Graphics and packages in Julia

Visualization is a key topic in scientific computing. Currently there are several options available for producing different types of graphics in Julia.

Coming from Python, one of the most accessible (and full-featured) is PyPlot, which is a Julia wrapper to the pyplot submodule of the Python matplotlib library.

Installing packages

To install the PyPlot package, if it is not already installed, we do



In [1]:

    
Pkg.add("PyPlot")









    



INFO: Nothing to be done
INFO: METADATA is out-of-date — you may not have the latest version of PyPlot
INFO: Use `Pkg.update()` to get the latest versions of your packages

If the package requested is already installed, this will be reported with the message INFO: Nothing to be done, as shown above. It will also warn you if there may be a new version of the package available.

Pkg is the package manager. It uses git repositories, which are each cloned into their own sub-directory of the .julia directory in your home directory.

The list of packages currently available is at http://pkg.julialang.org/; it is growing rapidly.

Pkg checks each time to see if the METADATA.jl repository has been updated; this repository contains the information about available packages.

Pkg.update() will update to the latest versions of installed packages. (Currently this is an all-or-nothing operation, updating all installed packages.)

Using packages

To make the package accessible in our code, we use



In [2]:

    
using PyPlot









    



INFO: Loading help data...

using is analogous to from [package] import * in Python; it makes all names in the package available. We could instead use import PyPlot, in which case all names would be available as PyPlot.plot, etc.



In [4]:

    
x = rand(10)
y = rand(10)

p = plot(x, y, "ro-")









    












    Out[4]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x11880b790>



In [5]:

    
p









    Out[5]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x11880b790>



In [ ]:

An alternative is to use import instead:



In [3]:

    
import PyPlot



In [6]:

    
PyPlot.figure(figsize=(4,2))
PyPlot.plot(rand(10), rand(10))









    












    Out[6]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x10d548e50>



In [ ]:

    
PyPlot.save

Example: Eigenvalues of random matrices



In [3]:

    
L = 1000

diffs = []

for i in 1:10
    M = randn(L, L);
    M = Symmetric(M)

    lamb = eigvals(M);
    
    diffs = [diffs, diff(lamb)];
end

h = hist(diffs, 300)
plot(h[1][1:end-1], h[2])









    












    Out[3]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x11589ac10>

Gadfly

Gadfly is a native Julia plotting package, based on the Grammar of Graphics syntax, and thus with a similar flavour to R's ggplot package.



In [1]:

    
using Gadfly



In [2]:

    
xs = 1:10
ys = rand(10)

plot(x=xs, y=ys)









    Out[2]:

The plot can be panned and zoomed directly in the browser.

Different geometries are available:



In [3]:

    
plot(x=xs, y=ys, Geom.line)









    Out[3]:



In [7]:

    
plot(x=rand(10), y=rand(10), Geom.point, Geom.line(preserve_order=true))









    Out[7]:

Note that the lines are drawn between points ordered in the $x$-direction. To avoid this, we use an argument to Geom.line:



In [8]:

    
p = plot(layer(x=rand(10), y=rand(10), color=[1], Geom.point, Geom.line(preserve_order=true)),
layer(x=rand(10), y=rand(10), Geom.point, Geom.line(preserve_order=true)),
Guide.XLabel("first"), Guide.YLabel("second"))









    Out[8]:

We can write to a PDF:



In [9]:

    
draw(PDF("stuff.pdf", 10cm, 5cm), p)



In [11]:

    
;open stuff.pdf

DataFrames

The DataFrames package provides pandas-like functionality.



