How can I rotate a function?

Question

I am trying to draw the following picture, however I am wondering how can I rotate the gaussian function, like in the first plot?

enter image description here

\documentclass[10pt, compress, usetitleprogressbar]{beamer}  
%Tikz for drawing
\usepackage{tikz}
\usetikzlibrary{calc,patterns,decorations.pathmorphing,decorations.markings}
\usetikzlibrary{shapes,arrows}
\usetikzlibrary{calc}
\usetikzlibrary{positioning}
\usetikzlibrary{shapes.multipart}

\pgfmathdeclarefunction{gauss}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
}
\pgfmathdeclarefunction{cline}{2}{%
  \pgfmathparse{#1*x+#2}%
}
\begin{tikzpicture}[auto, scale=0.58, every
    node/.style={transform shape}]
    \begin{axis}[very thick,cyan!30!black,          
        no markers, domain=0:6, samples=100,    
        axis lines*=left, xlabel=Measured Value (x), ylabel=Probability Density,
        height=5cm, width=7cm,
        xtick=\empty, ytick=\empty,         
        enlargelimits=false, clip=false, axis on top,
        grid = major, name=plot1, ymax=1
      ]  
      \addplot [very thick,cyan!50!black, fill=cyan!10, rotate
      around={-90:(9,9)},] {gauss(3,0.5)};
    \end{axis}

    \begin{axis}[very thick,cyan!30!black,
        no markers, domain=0:6, samples=100,    
        axis lines*=left, xlabel=Measured Value (x), ylabel=Probability Density,
        height=5cm, width=7cm,
        xtick=\empty, ytick=\empty,
        %xtick={-3, -2, -1, 0, 1, 2, 3}, ytick=empty,
        enlargelimits=false, clip=false, axis on top,
        grid = major, name=plot2,
         at=(plot1.right of south east), anchor=left of south west,
         ymax=1
      ]  
      \addplot [very thick,cyan!50!black, fill=cyan!10] {cline(1,0.5)};
    \end{axis}

    \begin{axis}[very thick,cyan!30!black,
        no markers, domain=0:6, samples=100,    
        axis lines*=left, xlabel=Measured Value (x), ylabel=Probability Density,
        height=5cm, width=7cm,
        xtick=\empty, ytick=\empty,
        enlargelimits=false, clip=false, axis on top,
        grid = major, name=plot3,
        at=(plot2.below south west), anchor=above north west,
        ymax=1]
      ]  
      \addplot [very thick,cyan!50!black, fill=cyan!10] {gauss(3,0.5)};
    \end{axis}

\end{tikzpicture}
\end{document}

This would be easier using a regular TikZ plot rather than pgfplots. — John Kormylo, May 06 '15 at 21:16

score 5 · Accepted Answer · answered May 07 '15 at 08:20

Try

\documentclass[tikz,border=5mm]{standalone}
    \usetikzlibrary{positioning}

\pgfmathdeclarefunction{gauss}{2}{%
  \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((\x-#1)^2)/(2*#2^2))}%
}
        \begin{document}
    \begin{tikzpicture}[
node distance = 4mm,
         font = \small\sffamily,
     N/.style = {name=n#1, 
                 shape=rectangle,fill=gray!10,
                 minimum size=44mm,
                 node contents={}},
        domain = 0:4,
       samples = 20,
                        ]
\node[N=1,above right];
    \draw[<-]   (n1.south west) --
        node[left] {\rotatebox{90}{calculated value $(y)$}}
                (n1.north west);
    \draw[->]   (n1.north west) --
        node[above] {probability density}
                (n1.north east);
\draw[draw=cyan!50!black, fill=cyan!10, very thick, smooth,
%      transform canvas={yshift=4mm}
      ]
      plot ({gauss(2,0.4)},\x);
%---
\node[N=2,right=of n1];
    \draw[->]   (n2.south west) -- (n2.north west) node[above] {$(y)$};
    \draw[->]   (n2.south west) -- (n2.south east) node[right] {$(x)$};
    \draw[very thick, shorten <=2mm]   
                (n2.south west) -- node[pos=0.75,below,sloped] {$y(x)=a+bx$} (n2.north east) ;
%---
\node[N=3,below=of n2];
    \draw[->]   (n3.south west) --
        node[left] {\rotatebox{90}{measured  value $(y)$}}
                (n3.north west);
    \draw[->]   (n3.south west) --
        node[below] {probability density}
                (n3.south east);
\draw[draw=cyan!50!black, fill=cyan!10, very thick, smooth,
      transform canvas={xshift=48mm, yshift=-48mm}
      ]
      plot (\x,{gauss(2,0.4)});
%---
\draw[dashed]   ([yshift=-2mm] n1.west) -| ([xshift=-2mm] n3.south);
\end{tikzpicture}
        \end{document}

