Data Manipulation and Visualization Techniques in Julia

13 min read

By Anshul Tayal

In this article, we’ll look at data manipulation and visualization techniques in Julia. However, I’ll not get into the details of each parameter of every function, as the objective of this series is to use Julia as a tool to achieve our goal, i.e. building and backtesting trading strategies. So, we’ll stay focused on that.

You can refer to the detailed documentation of a function if you need it to solve any particular challenge you face while programming.

This article is divided into the following sections:


In my previous posts in this Julia programming series, I introduced the language and started with the basic syntax of Julia programming. You can check that out as well.


Data manipulation

You need to understand the data structures dealing with large heterogeneous data sets whenever you work with any programming language. In the Julia world, they are called dataframes.

Julia’s DataFrames.jl package provides a way to structure and manipulate data.

It can be installed using the “Pkg” module.

Creating new dataframes

Here’s an example of creating a new dataframe.

Output:

Name Team Work_experience
String String Int64
Vivek EPAT 15
Viraj Marketing 8
Rohan Sales 7
Ishan Quantra 10
a b
Float64 Float64
0.845011 0.720306
0.647665 0.0409036
0.427267 0.221369
0.413642 0.374832
0.477994 0.118461
0.0849006 0.157679
0.0477405 0.845332
0.518909 0.159305
0.93499 0.259579
0.60034 0.115911

Column names can be accessed using the names() function.

Output:

3-element Vector{String}:
"Name"
"Team"
"Work_experience"

3-element Vector{Symbol}:
:Name
:Team
:Work_experience

Renaming columns can be done using the rename() function.

name team work experience
String String Int64
Vivek EPAT 15
Viraj Marketing 8
Rohan Sales 7
Ishan Quantra 10

Indexing and summarising data

Indexing dataframes to use particular rows or columns for manipulation is a fundamental operation, and summarising data helps us understand it better. In Julia, summary stats of any dataset can be printed using the describe() function.

variable mean min median max nmissing eltype
Symbol Float64 Float64 Float64 Float64 Int64 DataType
a 0.499846 0.0477405 0.498452 0.93499 0 Float64
b 0.301368 0.0409036 0.190337 0.845332 0 Float64

Another way to find the number of rows and columns in a dataframe is using ncol() and nrow() functions.

Output:
2
10

Let’s look at multiple methods of accessing rows and columns of a dataframe.

Output:
4-element Vector{String}:
"Vivek"
"Viraj"
"Rohan"
"Ishan"

4-element Vector{String}:
"EPAT"
"Marketing"
"Sales"
"Quantra"

3-element Vector{String}:
"EPAT"
"Marketing"
"Sales"
name team work experience
String String Int64
Vivek EPAT 15
name team
String String
Vivek EPAT
Viraj Marketing
Rohan Sales
Ishan Quantra

Basic mathematical operations

As discussed in my previous post, basic arithmetic operations can be performed on individual columns.

10-element Vector{Float64}:

-0.5474996670806442
 0.5174063588946236
-0.564150142575268
 0.12873854328766576
 0.2741519215981265
 0.20241852864291987
 0.09324017568958975
-0.41716724316286524
 0.2693306887583933
-0.5967498723478988

You’ll have to use the “.” operator for element-wise division.

10-element Vector{Float64}:

0.06754620232737023
3.013387340201863
0.4169119702423886
1.2293455286486041
1.4462537614868343
8.482279426917298
1.1103752688515762
0.21238611891693882
3.1244976300403002
0.38733760512833965

Basic operations

Rearranging columns

r” is a regex search string. Here, any column with a string “work” will be selected and moved to the first place. You can write the full column name as well.

work experience name team
Int64 String String
15 Vivek EPAT
8 Viraj Marketing
7 Rohan Sales
10 Ishan Quantra

Adding a new column in a dataframe

Here we add another column, “c”, to the dataframe df_2.

a b c
Float64 Float64 Float64
0.845011 0.720306 0.962749
0.647665 0.0409036 0.10846
0.427267 0.221369 0.197592
0.413642 0.374832 0.967406
0.477994 0.118461 0.0233091
0.0849006 0.157679 0.936764
0.0477405 0.845332 0.296003
0.518909 0.159305 0.514714
0.93499 0.259579 0.620951
0.60034 0.115911 0.0224133

Dataframe-to-matrix conversion

10×3 Matrix{Float64}:

0.0396604  0.58716    0.741712
0.774389   0.256983   0.429361
0.403371   0.967521   0.989583
0.690069   0.56133    0.50599
0.888493   0.614341   0.152574
0.229472   0.0270531  0.932589
0.937996   0.844756   0.0745573
0.112492   0.52966    0.712178
0.396105   0.126774   0.397762
0.377277   0.974027   0.685073

Grouping data

Let’s look at ways to group data, which comes in handy while summarising data.

