100 Julia exercises

This is Julia version of 100 numpy exercises

Latest version of 100 numpy excercises are available at this repository.

You can see executed results here

Neophyte

1. Import the numpy package under the name np

# nothing to do

2. Print the Julia version

VERSION

3. Create a null vector of size 10

Z = zeros(10)

4. Create a null vector of size 10 and set the fifth value to 1

Z = zeros(10)
Z[5] = 1
Z

5. Create a vector with values ranging from 10 to 99

Z = [10:99]

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

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

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

nz = find([1,2,0,0,4,0])

8. Create a 3x3 identity matrix

Z = eye(3)

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

Z = diagm(1:4, -1)

10. Create a 10x10x10 array with random values

rand(10, 10, 10)

Novice

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

Z = zeros(Int64,8,8)
Z[1:2:end, 2:2:end] = 1
Z[2:2:end, 1:2:end] = 1
Z

# Another solution
# Author: harven
[(i+j)%2 for i=1:8, j=1:8]

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

Z = rand(10, 10)
Zmin, Zmax = minimum(Z), maximum(Z)

# It can also be written as follows.
# Author: hc_e
# http://qiita.com/chezou/items/d7ca4e95d25835a5cd01#comment-1c20073a44695c08f523
Zmin, Zmax = extrema(Z)

3. Create a checkerboard 8x8 matrix using the tile function

# numpy's tile equal to repmat
Z = repmat([0 1;1 0],4,4)

4. Normalize a 5x5 random matrix (between 0 and 1)

Z = rand(5, 5)
Zmin, Zmax = minimum(Z), maximum(Z)
Z = (Z .- Zmin)./(Zmax - Zmin)

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

Z = ones(5,3) * ones(3,2)

6. Create a 10x10 matrix with row values ranging from 0 to 9

(zeros(Int64,10,10) .+ [0:9])'

# Alternate solution
# Author: Leah Hanson
[y for x in 1:10, y in 0:9]

7. Create a vector of size 1000 with values ranging from 0 to 1, both excluded

linspace(0,1, 1002)[2:end - 1]

8. Create a random vector of size 100 and sort it

Z = rand(100)
sort(Z) # returns a sorted copy of Z; leaves Z unchanged

# Alternate solution
# Author: Leah Hanson
Z = rand(100)
sort!(Z) # sorts Z in-place; returns Z

9. Consider two random matrices A anb B, check if they are equal.

A = rand(0:2, 2,2)
B = rand(0:2, 2,2)
A == B

10. Create a random vector of size 1000 and find the mean value

Z = rand(1000)
m = mean(Z)

Apprentice

1. Make an array immutable (read-only)

julia> Pkg.add("ImmutableArrays")
julia> using ImmutableArrays
julia> Matrix4x4(rand(4,4))
4x4 ImmutableArrays.Matrix4x4{Float64}:
 0.0724154  0.0840244  0.291123  0.853076
 0.0994344  0.686174   0.214841  0.248117
 0.996963   0.680124   0.405399  0.180246
 0.232086   0.0424678  0.375087  0.799278

2. Consider a random 10x2 matrix representing Cartesian coordinates, convert them to polar coordinates

Z = rand(10,2)
X, Y = Z[:,1], Z[:,2]
R = sqrt(X.^2 + Y.^2)
T = atan2(Y,X)

3. Create random vector of size 100 and replace the maximum value by 0

Z = rand(100)
Z[indmax(Z)] = 0

4. Create a structured array with x and y coordinates covering the [0,1]x[0,1] area.

# There is no official `meshgrid` function.
# See also: https://github.com/JuliaLang/julia/issues/4093
# assume using https://github.com/JuliaLang/julia/blob/master/examples/ndgrid.jl
include("/Applications/Julia-0.3.0-prerelease-547facf2c1.app/Contents/Resources/julia/share/julia/examples/ndgrid.jl")
X = linspace(0,1,10)
Zx, Zy = meshgrid(X, X)

# Another solution
# Author: Alireza Nejati
[(x,y) for x in linspace(0,1,10), y in linspace(0,1,10)]

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

for dtype in (Int8, Int16, Int32, Int64)
    println(typemin(dtype))
    println(typemax(dtype))
end

# Another solution
# Author: harven
# typemin, typemax returns -Inf, Inf
print(map!(t -> (typemin(t),typemax(t)), subtypes(Signed)))

for dtype in (Float32, Float64)
    println(typemin(dtype))
    println(typemax(dtype))
    println(eps(dtype))
end

6. Create a structured array representing a position (x,y) and a color (r,g,b)

# Julia doesn't have StructArray
# see also: https://github.com/JuliaLang/julia/issues/1263
# use DataFrames

7. Consider a random vector with shape (100,2) representing coordinates, find point by point distances

Z = rand(10,2)
X,Y = Z[:,1], Z[:,2]
D = sqrt((X.-X').^2 + (Y .- Y').^2)

8. Generate a generic 2D Gaussian-like array

X, Y = meshgrid(linspace(-1,1,100),linspace(-1,1,100))
D = sqrtm(X*X + Y*Y)
sigma, mu = 1.0, 0.0
G = exp(-( (D.-mu)^2 / ( 2.0 * sigma^2 ) ) )

# Another solution
# Author: Billou Beilour
sigma, mu = 1.0, 0.0
G = [ exp(-(x-mu).^2/(2.0*sigma^2) -(y-mu).^2/(2.0*sigma^2) ) for x in linspace(-1,1,100), y in linspace(-1,1,100) ]

# It also written
# Author: Billou Beilour
sigma, mu = 1.0, 0.0
x,y = linspace(-1,1,100), linspace(-1,1,100)
G = zeros(length(x),length(y))

for i in 1:length(x), j in 1:length(y)
    G[i,j] = exp(-(x[i]-mu).^2/(2.0*sigma^2) -(y[j]-mu).^2/(2.0*sigma^2) )
end

9. Consider the vector [1, 2, 3, 4, 5]. How to build a new vector with 3 consecutive zeros interleaved between each value?

