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%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
sns.set_style('white')
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from scipy.interpolate import griddata
In this example the values of a scalar field $f(x,y)$ are known at a very limited set of points in a square domain:
Create arrays x
, y
, f
:
x
should be a 1d array of the x coordinates on the boundary and the 1 interior point.y
should be a 1d array of the y coordinates on the boundary and the 1 interior point.f
should be a 1d array of the values of f at the corresponding x and y coordinates.You might find that np.hstack
is helpful.
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x = np.hstack((np.linspace(-4,4,9), np.full(11, -5), np.linspace(-4,4,9), np.full(11, 5), [0]))
y = np.hstack((np.full(9,-5), np.linspace(-5, 5,11), np.full(9,5), np.linspace(-5,5,11), [0]))
f = np.hstack((np.zeros(20), np.zeros(20),[1.0]))
print(f)
The following plot should show the points on the boundary and the single point in the interior:
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plt.scatter(x, y);
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assert x.shape==(41,)
assert y.shape==(41,)
assert f.shape==(41,)
assert np.count_nonzero(f)==1
Use meshgrid
and griddata
to interpolate the function $f(x,y)$ on the entire square domain:
xnew
and ynew
should be 1d arrays with 100 points between $[-5,5]$.Xnew
and Ynew
should be 2d versions of xnew
and ynew
created by meshgrid
.Fnew
should be a 2d array with the interpolated values of $f(x,y)$ at the points (Xnew
,Ynew
).
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xnew = np.linspace(-5, 5, 100)
ynew = np.linspace(-5, 5, 100)
Xnew, Ynew = np.meshgrid(xnew, ynew)
Fnew = griddata((x, y), f , (Xnew, Ynew), method='cubic')
plt.imshow(Fnew, extent=(-5,5,-5,5))
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assert xnew.shape==(100,)
assert ynew.shape==(100,)
assert Xnew.shape==(100,100)
assert Ynew.shape==(100,100)
assert Fnew.shape==(100,100)
Plot the values of the interpolated scalar field using a contour plot. Customize your plot to make it effective and beautiful.
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plt.contourf(Xnew, Ynew, Fnew, cmap='hot')
plt.colorbar(label='Z')
plt.box(False)
plt.title("The interpolated 2d grid of our data.")
plt.xlabel('X')
plt.ylabel('Y');
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assert True # leave this to grade the plot
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