add pgfplot

[ksagiyam]

Description

Enable outputting Function data for LaTeX tikz plots. Not for large Functions.

Example:

from firedrake import *
  

mesh = TorusMesh(31, 13, 2.0, 0.5, quadrilateral=False, print_latex_example=True)
x, y, z = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 2)
f = Function(V, name="torus_tri").interpolate(x)
pgfplot(f, "./pgfplot_example_torus_tri.txt", degree=2)

generates an output file "./pgfplot_example_torus_tri.txt" and prints an example usage in LaTeX:

===========================================================================================
% pgfplot_example.tex

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{figure}[ht]
\begin{tikzpicture}
\begin{axis}[title=torus tri,
             xmin=-2.49, xmax= 2.50,
             ymin=-2.50, ymax= 2.50,
             zmin=-0.50, zmax= 0.50,
             xlabel={$x$},
             ylabel={$y$},
             zlabel={$z$},
             % xtick={0, 1, 2},
             % xticklabels={0, 1, 2},
             % ytick={0, 1},
             % yticklabels={0, 1},
             % ztick={0, 1},
             % zticklabels={0, 1},
             % axis equal,
             axis equal image,
             colorbar,
             colormap/hot, % hot, cool, bluered, greenyellow, redyellow, violet, blackwhite
             colorbar/width=10pt,
             view={30}{45},
             width=300pt,
             height=300pt,
             % axis line style={draw=none},
             % tick style={draw=none},
            ]
\addplot3[patch,
          patch type=triangle quadr,
          point meta=explicit,
          shader=faceted interp, % interp, faceted, faceted interp
          opacity=1.,
         ] table[x=x, y=y, z=z, meta=torus_tri] {./pgfplot_example_torus_tri.txt};
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}
===========================================================================================

Run:

lualatex -shell-escape pgfplot_example.tex

For more details, see:

https://pgfplots.sourceforge.net/gallery.html
http://www.bakoma-tex.com/doc/latex/pgfplots/pgfplots.pdf

Associated Pull Requests:

Fixes Issues:

Checklist for author:

• I have linted the codebase (make lint in the firedrake source directory).
• My changes generate no new warnings.
• All of my functions and classes have appropriate docstrings.
• I have commented my code where its purpose may be unclear.
• I have included and updated any relevant documentation.
• Documentation builds locally (make linkcheck; make html; make latexpdf in firedrake/docs directory)
• I have added tests specific to the issues fixed in this PR.
• I have added tests that exercise the new functionality I have introduced
• Tests pass locally (pytest tests in the firedrake source directory) (useful, but not essential if you don't have suitable hardware).
• I have performed a self-review of my own code using the below guidelines.

Checklist for reviewer:

• Docstrings present
• New tests present
• Code correctly commented
• No bad "code smells"
• No issues in parallel
• No CI issues (excessive parallelism/memory usage/time/warnings generated)
• Upstream/dependent branches and PRs are ready

Feel free to add reviewers if you know there is someone who is already aware of this work.

Please open this PR initially as a draft and mark as ready for review once CI tests are passing.

[ksagiyam]

mesh = TorusMesh(31, 13, 2.0, 0.5, quadrilateral=False)
x, y, z = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 2)
f = Function(V, name="torus_tri").interpolate(x)
pgfplot(f, "./pgfplot_example_torus_tri.txt", degree=2)

torus_tri.pdf

[ksagiyam]

mesh = TorusMesh(31, 13, 2.0, 0.5, quadrilateral=True)
x, y, z = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 2)
f = Function(V, name="torus_quad").interpolate(x)
pgfplot(f, "./pgfplot_example_torus_quad.txt", degree=2)

torus_quad.pdf

[ksagiyam]

mesh = UnitBallMesh(refinement_level=3)
x, y, z = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 2)
f = Function(V, name="ball").interpolate(x)
pgfplot(f, "./pgfplot_example_ball.txt", degree=2)

ball.pdf

[ksagiyam]

mesh = BoxMesh(32, 16, 16, 2.0, 1.0, 1.0, hexahedral=True)
x, y, z = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 2)
r = sqrt(x**2 + y**2 + z**2)
f = Function(V, name="box").interpolate(sin(16 * r) / (r + 1.e-6))
pgfplot(f, "./pgfplot_example_box.txt", degree=2)

box.pdf

[connorjward]

Cool!

[connorjward]

Surely this should be part of firedrake.plot? Perhaps we should make firedrake.plot a subpackage. If we are careful with namespacing this shouldn't affect an end user at all.

[ksagiyam]

Thanks! Yes, we can.

[connorjward]

Does this work in parallel? The docstring should probably make it clear either way.

[ksagiyam]

Yes. Updated docstring.

[dham]

Wow. Just wow.