Confidence Interval 3 dimensional plot - python

I have a 3-dimensional plot and I am able to plot it with the code written below.
Considering that my point distribution is represented by a 100x100 matrix, is it possible to plot a confidence interval on my data? In the code below, my data are called "result", while the upper bound and lower bound that I want to show are called "upper_bound" and "lower_bound".
For example, I am asking if exist something like this, but in 3 dimension (instead of 2 dimension like the picture below)
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
interval = np.random.normal(0, 1, size=(100, 100))
x = np.arange(0.1,1.1,0.01)
y = np.linspace(-np.pi,np.pi,100)
X,Y = np.meshgrid(x,y)
result = []
for i,j in zip(X,Y):
result.append(np.log(i)+np.sin(j))
upper_bound = np.array(result)+interval
lower_bound = np.array(result)-interval
fig = plt.figure()
fig.set_figwidth(20)
fig.set_figheight(6)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, np.array(result))
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()

Check out this 3d surface plot using plotly graph objects:
import plotly.graph_objects as go
import numpy as np
x = np.arange(0.1,1.1,0.01)
y = np.linspace(-np.pi,np.pi,100)
X,Y = np.meshgrid(x,y)
result = []
for i,j in zip(X,Y):
result.append(np.log(i)+np.sin(j))
upper_bound = np.array(result)+1
lower_bound = np.array(result)-1
fig = go.Figure(data=[
go.Surface(z=result),
go.Surface(z=upper_bound, showscale=False, opacity=0.3,colorscale='purp'),
go.Surface(z=lower_bound, showscale=False, opacity=0.3,colorscale='purp'),
])
fig.show()
This plots 3 surfaces, the one for your results and the 2 bounds. However if you'd like something that looks more like a filled volume you'd have to add volume graphs with scaling opacity.

