
pwd() #Present working directory

"D:\\Dropbox (Personal)\\Tricks.of.the.trade\\Julia"


readdir() #Read the content of this directory

4-element Array{String,1}:
 ".ipynb_checkpoints"
 "00_Julia_introduction.html"
 "00_Julia_introduction.ipynb"
 "00_Julia_introduction.jl"


readdir(join=true) #Show the full path of the contents

4-element Array{String,1}:
 "D:\\Dropbox (Personal)\\Tricks.of.the.trade\\Julia\\.ipynb_checkpoints"
 "D:\\Dropbox (Personal)\\Tricks.of.the.trade\\Julia\\00_Julia_introduction.html"
 "D:\\Dropbox (Personal)\\Tricks.of.the.trade\\Julia\\00_Julia_introduction.ipynb"
 "D:\\Dropbox (Personal)\\Tricks.of.the.trade\\Julia\\00_Julia_introduction.jl"


] status

Status `C:\Users\Raghav\.julia\environments\v1.5\Project.toml`
  [5ae59095] Colors v0.12.4
  [a81c6b42] Compose v0.8.2
  [a93c6f00] DataFrames v0.21.7
  [5789e2e9] FileIO v1.4.3
  [c91e804a] Gadfly v1.3.0
  [f67ccb44] HDF5 v0.13.6
  [47d2ed2b] Hyperscript v0.0.3
  [7073ff75] IJulia v1.21.3
  [6a3955dd] ImageFiltering v0.6.15
  [6218d12a] ImageMagick v1.1.6
  [86fae568] ImageView v0.10.9
  [916415d5] Images v0.22.4
  [c601a237] Interact v0.10.3
  [c3e4b0f8] Pluto v0.11.14
  [438e738f] PyCall v1.91.4
  [d330b81b] PyPlot v2.9.0
  [24249f21] SymPy v1.0.28
  [10745b16] Statistics


α = 1/137

0.0072992700729927005


typeof(α)

Float64

π

π = 3.1415926535897...


typeof(π)

Irrational{:π}


round(π)

3.0

Inf

Inf


1/Inf

0.0


1 == 1.0

true


isequal(1,1.0)

true


1 === 1.0

false


exp(π^π)/(1/α + 1/π)

4.984094478274027e13


z = 1 + 3*im

1 + 3im


typeof(z)

Complex{Int64}


abs(z)

3.1622776601683795


exp(-im*z)

10.852261914197959 - 16.901396535150095im


100 ÷ 9

11


div(100,9)

11


mod(100,13)

9


mod2pi(7)

0.7168146928204135


mod(7,2*π)

0.7168146928204138


sqrt(α)

0.0854357657716761


cbrt(α)

0.19398127563103507


log(α) #Natural log

-4.919980925828125


log10(α)

-2.1367205671564067


exp(α)

1.0073259746799632


xr = 10*randn(5) # Generate an array of five random numbers (normally-distributed)

5-element Array{Float64,1}:
 -12.821956993273712
  -8.683820552480404
 -12.432308497818362
  21.983405018630076
  -9.21796091049308


xr[1] # First element of the array 'xr'

-12.821956993273712


xr[end] # Last element of the array 'ar'

-9.21796091049308


tmp = xr[2:4] # Slicing an array to grab 2nd to 4th elements

3-element Array{Float64,1}:
  -8.683820552480404
 -12.432308497818362
  21.983405018630076


xr[xr .> 0] #Select elements of the array that meet a certain criteria

1-element Array{Float64,1}:
 21.983405018630076


exp.(sin.(xr))

5-element Array{Float64,1}:
 0.7766132637390659
 0.5091591606896105
 1.1430051631348843
 1.0077735373808017
 0.8143656389765686


x= [1, 2, 3]
y= x # point 'y' to 'x'

3-element Array{Int64,1}:
 1
 2
 3


println(x, typeof(x))
println(y, typeof(y))
x === y #evaluates to true only if both are referring to the same object in memory

[1, 2, 3]Array{Int64,1}
[1, 2, 3]Array{Int64,1}

true


x[1]= 0
x[2]= 0
println(x, typeof(x))
println(y, typeof(y))
x === y

[0, 0, 3]Array{Int64,1}
[0, 0, 3]Array{Int64,1}

true


y[1]= 1
y[3]= -1
println(x, typeof(x))
println(y, typeof(y))
x === y

[1, 0, -1]Array{Int64,1}
[1, 0, -1]Array{Int64,1}

true


x= [-π,0,π]
println(x, typeof(x))
println(y, typeof(y))
x === y

[-3.141592653589793, 0.0, 3.141592653589793]Array{Float64,1}
[1, 0, -1]Array{Int64,1}

false


a = [1,2,3, [4,5,6]]
b= copy(a)
c= deepcopy(a)
println(a)
println(b)
println(c)
println(b === a)
println(c === a)

Any[1, 2, 3, [4, 5, 6]]
Any[1, 2, 3, [4, 5, 6]]
Any[1, 2, 3, [4, 5, 6]]
false
false


a[1:3]= [0,0,0]
println(a)
println(b)
println(c)

Any[0, 0, 0, [4, 5, 6]]
Any[1, 2, 3, [4, 5, 6]]
Any[1, 2, 3, [4, 5, 6]]


a[4][1:3]= [0,0,0]
println(a)
println(b)
println(c)

Any[0, 0, 0, [0, 0, 0]]
Any[1, 2, 3, [0, 0, 0]]
Any[1, 2, 3, [4, 5, 6]]


a[4]= [1,2,3,4,5,6,7,8,9,0]
println(a)
println(b)
println(c)