In [9]:

    
Pkg.add("DataFrames")









    



INFO: Nothing to be done
INFO: METADATA is out-of-date — you may not have the latest version of DataFrames
INFO: Use `Pkg.update()` to get the latest versions of your packages

Gadfly has excellent integration with DataFrames:



In [10]:

    
Pkg.add("RDataSets")









    



INFO: Nothing to be done
INFO: METADATA is out-of-date — you may not have the latest version of RDataSets
INFO: Use `Pkg.update()` to get the latest versions of your packages



In [12]:

    
using Gadfly
using RDatasets



In [13]:

    
irises = dataset("datasets", "iris")
head(irises)









    Out[13]:




SepalLength SepalWidth PetalLength PetalWidth Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 3.1 1.5 0.2 setosa
5 5.0 3.6 1.4 0.2 setosa
6 5.4 3.9 1.7 0.4 setosa



In [14]:

    
typeof(irises)









    Out[14]:





DataFrame (constructor with 22 methods)



In [15]:

    
plot(irises, x="SepalLength", y="SepalWidth", Geom.point)









    Out[15]:



In [17]:

    
cars = dataset("car", "SLID")
head(cars)









    Out[17]:




Wages Education Age Sex Language
1 10.56 15.0 40 Male English
2 11.0 13.2 19 Male English
3 NA 16.0 49 Male Other
4 17.76 14.0 46 Male Other
5 NA 8.0 71 Male English
6 14.0 16.0 50 Female English



In [18]:

    
plot(cars, x="Wages", color="Language", Geom.histogram)









    Out[18]:

Modules

A module is a way to encapsulate code in a namespace. The syntax is as follows

module NAME

import Base.show, Base.getindex   # imports to extend Base functions
export A, B   # exports

...

end

We can then do using NAME to use the functionality.

Example: Eigenvalues of random matrices



In [19]:

    
import PyPlot









    



INFO: Loading help data...



In [21]:

    
plt = PyPlot









    Out[21]:





PyPlot



In [20]:

    
help("import")









    



No help information found.



In [22]:

    
plt.plot









    Out[22]:





plot (generic function with 1 method)



In [25]:

    
macroexpand(:(@time begin sin(10); @time cos(10) end ))









    Out[25]:





:(begin  # util.jl, line 50:
        local #3284#b0 = Base.gc_bytes() # line 51:
        local #3285#t0 = Base.time_ns() # line 52:
        local #3286#g0 = Base.gc_time_ns() # line 53:
        local #3287#val = begin  # In[25], line 1:
                    sin(10) # line 1:
                    begin  # util.jl, line 50:
                        local #3291#b0 = Base.gc_bytes() # line 51:
                        local #3292#t0 = Base.time_ns() # line 52:
                        local #3293#g0 = Base.gc_time_ns() # line 53:
                        local #3294#val = cos(10) # line 54:
                        local #3295#g1 = Base.gc_time_ns() # line 55:
                        local #3296#t1 = Base.time_ns() # line 56:
                        local #3297#b1 = Base.gc_bytes() # line 57:
                        Base.time_print(Base.-(#3296#t1,#3292#t0),Base.-(#3297#b1,#3291#b0),Base.-(#3295#g1,#3293#g0)) # line 58:
                        #3294#val
                    end
                end # line 54:
        local #3288#g1 = Base.gc_time_ns() # line 55:
        local #3289#t1 = Base.time_ns() # line 56:
        local #3290#b1 = Base.gc_bytes() # line 57:
        Base.time_print(Base.-(#3289#t1,#3285#t0),Base.-(#3290#b1,#3284#b0),Base.-(#3288#g1,#3286#g0)) # line 58:
        #3287#val
    end)



In [ ]:

    
i = 0
@time @until

	SepalLength	SepalWidth	PetalLength	PetalWidth	Species
1	5.1	3.5	1.4	0.2	setosa
2	4.9	3.0	1.4	0.2	setosa
3	4.7	3.2	1.3	0.2	setosa
4	4.6	3.1	1.5	0.2	setosa
5	5.0	3.6	1.4	0.2	setosa
6	5.4	3.9	1.7	0.4	setosa

	Wages	Education	Age	Sex	Language
1	10.56	15.0	40	Male	English
2	11.0	13.2	19	Male	English
3	NA	16.0	49	Male	Other
4	17.76	14.0	46	Male	Other
5	NA	8.0	71	Male	English
6	14.0	16.0	50	Female	English