Superimpose a line on a histogram in Gnuplot - c++

Question

I use C++ in Xcode on Mac and a pipe method to communicate with Gnuplot. I am interested in converting my arrays into graphs directly through the program, after I run it. Using
FILE *f = popen("gnuplot -persist", "w");
I open the file and then communicate using fprintf.
Now, I have some data in arrays of interest. w is a "proposed" array of standard normal variables and I intend to check if it is indeed a Gaussian distribution with mean = 0 and variance = 1 .To do that I plot a histogram. After that I want to superimpose a real Gaussian function, which has ex as a x coordinate values and gauss as y coordinate values directly on the histogram. How can I do that?
Here's the code so far:
double start = -4; //min
double end = 4 ; //max
double numberofbins = 100;
double width = (end-start)/numberofbins ;
fprintf (f,
"set ylabel '# of elements'\n"
"set xlabel 'The numbers'\n"
"Min = %g\n" //where binning starts
"Max = %g\n" // where binning ends
"n = %g\n" // the number of bins
"width = 10**(-1)\n" // binwidth; (Max-Min)/n
"bin(x) = width*(floor((x-Min)/width)+0.5) + Min\n"
"f(x)= e**((-x**2)/2) / sqrt(2*pi)\n"
"plot '-' using (bin($1)):(1) smooth freq with boxes,'' u $2:$3 with lines linestyle 1\n",start,end,numberofbins)
for (int i= 0; i < numberofpoints; i++){
fprintf(f, "%g %g %g\n", w[i], ex[i], gauss[i]);
}
fclose(f);
Here is the result if I run the demonstrated code:
As we can see, the binning was successful but the line was omitted and gives the following error:
gnuplot> plot '-' using (bin($1)):(1) smooth freq with boxes,'' u $2:$3 with lines linestyle 1
^
line 100000: column() called from invalid context
I have checked online but nobody is practicing communicating with Gnuplot that way.
If I plot only the 2:3 part (without binning), I get this graph:
Thus, the problem might be with the compatibility of these two plots.

Answer 1

there are different ways to plot "inline" data
plot '-' u 1:2 w lines
1 11
2 22
3 33
e
From gnuplot help special-filenames
If you use both '-' and '' on the same plot command, you'll need to
have two sets of inline data, ...
This means:
plot '-' u 1:2 w boxes, '' u 1:2 w lines
1 11
2 22
3 33
e
1 11
2 22
3 33
e
So, instead, I would generate a datablock in the beginning of your generated command string and reuse the data as many times as you need it during your plotting command.
$Data <<EOD
1 11
2 22
3 33
EOD
plot $Data u 1:2 w boxes, '' u 1:2 w lines

Answer 2

I have solved the problem by creating a second y axis on the same graph and plotting according to it. The code used was:
fprintf (f,
"set xlabel 'The numbers'\n"
"Min = %g\n" //where binning starts
"Max = %g\n" // where binning ends
"n = %g\n" // the number of bins
"width = 10**(-1)\n" // binwidth; (Max-Min)/n
"bin(x) = width*(floor((x-Min)/width)+0.5) + Min\n"
"set ytics 100 nomirror tc lt 1\n"
"set ylabel '# of elements' tc lt 1\n"
"set y2tics 0.4 nomirror tc lt 2\n"
"set y2label 'Theoretical Gaussian' tc lt 2\n"
"plot '-' using (bin($1)):(1) smooth freq with boxes title 'Generator Histogram','-' u 1:2 with l axes x1y2 title 'Theoretical Gaussian (mean=0, std = 1)'\n",start,end,numberofbins) ;
for (int i= 0; i < numberofpoints; i++){
fprintf(f, "%g\n", w[i]);
}
fprintf(f,"e\n");
for (int i= 0; i < numberofpoints; i++){
fprintf(f, "%g %g\n",ex[i], gauss[i]);
}
fprintf(f,"e\n");
fclose(f);
which plots this: