Main Page

Creation
Combination
Removal
Indexing
Size and Shape
Resize and Reshape
Element Wise Operations
Comprehension
Broadcasting

Vector and Matrix

Creation

Empty vector

Matlab (2020b)	Julia (1.6)
`[]`	`[]`

Row vector

Matlab (2020b)	Julia (1.6)
`[1 2 3] [1, 2, 3]`	`[1 2 3] # Matrix with 1 row # 1×3 Matrix{Int64}: # 1 2 3`

Column vector

Matlab (2020b)	Julia (1.6)
`[1; 2; 3]`	`[1; 2; 3] # comma in between makes it a vector (column) [1, 2, 3] # 3-element Vector{Int64}: # 1 # 2 # 3`

Assignment

Matlab (2020b)	Julia (1.6)
`% copy by value a = b` copy by value is the only assignment possible in matlab, although it is technically assigned by reference until change on `b` is requested.	`# copy by value a = copy(b) # copy by reference a = b`

Range of numbers

Matlab (2020b)	Julia (1.6)
Not really a concept of range of numbers as in Julia	`# range of numbers between 1 to 3 1:3 # range of numbers between 1 to 10 with step of 2 1:2:10`

Explicit range of numbers

Matlab (2020b)	Julia (1.6)
`1:3 % [1 2 3] 1:2:10 % [1 3 5 7 9]`	`collect(1:3)' collect(1:2:10)' # Note: transpose (') to make same dimension as in matlab, which is row vector, since collect returns column vector`

NaN and Inf

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`nan(a) NaN(a) nan(a, b) NaN(a, b) inf(a) Inf(a) inf(a, b) Inf(a, b)`	`# needs explicit dimension repeat([NaN], a, a) repeat([NaN], a, b) # needs explicit dimension repeat([Inf], a, a) repeat([Inf], a, b)`

nan(a)
NaN(a)

nan(a, b)
NaN(a, b)

inf(a)
Inf(a)

inf(a, b)
Inf(a, b)

# needs explicit dimension
repeat([NaN], a, a)

repeat([NaN], a, b)


# needs explicit dimension
repeat([Inf], a, a)

repeat([Inf], a, b)

Built in functions

Matlab (2020b)	Julia (1.6)	Notes
`zeros(m)`	`zeros(m, m)`
`zeros(m, n)`	`zeros(m, n)`
`uint8(zeros(m))`	`zeros(UInt8, m, m)`	zero numbers with defined type, e.g. UInt8
`uint8([0 0 0]])`	`UInt8[0 0 0]`	zero numbers with defined type, e.g. UInt8
`ones(m)`	`ones(m, m)`	Types can also be specified, see zeros
`ones(m, n)`	`ones(m, n)`	Types can also be specified, see zeros
`a = eye(m)`	`a = I(m)`	Identity matrix, needs `using LinearAlgebra` in Julia
`diag(x)`	`Diagonal(x)`	create diagonal matrix
`rand(m)`	`rand(m, m)`	Julia needs explicit dimension
`rand(m, 1)`	`rand(m)`	Julia returns column vector
`rand(m, 1)`	`rand(m, 1)`	Julia returns matrix size (m, 1)
`rand(m, n)`	`rand(m, n)`
`randn(m)`	`randn(m, m)`	Julia needs explicit dimension
`randn(m, n)`	`randn(m, n)`
`true(m)`	`trues(m, m)`	Julia needs explicit dimension
`true(m, n)`	`trues(m, n)`
`false(m)`	`falses(m, m)`	Julia needs explicit dimension
`false(m, n)`	`falses(m, n)`

Combination

Horizontal concatenation

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`% Concatenate without comma (,) [[1 2] [3 4]] % Concatenate with horzcat horzcat([1 2], [3 4]) % Concatenate with comma (,) [[1, 2], [3, 4]]`	`# Concatenate without comma (,) [[1 2] [3 4]] # Concatenate with hcat hcat([1 2], [3 4]) # Concatenating with comma will concatenate vectors [[1 2], [3 4]] # 2-element Vector{Matrix{Int64}}: # [1 2] # [3 4] [[1; 2], [3; 4]] # 2-element Vector{Vector{Int64}}: # [1, 2] # [3, 4] [[1, 2], [3, 4]] # 2-element Vector{Vector{Int64}}: # [1, 2] # [3, 4]`

% Concatenate without comma (,)
[[1 2] [3 4]]

