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Vinod V
Vinod V

Posted on • Updated on

100 Julia exercises

Here is a Julia version of exercises with solutions which is based on the exercises given here: https://github.com/rougier/numpy-100

1. Import the julia package LinearAlgebra under the name la 

import LinearAlgebra as la #or
import LinearAgebra
const la = LinearAlgebra
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2. Print the version of julia package Javis 

] 
status Javis
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3. Create a zero vector of size 10 and of type Int64 

a = zeros(Int64,10)
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4. How to find the memory size of any array in bytes 

sizeof(a)
length(a)*sizeof(eltype(a))
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5. How to get the documentation of the Julia zero function from the command line? 

?zeros
a = @doc zeros # documentation is copied to a
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6. Create a Int vector of size 10 but the fifth value which is 1 (in two lines of code) 

a = zeros(Int,10)
a[5] = 1
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7. Create a vector with values ranging from 10 to 49 

a = [10:49;]
a = collect(10:49)
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8. Return the reverse of a vector (first element becomes last) 

a[end:-1:1] #faster
reverse(a)
reverse!(a) #inplace
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9. Create a 3x3 matrix with values ranging from 0 to 8 

a = reshape(0:8,3,3)
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10. Find indices of non-zero elements from [1,2,0,0,4,0] 

findall(!isequal(0),a)
findall(!iszero,a)
findall(!=(0),a)
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11. Create a 3x3 identity matrix 

using LinearAlgebra
a = I(3)
a = Matrix(1.0I,3,3)
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12. Create a 3x3x3 array with random values 

a = rand(3,3,3) #numbers in the range 0 to 1
b = randn(3,3,3) #Gaussian random numbers
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13. Create a 10x10 array with random values and find the minimum and maximum values 

a = rand(10,10)
minm = minimum(a)
maxm = maximum(a)
minm, maxm = extrema(a)
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14. Create a random vector of size 30 and find the mean value 

using Statistics
a = rand(30) #rand(30,)
b = mean(a)
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15. Create a 2d array with 1 on the border and 0 inside 

a = zeros(5,5)
a[1,:] .= 1
a[end,:] .= 1
a[2:end-1,1] .= 1 
a[2:end-1,end] .= 1
a[:,1] .= 1;a[:,end] .= 1 #Last two steps can be replaced by this line
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16. How to add a border (filled with 0's) around an existing array? 

a = rand(5,5)
b = zeros(Float64,size(a,1)+2,size(a,2)+2)# b = zeros(eltype(a), size(a) .+ 1)
b[2:end-1,2:end-1] = a
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17. What is the result of the following expression? (★☆☆) 

 (0 * NaN) >= NaN : false
NaN == NaN : false
NaN > NaN : false
NaN - NaN : NaN
NaN in Set([NaN]) : true
NaN in [NaN] : false
0.3 == 3 * 0.1 : false #floating point rounding error
isapprox(0.3 , 3 * 0.1) : true
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18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal 

a = Bidiagonal(zeros(5,),collect(1:4),:L)
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19. Create a 8x8 matrix and fill it with a checkerboard pattern 

a = zeros(Int64,8,8)
a[1:2:end,1:2:end] .= 1
a[2:2:end,2:2:end] .= 1 #or
a = [Int(isodd(i+j)) for i in 1:8, j in 1:8]
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20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? 

m = 100
n,p,r = 6,7,8
page = Int64(ceil(m/n/p))
col = Int64(ceil((m-(page-1)*n*p)/n))
row = Int64(ceil((m-(page-1)*n*p-(col-1)*n)/n))

CartesianIndices((6,7,8))[m] #builtin command
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21. Create a checkerboard 8x8 matrix using the repeat function (★☆☆) 

repeat([1 0;0 1],4,4)
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22. Normalize a 5x5 random matrix (★☆☆) 

a = randn(5,5)
a = a .- minimum(a)
a = a./maximum(a)
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23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆) 

mutable struct color
  R::UInt8
  G::UInt8
  B::UInt8
  A::UInt8
end
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24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) 

a = rand(5,3);b = rand(3,2)
c = a*b
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25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆) 

a = 3;b = 8;
x = rand(1:10,20) # collect(1:10)
x[a .<= x .<= b] .= -x[a .<= x .<= b] #or
x[a .<= x .<= b] .*= -1.
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26. What is the output of the following script? (★☆☆) [Python only]
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27. Consider an integer vector Z, which of these expressions are legal? 

