ex-4: fit plot added

ex-4/main.c

@@ -9,13 +9,14 @@
 
 // Process CLI arguments.
 //
-int parser(size_t *N, size_t *n, double *p_max, char argc, char **argv)
+int parser(size_t *N, size_t *n, double *p_max, char argc, char **argv, size_t *go)
   {
   for (size_t i = 1; i < argc; i++)
     {
          if (!strcmp(argv[i], "-n")) *N     = atol(argv[++i]);
     else if (!strcmp(argv[i], "-b")) *n     = atol(argv[++i]);
     else if (!strcmp(argv[i], "-p")) *p_max = atof(argv[++i]);
+    else if (!strcmp(argv[i], "-o")) *go = 1;
     else
       {
       fprintf(stderr, "Usage: %s -[hnbp]\n", argv[0]);
@@ -23,6 +24,7 @@ int parser(size_t *N, size_t *n, double *p_max, char argc, char **argv)
       fprintf(stderr, "\t-n N\tThe number of events to generate. (default: 50000)\n");
       fprintf(stderr, "\t-b N\tThe number of bins of the histogram. (default: 50)\n");
       fprintf(stderr, "\t-p PMAX\tThe maximum value of momentum. (default: 10)\n");
+      fprintf(stderr, "\t-o \tPrint histogram to stdout.\n");
       return 0;
       }
     }
@@ -35,18 +37,19 @@ int main(int argc, char **argv)
 
   // Set default options.
   //
-  size_t N = 50000;          // number of events.
+  size_t N = 50000;
-  size_t n = 50;             // number of bins.
+  size_t n = 50;
-  double p_max = 10;         // maximum value of momentum module.
+  double p_max = 10;
-  int res = parser(&N, &n, &p_max, argc, argv);
+  size_t go = 0;
-  if (res == 1)
+  int res = parser(&N, &n, &p_max, argc, argv, &go);
+  if (go == 0)
     {
     printf("\nGenerating histogram with:\n"
                        "%ld points\n"
                        "%ld bins\n"
                        "p_max = %.3f\n\n", N, n, p_max);
     }
-  else return EXIT_FAILURE;
+  else if (res == 0) return EXIT_FAILURE;
 
   // printf("step: \t%.5f\n", step);
 
@@ -116,12 +119,15 @@ int main(int argc, char **argv)
   // Compute the mean value of each bin and print it to stodut
   // together with other useful things to make the histogram.
   //
-  // printf("bins: \t%ld\n", n);
+  if (go == 1)
-  // printf("step: \t%.5f\n", step);
+    {
+    printf("bins: \t%ld\n", n);
+    printf("step: \t%.5f\n", step);
+    }
   for (size_t i = 0; i < n; i++)
     {
     histo[i].sum = histo[i].sum / histo[i].amo;    // Average P_v
-    //printf("\n%.5f", histo[i].sum);
+    if (go == 1) printf("\n%.5f", histo[i].sum);
     };
   
   // Compare the histigram with the expected function:
@@ -165,9 +171,12 @@ int main(int argc, char **argv)
 
   double result = x;
   double res_chi = chi2(result, &params);
-  printf("Results:\n");
+  if (go == 0)
-  printf("χ² = %.3f\n", res_chi);
+    {
-  printf("p_max = %.3f\n", result);
+    printf("Results:\n");
+    printf("χ² = %.3f\n", res_chi);
+    printf("p_max = %.3f\n", result);
+    }
 
   // Compute the second derivative of χ² in its minimum for the result error.
   //   
@@ -195,9 +204,19 @@ int main(int argc, char **argv)
     B = exp2d(x, result) * (1 - pow((histo[i].sum / expecto), 2));
     error = error + A + B;
     };
-    error = 1/error;
+  error = 1/error;
-  printf("ΔP_max = %.3f\n\n", error);
+  if (go == 0) printf("ΔP_max = %.3f\n", error);
 
+  // Check compatibility
+  //
+  double t = fabs(result - p_max)/error;
+  double alpha = 1 - erf(t/sqrt(2));
+  if (go == 0)
+    {
+    printf("\nCompatibility:\n");
+    printf("t = %.3f\n", t);
+    printf("α = %.3f\n\n", alpha);
+    }
 
   // Free memory.
   //

ex-4/note.py

@@ -12,7 +12,6 @@ def main():
     y = f(x)
 
     plt.rcParams['font.size'] = 20
-    plt.figure()
     plt.title('Expected distribution', loc='right')
     plt.ylabel('$\\langle |P_v| \\rangle$')
     plt.xlabel('$P_h$')

notes/sections/4.md

@@ -247,8 +247,11 @@ where $\Delta p_{\text{max}}$ is the absolute error of $p_{\text{max}}$. At 95%
 confidence level, the values are compatible if $p > 0.05$.
 In this case:
 
-  - t = 0.278
+  - t = 0.295
-  - p = 0.781
+  - p = 0.768
 
 which allows to assert that the sampled points actually follow the predicted
-distribution.
+distribution. In @fig:fit, the fit function superimposed on the histogram is
+shown.
+
+![Fitted data.](images/fit.pdf){#fig:fit}