Related

Making a 4-D scatter plot using Matplotlib in Python

Essentially, I'm trying to make a 4-D scatter plot with 4 columns of data (see sample below).
X (mm) Y (mm) Z (mm) Diameter (mm)
11.096 11.0972 13.2401 124.279
14.6836 11.0389 8.37134 138.949
19.9543 11.1025 31.1912 138.949
15.4079 10.9505 31.1639 152.21
20.6372 14.5175 6.94501 152.211
20.47 11.225 31.3612 152.211
19.0432 11.3234 8.93819 152.213
29.4091 10.1331 26.6354 186.417
12.9391 10.6616 28.9523 186.418
29.9102 10.4828 25.1129 186.418
30.5483 12.163 15.9116 186.418
19.0631 10.5784 30.9791 186.418
9.65332 10.8563 12.975 186.419
8.4003 11.0417 17.0181 186.419
26.0134 10.6857 9.41572 186.419
13.7451 11.1495 28.7108 186.419
The first three columns of data (X, Y, Z) are the coordinate positions of the 4th column of data (Diameter) so I was able to generate a 3-D scatter plot of these positions. However, I'm trying to plot these Diameters with different color markers based on certain threshold values (ie. Diameters that are less than 100 mm are red, 101-200 mm are blue, 201-300 mm are green, etc.) Once the color of the markers are determined, it would plot these markers based on its X, Y, Z coordinates. I tried writing a simple for loop to do this, but for some reason it becomes very slow/laggy and will only plot one color too. Can anyone see if there's something wrong with my approach? Thanks!
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import pandas
import os
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
os.chdir(r'C:\Users\Me\Documents')
data = pandas.read_excel("Diameter Report", "Data")
X = data['X (mm)'].values.tolist()
Y = data['Y (mm)'].values.tolist()
Z = data['Z (mm)'].values.tolist()
dims = data['Diameter (mm)'].values.tolist()
for i in dims:
if i < int(100):
ax.plot(X, Y, Z, c='r', marker='o')
elif i >= int(101) and i <200:
ax.plot(X, Y, Z, c='b', marker='o')
elif i >= int(201) and i <300:
ax.plot(X, Y, Z, c='g', marker='o')
ax.set_xlabel('Center X (mm)')
ax.set_ylabel('Center Y (mm)')
ax.set_zlabel('Center Z (mm)')
plt.show()
It seems the thresholds for the values are equally spaced, so you can just divide by 100 and truncate further decimal places. This allows to plot a single scatter instead of hundreds of plots.
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import pandas
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
data = pandas.read_excel("Diameter Report", "Data")
X = data['X (mm)'].values
Y = data['Y (mm)'].values
Z = data['Z (mm)'].values
dims = data['Diameter (mm)'].values
ax.scatter(X,Y,Z, c=(dims/100).astype(int), marker="o", cmap="brg")
ax.set_xlabel('Center X (mm)')
ax.set_ylabel('Center Y (mm)')
ax.set_zlabel('Center Z (mm)')
plt.show()
The more general case of arbitrary boundaries would probably best be solved using a BoundaryNorm and a colormap with as many different colors as classifications.
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib.colors as mcolors
import pandas as pd
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
d = np.random.rand(10,4)
d[:,3] = np.random.randint(1,300, 10)
data = pd.DataFrame(d, columns=["X (mm)","Y (mm)","Z (mm)","Diameter (mm)"])
X = data['X (mm)'].values
Y = data['Y (mm)'].values
Z = data['Z (mm)'].values
dims = data['Diameter (mm)'].values
bounds = [0,100,200,300]
colors = ["b", "r", "g"]
cmap = mcolors.ListedColormap(colors)
norm = mcolors.BoundaryNorm(bounds, len(colors))
sc = ax.scatter(X,Y,Z, c=dims, marker="o", cmap=cmap, norm=norm)
ax.set_xlabel('Center X (mm)')
ax.set_ylabel('Center Y (mm)')
ax.set_zlabel('Center Z (mm)')
fig.colorbar(sc)
plt.show()
Here is a slightly more general solution where you can explicitly specify the ranges you want regardless of the spacing. I did not have the complete data so I modified your limits from 100, 200, 300 to 140, 180, 200 based on the provided data.
A couple of things:
You probably want to use scatter3d as you mentioned it in your question instead of plot.
I am using NumPy to read in the data because this way you will have the data as NumPy arrays which make the masking and slicing easy.
Here I am creating 3 conditional masks depending on the magnitude of dims.
Next, you store these masks in a list and then iterate over it to use one mask at a time.
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import pandas
import numpy as np
import os
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
X, Y, Z, dims = np.loadtxt('sample.txt', unpack=True, skiprows=1)
mask1 = (dims<140)
mask2 = ((dims>=140) & (dims<180))
mask3 = ((dims>=180) & (dims<200))
masks = [mask1, mask2, mask3]
colors = ['r', 'b', 'g'] # color order as you specified in the question
for mask, color in zip(masks, colors):
ax.scatter3D(X[mask], Y[mask], Z[mask], c=color)
ax.set_xlabel('Center X (mm)')
ax.set_ylabel('Center Y (mm)')
ax.set_zlabel('Center Z (mm)')
plt.show()

Plotting scatter density plots in python [duplicate]

