Publication-quality plots in Julia using PGFPlotsX

Shuvomoy Das Gupta

November 30, 2021

In this blog, we discuss how to draw publication quality blogs in Julia. We will use the package PGFPlotsX.

Table of contents

  1. First Example
  2. Saving a plot
  3. Drawing multiple functions on the same plot
  4. Plotting error bars
  5. The same error bar, but fancier
  6. Multiple plots with error bars

First, we install the package, of course.

In [1]:

# using Pkg
# Pkg.add("PGFPlotsX")
using PGFPlotsX

First Example

We start with a very easy example. We plot x2x^2 vs xx. To insert Latex compatible code we use the package using LaTeXStrings.

In [2]:

using LaTeXStrings

In [3]:

x = range(0.1,stop=5, length = 50);
y = x.^2;

In [4]:

plot1 = @pgf Axis(
    {
        xmajorgrids, # show grids along x axis
        ymajorgrids, # show grids along y axis
        xlabel = L"x",  # L"()" shows $()$ in latex math
        ylabel = L"f(x)=x^2" 
    },
    Plot(
        {
            "no marks",
            style = "{ultra thick}",
            # style determines the linewidth: ultra thin, very thin, semithick, thick, very thick, ultra thick 
            color = "blue" 
            # other possible colors are red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, purple, teal, violet and white
        },
        Coordinates(x, y)
    )
)

Out[4]:

Saving a plot

We can save the plot above by running the following command.

In [5]:

pgfsave("first_plot.tex", plot1) # will save a tex file
pgfsave("firt_plot.pdf", plot1) # will save a pdf file
pgfsave("first_plot.svg", plot1) # will save a svg file

Drawing multiple functions on the same plot

As our second example, let us plot both x2x^2 and log⁡(x)\log(x) over R++\mathbf{R}_{++} on the same plot.

In [6]:

x = range(.1,stop=10, length = 100);
y = x.^2;
z = log.(x);

In [7]:

@pgf Axis(
    {
        xmajorgrids, # show grids along x axis
        ymajorgrids, # show grids along y axis
        xlabel = L"x",  # L"()" shows $()$ in latex math
        ylabel = L"Comparison between $x^2$ and $\log(x)$"
    },
    PlotInc(
        {
            "no marks",
            style = "{ultra thick}",
            # style determines the linewidth: ultra thin, very thin, semithick, thick, very thick, ultra thick 
            color = "blue" 
            # other possible colors are red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, purple, teal, violet and white
        },
        Coordinates(x, y)
    ), 
   LegendEntry(L"x^2"),
    PlotInc(
        {
            "no marks",
            style = "{ultra thick}",
            # style determines the linewidth: ultra thin, very thin, semithick, thick, very thick, ultra thick 
            color = "red" 
            # other possible colors are red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, purple, teal, violet and white
        },
        Coordinates(x, z)
    ),
  LegendEntry(L"\log(x)")
)

Out[7]:

Plotting error bars

An error bar shows the reliability of a data point.

Consider the hypothetical scenario. Suppose, there are mm different scenarios for a potential experiment, and for each value of mm we want to measure some entity xmtruex^{\rm{true}}_{m}. Unfortunately, our measuring instrument has some error, so we need to take multiple measurements for each mm. For each value of mm, we can have nn different measurements of xmtruex^{\rm{true}}_{m}. Suppose, for each value of mm, we have the measured data points xm(1),xm(2),…,xm(n){x^{(1)}_m, x^{(2)}_m, \ldots, x^{(n)}_m}. We can compute the mean for each value of mm, which we denote by xˉm\bar{x}_m, however it is likely to have some error from the real xmtruex^{\rm{true}}_{m}, which we can quantify via computing the reliability. For each value of mm, compute the standard deviation σm\sigma_m of the observed data points, and then create the confidence interval:

[xˉm−σmn,xˉm+σmn], [\bar{x}_m - \frac{\sigma_m}{\sqrt{n}}, \bar{x}_m + \frac{\sigma_m}{\sqrt{n}}],

which is also called one standard error band around the mean. To change the width of this confidence interval, we can also use some mulitple of the estimate of the standard deviation of the mean.