Z = [1,2,3,4,5]
nz = 3
Z0 = zeros(length(Z) + (length(Z)-1)*(nz))
Z0[1:nz+1:end] = Z

10. Find the nearest value from a given value in an array

Z = [3,6,9,12,15]
Z[indmin(abs(Z .- 10))]

Journeyman

1. Consider the following file:

1,2,3,4,5
6,,,7,8
,,9,10,11

How to read it?

using DataFrames
readtable("missing.dat")

2. Consider a generator function that generates 10 integers and use it to build an array

function mygenerator()
    for n=1:10
        produce(n)
    end
end
collect(Int,Task(mygenerator))

3. Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices)?

using StatsBase
Z = ones(10)
I = rand(0:length(Z), 20)
Z += counts(I, 1:length(Z))

4. How to accumulate elements of a vector (X) to an array (F) based on an index list (I)?

using StatsBase
X = WeightVec([1,2,3,4,5,6])
I = [1,3,9,3,4,1]
F = counts(I, maximum(I), X)

5. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors

w,h = 16,16
I = convert(Array{Uint8}, rand(0:2, (h,w,3)))
F = I[:,:,1] * 256 * 256 + I[:,:,2]*256 + I[:,:,3]
n = length(unique(F))
unique(I)

6. Considering a four dimensional array, how to get sum over the last two axis at once?

A = rand(0:10, (3,4,3,4))
x,y = size(A)[1:end-2]
z = prod(size(A)[end-1:end])
calc_sum = sum(reshape(A, (x,y,z)),3)

7. Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices?

using StatsBase
D = WeightVec(rand(100))
S = rand(0:10,100)
D_sums = counts(S, maximum(S), D)
D_counts = counts(S, maximum(S))
D_means = D_sums ./ D_counts

Craftsman

1. Consider a one-dimensional array Z, build a two-dimensional array whose first row is (Z[0],Z[1],Z[2]) and each subsequent row is shifted by 1 (last row should be (Z[-3],Z[-2],Z[-1])

# I don't find any function like stride_tricks.as_stride
function rolling(A, window)
       Z = zeros(length(A)-2, window)
       for i in 1:(length(A) - window +1)
           Z[i,:] = A[i:i+2]
       end
       return Z
end

rolling(0:100, 3)

2. Consider a set of 100 triplets describing 100 triangles (with shared vertices), find the set of unique line segments composing all the triangles.

faces = rand(0:100, 100, 3)
face2 = kron(faces,[1 1])

F = circshift(sortcols(face2),(0,1))
F = reshape(F, (convert(Int64,length(F)/2),2))
F = sort(F,2)
G = unique(F,1)

3. Given an array C that is a bincount, how to produce an array A such that np.bincount(A) == C?

using StatsBase
O = [1 1 2 3 4 4 6]
C = counts(O, maximum(O))
A = foldl(vcat,[kron(ones(Int64, C[i]), i) for i in 1:length(C)])

4. How to compute averages using a sliding window over an array?

function moving_average(A, n=3)
  ret = cumsum(A)
  ret[n+1:end] = ret[n+1:end] - ret[1:end-n]
  return ret[n:end-1] / n
end
Z = 0:20
moving_average(Z, 3)

Artisan

1. Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])

Z = rand(0:5,100,3)
E = prod(Z[:,2:end] .== Z[:,1:end-1],2)
U = Z[find(~E), :]

2. Convert a vector of ints into a matrix binary representation.

I = [0 1 2 3 15 16 32 64 128]
B = foldl(hcat,[reverse(int(bool(i & (2 .^ (0:8))))) for i in I])'

Adept

1. Consider an arbitrary array, write a function that extracts a subpart with a fixed shape and centered on a given element (pad with a fill value when necessary)

# Not solve yet

Expert

1. Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A that contain elements of each row of B regardless of the order of the elements in B?

# I can't execute numpy version...

2. Extract all the contiguous 3x3 blocks from a random 10x10 matrix.

# Not solve yet

3. Create a 2D array subclass such that Z[i,j] == Z[j,i]

# There is Symmetric class in julia but immutable
# https://github.com/JuliaLang/julia/blob/master/base/linalg/symmetric.jl
# See also: https://github.com/JuliaLang/julia/pull/1533

4. Consider a set of p matrices with shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of the p matrix products at once? (result has shape (n,1))

# Author: Alireza Nejati
p, n = 10, 20
M = ones(n,n,p)
V = ones(n,p)
S = reduce(+, [M[i,:,j]*V[i] for i = 1:n, j = 1:p])'
S

Master

1. Given a two dimensional array, how to extract unique rows?

Z = rand(0:2, 6,3)
uZ = unique(Z,1)

Archmaster