Issue
I am trying to plot different norms with contourf and contour. I have succeeded with all norms except zero-norm and inf-norm. What is the right way to draw similar graphs for 0-norm and inf-norm?
Here is my code:
`p_values = [0., 0.04, 0.5, 1, 1.5, 2, 7, np.inf]
xx, yy = np.meshgrid(np.linspace(-3, 3, num=101), np.linspace(-3, 3, num=101))
fig, axes = plt.subplots(ncols=(len(p_values) + 1)// 2,
nrows=2, figsize=(14, 7))
for p, ax in zip(p_values, axes.flat):
if p != 0:
zz = ((np.abs((xx))**p) + (np.abs((yy))**p))**(1./p)
else:
zz = np.full_like(xx, np.sum(xx !=0))
ax.contourf(xx, yy, zz, 30, cmap='bwr')
ax.contour(xx,yy,zz, [1], colors='red', linewidths = 2)
proxy = [plt.Rectangle((0,0),1,1, facecolor='red')]
plt.show()`
Solution
First, let me mention that numpy provides numpy.linalg.norm
which could simplify things, when calculating norms. In the remainder I will stick to the attempt from the question to calculate the norm manually though.
L∞ norm
The L∞ norm would be the suppremum of the two arrays. This can easily be calculated using numpy.maximum
.
zz = np.maximum(np.abs(xx),np.abs(yy))
L0 "norm"
The L0 "norm" would be defined as the number of non-zero elements. For the 2D case it can hence take the values 0 (both zero), 1 (one zero), or 2 (both non-zero). Depicting this function as a contour plot is not really succefull because the function essentially deviates from 2 only along two lines in the plot. Using an imshow
plot would show it though.
zz = (xx != 0).astype(int) + (yy != 0).astype(int)
ax.imshow(zz, cmap='bwr', aspect="auto")
Complete example.
In total the plot could then look like
import matplotlib.pyplot as plt
import numpy as np
p_values = [0., 0.04, 0.5, 1, 1.5, 2, 7, np.inf]
xx, yy = np.meshgrid(np.linspace(-3, 3, num=101), np.linspace(-3, 3, num=101))
fig, axes = plt.subplots(ncols=(len(p_values) + 1)// 2,
nrows=2, figsize=(14, 7))
for p, ax in zip(p_values, axes.flat):
if p == 0:
zz = (xx != 0).astype(int) + (yy != 0).astype(int)
ax.imshow(zz, cmap='bwr', extent=(xx.min(),xx.max(),yy.min(),yy.max()), aspect="auto")
else:
if np.isinf(p):
zz = np.maximum(np.abs(xx),np.abs(yy))
else:
zz = ((np.abs((xx))**p) + (np.abs((yy))**p))**(1./p)
ax.contourf(xx, yy, zz, 30, cmap='bwr')
ax.contour(xx,yy,zz, [1], colors='red', linewidths = 2)
plt.show()
Answered By - ImportanceOfBeingErnest
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