In-built datasets in Julia

The package RDatasets.jl in Julia helps you import all the in-build packages in R that can be used for testing purposes.

Here’s how you can find out the list of available datasets. It has 763 datasets.

We’ll work with one of the in-built datasets (“iris”) in this section. “iris” provides the data for multiple measurements of 3 plant species and 4 features for each of them. More details about this dataset can be found here.

The following snapshot shows the variables in the iris dataset.

iris dataset
Source
SepalLength SepalWidth PetalLength PetalWidth Species
Float64 Float64 Float64 Float64 Cat…
5.1 3.5 1.4 0.2 setosa
4.9 3.0 1.4 0.2 setosa
4.7 3.2 1.3 0.2 setosa
4.6 3.1 1.5 0.2 setosa
5.0 3.6 1.4 0.2 setosa
5.4 3.9 1.7 0.4 setosa
4.6 3.4 1.4 0.3 setosa
5.0 3.4 1.5 0.2 setosa
4.4 2.9 1.4 0.2 setosa
4.9 3.1 1.5 0.1 setosa
5.4 3.7 1.5 0.2 setosa
4.8 3.4 1.6 0.2 setosa
4.8 3.0 1.4 0.1 setosa
4.3 3.0 1.1 0.1 setosa
5.8 4.0 1.2 0.2 setosa
5.7 4.4 1.5 0.4 setosa
5.4 3.9 1.3 0.4 setosa
5.1 3.5 1.4 0.3 setosa
5.7 3.8 1.7 0.3 setosa
5.1 3.8 1.5 0.3 setosa
5.4 3.4 1.7 0.2 setosa
5.1 3.7 1.5 0.4 setosa
4.6 3.6 1.0 0.2 setosa
5.1 3.3 1.7 0.5 setosa
4.8 3.4 1.9 0.2 setosa
5.0 3.0 1.6 0.2 setosa
5.0 3.4 1.6 0.4 setosa
5.2 3.5 1.5 0.2 setosa
5.2 3.4 1.4 0.2 setosa
4.7 3.2 1.6 0.2 setosa

Here’s the summary of this dataset.

variable mean min median max nmissing eltype
Symbol Union… Any Union… Any Int64 DataType
SepalLength 5.84333 4.3 5.8 7.9 0 Float64
SepalWidth 3.05733 2.0 3.0 4.4 0 Float64
PetalLength 3.758 1.0 4.35 6.9 0 Float64
PetalWidth 1.19933 0.1 1.3 2.5 0 Float64
Species   setosa   virginica 0 CategoricalValue{String, UInt8}

Let’s look at some of the questions you might want to answer using the iris dataset.

We can perform arithmetic operations by grouping data based on various columns. Here’s how we can get the answer to the following question -

What’s the mean value of the sepal length of each species?

Species mm
Category Float64
setosa 5.006
versicolor 5.936
virginica 6.588

Another package that helps make the operations more intuitive is Pipe.jl. It lets you write operations as they are performed instead of the backward approach.

Species mm
Category Float64
setosa 5.006
versicolor 5.936
virginica 6.588
Species nrow
Category Float64
setosa 50
versicolor 50
virginica 50

Dealing with missing data

Julia has a “missing” object that is used for unavailable data. You can use skipmissing() function to perform operations ignoring the missing values.

Output:

a b
Int64? String?
1 Apple
missing Orange
3 missing
7 Grapes

You can use dropmissing() function to remove the missing values.

a b
Int64 String
1 Apple
7 Grapes

More details for dealing with missing values can be found here.


Importing and exporting data as CSV and Excel files

Reading data is the first step in analysing any kind of data. Most of the information we come across is either in CSV or excel format, so we’ll focus on these two. We will work with CSV.jl and XLSX.jl for dealing with CSV and Excel files.

Reading and writing CSV files

We’ll read a CSV file (infy.csv), as a dataframe, containing historical stock price data for Infosys downloaded from Yahoo finance for the period 21-Dec-2020 to 22-Dec-2021.

