Hi,
I still not have a solution for plotting the complex valued functions with
mayavi.
It is not clear to me whether there is an issue of VTK itself or of a
not-yet-implemented
function in mayavi. However, I was able to do exactly what I wanted using
matplotlib;
unfortunately, this has to stay 2D. I was hoping to be able to do something
similar
for 3-dimensional functions in mayavi...
Here is the exercise: given the function f(x,y) = (-1.+(x+1.j*y)**3)**2
we have to plot z = f(x,y) for x an y between -2 and 2. As z is complex, we
follow the
convention of Thaller (quantum mechanics): the color of each point is first
computed in the
hsv system, where h (hue) is given by the angle of z, s is always 1 and v
(value) is related to the
absolute value of z (by the stereographic projection) such that a point of
absolute value 0 is completely dark.
After that, the hsv codes are traduced into the rgb system and then the points
with their own colors are ploted with the imshow function of matplotlib.
The proposed function to plot is nice, because we'll recognize 3 dark points:
it has 3 zeros. The phase spectrum appears 2 times around each dark point,
meaning that each of the zeros has multiplicity 2.
If you run the implementation below (which uses matplotlib), you'll agree, I
hope, that such a visualization is
more helpful that a classical one, and hence it is worthwhile to find a
solution in mayavi, too...
Would it be possible in mayavi to plot only the points, but each with its own
color and without modifying their size?
Vasile
----------
from matplotlib.colors import hsv_to_rgb
import numpy as np
# create the grid
x, y = np.mgrid[-2:2:0.01, -2:2:0.05]
z = -1.+(x+1.j*y)**3
z = z**2 # function to be ploted
# funny think in matplotlib: the axes are inversed :(
z = z.transpose(); x = x.transpose(); y = y.transpose()
# go for the hue from the phase
phase = np.angle(-z) # to get exactly Thallers colors
A = 0.5*(phase+np.pi)/np.pi
# go for the value in the hsv scheme
R = abs(z)**2; M = 0.1#R.min() # M is needed in the projection
theta = np.pi - 2*np.arctan(np.sqrt(R/M))
# prepare the points to be ploted
Nx,Ny = z.shape
hsv_colors = np.empty((Nx, Ny,3))
hsv_colors[:, :, 0] = A
hsv_colors[:, :, 1] = 1.
hsv_colors[:, :, 2] = 1.-theta/np.pi
z_rgb = hsv_to_rgb(hsv_colors)
# and plot them
import matplotlib.pyplot as plt
fig = plt.figure()
plt.imshow(z_rgb, origin='lower', extent=[-2,2,-2,2])
plt.xlabel('x')
plt.ylabel('y')
fig = plt.figure()
# look only at the absolute value
plt.imshow(R, origin='lower', extent=[-2,2,-2,2])
plt.xlabel('x')
plt.ylabel('y')
plt.show()
________________________________________
From: Gradinaru Vasile Catrinel [vasile.gradin...@sam.math.ethz.ch]
Sent: Friday, June 10, 2011 11:44 AM
To: Gael Varoquaux
Cc: enthought-...@enthought.com; mayavi-users@lists.sourceforge.net
Subject: Re: [MayaVi-users] [Enthought-Dev] complex valued function with
"QM-standard" color convention?
Hi,
having only 0 and pi is just what I wanted: a simple example allows me to find
faster the bugs...
Since the v in the hsv scheme is constant (hue-saturation-value) we see the
jump.
Having the v set by the (squared) absolute value of z=f(x,y) would allow the
points near to 0 to be darker
and maybe to not allow the eyes to realize too much of the jump.
Do you know if there is an efficient way to plot only the points with their
associated colors
(each point comes with its own color)?
Vasile
________________________________________
From: Gael Varoquaux [gael.varoqu...@normalesup.org]
Sent: Friday, June 10, 2011 9:01 AM
To: Gradinaru Vasile Catrinel
Cc: enthought-...@enthought.com; mayavi-users@lists.sourceforge.net
Subject: Re: [MayaVi-users] [Enthought-Dev] complex valued function with
"QM-standard" color convention?
Hi,
I had a quick look at your code, and it seems jst fine. It even seems to
run fine, at least the Mayavi part. The 'angle(z)' variable that you are
passing in is only made of 0 and pi values, thus I am not surprised that
the mesh shows only two colors. Maybe that's where the problem lies?
Cheers,
Gael
On Thu, Jun 09, 2011 at 03:00:36PM +0000, Gradinaru Vasile Catrinel wrote:
> from numpy import real, imag, conj, abs, mgrid
> x, y = mgrid[-2:2:0.05, -2:2:0.05]
> u = x*exp(-0.25*x**2)
> v = y*exp(-0.25*y**2)
> z = u*v
> surfCF(x, y, angle(z), abs(z)**2)
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