Four Beautiful Python, R, MATLAB, and Mathematica plots with LaTeX

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1. MATLAB plotting with LaTeX

First, here’s an example using Plotly’s MATLAB API. This is a visualization of Bessel Functions of the first kind, solutions for a differential equation. It’s a useful function for studying and understanding heat conduction, how waves travel, and more. The MATLAB code below creates our plot.

1. plot(X,J,'LineWidth',1.5)
   
2. axis([0 20 -.5 1])
   
3. grid on
   
4. legend('J_0','J_1','J_2','J_3','J_4','Location','Best')
   
5. title('Bessel Functions of the First Kind for v = 0,1,2,3,4')
   
6. xlabel('X')
   
7. ylabel('J_v(X)')
   
8. X = 0:0.1:20;
   
9. X = 0:0.1:20;
   
10. J = zeros(5,201);
    
11. for i = 0:4
    
12.     J(i+1,:) = besselj(i,X);
    
13. end
    
14. plot(X,J,'LineWidth',1.5)
    
15. axis([0 20 -.5 1])
    
16. grid on
    
17. legend('J_0','J_1','J_2','J_3','J_4','Location','Best')
    
18. title('Bessel Functions of the First Kind for v = 0,1,2,3,4')
    
19. xlabel('X')
    
20. ylabel('J_v(X)')
    
21. fig2plotly();

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The code generates a web-based version of our plot. We can apply a theme to change the colors, layouts, and fonts.

Then, we can share the plot in an iframe, as seen below.

The x axis contains the following formula. Plotly renders the LaTeX version of it.

$x^2 frac{d^2 y}{dx^2} + x frac{dy}{dx} + (x^2 – alpha^2)y = 0$

The plot is saved at a URL: https://plot.ly/~MattSundquist/2135. The URL contains the data, plot and code to translate the plot between MATLAB, R, Python, Julia, and JavaScript.

2. Python and matplotlib plotting with LaTeX

We can make matplotlib and Python plots into web-based plots. This is an example using Plotly’s Python API. Here we’re using a Gaussian distribution to study random variables and see where they fall on what is sometimes called a “bell curve.” We can add the standard deviation formula to our plot.

1. import matplotlib.pyplot as plt   # side-stepping mpl's backend
   
2. import plotly.plotly as py
   
3. import plotly.tools as tls
   
4. from plotly.graph_objs import *
   
5. %matplotlib inline
   
6. py.sign_in("IPython.Demo", "1fw3zw2o13")
   
7. fig1 = plt.figure()
   
8. 
   
9. import matplotlib.pyplot as plt
   
10. import numpy as np
    
11. 
    
12. x = np.linspace(-2.0, 2.0, 10000) # The x-values
    
13. sigma = np.linspace(0.4, 1.0, 4) # Some different values of sigma

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1. # Here we evaluate a Gaussians for each sigma
   
2. gaussians = [(2*np.pi*s**2)**-0.5 * np.exp(-0.5*x**2/s**2) for s in sigma]
   
3. 
   
4. ax = plt.axes()
   
5. 
   
6. for s,y in zip(sigma, gaussians):
   
7.     ax.plot(x, y, lw=1.25, label=r"$sigma = %3.2f$"%s)
   
8. 
   
9. formula = r"$y(x)=frac{1}{sqrt{2pisigma^2}}e^{-frac{x^2}{2sigma^2}}$"
   
10. 
    
11. ax.text(0.05, 0.80, formula, transform=ax.transAxes, fontsize=20)
    
12. ax.set_xlabel(r"$x$", fontsize=18)
    
13. ax.set_ylabel(r"$y(x)$", fontsize=18)
    
14. ax.legend()
    
15. plt.show()

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Here is our plot:

The annotation looks like this in the GUI:

3. R plotting with LaTeX

We can make plots with R. Here’s an example using the Plotly R API.

1. library(plotly)
   
2. py <- plotly(username="R-demo-account", key="yu680v5eii")
   
3. 
   
4. trace1 <- list(
   
5.   x = c(1, 2, 3, 4),
   
6.   y = c(1, 4, 9, 16),
   
7.   name = "$alpha_{1c} = 352 pm 11 text{ km s}^{-1}$",
   
8.   type = "scatter"
   
9. )
   
10. trace2 <- list(
    
11.   x = c(1, 2, 3, 4),
    
12.   y = c(0.5, 2, 4.5, 8),
    
13.   name = "$beta_{1c} = 25 pm 11 text{ km s}^{-1}$",
    
14.   type = "scatter"
    
15. )
    
16. data <- list(trace1, trace2)
    
17. layout <- list(
    
18.   xaxis = list(title = "$sqrt{(n_text{c}(t|{T_text{early}}))}$"),
    
19.   yaxis = list(title = "$d, r text{ (solar radius)}$")
    
20. )
    
21. response <- py$plotly(data, kwargs=list(layout=layout, filename="latex", fileopt="overwrite"))
    
22. url <- response$url

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The title was added in the GUI, and is written as ‘$LaTeX$’. We embed with this snippet; every Plotly graph can similarly be embedded in websites, blogs, and notebooks.

<iframe width="500" height="500" frameborder="0" seamless="seamless" scrolling="no" src="https://plot.ly/~MattSundquist/2138.embed?width=500&height=500"></iframe>
4. Mathematica plotting with LaTeX

A user-contributed Mathematica API is in the works, which lets us turn our Mathematica plots into D3, web-based plots. Here is our code:

1. Plotly[Sin[Exp[x]], {x, -Pi, Pi}, AxesLabel -> {"e", "s"}]

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And our plot:

Plotly is free for public projects, entirely online, and you own your data. Learn more on our site.

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