Interpolation Exercise 2

In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np

In [2]:
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 [3]:
xb = np.array([-5,-4,-3,-2,-1,0,1,2,3,4,5])
yb = np.array([-5,-5,-5,-5,-5,-5,-5,-5,-5,-5,-5])
yt = np.array([5]*11)
yc = np.array(0)
x = np.hstack((xb,xb,yb[1:10],yt[1:10],yc))
y = np.hstack((yb,yt,xb[1:10],xb[1:10],yc))
f1 = np.array([0]*40)
f2 = [1]
f = np.hstack((f1,f2))

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

In [4]:
plt.scatter(x, y);

In [5]:
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).
  • Use cubic spline interpolation.

In [6]:
xnew = np.array[-5,5,100]
ynew = np.array[-5,5,100]
Xnew,Ynew = np.meshgrid(xnew,ynew)
Fnew = griddata((x,y),f,(Xnew,Ynew), method = 'cubic')

TypeError                                 Traceback (most recent call last)
<ipython-input-6-81c1e6f88716> in <module>()
----> 1 xnew = np.array[-5,5,100]
      2 ynew = np.array[-5,5,100]
      3 Xnew,Ynew = np.meshgrid(xnew,ynew)
      4 Fnew = griddata((x,y),f,(Xnew,Ynew), method = 'cubic')

TypeError: 'builtin_function_or_method' object is not subscriptable

In [7]:
assert xnew.shape==(100,)
assert ynew.shape==(100,)
assert Xnew.shape==(100,100)
assert Ynew.shape==(100,100)
assert Fnew.shape==(100,100)

NameError                                 Traceback (most recent call last)
<ipython-input-7-32f87223a985> in <module>()
----> 1 assert xnew.shape==(100,)
      2 assert ynew.shape==(100,)
      3 assert Xnew.shape==(100,100)
      4 assert Ynew.shape==(100,100)
      5 assert Fnew.shape==(100,100)

NameError: name 'xnew' is not defined

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

In [8]:

NameError                                 Traceback (most recent call last)
<ipython-input-8-460668c43941> in <module>()
----> 1 plt.contourf(Fnew)
      2 ax = plt.gca()
      3 plt.title('Interpolated Scaler Field')
      4 plt.xlabel('X')
      5 plt.ylabel('Y')

NameError: name 'Fnew' is not defined

In [ ]:
assert True # leave this to grade the plot