I'd like to make a scatter plot where each point is colored by the spatial density of nearby points.
I've come across a very similar question, which shows an example of this using R:
R Scatter Plot: symbol color represents number of overlapping points
What's the best way to accomplish something similar in python using matplotlib?
In addition to hist2d or hexbin as #askewchan suggested, you can use the same method that the accepted answer in the question you linked to uses.
If you want to do that:
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde
# Generate fake data
x = np.random.normal(size=1000)
y = x * 3 + np.random.normal(size=1000)
# Calculate the point density
xy = np.vstack([x,y])
z = gaussian_kde(xy)(xy)
fig, ax = plt.subplots()
ax.scatter(x, y, c=z, s=100)
plt.show()
If you'd like the points to be plotted in order of density so that the densest points are always on top (similar to the linked example), just sort them by the z-values. I'm also going to use a smaller marker size here as it looks a bit better:
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde
# Generate fake data
x = np.random.normal(size=1000)
y = x * 3 + np.random.normal(size=1000)
# Calculate the point density
xy = np.vstack([x,y])
z = gaussian_kde(xy)(xy)
# Sort the points by density, so that the densest points are plotted last
idx = z.argsort()
x, y, z = x[idx], y[idx], z[idx]
fig, ax = plt.subplots()
ax.scatter(x, y, c=z, s=50)
plt.show()
Plotting >100k data points?
The accepted answer, using gaussian_kde() will take a lot of time. On my machine, 100k rows took about 11 minutes. Here I will add two alternative methods (mpl-scatter-density and datashader) and compare the given answers with same dataset.
In the following, I used a test data set of 100k rows:
import matplotlib.pyplot as plt
import numpy as np
# Fake data for testing
x = np.random.normal(size=100000)
y = x * 3 + np.random.normal(size=100000)
Output & computation time comparison
Below is a comparison of different methods.
1: mpl-scatter-density
Installation
pip install mpl-scatter-density
Example code
import mpl_scatter_density # adds projection='scatter_density'
from matplotlib.colors import LinearSegmentedColormap
# "Viridis-like" colormap with white background
white_viridis = LinearSegmentedColormap.from_list('white_viridis', [
(0, '#ffffff'),
(1e-20, '#440053'),
(0.2, '#404388'),
(0.4, '#2a788e'),
(0.6, '#21a784'),
(0.8, '#78d151'),
(1, '#fde624'),
], N=256)
def using_mpl_scatter_density(fig, x, y):
ax = fig.add_subplot(1, 1, 1, projection='scatter_density')
density = ax.scatter_density(x, y, cmap=white_viridis)
fig.colorbar(density, label='Number of points per pixel')
fig = plt.figure()
using_mpl_scatter_density(fig, x, y)
plt.show()
Drawing this took 0.05 seconds:
And the zoom-in looks quite nice:
2: datashader
Datashader is an interesting project. It has added support for matplotlib in datashader 0.12.
Installation
pip install datashader
Code (source & parameterer listing for dsshow):
import datashader as ds
from datashader.mpl_ext import dsshow
import pandas as pd
def using_datashader(ax, x, y):
df = pd.DataFrame(dict(x=x, y=y))
dsartist = dsshow(
df,
ds.Point("x", "y"),
ds.count(),
vmin=0,
vmax=35,
norm="linear",
aspect="auto",
ax=ax,
)
plt.colorbar(dsartist)
fig, ax = plt.subplots()
using_datashader(ax, x, y)
plt.show()
It took 0.83 s to draw this:
There is also possibility to colorize by third variable. The third parameter for dsshow controls the coloring. See more examples here and the source for dsshow here.
3: scatter_with_gaussian_kde
def scatter_with_gaussian_kde(ax, x, y):
# https://stackoverflow.com/a/20107592/3015186
# Answer by Joel Kington
xy = np.vstack([x, y])
z = gaussian_kde(xy)(xy)
ax.scatter(x, y, c=z, s=100, edgecolor='')
It took 11 minutes to draw this:
4: using_hist2d
import matplotlib.pyplot as plt
def using_hist2d(ax, x, y, bins=(50, 50)):
# https://stackoverflow.com/a/20105673/3015186
# Answer by askewchan
ax.hist2d(x, y, bins, cmap=plt.cm.jet)
It took 0.021 s to draw this bins=(50,50):
It took 0.173 s to draw this bins=(1000,1000):
Cons: The zoomed-in data does not look as good as in with mpl-scatter-density or datashader. Also you have to determine the number of bins yourself.
5: density_scatter
The code is as in the answer by Guillaume.
It took 0.073 s to draw this with bins=(50,50):
It took 0.368 s to draw this with bins=(1000,1000):
Also, if the number of point makes KDE calculation too slow, color can be interpolated in np.histogram2d [Update in response to comments: If you wish to show the colorbar, use plt.scatter() instead of ax.scatter() followed by plt.colorbar()]:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.colors import Normalize
from scipy.interpolate import interpn
def density_scatter( x , y, ax = None, sort = True, bins = 20, **kwargs ) :
"""
Scatter plot colored by 2d histogram
"""
if ax is None :
fig , ax = plt.subplots()
data , x_e, y_e = np.histogram2d( x, y, bins = bins, density = True )
z = interpn( ( 0.5*(x_e[1:] + x_e[:-1]) , 0.5*(y_e[1:]+y_e[:-1]) ) , data , np.vstack([x,y]).T , method = "splinef2d", bounds_error = False)
#To be sure to plot all data
z[np.where(np.isnan(z))] = 0.0
# Sort the points by density, so that the densest points are plotted last
if sort :
idx = z.argsort()
x, y, z = x[idx], y[idx], z[idx]
ax.scatter( x, y, c=z, **kwargs )
norm = Normalize(vmin = np.min(z), vmax = np.max(z))
cbar = fig.colorbar(cm.ScalarMappable(norm = norm), ax=ax)
cbar.ax.set_ylabel('Density')
return ax
if "__main__" == __name__ :
x = np.random.normal(size=100000)
y = x * 3 + np.random.normal(size=100000)
density_scatter( x, y, bins = [30,30] )
You could make a histogram:
import numpy as np
import matplotlib.pyplot as plt
# fake data:
a = np.random.normal(size=1000)
b = a*3 + np.random.normal(size=1000)
plt.hist2d(a, b, (50, 50), cmap=plt.cm.jet)
plt.colorbar()

