3

This question was answered in this post, but I would like a small adaptation of it.

I would like to take the top solution of the above post. Instead of a single bi-variate distribution, I would like to have a grid of such distributions. The grid should be rectangular with controllable positions for each source.

I would then like to adapt this resulting image to remove all of the axes to leave behind just the surface distribution.

The grid I would like should be something like that here. But the position of each circle should be a 2D Gaussian.

Desired output

Something like this, with and without projections on the axes.

enter image description here

The distribution

Each source on the grid should have the following distribution:

$$f(x, y) = \frac{1}{2\pi \sigma_x \sigma_y}\exp[-\frac{(x-\mu_x)^2}{\sigma_x^2} + -\frac{(y-\mu_y)^2}{\sigma_y^2}]$$.

with $\sigma_x = \sigma_y$ and varying values for $\mu_x$ and $\mu_y$ for the different sources. Note that this distribution has a diagonal form for the covariance matrix with elements $\sigma_x$ and $\sigma_y$ on the diagonal.

Sid
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  • 1
    And, where is your problem? What have you done so far? – Huang_d Jun 16 '17 at 15:28
  • @Huang_d, getting a second distribution using the \addplot3 [surf] plot at a different location. It does not produce 2 seperate distributions. – Sid Jun 16 '17 at 15:31
  • One big problem (if I understand correctly) is, you won't be able to draw several intersecting surfaces using PgfPlots, as it won't be able to decide correctly which is in the front / in the back. – marsupilam Jun 16 '17 at 15:31
  • @marsupilam, I see. Is there an alternative way to achieve this? – Sid Jun 16 '17 at 15:41
  • You could draw each surface only on the relevant domain and put them side by side. Do you have a model picture of what you would like, or more details of which gaussians you want and what grid you are thinking of ? – marsupilam Jun 16 '17 at 15:46
  • @marsupilam see updated question for a link to a grid picture. – Sid Jun 16 '17 at 15:54
  • I would recommend generating the data outside of LaTeX, using Matlab or Python, for instance, and only using PGFPlots do generate the plot. As marsupilam said, it would be helpful to see a sketch of the desired result, or at least a more detailed description. – Jake Jun 16 '17 at 15:54

1 Answers1

1

I wonder if I'll ever understand the thing with loops in pgfplots.

The output

enter image description here

The (simplistic) code

@Jake is right in pointing out this is a lot of computations for pgfplots, and you may be well-advised to pre-compute the functions via an external tool

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
  [
    declare function=
    {
      gaussian(\x)= exp(-.5*\x^2);
      gaussianDouble(\x,\y)= gaussian(\x)*gaussian(\y);
    }
]
\begin{axis}
  \foreach\i in {0,4,...,12}
  {
    \foreach\j in {0,4,...,12}
    {
      \addplot3[surf, samples=20, domain=-2:2, y domain=-2:2]({x+\i},{y-\j},{gaussianDouble(x,y)});
    }
  }
\end{axis}
\end{tikzpicture} 
\end{document}

In Scilab

Not an answer, but is this what you want ?

If so, may I edit your question to include the pic in it ?

The output

enter image description here

The (Scilab) code

function z=normal(x,y)
  norm = x.^2 + y.^2
  z = exp(-.5*norm)
endfunction
clf()
x=linspace(-3,3,30)
[X,Y]=meshgrid(x)
for i=0:2:10
  for j=0:2:10
    surf(X+i,Y+j,normal(X,Y))
  end
end
f=gcf()
f.color_map = autumncolormap(32);
marsupilam
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  • Yes, this is what I would like thanks - with and without a distribution shown projected on the xz and yz axes (much like the original post in question). I would still prefer it in TikZ, but you are most welcome to edit the question to illustrate the desired output. – Sid Jun 16 '17 at 16:27
  • @Sid Alright, then, you would need to tell us the x and y step of the lattice you are using, and the covariance matrix for the Gaussian distributions. Otherwise, no computation can be done... – marsupilam Jun 16 '17 at 16:31
  • Added the form of the distribution to the question. – Sid Jun 16 '17 at 17:00
  • It's true that it takes 20-30 seconds in pgfplots, but remember that you only have to compile it once. You can then subsequently include it using \includegraphics. – JPi Jun 16 '17 at 18:30
  • @JPi Sure, but I chose a rather low samples value and few bumps... It's unlikely you can get stellar graphics using this simple approach. – marsupilam Jun 16 '17 at 18:37
  • Right, though mostly because of tex memory limitations... – JPi Jun 16 '17 at 18:58