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

from scipy.interpolate import griddata

"""
Explanation: Interpolation Exercise 2
End of explanation
"""


# YOUR CODE HERE
raise NotImplementedError()

"""
Explanation: 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.
End of explanation
"""


plt.scatter(x, y);

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

"""
Explanation: The following plot should show the points on the boundary and the single point in the interior:
End of explanation
"""


# YOUR CODE HERE
raise NotImplementedError()

assert xnew.shape==(100,)
assert ynew.shape==(100,)
assert Xnew.shape==(100,100)
assert Ynew.shape==(100,100)
assert Fnew.shape==(100,100)

"""
Explanation: 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.
End of explanation
"""


# YOUR CODE HERE
raise NotImplementedError()

assert True # leave this to grade the plot

"""
Explanation: Plot the values of the interpolated scalar field using a contour plot. Customize your plot to make it effective and beautiful.
End of explanation
"""


