 
-// Wrapper for the gsl_function.
+// exp() wrapper for the gsl_function structure
 //
 double function (double * x, size_t dim, void * params)
   {
@@ -19,13 +19,13 @@ void results (size_t calls, double result, double error, double chi)
   {
   if (calls != 0)
     {
-    printf ("%.0e\t", (double)calls);
+    printf ("%6.0e | ", (double)calls);
     }
-  printf ("%.10f\t", result);
+  printf ("%5f | ", result);
-  printf ("%.10f\t", error);
+  printf ("%5f | ", error);
   if (chi != 0)
     {
-    printf ("%.3f\t", chi);
+    printf ("%5f", chi);
     }
   } 
 
@@ -52,6 +52,12 @@ int main(int argc, char** argv)
   expo.dim = 1;
   expo.params = NULL;
 
+  // Print the results table header
+  printf(" Calls |  Plain   |  Error   |  MISER   |"
+         "  Error   |  VEGAS   |  Error   | χ²\n");
+  printf(" ------|----------|----------|----------|"
+         "----------|----------|----------|---------\n");
+
   // Compute the integral for the following number of function calls:
   //          50
   //         500
@@ -62,7 +68,7 @@ int main(int argc, char** argv)
   //  50'000'000
   // with the three MC methods: plain MC, MISER and VEGAS.
   //
-  while (calls < 50000001)
+  while (calls <= 5000000)
     {
     // Plain MC
     gsl_monte_plain_state *sMC = gsl_monte_plain_alloc (dims);
@@ -82,7 +88,7 @@ int main(int argc, char** argv)
     gsl_monte_vegas_state *sVE = gsl_monte_vegas_alloc (dims);
     gsl_monte_vegas_integrate (&expo, lower, upper, dims, calls,
                                r, sVE, &integral, &error);
-      
+
     // In order to see the parameters of the VEGAS integration, decomment this
     // paragraph:
     //

ex-5/plot.py

@@ -4,19 +4,26 @@ import matplotlib.pyplot as plt
 import numpy             as np
 import sys
 
-calls, I_MC, σ_MC, I_MI, σ_MI, I_VE, σ_VE, chi = np.loadtxt(sys.stdin, unpack=True)
+table = np.loadtxt(sys.stdin, unpack=True, skiprows=2, delimiter='|')
+calls, I_MC, σ_MC, I_MI, σ_MI, I_VE, σ_VE, chi = table
 exact = 1.7182818285
 
 plt.rcParams['font.size'] = 17
+
 plt.figure()
 plt.title('Plain MC', loc='right')
 plt.ylabel('$I^{oss}$')
 plt.xlabel('calls')
-plt.axhline(y=exact,  color='#c556ea',  linestyle='-', label='Exact value')
+plt.xscale('log')
 
-plt.errorbar(calls, I_MC, linestyle='', marker='o', yerr=σ_MC, color='#92182b', label='Plain MC')
+plt.axhline(y=exact,  color='#c556ea',  linestyle='-',
-plt.errorbar(calls, I_MI, linestyle='', marker='o', yerr=σ_MI, color='black',   label='MISER')
+            label='Exact value')
-plt.errorbar(calls, I_VE, linestyle='', marker='o', yerr=σ_VE, color='gray',    label='VEGAS')
+plt.errorbar(calls, I_MC, linestyle='', marker='o',
+             yerr=σ_MC, color='#92182b', label='Plain MC')
+plt.errorbar(calls, I_MI, linestyle='', marker='o',
+             yerr=σ_MI, color='black',   label='MISER')
+plt.errorbar(calls, I_VE, linestyle='', marker='o',
+             yerr=σ_VE, color='gray',    label='VEGAS')
 
 plt.legend()
 plt.show()