% Concatenate with horzcat
horzcat([1 2], [3 4])

% Concatenate with comma (,)
[[1, 2], [3, 4]]

# Concatenate without comma (,)
[[1 2] [3 4]]

# Concatenate with hcat
hcat([1 2], [3 4])

# Concatenating with comma will concatenate vectors
[[1 2], [3 4]]
# 2-element Vector{Matrix{Int64}}:
#  [1 2]
#  [3 4]

[[1; 2], [3; 4]]
# 2-element Vector{Vector{Int64}}:
#  [1, 2]
#  [3, 4]

[[1, 2], [3, 4]]
# 2-element Vector{Vector{Int64}}:
#  [1, 2]
#  [3, 4]

Vertical concatenation

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`% Concatenate with semicolon (;) [[1; 2], [3; 4]] % Concatenate with vertcat vertcat([1; 2], [3; 4])`	`# Concatenate with semicolon (;) [[1; 2]; [3; 4]] # Concatenate with vcat vcat([1; 2], [3; 4]) # [1,2] and [3,4] are column vectors [[1, 2]; [3, 4]] vcat([1, 2], [3, 4]) # 4-element Vector{Int64}: # 1 # 2 # 3 # 4`

% Concatenate with semicolon (;)
[[1; 2], [3; 4]]

% Concatenate with vertcat
vertcat([1; 2], [3; 4])

# Concatenate with semicolon (;)
[[1; 2]; [3; 4]]

# Concatenate with vcat
vcat([1; 2], [3; 4])

# [1,2] and [3,4] are column vectors
[[1, 2]; [3, 4]]
vcat([1, 2], [3, 4])
# 4-element Vector{Int64}:
#  1
#  2
#  3
#  4

Horizontal concatenation of column vectors

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`% Comma or space to append horizontally [[1; 2] [3; 4]] [[1; 2], [3; 4]] horzcat([1; 2], [3; 4]) % All above will return the same % ans = % % 1 3 % 2 4`	`# DO NOT use comma to append horizontally # comma makes column vector [[1; 2] [3; 4]] [[1, 2] [3, 4]] hcat([1; 2], [3; 4]) # All above will return the same # 2×2 Matrix{Int64}: # 1 3 # 2 4 # Otherwise, using comma returns vector of vector [[1; 2], [3; 4]] # 2-element Vector{Vector{Int64}}: # [1, 2] # [3, 4]`

% Comma or space to append horizontally
[[1; 2] [3; 4]]
[[1; 2], [3; 4]]

horzcat([1; 2], [3; 4])

% All above will return the same
% ans =
% 
%      1     3
%      2     4

# DO NOT use comma to append horizontally
# comma makes column vector
[[1; 2] [3; 4]]
[[1, 2] [3, 4]] 

hcat([1; 2], [3; 4])

# All above will return the same
# 2×2 Matrix{Int64}:
#  1  3
#  2  4

# Otherwise, using comma returns vector of vector
[[1; 2], [3; 4]]
# 2-element Vector{Vector{Int64}}:
#  [1, 2]
#  [3, 4]

Concatenating range

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`[1:3, 4:6] % Result: [1 2 3 4 5 6] [(1:3)', (4:6)'] % ans = % % 1 4 % 2 5 % 3 6 [1:3, 4:6]' % With transpose % ans = % % 1 % 2 % 3 % 4 % 5 % 6 [(1:3)'; (4:6)'] % With transpose % ans = % % 1 % 2 % 3 % 4 % 5 % 6`	`# Range notation returns column vector, tranpose is needed # No comma to concatenate horizontally [(1:3)' (4:6)'] # Result: [1 2 3 4 5 6] [1:3; 4:6]' # Result: [1 2 3 4 5 6] [1:3 4:6] # 3×2 Matrix{Int64}: # 1 4 # 2 5 # 3 6 [1:3; 4:6] # 6-element Vector{Int64}: # 1 # 2 # 3 # 4 # 5 # 6 # Comma returns vector of range, instead of the individual numbers [1:3, 4:6] #2-element Vector{UnitRange{Int64}}: # 1:3 # 4:6`

[1:3, 4:6] % Result: [1 2 3 4 5 6]

[(1:3)', (4:6)']
% ans =
% 
%      1     4
%      2     5
%      3     6

[1:3, 4:6]' % With transpose
% ans =
% 
%      1
%      2
%      3
%      4
%      5
%      6