Python/Matplotlib: 2d random walk with kde joint density contour in a 3d plot

I'm struggling with creating a quite complex 3d figure in python, specifically using iPython notebook. I can partition the content of the graph into two sections:
The (x,y) plane: Here a two-dimensional random walk is bobbing around, let's call it G(). I would like to plot part of this trajectory on the (x,y) plane. Say, 10% of all the data points of G(). As G() bobs around, it visits some (x,y) pairs more frequently than others. I would like to estimate this density of G() using a kernel estimation approach and draw it as contour lines on the (x,y) plane.
The (z) plane: Here, I would like to draw a mesh or (transparent) surface plot of the information theoretical surprise of a bivariate normal. Surprise is simply -log(p(i)) or the negative (base 2) logarithm of outcome i. Given the bivariate normal, each (x,y) pair has some probability p(x,y) and the surprise of this is simply -log(p(x,y)).
Essentially these two graphs are independent. Assume the interval of the random walk G() is [xmin,xmax],[ymin,ymax] and of size N. The bivariate normal in the z-plane should be drawn from the same interval, such that for each (x,y) pair in the random walk, I can draw a (dashed) line from some subset of the random walk n < N to the bivariate normal. Assume that G(10) = (5,5) then I would like to draw a dashed line from (5,5) up the Z-axes, until it hits the bivariate normal.
So far, I've managed to plot G() in a 3-d space, and estimate the density f(X,Y) using scipy.stats.gaussian_kde. In another (2d) graph, I have the sort of contour lines I want. What I don't have, is the contour lines in the 3d-plot using the estimated KDE density. I also don't have the bivariate normal plot, or the projection of a few random points from the random walk, to the surface of the bivariate normal. I've added a hand drawn figure, which might ease intuition (ignore the label on the z-axis and the fact that there is no mesh.. difficult to draw!)
Any input, even just partial, such as how to draw the contour lines in the (x,y) plane of the 3d graph, or a mesh of a bivariate normal would be much appreciated.
Thanks!
import matplotlib as mpl
import matplotlib.pyplot as plt
import random
import numpy as np
import seaborn as sns
import scipy
from mpl_toolkits.mplot3d import Axes3D
%matplotlib inline
def randomwalk():
mpl.rcParams['legend.fontsize'] = 10
xyz = []
cur = [0, 0]
for _ in range(400):
axis = random.randrange(0, 2)
cur[axis] += random.choice([-1, 1])
xyz.append(cur[:])
x, y = zip(*xyz)
data = np.vstack([x,y])
kde = scipy.stats.gaussian_kde(data)
density = kde(data)
fig1 = plt.figure()
ax = fig1.gca(projection='3d')
ax.plot(x, y, label='Random walk')
sns.kdeplot(data[0,:], data[1,:], 0)
ax.scatter(x[-1], y[-1], c='b', marker='o') # End point
ax.legend()
fig2 = plt.figure()