Z.^Z #valid
2 << Z >> 2 #not valid
Z <- Z # Z < (-Z)
1im*Z #valid
Z/1/1 #valid,converted to float vector
Z<Z>Z #valid
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28. What are the result of the following expressions? (★☆☆) 

[0]/[0] : 1x1 Matrix Float64 0.0
[0] ./ [0] : NaN
[0]// [0] : MethodError
[0] .÷ [0] : DivideError
Float64(Int64([NaN])) : MethodError
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29. How to round away from zero a float array ? (★☆☆) 

round.(-4.5, RoundNearestTiesAway)
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30. How to find common values between two arrays? (★☆☆) 

intersect(A,B) #A and B are sets
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31. How to ignore all Julia warnings (not recommended)? (★☆☆)

32. Is the following expressions true? [Python only]★☆☆) 

np.sqrt(-1) == np.emath.sqrt(-1)
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33. How to get the dates of yesterday, today and tomorrow? (★☆☆) 

using Dates
tod = today()
tom = tod + Day(1)
yes = tod + Day(-1)
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34. How to get all the dates corresponding to the month of July 2016? (★★☆) 

using Dates
mon = collect(Date(2016,7,1):Day(1):Date(2016,7,31))
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35. How to compute ((A+B)*(-A/2)) in place (without copy)? (★★☆) 

A = rand(2,2);B = rand(2,2)
@. A = ((A+B)*(-A/2))
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36. Extract the integer part of a random array of positive numbers using 4 different methods (★★☆) 

A = 10*rand(1,10)
Int64.(trunc.(A))
B = parse.(Int64,[split(string(x),".")[1] for x in A])
Int64.(floor.(A))
Int64.(ceil.(A)) .- 1
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37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆) 

a = rand(0:4,5,5)
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38. Consider a generator function that generates 10 integers and use it to build an array (★☆☆) 

a = collect(1:10)
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39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆) 

a = rand(10)
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40. Create a random vector of size 10 and sort it (★★☆) 

a = rand(10,)
sort!(a)
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41. How to sum a small array faster than np.sum?Python only

42. Consider two random array A and B, check if they are equal (★★☆) 

isequal(A,B)
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43. Make an array immutable (read-only) (★★☆)

44. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆) 

a = rand(10,2);
ang = angle.(a[:,1] .+ 1im*a[:,2])
r = hypot.(a[:,1] .+ a[:,2])# sqrt.(a[:,1].^2 .+ a[:,2].^2)
p = r.*cis.(ang)  # r.*exp.(1im*ang) 
#or
to_polar(x, y) = hypot(x, y) * cis(angle(x+im*y))
[to_polar(x...) for x in eachrow(a)] #or
[to_polar(a[i, 1], a[i, 2]) for i in axes(a, 1)]
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45. Create random vector of size 10 and replace the maximum value by 0 (★★☆) 

a = rand(10)
a[a .== maximum(a)] .= 0
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46. Create a structured array with x and y coordinates covering the [0,1]x[0,1] area (★★☆) 

mutable struct xy
x:Float64
y:Float64
end
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47. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) (★★☆) 

X = rand(5);Y = rand(5);
C = [1/(xi-yi) for xi in X, yi in Y]#or
C = 1 ./ (X .- Y')
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48. Print the minimum and maximum representable value for each Julia scalar type 

typemin()
typemax()
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49. How to print all the values of an array? (★★☆) 

print(a)
display(a)
foreach(println, a) #prints full array
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50. How to find the closest value (to a given scalar) in a vector? (★★☆) 

a = rand(10)
x = 0.5 #given scalar
b = abs.(a .- x)
a[findmin(b)[2]]
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I will update remaining exercises in due course.

Top comments (2)

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logankilpatrick profile image
Logan Kilpatrick •

It would be great to get these setup and linked on GitHub as well! Let me know if you want to put them in the Julia Community GitHub organization.

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maxkapur profile image
Max Kapur • • Edited

I think #44 can be done more simply:

using LinearAlgebra: norm
a = rand(10, 2)
mapreduce(vcat, eachrow(a)) do r
    [norm(r) atan(r...)]
end
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Similarly for #50:

A = rand(10)
x = 0.5
findmin(a -> abs(a - x), A)
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(or minimum(a -> abs(a - x), A) if you just want the value of abs(a - x) as in your solution)