[(1:3)'; (4:6)'] % With transpose
% ans =
% 
%      1
%      2
%      3
%      4
%      5
%      6

# Range notation returns column vector, tranpose is needed
# No comma to concatenate horizontally
[(1:3)' (4:6)'] # Result: [1 2 3 4 5 6]

[1:3; 4:6]' # Result: [1 2 3 4 5 6]

[1:3 4:6]
# 3×2 Matrix{Int64}:
#  1  4
#  2  5
#  3  6

[1:3; 4:6]
# 6-element Vector{Int64}:
#  1
#  2
#  3
#  4
#  5
#  6

# Comma returns vector of range, instead of the individual numbers
[1:3, 4:6]
#2-element Vector{UnitRange{Int64}}:
# 1:3
# 4:6

Expand matrix

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`A = [10 20 30; 60 70 80]; A(3, 4) = 1 % A = % % 10 20 30 0 % 60 70 80 0 % 0 0 0 1`	`# expanding matrix in Julia is done by initializing matrix with larger size, and copy the first few elements into it A = [10 20 30; 60 70 80]; B = zeros(eltype(A), 3, 4); B[1:2, 1:3] = A; A = B; A[3,4] = 1; A # 3×4 Matrix{Int64}: # 10 20 30 0 # 60 70 80 0 # 0 0 0 1 # Directly expanding matrix result in error A = [10 20 30; 60 70 80]; A[3,4] = 1; # ERROR: BoundsError: attempt to access 2×3 Matrix{Int64} at index [3, 4]`

A = [10  20  30; 60  70  80];
A(3, 4) = 1
% A =
% 
%     10    20    30     0
%     60    70    80     0
%      0     0     0     1

# expanding matrix in Julia is done by initializing matrix with larger size, and copy the first few elements into it
A = [10  20  30; 60  70  80];
B = zeros(eltype(A), 3, 4);
B[1:2, 1:3] = A;
A = B;
A[3,4] = 1;
A
# 3×4 Matrix{Int64}:
#  10  20  30  0
#  60  70  80  0
#   0   0   0  1

# Directly expanding matrix result in error
A = [10  20  30; 60  70  80];
A[3,4] = 1;
# ERROR: BoundsError: attempt to access 2×3 Matrix{Int64} at index [3, 4]

Removal

Remove single row

Matlab (2020b)	Julia (1.6)
`A = rand(3, 3) A(2, :) = []`	`A = rand(3, 3) A = A[1:end .!= 2, :]`

Remove single column

Matlab (2020b)	Julia (1.6)
`% Matlab (2020b) A = rand(3, 3) A(:, 2) = []`	`# Julia (1.6) A = rand(3, 3) A = A[:, 1:end .!= 2]`

Remove multiple rows

Matlab (2020b)	Julia (1.6)
`A = rand(4, 4) A([2, 3], :) = []`	`A = rand(4, 4) A = A[setdiff(1:end, [2, 3]), :]`

Remove multiple rows and column

Matlab (2020b)	Julia (1.6)
`A = rand(4, 4) % 2 steps removal, first row then column A([2, 3], :) = [] A(:, 1) = []`	`A = rand(4, 4) A = A[setdiff(1:end, [2, 3]), 1:end .!= 1]`

Remove dimension

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`A = rand(1, 2, 1, 3) % Remove all dimensions of length 1 A = squeeze(A)`	`A = rand(1, 2, 1, 3) # Remove all dimensions of length 1 dropdims(A, dims=tuple(findall(size(A) .== 1)...)) # remove dimension 3, if it has size 1 dropdims(A, dims=3) # error if dimension to be removed is not 1 dropdims(A, dims=2) # ERROR: ArgumentError: dropped dims must all be size 1`

A = rand(1, 2, 1, 3)

% Remove all dimensions of length 1
A = squeeze(A)

A = rand(1, 2, 1, 3)

# Remove all dimensions of length 1
dropdims(A, dims=tuple(findall(size(A) .== 1)...))

# remove dimension 3, if it has size 1
dropdims(A, dims=3)

# error if dimension to be removed is not 1
dropdims(A, dims=2)
# ERROR: ArgumentError: dropped dims must all be size 1

Indexing

Indexing bracket

Matlab (2020b)	Julia (1.6)
`% Matlab uses normal bracket () X = A(I_1, I_2, ..., I_n) % Note: A is n-dimensional array`	`# Julia uses square bracket [] X = A[I_1, I_2, ..., I_n] # Note: A is n-dimensional array`