sns.kdeplot(data[0,:], data[1,:])
Calling randomwalk() initialises and plots this:
Edit #1:
Made some progress, actually the only thing I need is to restrict the height of the dashed vertical lines to the bivariate. Any ideas?
import matplotlib as mpl
import matplotlib.pyplot as plt
import random
import numpy as np
import seaborn as sns
import scipy
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.mlab import bivariate_normal
%matplotlib inline
# Data for random walk
def randomwalk():
mpl.rcParams['legend.fontsize'] = 10
xyz = []
cur = [0, 0]
for _ in range(40):
axis = random.randrange(0, 2)
cur[axis] += random.choice([-1, 1])
xyz.append(cur[:])
# Get density
x, y = zip(*xyz)
data = np.vstack([x,y])
kde = scipy.stats.gaussian_kde(data)
density = kde(data)
# Data for bivariate gaussian
a = np.linspace(-7.5, 7.5, 20)
b = a
X,Y = np.meshgrid(a, b)
Z = bivariate_normal(X, Y)
surprise_Z = -np.log(Z)
# Get random points from walker and plot up z-axis to the gaussian
M = data[:,np.random.choice(20,5)].T
# Plot figure
fig = plt.figure(figsize=(10, 7))
ax = fig.gca(projection='3d')
ax.plot(x, y, 'grey', label='Random walk') # Walker
ax.scatter(x[-1], y[-1], c='k', marker='o') # End point
ax.legend()
surf = ax.plot_surface(X, Y, surprise_Z, rstride=1, cstride=1,
cmap = plt.cm.gist_heat_r, alpha=0.1, linewidth=0.1)
#fig.colorbar(surf, shrink=0.5, aspect=7, cmap=plt.cm.gray_r)
for i in range(5):
ax.plot([M[i,0], M[i,0]],[M[i,1], M[i,1]], [0,10],'k--',alpha=0.8, linewidth=0.5)
ax.set_zlim(0, 50)
ax.set_xlim(-10, 10)
ax.set_ylim(-10, 10)
Final code,
import matplotlib as mpl
import matplotlib.pyplot as plt
import random
import numpy as np
import seaborn as sns
import scipy
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.mlab import bivariate_normal
%matplotlib inline
# Data for random walk
def randomwalk():
mpl.rcParams['legend.fontsize'] = 10
xyz = []
cur = [0, 0]
for _ in range(50):
axis = random.randrange(0, 2)
cur[axis] += random.choice([-1, 1])
xyz.append(cur[:])
# Get density
x, y = zip(*xyz)
data = np.vstack([x,y])
kde = scipy.stats.gaussian_kde(data)
density = kde(data)
# Data for bivariate gaussian
a = np.linspace(-7.5, 7.5, 100)
b = a
X,Y = np.meshgrid(a, b)
Z = bivariate_normal(X, Y)
surprise_Z = -np.log(Z)
# Get random points from walker and plot up z-axis to the gaussian
M = data[:,np.random.choice(50,10)].T
# Plot figure
fig = plt.figure(figsize=(10, 7))
ax = fig.gca(projection='3d')
ax.plot(x, y, 'grey', label='Random walk') # Walker
ax.legend()
surf = ax.plot_surface(X, Y, surprise_Z, rstride=1, cstride=1,
cmap = plt.cm.gist_heat_r, alpha=0.1, linewidth=0.1)
#fig.colorbar(surf, shrink=0.5, aspect=7, cmap=plt.cm.gray_r)
for i in range(10):
x = [M[i,0], M[i,0]]
y = [M[i,1], M[i,1]]
z = [0,-np.log(bivariate_normal(M[i,0],M[i,1]))]
ax.plot(x,y,z,'k--',alpha=0.8, linewidth=0.5)
ax.scatter(x, y, z, c='k', marker='o')

