From mathematics to a nice figure in a LaTeX document

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1 From mathematics to a nice figure in a L A T E Xdocument: a post-processing chain Matthieu Haefele High Level Support Team Max-Planck-Institut für Plasmaphysik, München, Germany Autrans, Septembre 2011, École d été Masse de données : structuration, visualisation

Max-Planck-Institut für Plasmaphysik, München, Germany Autrans,

2 A post-processing chain Numerical scheme to find an approximation Python/numpy C/F90/MPI/HDF5... Approximation of the solution Little physics problem pencil and paper Analytical solution Python/numpy Solution evaluation Python/pylab gnuplot The answer in a nice pdf latex nice eps figure with label inkscape svg figure nice eps figure VisIt/paraview

.. Approximation of the solution Little physics problem pencil and paper Analytical

3 Learn Python in 1 slide! def myfunction ( foo, bar = 3 ) : This f u n c t i o n computes something u s e f u l p r i n t I was c a l l e d with, foo, bar p i =3.14 for i in range ( 1 1 ) : i f i %2==0: # Writes p i i = XX p r i n t p i, i, =, i p i else : # Writes i p i = XX p r i n t i, p i =, i p i myfunction ( s u p e r s t r i n g )

4 Main Python packages to do numerics numpy: implementation of n-d arrays matplotlib/pylab: 1D, 2D graphics scipy: package based on numpy that soves different dedicated problems h5py: Python bindings for the HDF5 library f2py, swig: tools to automate the creation of Python bindings from C/F90 codes...

different dedicated problems h5py: Python bindings for the HDF5 library

5 Correction of exo1 in Python import numpy import h5py tab = numpy. zeros ( ( 2 2, 2 0 ), dtype=numpy. i n t 3 2 ) f = h5py. F i l e ( m y f i l e. hdf5, w ) f [ MyDataset ]= tab tab = numpy. ones ( ( 8, 8 ), dtype=numpy. i n t 3 2 ) f [ MyDataset ] [ 3 : 1 1, 2 : 1 0 ] = tab f. close ( )

6 Gnuplot open source software can produce 2D and 3D plots analytic or numeric functions

7 Using gnuplot interactively set xrange [0:4* ] plot sin(x), sin(x /2), "data.txt" u 1:2 w l pause -1 x [0 : 4π] plot on the same figure: sin(x) sin(x π 2 ) The second column of the file named data.txt, and plot with lines (w l) pause -1 means: do not close the window before I hit the Enter key

8 Using gnuplot non interactively set terminal svg set output "myfig.svg" set xrange [0:4* ] plot sin(x), sin(x /2), "data.txt" u 1:2 w l Same figure A svg file is created instead of opening a window

14159] plot sin(x), sin(x-3.14159/2), "data.

9 Resulting picture sin(x) sin(x /2) "data.txt" u 1:

10 Inkscape software Free and open source software Vector graphics edition/creation Standard Vector Graphics format based (SVG), the W3C standard Similar capacities as Illustrator, Freehand, CorelDraw or Xara X

Graphics format based (SVG), the W3C standard

11 Vector (svg, ps,... ) vs Raster (png, jpg, tiff,... ) Raster is an array of dots that appear to be shapes Pro: With sufficient resolution can be photo-realistic Con: Takes up lots of space even for simple geometric representations Con: Difficult to split into component pieces for further editing Vector is real 2D shapes Pro: Geometric representations scalable to any resolution Pro: Easy to edit component pieces Con: Difficult to do photo-realistic images at small file sizes

Takes up lots of space even for simple geometric representations Con: Difficult to split into component pieces for

12 A post-processing chain Numerical scheme to find an approximation Python/numpy C/F90/MPI/HDF5... Approximation of the solution Little physics problem pencil and paper Analytical solution Python/numpy Solution evaluation Python/pylab gnuplot The answer in a nice pdf latex nice eps figure with label inkscape svg figure nice eps figure VisIt/paraview

13 Hands on Let us consider the following magnetic diffusion equation B y (x, t) t = η 2 B y (x, t) with an initial discontinuous field given by { B0 for x > 0 B y (x, 0) = B 0 for x < 0 Please find the analytical solution and produce a L A T E X generated pdf file containing figures that illustrates this diffusion.

B y (x, 0) = B 0 for x < 0 Please find the analytical solution and produce a L

14 Hands on correction t The analytical solution is B y (x, t) = B 0 erf(ξ) with ξ = x/ 4ηt and the error function erf(ξ) = 2 π 1/2 Illustration with η = 1 and B 0 = 2 ξ 0 e u2 du x B(x,t)

ξ 0 e u2 du 2 1.5 1 0.5 0-0.5-1 -1.5-2 0-4 -2 0 2 4 4 2 0 2 4 x 20 15 10 5-1.000-0.

15 Part of the process in numerical science.xmf.xml.png gfortran, ifort mpiexec VisIt.f90.txt???.exe.avi.h5 Physics Math python + pylab convert.py python.gp.txt gnuplot.svg inkscape.eps.tex latex pdflatex.aux.bib bibtex.aux.tex.bbl latex pdflatex.aux latex.dvi dvips.ps ps2pdf pdflatex.pdf

h5 Physics Math python + pylab convert.py python.gp.txt gnuplot.

Scientific Visualization

.PRACE Winter School 2013 Scientific Visualization SOME CONCEPTS, TOOLS & LIBRARIES Nicolas P. Rougier Introduction Audience Yourself Scientific community Students Media Criterion Quality Speed Development