Multi dimension indexing using range

Matlab (2020b)	Julia (1.6)
`A = rand(10, 10) % Matlab uses normal bracket () X = A(1:2:10, 2:2:10)`	`A = rand(10, 10) # Julia uses square bracket [] X = A[1:2:10, 2:2:10]`

Select a few rows and a few columns

Matlab (2020b)	Julia (1.6)
`A = rand(5, 5) % Matlab uses normal bracket () A([1, 3], [4, 5])`	`A = rand(5, 5) # Julia uses square bracket [] A[[1, 3], [4, 5]]`

Index with 'end' keyword

Matlab (2020b)	Julia (1.6)
`A = rand(5, 5) A(2:3, 2:end-1)`	`A = rand(5, 5) A[2:3, 2:end-1]`

Select no element

Matlab (2020b)	Julia (1.6)
`A = rand(5, 5) A([])`	`A = rand(5, 5) A[[]]`

Select specific row

Matlab (2020b)	Julia (1.6)
`A = rand(5, 5) A(2, :)`	`A = rand(5, 5) (A[2, :])' # Julia always returns column vector, needs transpose`

Select specific column

Matlab (2020b)	Julia (1.6)
`A = rand(5, 5) A(:, 2)`	`A = rand(5, 5) A[:, 2]`

Vectorizing matrix

Matlab (2020b)	Julia (1.6)
`A = rand(2, 3) A(:)`	`A = rand(2, 3) A[:]`

Indexing by boolean

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`A = rand(1, 4) A([true, true, false, false]) % returns as row vector, since A is row vector A = rand(4, 1) A([true, true, false, false]) % returns as column vector, since A is column vector`	`A = rand(1, 4) (A[[true, true, false, false]])' # Always returns column vector regardless of A size. Needs transpose to get row vector A = rand(4, 1) A[[true, true, false, false]] # Always returns column vector regardless of A size.`

A = rand(1, 4)
A([true, true, false, false])
% returns as row vector, since A is row vector

A = rand(4, 1)
A([true, true, false, false])
% returns as column vector, since A is column vector

A = rand(1, 4)
(A[[true, true, false, false]])'
# Always returns column vector regardless of A size. Needs transpose to get row vector

A = rand(4, 1)
A[[true, true, false, false]]
# Always returns column vector regardless of A size.

Assigning parts of matrix

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`% Number of element in X must be the same as the place in A to fill in A(I_1, I_2, ..., I_n) = X`	`# Number of element in X must be the same as the place in A to fill in A[I_1, I_2, ..., I_n] = X # Also uses dot notation A[I_1, I_2, ..., I_n] .= X`

% Number of element in X must be the same as the place in A to fill in
A(I_1, I_2, ..., I_n) = X

# Number of element in X must be the same as the place in A to fill in
A[I_1, I_2, ..., I_n] = X

# Also uses dot notation
A[I_1, I_2, ..., I_n] .= X

Size and Shape

Finding element type

Matlab (2020b)	Julia (1.6)
`class(A)`	`eltype(A)`

Number of element, dimension, shape

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`A = rand(2, 3) numel(A) % Result 6 length(A) % Result 3 (largest dimension) ndims(A) % Result 2 size(A) % Result [2, 3] size(A, 1) % Result 2 size(A, 2) % Result 3`	`A = rand(2, 3) length(A) # Result 6 ndims(A) # Result 2 size(A) # Result (2, 3) tuple size(A, 1) # Result 2 size(A, 2) # Result 3`

A = rand(2, 3)
numel(A)   % Result 6
length(A)  % Result 3 (largest dimension)
ndims(A)   % Result 2
size(A)    % Result [2, 3]
size(A, 1) % Result 2
size(A, 2) % Result 3

A = rand(2, 3)
length(A)  # Result 6
ndims(A)   # Result 2
size(A)    # Result (2, 3) tuple
size(A, 1) # Result 2
size(A, 2) # Result 3