Here’s a summary for this data.

variable mean min median max nmissing eltype
Symbol Union… Any Union… Any Int64 DataType
Date   2020-12-22   2021-12-21 0 Date
Open 20.5674 16.39 20.63 24.05 0 Float64
High 20.7164 16.69 20.775 24.5 0 Float64
Low 20.4097 16.36 20.51 23.94 0 Float64
Close 20.5685 16.58 20.725 24.22 0 Float64
Adj Close 20.3422 16.2664 20.5451 24.22 0 Float64
Volume 7.09982e6 1320600 6.43815e6 22911800 0 Int64

Here, we calculate the range -

Date Open High Low Close Adj Close Volume range
Date Float64 Float64 Float64 Float64 Float64 Int64 Float64
2020-12-22 16.39 16.74 16.36 16.58 16.2664 6714400 0.379999
2020-12-23 16.9 16.93 16.57 16.59 16.2762 5913500 0.36
2020-12-24 16.68 16.69 16.52 16.6 16.286 1320600 0.170001
2020-12-28 16.73 16.84 16.72 16.77 16.4528 4239300 0.120001
2020-12-29 16.9 16.9 16.67 16.76 16.443 8473700 0.23
2020-12-30 16.87 17.0 16.83 16.93 16.6098 3877200 0.17
2020-12-31 17.01 17.03 16.89 16.95 16.6294 3693700 0.140002
2021-01-04 17.39 17.43 17.06 17.25 16.9237 12597600 0.370001
2021-01-05 17.32 17.67 17.32 17.65 17.3162 8109900 0.35
2021-01-06 17.4 17.79 17.34 17.73 17.3946 9136300 0.450001
2021-01-07 17.36 17.55 17.26 17.55 17.2181 10272000 0.289999
2021-01-08 18.07 18.61 18.02 18.59 18.2384 17802400 0.590001
2021-01-11 18.68 18.86 18.55 18.76 18.4052 12220600 0.310002
2021-01-12 18.92 18.94 18.54 18.6 18.2482 10629100 0.4
2021-01-13 19.03 19.07 18.4 18.43 18.0814 18409900 0.67
2021-01-14 18.57 18.65 18.14 18.22 17.8754 13286100 0.510001
2021-01-15 18.19 18.38 18.11 18.17 17.8263 7443000 0.269998
2021-01-19 18.08 18.18 17.95 18.12 17.7773 7179600 0.229999
2021-01-20 18.37 18.47 18.29 18.4 18.052 5408500 0.179998
2021-01-21 18.39 18.4 18.15 18.2 17.8558 7963400 0.25
2021-01-22 18.23 18.27 18.06 18.18 17.8361 5663500 0.210001
2021-01-25 18.15 18.22 17.84 17.92 17.5811 6012600 0.379999
2021-01-26 17.92 17.92 17.75 17.85 17.5124 5472600 0.17
2021-01-27 17.65 17.89 17.44 17.47 17.1396 11388300 0.449998
2021-01-28 17.46 17.75 17.41 17.64 17.3064 7877600 0.34
2021-01-29 17.16 17.23 16.88 16.88 16.5607 9671400 0.350001
2021-02-01 17.19 17.42 17.05 17.38 17.0513 5829200 0.370001
2021-02-02 17.45 17.51 17.34 17.44 17.1101 4119800 0.17
2021-02-03 17.6 17.75 17.49 17.65 17.3162 4677800 0.26
2021-02-04 17.54 17.64 17.36 17.59 17.2573 4439600 0.279998

This updated dataframe can be saved using CSV.write() function.

Reading and writing excel files

We’ll use the XLSX.jl package in Julia to read and write excel files.

