# Plotting 2D column-shaped results with python

Ok, so you have your computational output of a set of 2D points. You have been lazy and done the obvious stuff: arrange them in columns, with the first one being the x coordinates, second one the y coordinate, then come the fields, which may be scalar (one column each), or vector (two columns each, one for each coordinate). How to visualize them?

With python, start with

`ipython --pylab`

Then, read the data

In [4]: dt = loadtxt( ‘1/mesh.dat’ )

In [5]: shape( dt )
Out[5]: (1024, 27)

Notice the last command tells us we have 1024 data points, and 27 fields (well, 25 + positions). For convinience, assign columns to arrays:

In [6]: x=dt[:,0]; y=dt[:,1]; al=dt[:,4]

Now x and y are positions, and “al” is the scalar field for the fifth column (number 4, since counters start at 0 in python).

To visualize the positions,

In [7]: scatter( x , y )

A scalar field may be visualized with a color map:

In [9]: scatter( x , y , c = al )

The “c=” means the color is taken from field al. One may fiddle with colormaps and symbol sizes:

In [9]: scatter( x , y , c = al , cmap= plt.cm.Blues, s=8 )

To know the range we are plotting, produce a color bar:

In [19]: colorbar()

Remember each plotting is overlaid on the previous one, so it is necessary to blank the plot from time to time:

In [11]: clf()

For vector fields, assign coordinates to two separate arrays:

In [20]: vx=dt[:,8]; vy=dt[:,9]

Then, use “quiver” to get a vector plot:

In [22]: quiver( x, y, vx , vy )

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# from gnuplot to python

Part of my moving to python for science.

I have lately been using gnuplot to monitor the progress and end results of my simulations.  These are 2D hydrodynamic simulations, which involve 2D scalar and vector fields.

2D plots

With gnuplot, I used to run stuff like

plot ‘8000/points.dat’ u 1:2

for a 2D plot of a scalar field. On column 1 I have the x values of the coordinates and on column 2 the y values, so this just plots the coordinates. The “8000” is the directory for time step 8000, where the data file is saved.

OK, now running ipython –pylab I have to run

dt = pylab.loadtxt(‘8000/points.dat’)

ss=scatter(dt[:,0],dt[:,1],c=dt[:,11],s=50)

2D scatter plot with colors

Important things to notice:

• python starts numbering c-style: at 0! so, despite pylab having been designed in order to mimic matlab syntax, there is a clear departure here.
• it’s easy to assign a color to the points, in this case column 12 (11 for python) is a density field. The default color scale looks ok (it goes from blue to red).
• the size is set to 50 for a nice full-screen view.
• New plots will appear on top of this one. If this is not desired, close the window, or run pylab.clf()

Vector plots

This is quite easy in gnuplot:

plot ‘8000/points.dat’ u 1:2:(\$5/10):(\$6/10) w vec

On columns 5 and 6 I store the x and y components of the velocity. In this example they are reduced ten-fold in order to hace a decent plot (and this has to set by hand…).

Now we may run:

st=quiver(dt[:,0],dt[:,1],dt[:,4],dt[:,5],dt[11])

which does the same. A bonus is that the vector length is automatically calculated from the average vector length. This may the right solution, if not the option “scale=xx” may be used. The higher xx is, the shorter the arrows (??). The fifth entry is a color code, which does not look to good at present because, I think, they are taken as RGB values, unlike with scatter.

Vector plot — funny senseless colors

3D plots

This one’s harder. To get a scatter 3D plot of three columns I used to run

splot ‘8000/points.dat’ u 1:2:12

Now, it’s more like

from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()

ax = fig.add_subplot(111, projection=’3d’)

ax.scatter(dt[:,0],dt[:,1],dt[:,11])

fig.show()

That produces a quite nice scatter plot with tick marks on the three axes.

3D scatter plot