how histogram in Gnuplot works

Question

I try to reproduce a simple histogram with Gnuplot with the simple macro:

reset
n=9 #number of intervals
width=1 #interval width
hist(x,width)=width*floor(x/width)
set terminal pngcairo size 800,500 enhanced font 'Verdana,14'
set output "test.png"
set boxwidth width
set style fill transparent solid 0.5 border #fillstyle

set xrange [*:*]
set yrange [0:2.]

set xlabel "x"
set ylabel "Freq."

plot "const.dat" u (hist($1,width)) smooth freq w boxes lc rgb "orange" notitle

whit the follow data:

 1.1
 1.1
 1.1
 1.1
 1.1
 1.1
 1.1
 1.1

Now I like to understand how the hist(x,width) works in the sense:

hist(x,width)=width*floor(x/width)

works with every numbers taking the width=1 and then:

hist(1.1,1)=1*floor(1.1/1)=1

and so on, right?

Now (hist($1,width)) take all the elements in the columns and applay the hist function to everyone.

And I can be able to make the follow plot with the macro above:!

Question: If I use (hist($1,width)):(1.0) I Don't understand whit the plots change as all the elements stay in one single boxes (from 0.5 to 1.5) ?

Answer 1

In the first case you specify only a single column in the using statement. Since you need at least two (x and y-value), the specified value (your hist(...)) is used as y-value and the row number as x-value. The statement smooth frequency works such, that it takes all points with the same x-value and sums up the corresponding y-values. In your first example you have no equal x-values since the row number is used.

In the second example, you use the hist(...) value as x-value, which is 1 for all rows. The y-value is 1.0. So you get a single box at x=1 and y=8 (the number of rows).