Here’s how it can be done -

Date Open High Low Close Adj Close Volume
Any Any Any Any Any Any Any
2020-12-22 16.39 16.74 16.36 16.58 16.2664 6714400
2020-12-23 16.9 16.93 16.57 16.59 16.2762 5913500
2020-12-24 16.68 16.69 16.52 16.6 16.286 1320600
2020-12-28 16.73 16.84 16.72 16.77 16.4528 4239300
2020-12-29 16.9 16.9 16.67 16.76 16.443 8473700
2020-12-30 16.87 17.0 16.83 16.93 16.6098 3877200
2020-12-31 17.01 17.03 16.89 16.95 16.6294 3693700
2021-01-04 17.39 17.43 17.06 17.25 16.9237 12597600
2021-01-05 17.32 17.67 17.32 17.65 17.3162 8109900
2021-01-06 17.4 17.79 17.34 17.73 17.3946 9136300
2021-01-07 17.36 17.55 17.26 17.55 17.2181 10272000
2021-01-08 18.07 18.61 18.02 18.59 18.2384 17802400
2021-01-11 18.68 18.86 18.55 18.76 18.4052 12220600
2021-01-12 18.92 18.94 18.54 18.6 18.2482 10629100
2021-01-13 19.03 19.07 18.4 18.43 18.0814 18409900
2021-01-14 18.57 18.65 18.14 18.22 17.8754 13286100
2021-01-15 18.19 18.38 18.11 18.17 17.8263 7443000
2021-01-19 18.08 18.18 17.95 18.12 17.7773 7179600
2021-01-20 18.37 18.47 18.29 18.4 18.052 5408500
2021-01-21 18.39 18.4 18.15 18.2 17.8558 7963400
2021-01-22 18.23 18.27 18.06 18.18 17.8361 5663500
2021-01-25 18.15 18.22 17.84 17.92 17.5811 6012600
2021-01-26 17.92 17.92 17.75 17.85 17.5124 5472600
2021-01-27 17.65 17.89 17.44 17.47 17.1396 11388300
2021-01-28 17.46 17.75 17.41 17.64 17.3064 7877600
2021-01-29 17.16 17.23 16.88 16.88 16.5607 9671400
2021-02-01 17.19 17.42 17.05 17.38 17.0513 5829200
2021-02-02 17.45 17.51 17.34 17.44 17.1101 4119800
2021-02-03 17.6 17.75 17.49 17.65 17.3162 4677800
2021-02-04 17.54 17.64 17.36 17.59 17.2573 4439600

We can write an excel file using the writetable() function.

Julia has in-built read() and write() open() close() functions to work with text files. More details can be found here.

Data can be written in .jld format as well. .jld is Julia’s data format built using the JLD.jl package.

Details for the following packages can be found here -


Data visualization

Data visualization is crucial for understanding and analysing data. We’ll now look at some of the plots using Plots.jl. Plots.jl is one of the commonly used plotting libraries in Julia.

Line plot

Here’s a simple line plot.

line plot
line plot with 2 lines

Attributes of a plot

The following attributes can be added to the plot. These attributes can be used for all the plots discussed in this article.

  • xlabel - For x-axis label
  • ylabel - For y-axis label
  • title - Title of the plot
  • ylims - Range of y-axis
  • xlims - Range of the x-axis
  • label - Label names in the legend
  • linewidth/lw - For adjusting the width of the line
  • color - For adding specific colours to the lines
  • legend - Require legend or not and position of the legend. It can take: “topleft”, “topright”, “bottomleft”, “bottomright”, “right”, “bottom”, “top”, “right”, true, false
  • layout - For adding multiple plots in the same image.
  • size - Size of the plot

This list is not exhaustive; many attributes can be used. However, as I have mentioned earlier, we’ll stay focused on the question: How do we use Julia to achieve our goal?

The attributes presented above are most commonly used and should suffice for creating plots.

Here’s an example that combines all the features mentioned above.

formatted line plot

Scatter plot

Scatter plots can be generated using multiple methods. Here are a few examples -

scatter plot

Heatmap

heatmap for 10x20 matrix

Histogram

distribution of sepal length

Pie chart

pie chart

Here’s a sample layout with different plots.

4 plots (2x2 layout)

Plotting mathematical functions

Here are some plots of mathematical functions.

sin and cosine wave plot
tangent wave plot

Saving plots

The plot generated can be saved in various formats using the savefig() function.

Animated plots

We can also use the plots and covert and save them as gifs or videos.

gif of cosine wave plot
git of scatter plot

Lorenz attractor

The following is the code of the Lorenz attractor as seen in the Julia documentation:

gif of Lorenz attractor

More details about animated plots can be found here.

Various packages for plotting in Julia

Plots.jl is the basic plotting library in Julia. There are other packages for visualization such as -

  • GadFly.jl
  • GoogleCharts.jl
  • Makie.jl
  • PyPlot.jl
  • PGFPlotsX.jl
  • UnicodePlots.jl and
  • VegaLite.jl

Conclusion

This article covers the foundations of data manipulation and visualization using Julia.

In the following article, we’ll look at methods to get timeseries data for stock prices and analyse it using the tools presented in this article. Until then, take this article as a building block and explore the aspects you found interesting in detail!

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