100 Julia exercises with solutions

100_Julia_exercises_First50

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`


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import LinearAlgebra as la #or
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import LinearAgebra
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const la = LinearAlgebra

2. Print the version of julia package Javis


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] 
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status Javis

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


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a = zeros(Int64,10)

4. How to find the memory size of any array in bytes


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sizeof(a)
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length(a)*sizeof(eltype(a))

5. How to get the documentation of the Julia zero function from the command line?


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?zeros

6. Create a Int vector of size 10 but the fifth value which is 1 (in two lines of code)


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a = zeros(Int,10)
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a[5] = 1

7. Create a vector with values ranging from 10 to 49


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a = [10:49;]
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a = collect(10:49)

8. Return the reverse of a vector (first element becomes last)


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a[end:-1:1] #faster
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reverse(a)
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reverse!(a) #inplace

9. Create a 3x3 matrix with values ranging from 0 to 8


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a = reshape(0:8,3,3)

10. Find indices of non-zero elements from [1,2,0,0,4,0]


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findall(!isequal(0),a)
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findall(!iszero,a)
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findall(!=(0),a)

11. Create a 3x3 identity matrix


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using LinearAlgebra
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a = I(3)
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a = Matrix(1.0I,3,3)

12. Create a 3x3x3 array with random values


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a = rand(3,3,3) #numbers in the range 0 to 1
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b = randn(3,3,3) #Gaussian random numbers

13. Create a 10x10 array with random values and find the minimum and maximum values


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a = rand(10,10)
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minm = minimum(a)
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maxm = maximum(a)
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minm, maxm = extrema(a)

14. Create a random vector of size 30 and find the mean value


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using Statistics
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a = rand(30) #rand(30,)
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b = mean(a)

15. Create a 2d array with 1 on the border and 0 inside


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a = zeros(5,5)
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a[1,:] .= 1
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a[end,:] .= 1
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a[2:end-1,1] .= 1 
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a[2:end-1,end] .= 1
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a[:,1] .= 1;a[:,end] .= 1 #Last two steps can be replaced by this line

16. How to add a border (filled with 0's) around an existing array?


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a = rand(5,5)
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b = zeros(Float64,size(a,1)+2,size(a,2)+2)# b = zeros(eltype(a), size(a) .+ 1)
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b[2:end-1,2:end-1] = a

17. What is the result of the following expression? (★☆☆)


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 (0 * NaN) >= NaN : false
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NaN == NaN : false
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NaN > NaN : false
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NaN - NaN : NaN
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NaN in Set([NaN]) : true
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NaN in [NaN] : false
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0.3 == 3 * 0.1 : false #floating point rounding error
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isapprox(0.3 , 3 * 0.1) : true

18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal


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a = Bidiagonal(zeros(5,),collect(1:4),:L)

19. Create a 8x8 matrix and fill it with a checkerboard pattern


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a = zeros(Int64,8,8)
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a[1:2:end,1:2:end] .= 1
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a[2:2:end,2:2:end] .= 1 #or
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a = [Int(isodd(i+j)) for i in 1:8, j in 1:8]

20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element?


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m = 100
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n,p,r = 6,7,8
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page = Int64(ceil(m/n/p))
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col = Int64(ceil((m-(page-1)*n*p)/n))
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row = Int64(ceil((m-(page-1)*n*p-(col-1)*n)/n))
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CartesianIndices((6,7,8))[m] #builtin command

21. Create a checkerboard 8x8 matrix using the repeat function (★☆☆)


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repeat([1 0;0 1],4,4)

22. Normalize a 5x5 random matrix (★☆☆)


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a = randn(5,5)
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a = a .- minimum(a)
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a = a./maximum(a)

23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆)


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mutable struct color
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  R::UInt8
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  G::UInt8
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  B::UInt8
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  A::UInt8
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end

24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)


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a = rand(5,3);b = rand(3,2)
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c = a*b

25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆)


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a = 3;b = 8;
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x = rand(1:10,20) # collect(1:10)
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x[a .<= x .<= b] .= -x[a .<= x .<= b] #or
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x[a .<= x .<= b] .*= -1.

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?


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Z.^Z #valid
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2 << Z >> 2 #not valid
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Z <- Z # Z < (-Z)
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1im*Z #valid
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Z/1/1 #valid,converted to float vector
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Z<Z>Z #valid

28. What are the result of the following expressions? (★☆☆)


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[0]/[0] : 1x1 Matrix Float64 0.0
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[0] ./ [0] : NaN
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[0]// [0] : MethodError
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[0] .÷ [0] : DivideError
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Float64(Int64([NaN])) : MethodError

29. How to round away from zero a float array ? (★☆☆)


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round.(-4.5, RoundNearestTiesAway)

30. How to find common values between two arrays? (★☆☆)


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intersect(A,B) #A and B are sets

31. How to ignore all Julia warnings (not recommended)? (★☆☆)

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


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np.sqrt(-1) == np.emath.sqrt(-1)

33. How to get the dates of yesterday, today and tomorrow? (★☆☆)


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using Dates
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tod = today()
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tom = tod + Day(1)
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yes = tod + Day(-1)

34. How to get all the dates corresponding to the month of July 2016? (★★☆)


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using Dates
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mon = collect(Date(2016,7,1):Day(1):Date(2016,7,31))

35. How to compute ((A+B)*(-A/2)) in place (without copy)? (★★☆)


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A = rand(2,2);B = rand(2,2)
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@. A = ((A+B)*(-A/2))

36. Extract the integer part of a random array of positive numbers using 4 different methods (★★☆)


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A = 10*rand(1,10)
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Int64.(trunc.(A))
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B = parse.(Int64,[split(string(x),".")[1] for x in A])
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Int64.(floor.(A))
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Int64.(ceil.(A)) .- 1

37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆)


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a = rand(0:4,5,5)

38. Consider a generator function that generates 10 integers and use it to build an array (★☆☆)


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a = collect(1:10)

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


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a = rand(10)

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


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a = rand(10,)
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sort!(a)

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 (★★☆)


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isequal(A,B)

43. Make an array immutable (read-only) (★★☆)

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


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a = rand(10,2);
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ang = angle.(a[:,1] .+ 1im*a[:,2])
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r = hypot.(a[:,1] .+ a[:,2])# sqrt.(a[:,1].^2 .+ a[:,2].^2)
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p = r.*cis.(ang)  # r.*exp.(1im*ang) 
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#or
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to_polar(x, y) = hypot(x, y) * cis(angle(x+im*y))
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[to_polar(x...) for x in eachrow(a)] #or
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[to_polar(a[i, 1], a[i, 2]) for i in axes(a, 1)]

45. Create random vector of size 10 and replace the maximum value by 0 (★★☆)


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a = rand(10)
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a[a .== maximum(a)] .= 0

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


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mutable struct xy
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x:Float64
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y:Float64
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end

47. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) (★★☆)


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X = rand(5);Y = rand(5);
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C = [1/(xi-yi) for xi in X, yi in Y]#or
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C = 1 ./ (X .- Y')

48. Print the minimum and maximum representable value for each Julia scalar type


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typemin()
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typemax()

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


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print(a)
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display(a)
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foreach(println, a) #prints full array

50. How to find the closest value (to a given scalar) in a vector? (★★☆)


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a = rand(10)
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x = 0.5 #given scalar
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b = abs.(a .- x)
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a[findmin(b)[2]]

I will update remaining exercises in due course.