Using Julia in Jupyter

-- see the file on Using Python in Jupyter for some basics on Jupyter. This file is only about Julia.

Julia knows about integers, floating point numbers, even complex numbers like 1+2im.



In [1]:

    
2+2









    Out[1]:





4



In [2]:

    
2/3









    Out[2]:





0.6666666666666666



In [8]:

    
(1+2im)*(2+3im)









    Out[8]:





-5 + 10im

Julia already knows about sines and cosines, arrays, ranges of numbers. So you can save a lot of time and do calculations quickly. For instance, we can sum the integers from 1 to 100 as follows:



In [15]:

    
sum(1:100)









    Out[15]:





5050

We can compute the Riemann sum of the integral $\int_0^\pi \sin(x) dx$ as $$\sum_{k=1}^N \sin(x_k)\Delta_k$$ as:



In [17]:

    
sum(sin(0:.01:pi))*.01









    Out[17]:





1.9999900283082466



In [27]:

    
# Here is a matrix. Notice there are no commas. The semicolon separates the rows.
m = [10 20; 30 40]









    Out[27]:





2×2 Array{Int64,2}:
 10  20
 30  40



In [28]:

    
det(m)









    Out[28]:





-200.0



In [38]:

    
eig(m)









    Out[38]:





([-3.72281,53.7228],
[-0.824565 -0.415974; 0.565767 -0.909377])



In [40]:

    
eigval,eigvec = eig(m)









    Out[40]:





([-3.72281,53.7228],
[-0.824565 -0.415974; 0.565767 -0.909377])



In [41]:

    
# Check that the product of the eignvalues is the determinant.
prod(eigval)









    Out[41]:





-200.0



In [42]:

    
m*m









    Out[42]:





2×2 Array{Int64,2}:
  700  1000
 1500  2200



In [43]:

    
m^2









    Out[43]:





2×2 Array{Int64,2}:
  700  1000
 1500  2200



In [45]:

    
det(m^2)









    Out[45]:





40000.00000000014



In [46]:

    
exp(m)









    Out[46]:





2×2 Array{Float64,2}:
 22026.5         4.85165e8 
     1.06865e13  2.35385e17



In [47]:

    
expm(m)









    Out[47]:





2×2 Array{Float64,2}:
 5.12516e22  7.46955e22
 1.12043e23  1.63295e23

Plotting in Julia

To plot, we have to load in a package. The one we will use is called PyPlot, which is the same package as we used in Python plotting. (matplotlib.pyplot)

Notice the syntax for loading a package is very different in Julia.

Warning: Also note that this is a dangerous spot for the workshop, as this beta implementation of Julia tends to choke on loading packages. Especially if everyone in class tries to do it at once.



In [32]:

    
using PyPlot



In [33]:

    
plot([1,2,3,4])









    












    Out[33]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x314634cd0>



In [34]:

    
x = linspace(-3, 3)
y = x.^3 - 3*x
plot(x,y)









    












    Out[34]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x314807790>



In [35]:

    
n = 100
x = linspace(-3, 3, n)
y = linspace(-3,3,n)

xgrid = repmat(x',n,1)
ygrid = repmat(y,1,n)

z=exp(-xgrid.^2 - ygrid.^2)

plot_surface(x,y,z)









    












    Out[35]:





PyObject <mpl_toolkits.mplot3d.art3d.Poly3DCollection object at 0x314a7d0d0>



In [36]:

    
plot_surface(x,y,z,cmap="jet")









    












    Out[36]:





PyObject <mpl_toolkits.mplot3d.art3d.Poly3DCollection object at 0x314b4c150>



In [37]:

    
imshow(z)









    












    Out[37]:





PyObject <matplotlib.image.AxesImage object at 0x3153f6690>



In [ ]: