[Tex/LaTex] pgfplots: Syntax of Piecewise Defined Functions

pgfplotstikz-pgf

I read about piecewise defined functions today and saw this post which was actually about something else:

Label plots in pgfplots without entering coordinates manually

This is taken from there.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\thispagestyle{empty}   

\begin{tikzpicture}
 \begin{axis}[
        axis y line=center,
        axis x line=middle, 
        axis on top=true,
        xmin=-7,
        xmax=7,
        ymin=-4,
        ymax=4,
        clip=false
] 

\addplot[
    mark=none,
    domain=-4:6,
    samples=80,
    red,
    thick,
] {(x<-2)*-2 + (!(x<-2) && (x<3))*x + (!(x<3)) * 3}
    node[pos=0.1,pin=135:{\color{purple}$f(x)=-2$}] {}
    node[pos=0.6,pin=135:{\color{blue}$f(x)=x$}] {}
    node[pos=0.9,pin=135:{\color{green!70!black}$f(x)=3$}] {}
;
\end{axis}
\end{tikzpicture}

\end{document}

enter image description here

I get the syntax and(<condition1>,<condition2>) which is explained here for example but I do not understand the syntax in the example above

(x<-2)*-2 + (!(x<-2) && (x<3))*x + (!(x<3)) * 3

Can somebody explain it to me or am I just being blind? There is no and like in and(a,b) and what does the ! do? I guess it's a negation.

Update

Can I find this somewhere in a documentation or is this just common knowledge?

Best Answer

In pgfmath a true expression has the value 1, and a false expression has the value 0. That is, an expression such as (x<-2) is equivalent to a function f(x):

enter image description here

Hence, this works because:

(x<-2): This condition is ONLY true for x < -2. Hence this only contributes to the expression for x < -2. Hence (x<-2)*-2=-2 for x<-2, 0 otherwise.
(!(x<-2) && (x<3)): This has the value 1 for -2 <= x <= 2. Hence, in this range, this has the value of x.
!(x<3): This is 1 only for x >=3. Hence (!(x<3)) * 3=3 for x >=3, and zero otherwise.

If there is still any confusion, this table that computes the values of the various conditions should help:

enter image description here

Related Solutions

[Tex/LaTex] Question regarding piecewise syntax with pgfplot

It's simple math. :) But one should know that

and(<condition1>,<condition2>)

returns 1 when both conditions are true and 0 when at least one is false. So, when pgf is computing the value of func at 150 it does

(and(150>=0 , 150<=500) * (300 + 150*(12/10)) + (and(150>500, 150<=1000) * (600 + 150*(12/10))

which becomes

1 * (300 + 150*(12/10)) + 0 * (600 + 150*(12/10))

that is,

(300 + 150*(12/10))

When it's evaluating at 725, the same applies, but the result is

0 * (300 + 725*(12/10)) + 1 * (600 + 725*(12/10))

that is,

(600 + 725*(12/10))

In both cases the value is what's requested.

You need to correct the input if you want a graph which has an actual step at the discontinuity:

\begin{tikzpicture}[scale=0.8]
\begin{axis}
  [title={$C(x)$},
   ylabel=$y$,
   xlabel=$x$,
   grid=both,
   minor xtick={0,100,...,1000},
   xtick={0,200,...,1000},
   ytick={0,400,...,3200},
   samples=1000]
  \addplot[blue,domain=0:1000]{func(x)};
\end{axis}
\end{tikzpicture}

but the computation time will be longer. Also the function definition should be changed:

\pgfmathdeclarefunction{func}{1}{%
  \pgfmathparse{%
    (and(#1>=0  , #1<500)   * (300 + #1*(12/10)) +
    (and(#1>=500 , #1<=1000) * (600 + #1*(12/10))
  }%
}

so that the correct value is computed at 500 (you decide where the = should go).

enter image description here

[Tex/LaTex] pgfplots: percentage in matrix plot

It does not work in your MWE because you are overwriting it by also giving the option nodes near coors to the \addplot command. Remove the latter one (or specify format here), and it will print. I added a thinspace before the percentage sign, although it can also be recommended to load the siunitx package and let that format and typeset the values for you.

Anyway, here's the quickfixed version:

\documentclass[border=3pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{%
  width=5cm,
  height=18cm,
  compat=1.13,
  colormap={blackwhite}{gray(0cm)=(1); gray(1cm)=(0.5)},
  xticklabels={LPIBG, ALL, HPIBG},
  xtick={0,...,2},
  ytick=\empty
}

\begin{document}
\begin{tikzpicture}
\begin{axis}[%
  enlargelimits=false,
  xlabel style={font=\footnotesize},
  ylabel style={font=\footnotesize},
  legend style={font=\footnotesize},
  xticklabel style={font=\footnotesize},
  yticklabel style={font=\footnotesize},
  colorbar,
  colorbar style={%
    ytick={0,20,40,60,80,100},
    yticklabels={0,20,40,60,80,100},
    yticklabel={\pgfmathprintnumber\tick\,\%},
    yticklabel style={font=\footnotesize}
  },
  point meta min=0,
  point meta max=100,
  nodes near coords={\pgfmathprintnumber\pgfplotspointmeta\,\%},
  every node near coord/.append style={xshift=0pt,yshift=-7pt, black, font=\footnotesize},
]

\addplot[
matrix plot,
mesh/cols=3,
point meta=explicit]
table[meta=C]{
  x y C
  0 0 80
  1 0 36
  2 0 40
  0 1 64
  1 1 80
  2 1 60
  0 2 52
  1 2 84
  2 2 72
  0 3 72
  1 3 28
  2 3 32
  0 4 56
  1 4 84
  2 4 80
  0 5 72
  1 5 52
  2 5 44
  0 6 4
  1 6 84
  2 6 41
  0 7 37
  1 7 69
  2 7 84
  0 8 63
  1 8 53
  2 8 82
  0 9 78
  1 9 74
  2 9 39
  0 10 39
  1 10 63
  2 10 88
  0 11 76
  1 11 74
  2 11 49
  0 12 39
  1 12 6
  2 12 88
  0 13 46
  1 13 33
  2 13 75
  0 14 88
  1 14 67
  2 14 54
  0 15 79
  1 15 83
  2 15 75
  0 16 50
  1 16 46
  2 16 71
  0 17 92
  1 17 71
  2 17 75
  0 18 46
  1 18 33
  2 18 8
};
\end{axis}
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Question regarding piecewise syntax with pgfplot

[Tex/LaTex] pgfplots: percentage in matrix plot

Related Question