Interpolation Exercise 2



In [1]:

    
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
sns.set_style('white')



In [ ]:

    
from scipy.interpolate import griddata

Sparse 2d interpolation

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:

The square domain covers the region $x\in[-5,5]$ and $y\in[-5,5]$.
The values of $f(x,y)$ are zero on the boundary of the square at integer spaced points.
The value of $f$ is known at a single interior point: $f(0,0)=1.0$.
The function $f$ is not known at any other points.

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.



In [12]:

    
x=np.linspace(-5,5)
y=x
listf=[0,1,0]
f=np.array(listf)
f









    Out[12]:





array([0, 1, 0])

The following plot should show the points on the boundary and the single point in the interior:



In [13]:

    
plt.scatter(x, y);



In [14]:

    
assert x.shape==(41,)
assert y.shape==(41,)
assert f.shape==(41,)
assert np.count_nonzero(f)==1









    



---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-14-864d037f1b80> in <module>()
----> 1 assert x.shape==(41,)
      2 assert y.shape==(41,)
      3 assert f.shape==(41,)
      4 assert np.count_nonzero(f)==1

AssertionError:

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).
Use cubic spline interpolation.



In [ ]:

    
# YOUR CODE HERE
raise NotImplementedError()



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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.



In [ ]:

    
# YOUR CODE HERE
raise NotImplementedError()



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assert True # leave this to grade the plot