Python : PathPatch ,3D plotting & StreamPlot in Mathplotlib

Histograms

The hist() function generates histograms automatically and returns the bin counts or probabilities. This demo shows a few optional characteristics in addition to the basic histogram:

• Setting the number of data bins.
• The parameter of density, Which normalises the height of the bin so that the histogram integral is 1.
• The resulting histogram is an approximation of the probability density function.
• Setting the face color of the bars. Setting the opacity (alpha value).

import matplotlib 
import numpy as np 
import matplotlib.pyplot as plt 

np.random.seed(19680801) 

# example data 
mu = 100 # mean of distribution 
sigma = 15 # standard deviation of distribution 
x = mu + sigma * np.random.randn(437)
 
num_bins = 50 
fig, ax =plt.subplots()
 
# the histogram of the data 
n, bins, patches = ax.hist(x, num_bins, density=True) 
# add a 'best fit' line 
y = ((1 / (np.sqrt(2 * np.pi) *sigma))* np.exp(-0.5* (1 / sigma *(bins - mu))**2)) 
ax.plot(bins, y, '--') 
ax.set_xlabel('Smarts') 
ax.set_ylabel('Probability density') 
ax.set_title(r'Histogram of IQ: $\mu-1000$, $\sigma=15$') 
# Tweak spacing to prevent clipping of ylabel 
fig.tight_layout() 
plt.show() 
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Output:

PathPatch object

In Matplotlib, you can use the matplotlib. path module to add arbitrary paths:

import matplotlib.path as mpath 
import matplotlib.patches as mpatches 
import matplotlib.pyplot as plt 

fig, ax = plt.subplots()
 
Path = mpath.Path 
path_data = [ (Path.MOVETO, (1.58, -2.57)), 
                         (Path.CURVE4, (0.35, -1.1)), 
                         (Path.CURVE4, (-1.75, 2.0)), 
                         (Path.CURVE4, (0.375, 2.0)), 
                         (Path.LINETO, (0.85, 1.15)), 
                         (Path.CURVE4, (2.2, 3.2)), 
                         (Path.CURVE4, (3, 0.05)), 
                         (Path.CURVE4, (2.0, -0.5)), 
                         (Path.CLOSEPOLY, (1.58, -2.57)),]
                                                            
codes, verts = zip(*path_data) 
path = mpath.Path(verts, codes) 
patch = mpatches.PathPatch(path, facecolor='r', alpha=0.5) 
ax.add_patch(patch) 

# plot control points and connecting Lines 
x, y = zip(*path.vertices) 
line = ax.plot(x, y, 'go-' ) 

ax.grid() 
ax.axis('equal') 
plt.show() 
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Output:

Three-dimensional plotting

The mplot3d toolkit (see Getting Started and 3D Plotting) supports simple surface-inclusive 3d graphs with wireframe, scatter and bar charts.

import matplotlib.pyplot as plt 
from matplotlib import cm 
from matplotlib.ticker import LinearLocator 
import numpy as np
 
fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
 
# Make data. 
X = np.arange(-5, 5, 0.25) 
Y = np.arange(-5, 5, 0.25) 
X, Y = np.meshgrid(X, Y) 
R = np.sqrt(X**2 + Y**2) 
Z = np.sin(R)
 
# Plot the surface. 
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, linewidth=0, antialiased=False)
 
# Customize the z axis. 
ax.set_zlim(-1.01, 1.01) 
ax.zaxis.set_major_locator(LinearLocator(10)) 
# A StrMethodFormatter is used automatically 
ax.zaxis.set_major_formatter('{x:.02f}')
 
# Add a colour bar that maps the colours to the values. 
fig.colorbar(surf, shrink=0.5, aspect=5) 

plt.show() 
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Output:

Streamplot

For displaying 2D vector fields, a stream plot or streamline plot is used. A few features of the streamplot function are shown in this example:

Varying the color along a streamline. Varying the density of streamlines. Varying the line width along a streamline. Controlling the starting points of streamlines. Streamlines skipping masked regions and NaN values.

import numpy as np 
import matplotlib.pyplot as plt 
import matplotlib.gridspec as gridspec 

# Creating dataset 
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j] 
U = -1 - X**2 + Y 
V = 1 + X - Y**2
speed = np.sqrt(U**2 + V**2) 

fig = plt.figure(figsize =(20, 16)) 
gs = gridspec.GridSpec(nrows = 3, ncols = 2, height_ratios =[1, 1, 2]) 

# Create a mask 
mask = np.zeros(U.shape, dtype = bool) 
mask[40:60, 40:60] = True
U[:20, :20] = np.nan 
U = np.ma.array(U, mask = mask) 

ax = fig.add_subplot(gs[2:, :]) 
ax.streamplot(X, Y, U, V, color ='r') 
ax.set_title('Streamplot with Masking') 

ax.imshow(~mask, extent =(-w, w, -w, w), alpha = 0.5, 
		interpolation ='nearest', cmap ='gray', aspect ='auto') 
ax.set_aspect('equal') 
 
plt.tight_layout() 
plt.show() 
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Output:

Hope you enjoyed this article on PathPatch,3D plotting & StreamPlot in Matplotlib, Happy Programming 🙂