In [8]:

m_array = 1:10
measurements = 1:50
x_matrix_true = 0.5*m_array
x_matrix_noise = randn(length(m_array),length(measurements)) # made up data for this plot
x_matrix = x_matrix_true .+ x_matrix_noise
# so x_array[m, :] will give us the array of all measurements for scenario m; we are interested in computing the following arrays
using Statistics
x_mean = vec(mean(x_matrix, dims = 2)) # mean(matrix, dims = 2)computes the row-wise mean of a matrix
x_std = vec(std(x_matrix, dims = 2))  
x_sem = vec(x_std./sqrt(length(measurements))) # sem = standard error of the mean

Out[8]:

10-element Array{Float64,1}:
 0.1604034132861103 
 0.1460304429550008 
 0.1365847039486609 
 0.13948683707167778
 0.1319594461585211 
 0.14365778090865236
 0.1406170456066185 
 0.1418559017096794 
 0.15048702832975708
 0.13851376073434124

In [9]:

@pgf Axis(
    {
        xmajorgrids, # show grids along x axis
        ymajorgrids, # show grids along y axis
        "error bars/y dir=both",
        "error bars/y explicit",
        xlabel = L"$m$ (scenarios)",  # L"()" shows $()$ in latex math
        ylabel = L"$x$ (measurement)" 
    },
    Plot(
        {
            "no marks",
            style = "{very thick}",
            # style determines the linewidth: ultra thin, very thin, semithick, thick, very thick, ultra thick 
            color = "blue" 
            # other possible colors are red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, purple, teal, violet and white
        },
        Coordinates(m_array, x_mean; yerror = x_sem)
    )
)

Out[9]:

The same error bar, but fancier

The same plot, but with fancier options is below.

In [10]:

@pgf Axis(
    {
        xmajorgrids, # show grids along x axis
        ymajorgrids, # show grids along y axis
        "error bars/y dir=both",
        "error bars/error mark=diamond*",
        "error bars/y explicit",
        "error bars/error bar style={line width=1pt, dashed}",
        "error bars/error bar style={blue}",
        xlabel = L"$m$ (scenarios)",  # L"()" shows $()$ in latex math
        ylabel = L"$x$ (measurement)" 
    },
    Plot(
        {
            "no marks",
            style = "{ultra thick}",
            # style determines the linewidth: ultra thin, very thin, semithick, thick, very thick, ultra thick 
            color = "red" 
            # other possible colors are red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, purple, teal, violet and white
        },
        Coordinates(m_array, x_mean; yerror = x_sem)
    )
)

Out[10]:

Multiple plots with error bars

In a similar manner, we can plot multiple plots with error bars as follows.

In [11]:

m_array = 1:10
measurements = 1:50

x_matrix_true = 0.5*m_array
x_matrix_noise = randn(length(m_array),length(measurements)) 
x_matrix = x_matrix_true .+ x_matrix_noise

y_matrix_true = 0.5*sqrt.(m_array)
y_matrix_noise = randn(length(m_array),length(measurements)) 
y_matrix = y_matrix_true .+ y_matrix_noise

x_mean = vec(mean(x_matrix, dims = 2)) # mean(matrix, dims = 2)computes the row-wise mean of a matrix
x_std = vec(std(x_matrix, dims = 2))  
x_sem = vec(x_std./sqrt(length(measurements))) # sem = standard error of the mean

y_mean = vec(mean(y_matrix, dims = 2)) # mean(matrix, dims = 2)computes the row-wise mean of a matrix
y_std = vec(std(y_matrix, dims = 2))  
y_sem = vec(y_std./sqrt(length(measurements))) # sem = standard error of the mean

Out[11]:

10-element Array{Float64,1}:
 0.13382424056139092
 0.15169294891036073
 0.12455783827400334
 0.14694898448593774
 0.15490045368362218
 0.14199887043991172
 0.13742334894544558
 0.12821628839800778
 0.13339558092910958
 0.13009038005264217

In [12]:

@pgf Axis(
    {
        xmajorgrids, # show grids along x axis
        ymajorgrids, # show grids along y axis
        "error bars/y dir=both",
        "error bars/y explicit",
        "error bars/error bar style={line width=1pt}",
        xlabel = L"$m$ (scenarios)",  # L"()" shows $()$ in latex math
        ylabel = "measurement" 
    },
    PlotInc(
        {
            "no marks",
            style = "{ultra thick}",
            # style determines the linewidth: ultra thin, very thin, semithick, thick, very thick, ultra thick 
            color = "blue" 
            # other possible colors are red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, purple, teal, violet and white
        },
        Coordinates(m_array, x_mean; yerror = x_sem)
    ), 
   LegendEntry(L"x"),
    PlotInc(
        {
            "no marks",
            style = "{ultra thick}",
            # style determines the linewidth: ultra thin, very thin, semithick, thick, very thick, ultra thick 
            color = "red" 
            # other possible colors are red, green, blue, cyan, magenta, yellow, black, gray, darkgray, lightgray, brown, lime, olive, orange, pink, purple, teal, violet and white
        },
        Coordinates(m_array, y_mean; yerror = y_sem)
    ),
  LegendEntry(L"y")
)

Out[12]:

© Shuvomoy Das Gupta. Last modified: October 11, 2024. Website built with Franklin.jl and the Julia programming language.