Pgfplots and round-off error

Question

I have a graph that must show the oscillations in energy of a numerical scheme. The problem is that the energy is something like this:

-9.99999994950000e-01

and I have oscillations after 8 digits. At the moment, the graph is a straight line, so I can't see the oscillations.

How many digit pgfplots can use? Is there any way to see these oscillations?

Answer 1

The problem here is that you want to display a data range of, say, -9.99999994950000e-01 to -9.99999995000000e-01 . The relative precision which is required to provide meaningful results here is beyond the capabilities of pgfplots, sorry.

However, you can assist it - if you have a math tool at hand. A "math tool" can be LuaLaTeX ... suppose you had LuaLaTeX, then the following might be a solution:

\documentclass{standalone}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\def\SHIFT{-0.99999999}
\def\EXPONENT{9}%
    \begin{axis}[
        y coord trafo/.code={%
            \edef\pgfmathresult{\directlua{tex.print( (#1 - (\SHIFT))*10^(\EXPONENT) )}}%
            \message{#1 -> \pgfmathresult^^J}%
        },
        y coord inv trafo/.code={%
            \edef\pgfmathresult{\directlua{tex.print( #1*10^(-\EXPONENT) + (\SHIFT) )}}%
            \message{inv: #1 -> \pgfmathresult^^J}%
        },
        yticklabel style={
            /pgf/number format/precision=11,
            /pgf/number format/fixed zerofill,
        },
    ]
    \addplot table {
    0 -9.99999994950000e-01
    1 -9.99999995000000e-01
    2 -9.99999995010000e-01
    };
    \end{axis}
\end{tikzpicture}
\end{document}

It employs Lua's math capabilities in order to transform your input data into some range where pgfplots can apply its arithmetics. Later, it uses Lua again to transform the intermediate results back. The number printer is lossless (as it operates on symbols only).

Note that this affine transformation consisting of shifts and an exponent is very similar to what pgfplots does internally. It just can't cope with such high relative precisions.

If you do not have LuaLaTeX, you can still try to prepare your data. Apparently, the energy is being computed by some numeric algorithm. If you would apply such a transformation manually, you could display it. You would need to get meaningful tick labels, which is less elegant than my first approach, but still feasible (for example by providing them manually).