Any[0, 0, 0, [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]]
Any[1, 2, 3, [0, 0, 0]]
Any[1, 2, 3, [4, 5, 6]]


a = [1,3,17]

3-element Array{Int64,1}:
  1
  3
 17


a .^ 2

3-element Array{Int64,1}:
   1
   9
 289


a .+ 3 #Add 3 to each element of the array 'a'

3-element Array{Int64,1}:
  4
  6
 20


a .÷ 3 #Divide each element of the array 'a' by 3
# Note that this division is an integer division. \div + tab gives the above symbol

3-element Array{Int64,1}:
 0
 1
 5


a ./ 3
# This now is a full division. Notice that the values are now floating-point whereas earlier it was an integer

3-element Array{Float64,1}:
 0.3333333333333333
 1.0
 5.666666666666667


a .* 3

3-element Array{Int64,1}:
  3
  9
 51


array = [1 2 3 4 5; 7 8 9 10 0; 5 3 2 7 6] #creating a matrix (two-dimensional array) row-by-row

3×5 Array{Int64,2}:
 1  2  3   4  5
 7  8  9  10  0
 5  3  2   7  6


arr = [[1,7,5] [2,8,3] [3,9,2] [4,10,7] [5,0,6]] #creating a matrix column-by-column

3×5 Array{Int64,2}:
 1  2  3   4  5
 7  8  9  10  0
 5  3  2   7  6


x = [1,8,7] # An array with 3 rows (column-vector)

#=
Alternatives:
x = [1
    8
    7] 
#or
x = [1;8;7]
=#

3-element Array{Int64,1}:
 1
 8
 7


y = [7 6 5] # An array with 3 columns (row-vector)

1×3 Array{Int64,2}:
 7  6  5


x * y # Matrix multiplication

3×3 Array{Int64,2}:
  7   6   5
 56  48  40
 49  42  35


x .* y #element-by-element multiplication by broadcasting both matrices

3×3 Array{Int64,2}:
  7   6   5
 56  48  40
 49  42  35


y .* x

3×3 Array{Int64,2}:
  7   6   5
 56  48  40
 49  42  35


y * x

1-element Array{Int64,1}:
 90


A = x .+ y # element-by-element addition of two matrices

3×3 Array{Int64,2}:
  8   7   6
 15  14  13
 14  13  12


tmp = x ./ y # element-by-element division of two matrices

3×3 Array{Float64,2}:
 0.142857  0.166667  0.2
 1.14286   1.33333   1.6
 1.0       1.16667   1.4


function f(x,y,z)
    r = sqrt(x^2 + y^2 + z^2)
end

f (generic function with 1 method)


f(1,1,1)

1.7320508075688772


f(x)= 4*x.^2 # A one-line function

f (generic function with 2 methods)


f(2)

16


f([1,2,3,4,5])

5-element Array{Int64,1}:
   4
  16
  36
  64
 100


function g(x,y,z)
    r²= x^2 + y^2 + z^2
    r = sqrt(r²)
    return(round(r,digits=2),r²)
end

g (generic function with 1 method)


g(3,0,0)

(3.0, 9)


points = ((0,0,0), (3,0,0), (3,3,3))
for p in points
    (x,y,z)= (p[1],p[2],p[3])
    println("At ", p, ", function returns ", g(x,y,z))
end

At (0, 0, 0), function returns (0.0, 0)
At (3, 0, 0), function returns (3.0, 9)
At (3, 3, 3), function returns (5.2, 27)


using PyPlot #Here we are invoking the PyPlot package to start plotting stuff


foos = 10*randn(300)
plot(foos,"-k")

1-element Array{PyCall.PyObject,1}:
 PyObject <matplotlib.lines.Line2D object at 0x000000004F905AF0>


x = range(0,step=0.1,stop=6*π)
y = sin.(x)
plot(x, y)
xlabel("X value")
ylabel("Y value")
title("Sinθ")
grid("on")


scatter(x,y,alpha=0.5)
xlabel("X value")
ylabel("Y value")
title("Scatter plot of Sinθ")
grid("on")


x= range(-3*π,stop=3*π,length=201)
y= sinc.(x)
title("sinc function")
xlabel("x axis")
ylabel("y axis")
plot(x, y, linewidth=2.0, linestyle="--", color= "pink");


PyPlot.plt.hist(randn(1000),bins=10); # Histogram
PyPlot.title("Histogram")
grid("on")


f(x) = 4*x.^2
x = [-50,-25,0,25,50]
scatter(x,f(x));


xx = range(-100, stop =100, step=3)
scatter(xx,f(xx))

PyObject <matplotlib.collections.PathCollection object at 0x000000004BD458B0>


using PyCall


@pyimport pylab


@pyimport numpy as np


x = np.linspace(-π,π,1000)
y1 = np.sin(2*x .+ 5);
y2 = np.sin(2*x + np.cos(2*x) .+ 5);


plt = pylab
plt.plot(x, y1,"-b",label="sin(2x + 5)")
plt.plot(x, y2,"--g",label="sin(2x + cos(2x) + 5)")
plt.ylim(-1.25, 1.5)
plt.legend(loc="upper right")

PyObject <matplotlib.legend.Legend object at 0x000000005040DEB0>

Contents¶

Installation¶

Handly resources:¶

Julia terminal¶

Package manager¶

Shell Commands on Unix-like OS¶

Notebook¶

Pluto¶

Jupyter¶

Basic Jupyter notebook tips¶

Now finally let's try some Julia!¶

Basic operations¶

Integer division¶

Modulo operation¶

Power, logs and roots¶

Random numbers¶

Variables and Copies¶

Vectorized 'dot' operation¶

Multi-dimensional arrays¶

Function¶

Generate plots using PyPlot¶

PyCall¶