matplotlib scatterplot: adding 4th dimension by the marker shape

I would like to add a fourth dimension to the scatter plot by defining the ellipticity of the markers depending on a variable. Is that possible somehow ?
EDIT:
I would like to avoid a 3D-plot. In my opinion these plots are usually not very informative.
You can place Ellipse patches directly onto your axes, as demonstrated in this matplotlib example. To adapt it to use eccentricity as your "third dimension") keeping the marker area constant:
from pylab import figure, show, rand
from matplotlib.patches import Ellipse
import numpy as np
import matplotlib.pyplot as plt
N = 25
# ellipse centers
xy = np.random.rand(N, 2)*10
# ellipse eccentrities
eccs = np.random.rand(N) * 0.8 + 0.1
fig = plt.figure()
ax = fig.add_subplot(111, aspect='equal')
A = 0.1
for pos, e in zip(xy, eccs):
# semi-minor, semi-major axes, b and a:
b = np.sqrt(A/np.pi * np.sqrt(1-e**2))
a = A / np.pi / b
ellipse = Ellipse(xy=pos, width=2*a, height=2*b)
ax.add_artist(ellipse)
ax.set_xlim(0, 10)
ax.set_ylim(0, 10)
show()
Of course, you need to scale your marker area to your x-, y- values in this case.
You can use colorbar as the 4th dimension to your 3D plot. One example is as shown below:
import matplotlib.cm as cmx
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib
import numpy as np
def scatter3d(x,y,z, cs, colorsMap='jet'):
cm = plt.get_cmap(colorsMap)
cNorm = matplotlib.colors.Normalize(vmin=min(cs), vmax=max(cs))
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=cm)
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(x, y, z, c=scalarMap.to_rgba(cs))
scalarMap.set_array(cs)
fig.colorbar(scalarMap,label='Test')
plt.show()
x = np.random.uniform(0,1,50)
y = np.random.uniform(0,1,50)
z = np.random.uniform(0,1,50)
so scatter3D(x,y,z,x+y) produces:
with x+y being the 4th dimension shown in color. You can add your calculated ellipticity depending on your specific variable instead of x+y to get what you want.
To change the ellipticity of the markers you will have to create them manually as such a feature is not implemented yet. However, I believe you can show 4 dimensions with a 2D scatter plot by using color and size as additional dimensions. You will have to take care of the scaling from data to marker size yourself. I added a simple function to handle that in the example below:
import matplotlib.pyplot as plt
import numpy as np
data = np.random.rand(60,4)
def scale_size(data, data_min=None, data_max=None, size_min=10, size_max=60):
# if the data limits are set to None we will just infer them from the data
if data_min is None:
data_min = data.min()
if data_max is None:
data_max = data.max()
size_range = size_max - size_min
data_range = data_max - data_min
return ((data - data_min) * size_range / data_range) + size_min
plt.scatter(data[:,0], data[:,1], c=data[:,2], s=scale_size(data[:,3]))
plt.colorbar()
plt.show()
Result:

How can I make a scatter plot colored by density in matplotlib?

I'd like to make a scatter plot where each point is colored by the spatial density of nearby points.
I've come across a very similar question, which shows an example of this using R:
R Scatter Plot: symbol color represents number of overlapping points
What's the best way to accomplish something similar in python using matplotlib?
In addition to hist2d or hexbin as #askewchan suggested, you can use the same method that the accepted answer in the question you linked to uses.
If you want to do that:
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde
# Generate fake data
x = np.random.normal(size=1000)
y = x * 3 + np.random.normal(size=1000)
# Calculate the point density
xy = np.vstack([x,y])
z = gaussian_kde(xy)(xy)
fig, ax = plt.subplots()
ax.scatter(x, y, c=z, s=100)
plt.show()
If you'd like the points to be plotted in order of density so that the densest points are always on top (similar to the linked example), just sort them by the z-values. I'm also going to use a smaller marker size here as it looks a bit better:
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde
# Generate fake data
x = np.random.normal(size=1000)
y = x * 3 + np.random.normal(size=1000)
# Calculate the point density
xy = np.vstack([x,y])
z = gaussian_kde(xy)(xy)
# Sort the points by density, so that the densest points are plotted last
idx = z.argsort()
x, y, z = x[idx], y[idx], z[idx]
fig, ax = plt.subplots()
ax.scatter(x, y, c=z, s=50)
plt.show()
Plotting >100k data points?
The accepted answer, using gaussian_kde() will take a lot of time. On my machine, 100k rows took about 11 minutes. Here I will add two alternative methods (mpl-scatter-density and datashader) and compare the given answers with same dataset.
In the following, I used a test data set of 100k rows:
import matplotlib.pyplot as plt
import numpy as np
# Fake data for testing
x = np.random.normal(size=100000)
y = x * 3 + np.random.normal(size=100000)
Output & computation time comparison
Below is a comparison of different methods.
1: mpl-scatter-density
Installation
pip install mpl-scatter-density
Example code
import mpl_scatter_density # adds projection='scatter_density'
from matplotlib.colors import LinearSegmentedColormap
# "Viridis-like" colormap with white background
white_viridis = LinearSegmentedColormap.from_list('white_viridis', [
(0, '#ffffff'),
(1e-20, '#440053'),
(0.2, '#404388'),
(0.4, '#2a788e'),
(0.6, '#21a784'),
(0.8, '#78d151'),
(1, '#fde624'),
], N=256)
def using_mpl_scatter_density(fig, x, y):
ax = fig.add_subplot(1, 1, 1, projection='scatter_density')
density = ax.scatter_density(x, y, cmap=white_viridis)
fig.colorbar(density, label='Number of points per pixel')
fig = plt.figure()
using_mpl_scatter_density(fig, x, y)
plt.show()
Drawing this took 0.05 seconds:
And the zoom-in looks quite nice:
2: datashader
Datashader is an interesting project. It has added support for matplotlib in datashader 0.12.
Installation
pip install datashader
Code (source & parameterer listing for dsshow):
import datashader as ds
from datashader.mpl_ext import dsshow
import pandas as pd
def using_datashader(ax, x, y):
df = pd.DataFrame(dict(x=x, y=y))
dsartist = dsshow(
df,
ds.Point("x", "y"),
ds.count(),
vmin=0,
vmax=35,
norm="linear",
aspect="auto",
ax=ax,
)
plt.colorbar(dsartist)
fig, ax = plt.subplots()
using_datashader(ax, x, y)
plt.show()
It took 0.83 s to draw this:
There is also possibility to colorize by third variable. The third parameter for dsshow controls the coloring. See more examples here and the source for dsshow here.
3: scatter_with_gaussian_kde
def scatter_with_gaussian_kde(ax, x, y):
# https://stackoverflow.com/a/20107592/3015186
# Answer by Joel Kington
xy = np.vstack([x, y])
z = gaussian_kde(xy)(xy)
ax.scatter(x, y, c=z, s=100, edgecolor='')
It took 11 minutes to draw this:
4: using_hist2d
import matplotlib.pyplot as plt
def using_hist2d(ax, x, y, bins=(50, 50)):
# https://stackoverflow.com/a/20105673/3015186
# Answer by askewchan
ax.hist2d(x, y, bins, cmap=plt.cm.jet)
It took 0.021 s to draw this bins=(50,50):
It took 0.173 s to draw this bins=(1000,1000):
Cons: The zoomed-in data does not look as good as in with mpl-scatter-density or datashader. Also you have to determine the number of bins yourself.
5: density_scatter
The code is as in the answer by Guillaume.
It took 0.073 s to draw this with bins=(50,50):
It took 0.368 s to draw this with bins=(1000,1000):
Also, if the number of point makes KDE calculation too slow, color can be interpolated in np.histogram2d [Update in response to comments: If you wish to show the colorbar, use plt.scatter() instead of ax.scatter() followed by plt.colorbar()]:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.colors import Normalize
from scipy.interpolate import interpn
def density_scatter( x , y, ax = None, sort = True, bins = 20, **kwargs ) :
"""
Scatter plot colored by 2d histogram
"""
if ax is None :
fig , ax = plt.subplots()
data , x_e, y_e = np.histogram2d( x, y, bins = bins, density = True )
z = interpn( ( 0.5*(x_e[1:] + x_e[:-1]) , 0.5*(y_e[1:]+y_e[:-1]) ) , data , np.vstack([x,y]).T , method = "splinef2d", bounds_error = False)
#To be sure to plot all data
z[np.where(np.isnan(z))] = 0.0
# Sort the points by density, so that the densest points are plotted last
if sort :
idx = z.argsort()
x, y, z = x[idx], y[idx], z[idx]
ax.scatter( x, y, c=z, **kwargs )
norm = Normalize(vmin = np.min(z), vmax = np.max(z))
cbar = fig.colorbar(cm.ScalarMappable(norm = norm), ax=ax)
cbar.ax.set_ylabel('Density')
return ax
if "__main__" == __name__ :
x = np.random.normal(size=100000)
y = x * 3 + np.random.normal(size=100000)
density_scatter( x, y, bins = [30,30] )
You could make a histogram:
import numpy as np
import matplotlib.pyplot as plt
# fake data:
a = np.random.normal(size=1000)
b = a*3 + np.random.normal(size=1000)
plt.hist2d(a, b, (50, 50), cmap=plt.cm.jet)
plt.colorbar()

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