In your (not working) MWE I change the following:

instead of document class beamer I use standalone
I omit not used TikZ libraries and definition for function cline
I change the parameters for Gaus pdf
use the suggestion of John Kormylov and draw all elements in three nodes (to
easy see them, they are gray colored; in final version you can omit this fill) accommodate of picture size to size of beamer frame

For the Gauss pdf in first node I simple change the coordinates, so the function is not necessary rotate.

enter image description here

How do you decide which library would fit for the plotting application? — Mokus, May 07 '15 at 08:22
I select only library 'positioning', which enabled positioning of nodes on the way as I usual do. If you need other libraries for final look out of picture, than simple add them. — Zarko, May 07 '15 at 08:29

score 3 · Answer 2 · edited Apr 13 '17 at 12:34

You could do this one nicely in Metapost as well.

enter image description here

Once you have created a normal-shaped curve you can scale it and relocate it as needed.

prologues := 3;
outputtemplate := "%j%c.eps";

beginfig(0);
  % unit
  u := 1cm;

  % axes
  path xx, yy;
  xx = (origin -- 5 right) scaled u;
  yy = xx rotated 90;
  drawarrow xx; label.rt (btex $x$ etex, point 1 of xx);
  drawarrow yy; label.top(btex $y$ etex, point 1 of yy);

  % parameters, assuming y=a+bx  
  a = 0.6u; 
  b = 0.7;
  x_mean = 2.7u;

  % the regression line, and the normal curves
  path lm, Z, Zx, Zy;
  lm = (0,a) -- (5u,a+b*5u);

  % the regression mean point
  z0 = (x_mean, a+b*x_mean);

  % scale is arbitrary, so you only need the core of the probability distribution, 
  % and so the "3" is just to make it look nice
  Z  = ((-4,0) for x = -3.9 step .1 until 4: .. (x, 3 mexp(-128*(x**2))) endfor) scaled 1/2 u;

  margin = -2u;
  % for the x-axis you just want a copy of Z shifted down and across
  Zx = Z shifted (x0,margin);

  % for the y-axis you can make it more realistic if you scale it by the regression coefficient 
  % before you rotate it and shift it
  Zy = Z xscaled b rotated -90 shifted (margin,y0);

  % put in the lines connecting the measurements to the response
  alpha = 1.96 * 1/2 u;
  for i=-1 upto 1:
    draw (x0+(i*alpha),margin) -- (x0+(i*alpha),y0+(i*b*alpha)) -- (margin,y0+(i*b*alpha)) 
         cutbefore Zx cutafter Zy
         dashed if i=0: evenly else: withdots scaled 0.6 fi;
  endfor 

  % draw the lm line and the normal curves and then label them
  draw lm withcolor .67 red;
  draw Zx;
  draw Zy;

  label.bot(btex Measured value ($x$) etex, (x0,margin));
  label.lft(btex Response value ($y$) etex rotated 90, (margin,y0));
  label.top(btex $y=a+bx$ etex, point 1 of lm);

endfig;

end

How can I rotate a function?

2 Answers2