Numerical & Scientific Computing with Python: Contour Plots with Python

## Matplotlib Tutorial: Contour Plots

### Contour Plot

A contour line or isoline of a function of two variables is a curve along which the function has a constant value.

It is a cross-section of the three-dimensional graph of the function f(x, y) parallel to the x, y plane.

Contour lines are used e.g. in geography and meteorology.

In cartography, a contour line joins points of equal elevation (height) above a given level, such as mean sea level.

We can also say in a more general way that a contour line of a function with two variables is a curve which connects points with the same values.

#### Creating a "meshgrid"

# the following line is only necessary if working with "ipython notebook"
%matplotlib inline
import numpy as np
xlist = np.linspace(-3.0, 3.0, 3)
ylist = np.linspace(-3.0, 3.0, 4)
X, Y = np.meshgrid(xlist, ylist)
print(xlist)
print(ylist)
print(X)
print(Y)

[-3.  0.  3.]
[-3. -1.  1.  3.]
[[-3.  0.  3.]
[-3.  0.  3.]
[-3.  0.  3.]
[-3.  0.  3.]]
[[-3. -3. -3.]
[-1. -1. -1.]
[ 1.  1.  1.]
[ 3.  3.  3.]]

import numpy as np
xlist = np.linspace(-3.0, 3.0, 3)
ylist = np.linspace(-3.0, 3.0, 4)
X, Y = np.meshgrid(xlist, ylist)
Z = np.sqrt(X**2 + Y**2)
print(Z)

[[ 4.24264069  3.          4.24264069]
[ 3.16227766  1.          3.16227766]
[ 3.16227766  1.          3.16227766]
[ 4.24264069  3.          4.24264069]]


#### Calculation of the Values

import numpy as np
xlist = np.linspace(-3.0, 3.0, 3)
ylist = np.linspace(-3.0, 3.0, 4)
X, Y = np.meshgrid(xlist, ylist)
Z = np.sqrt(X**2 + Y**2)
print(Z)

[[ 4.24264069  3.          4.24264069]
[ 3.16227766  1.          3.16227766]
[ 3.16227766  1.          3.16227766]
[ 4.24264069  3.          4.24264069]]

import matplotlib.pyplot as plt
plt.figure()
cp = plt.contour(X, Y, Z)
plt.clabel(cp, inline=True,
fontsize=10)
plt.title('Contour Plot')
plt.xlabel('x (cm)')
plt.ylabel('y (cm)')
plt.show()


#### Changing the Colours and the Line Style

import matplotlib.pyplot as plt
plt.figure()
cp = plt.contour(X, Y, Z, colors='black', linestyles='dashed')
plt.clabel(cp, inline=True,
fontsize=10)
plt.title('Contour Plot')
plt.xlabel('x (cm)')
plt.ylabel('y (cm)')
plt.show()


#### Filled Contours

import numpy as np
import matplotlib.pyplot as plt
xlist = np.linspace(-3.0, 3.0, 100)
ylist = np.linspace(-3.0, 3.0, 100)
X, Y = np.meshgrid(xlist, ylist)
Z = np.sqrt(X**2 + Y**2)
plt.figure()
cp = plt.contourf(X, Y, Z)
plt.colorbar(cp)
plt.title('Filled Contours Plot')
plt.xlabel('x (cm)')
plt.ylabel('y (cm)')
plt.show()


#### Individual Colours

import numpy as np
import matplotlib.pyplot as plt
xlist = np.linspace(-3.0, 3.0, 100)
ylist = np.linspace(-3.0, 3.0, 100)
X, Y = np.meshgrid(xlist, ylist)
Z = np.sqrt(X**2 + Y**2)
plt.figure()
contour = plt.contourf(X, Y, Z)
plt.clabel(contour, colors = 'k', fmt = '%2.1f', fontsize=12)
c = ('#ff0000', '#ffff00', '#0000FF', '0.6', 'c', 'm')
contour_filled = plt.contourf(X, Y, Z, colors=c)
plt.colorbar(contour)
plt.title('Filled Contours Plot')
plt.xlabel('x (cm)')
plt.ylabel('y (cm)')
plt.show()


#### Levels

The levels were decided automatically by contour and contourf so far. They can be defined manually, by providing a list of levels as a fourth parameter. Contour lines will be drawn for each value in the list, if we use contour. For contourf, there will be filled colored regions between the values in the list.

import numpy as np
import matplotlib.pyplot as plt
xlist = np.linspace(-3.0, 3.0, 100)
ylist = np.linspace(-3.0, 3.0, 100)
X, Y = np.meshgrid(xlist, ylist)
Z = np.sqrt(X ** 2 + Y ** 2 )
plt.figure()
levels = [0.0, 0.2, 0.5, 0.9, 1.5, 2.5, 3.5]
contour = plt.contour(X, Y, Z, levels, colors='k')
plt.clabel(contour, colors = 'k', fmt = '%2.1f', fontsize=12)
contour_filled = plt.contourf(X, Y, Z, levels)
plt.colorbar(contour_filled)
plt.title('Plot from level list')
plt.xlabel('x (cm)')
plt.ylabel('y (cm)')
plt.show()


The last example of this chapter will be a "lovely" contour plot:

import matplotlib.pyplot as plt
import numpy as np
y, x = np.ogrid[-1:2:100j, -1:1:100j]
plt.contour(x.ravel(),
y.ravel(),
x**2 + (y-((x**2)**(1.0/3)))**2,
[1],
colors='red',)
plt.axis('equal')
plt.show()

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