gnuplot: variable values and definitions in plot command

Question

I just stumbled across the following:

According to the gnuplot manual a plot element may contain a definition.

Syntax: 

      plot {<ranges>} <plot-element> {, <plot-element>, <plot-element>}

Each plot element consists of a definition, a function, or a data source 
together with optional properties or modifiers: 

      plot-element:
           {<iteration>}
           <definition> | {sampling-range} <function> | <data source>
                        | keyentry
           {axes <axes>} {<title-spec>}
           {with <style>}

Check the following example:

For the first graph y=x+1 is plotted because a=1 was defined earlier. As expected.
For the second graph and the first plot command it should be the same but y=2*x+1 is plotted instead (twice).
In the third graph when a=1 is explicitely specified it is plotted as expected.

Why is gnuplot ignoring a=1 for the second graph? Have I misunderstood something?

Code:

### definitions in plot command
reset session

a = 1
b = 1
f(x) = a*x + b

set yrange[-40:40]
set multiplot layout 1,3
    plot     f(x)
    plot     f(x), a=2 f(x), a=3 f(x)
    plot a=1 f(x), a=2 f(x), a=3 f(x)
unset multiplot
### end of code

Result:

Ethan · Accepted Answer · 2020-09-24 05:08:53Z

4

Your diagnosis is slightly off. In the second panel the first, purple plot is superimposed with the a=3 plot rather than the a=2 plot.

Why? Because gnuplot accumulates all elements of the full plot before actually drawing any of them. This involves making two passes over the command line. One pass to parse and load data from any data sources mentioned (needed for example for autoscaling), then a second pass to evaluate any functions over the range (which might have determined by autoscaling). During the first pass here, a gets set to 2 and then to 3. At the start of the second pass a is still 3 and in the absence of an initial definition to change it that is what is used when f(x) is evaluated.

edited Sep 24, 2020 at 5:08

answered Sep 24, 2020 at 4:29

Ethan

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3 Comments

theozh Over a year ago

Thank you for your explanation. Ok, didn't know about the two passes. It's always good to know what's going on "behind the scenes".

Friedrich -- Слава Україні Over a year ago

I experienced the same issue. For most users the outcome will be unexpected.

Ethan Over a year ago

Perhaps. But consider that even if it were to act as you apparently expect the first time you issue a plot command, it would act differently on replot for exactly the same reason as the actual behavior - the value of variable a has changed in the interim.

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