contour_plot with several poles

asked 2019-03-25 22:57:22 +0100

stockh0lm
270 ●4 ●8 ●26

I have a 2d function with four poles that i would like to exclude from the plot because they hide interesting details of the rest of the plot. With just one pole i can omit one region. Now I want to omit all four like this:

show( contour_plot(pic, (x,-0.5,1.5), (z,-1,2), region=[((x)^2+(z)^2-.01), ((x)^2+(z-1)^2-.01), ((x-1)^2+(z)^2-.01), ((x-1)^2+(z-1)^2-.01)] ) )

that means i give a list of regions. That fails:

Traceback (most recent call last):
  File "e-feld.sage.py", line 68, in <module>
    show( contour_plot(pic, (x,-_sage_const_0p5 ,_sage_const_1p5 ), (z,-_sage_const_1 ,_sage_const_2 ), region=[((x)**_sage_const_2 +(z)**_sage_const_2 -_sage_const_p01 ), ((x)**_sage_const_2 +(z-_sage_const_1 )**_sage_const_2 -_sage_const_p01 ), ((x-_sage_const_1 )**_sage_const_2 +(z)**_sage_const_2 -_sage_const_p01 ), ((x-_sage_const_1 )**_sage_const_2 +(z-_sage_const_1 )**_sage_const_2 -_sage_const_p01 )] ) )
  File "/usr/lib/python2.7/dist-packages/sage/misc/decorators.py", line 411, in wrapper
    return func(*args, **kwds)
  File "/usr/lib/python2.7/dist-packages/sage/misc/decorators.py", line 411, in wrapper
    return func(*args, **kwds)
  File "/usr/lib/python2.7/dist-packages/sage/misc/decorators.py", line 492, in wrapper
    return func(*args, **options)
  File "/usr/lib/python2.7/dist-packages/sage/plot/contour_plot.py", line 848, in contour_plot
    include_endpoint=True)],
TypeError: 'tuple' object is not callable

Is it my syntax? Can I give a list of regions, at all? Or can I tone down the poles in some other way so that i can still see the contours of my plot?

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answered 2019-03-26 01:30:17 +0100

Juanjo

3213 ●5 ●41 ●86

(I'd tried to write the following lines as comments to @Emmanuel Charpentier's answer, but I had problems with formatting)

In the preceding answer, I think that the correct syntax is lambda x,z: (x^2+z^2.... Perhaps it is clearer to define before the region to be included. In order to color the excluded region, you can also plot it with region_plot and then combine everything in a single figure. Try, for example, the following complete example:

# Variables
var("x,y")

# f is a function with poles in (0,0), (1,0), (0,1), (1,1) 
f(x,y) = 1/(x^2+y^2) + 1/((x-1)^2+y^2) + 1/(x^2+(y-1)^2) + 1/((x-1)^2+(y-1)^2)

# Region where contour lines should be plotted
def region_to_include(x,y):
    return x^2+y^2>0.1 and x^2+(y-1)^2>0.1 and (x-1)^2+y^2>0.1 and (x-1)^2+(y-1)^2>0.1

# As an alternative:
#def region_to_include(x,y):
#    return (x^2+y^2-0.1) * (x^2+(y-1)^2-0.1) * ((x-1)^2+y^2-0.1) * ((x-1)^2+(y-1)^2-0.1)

# Region to be excluded
def region_to_exclude(x,y):
    return not region_to_include(x,y)

# Contour plot on the desired region
c = contour_plot(f(x,y), (x,-1,2), (y,-1,2), region=region_to_include, 
                 contours= 30, plot_points=200, cmap=colormaps.jet, colorbar=True)

# Plot of the region to be excluded
r = region_plot(region_to_exclude, (x,-1,2), (y,-1,2), 
                plot_points=300, incol="gray", bordercol="black", borderwidth=3)

# Final plot
show(c + r, frame=True, axes=False)

See this SageCell

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don't i do exactly what you do, in your example? why goes wrong with the poles on the left?

stockh0lm ( 2019-04-13 21:18:16 +0100 )edit

Since you don't provide the exact definition of the function whose contours you try to plot, I can't tell what happens in every pole.

Juanjo ( 2019-04-14 02:11:29 +0100 )edit

no, it was not a problem with the poles but a typo on my part. your example is perfectly fine but i had a .1 instead of 1, which made it miss the left poles.

stockh0lm ( 2019-04-14 09:04:29 +0100 )edit

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answered 2019-03-26 00:08:11 +0100

Emmanuel Charpentier
7774 ●6 ●51 ●154

updated 2019-03-26 08:10:01 +0100

From the docstring:

""region" - (default: None) If region is given, it must be a function of two variables. Only segments of the surface where region(x,y) returns a number >0 will be included in the plot."

Your region argument is a list of four expressions. Apparently, you wish to exclude the neighborhood of{(0, 0),(0,1),(1, 0), (1,1)}. I'd try:

region=lambda x,z: (x^2+z^2)>1/100)*(((x-1)^2+z^2)>1/100)*(x^2+(z-1)^2)>1/100)*(((x-1)^2+(z-1)^2)>1/100)

which should return True (i. e. 1) except in the target neighborhoods, where it should return 0.

HTH,

EDIT : lambda x, z:..., **NOT**lambda(x,z)...`. My deepest apologies.

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awesome, thank you for the idea to put this into a lambda function.

stockh0lm ( 2019-03-26 11:21:11 +0100 )edit

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