Testing matrix

# Julia (1.6)

# matlab isempty(A)
isempty(A)

# matlab isscalar(A)
isa(A, Union{Number, AbstractString, Char, Bool})

# matlab issorted(A)
issorted(A)

# matlab isvector(A)
isa(A, Array) && (sum(size(A) .!= 1) <= 1)

# matlab ismatrix(A)
isa(A, Union{Array, Matrix}) && (sum(size(A) .!= 1) > 1)

# matlab isrow(A)
isa(A, Union{Array, Matrix}) && (sum((size(A) .!= 1)[setdiff(1:ndims(A), 2)]) == 0)

# matlab iscolumn(A)
isa(A, Union{Array, Matrix}) && (ndims(A) == 1 || sum(size(A)[2:end] .!= 1) == 0)

Functions not available in Matlab

Julia (1.6)	Notes
`axes(A)`	a tuple containing the valid indices of A
`axes(A, n)`	a range expressing the valid indices along dimension n
`eachindex(A)`	an efficient iterator for visiting each position in A
`stride(A, k)`	the stride (linear index distance between adjacent elements) along dimension k
`strides(A)`	a tuple of the strides in each dimension

Resize and Reshape

Matlab (2020b)	Julia (1.6)	Notes
`reshape(A, 3, 2)`	`reshape(A, 3, 2)`	Reshape into different dimension
`reshape(A, [], 1)`	`reshape(A, :, 1)`	reshape into column vector
`reshape(A, 1, [])`	`reshape(A, 1, :)`	reshape into row vector
`transpose(A)`	`transpose(A)`	Transpose vector or matrix
`A'` `ctranspose(A)`	`A'` `adjoint(A)`	Complex conjugate transpose
`flip(A)`	`reverse(A, dims=1)`	Flip order of elements
`flip(A, 2)`	`reverse(A, dims=2)`	Flip order of elements in 2nd dimension
`rot90(A)`	`rotl90(A)`	Rotate array 90 degrees counterclockwise (left)
`rot90(A, 3)`	`rotl90(A, 3)` `rotr90(A)`	Rotate array 270 degrees counterclockwise (left) or 90 degree clockwise (right)
`rot90(A, 2)`	`rotl90(A, 2)` `rotr90(A, 2)` `rot180(A)`	Rotate array 180 degrees
`permute(A, [m, n, p])`	`permutedims(A, (m, n, p))`	Permute array dimensions
`circshift(A, n)`	`circshift(A, n)`	Shift array circularly
`circshift(A, n, m)`	`circshift(A, (n, m)`)	Shift matrix circularly. Julia uses tuple
`shiftdim(A)`		Shift array dimensions

Sort

Sorting vector and matrix

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`A = rand(4, 1) sort(A) sort(A, 'descend') % sort descending sort(A, 1) % works on vector and matrix sort(A, 2) % works on vector and matrix`	`A = rand(4) sort(A) sort(A, rev=true) # sort descending sort(A, dims=1) # error on using dimension on vector # ERROR: MethodError: no method matching sort!(::Vector{Float64}; dims=1) A = rand(4, 1) # this will return matrix, not vector sort(A) # this will fail # ERROR: UndefKeywordError: keyword argument dims not assigned sort(A, dims=1) # This will work. Julia needs explicit dimension for matrix sort(A, dims=2) # This will work. Julia needs explicit dimension for matrix`

A = rand(4, 1)

sort(A)
sort(A, 'descend') % sort descending

sort(A, 1) % works on vector and matrix
sort(A, 2) % works on vector and matrix

A = rand(4)

sort(A)
sort(A, rev=true) # sort descending

sort(A, dims=1) # error on using dimension on vector
# ERROR: MethodError: no method matching sort!(::Vector{Float64}; dims=1)

A = rand(4, 1) # this will return matrix, not vector
sort(A) # this will fail
# ERROR: UndefKeywordError: keyword argument dims not assigned

sort(A, dims=1) # This will work. Julia needs explicit dimension for matrix
sort(A, dims=2) # This will work. Julia needs explicit dimension for matrix

Outputing index of the sorted matrix

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`A = rand(4, 1) [B, idx] = sort(A) A = rand(4, 3) [B, idx] = sort(A) % also works on matrix`	`A = rand(4) idx = sortperm(A) B = A[idx] A = rand(4, 3) idx = sortperm(A) # Throw error on matrix # ERROR: MethodError: no method matching sortperm(::Matrix{Float64})`

A = rand(4, 1)
[B, idx] = sort(A)

A = rand(4, 3)
[B, idx] = sort(A) % also works on matrix

A = rand(4)
idx = sortperm(A)
B = A[idx]

A = rand(4, 3)
idx = sortperm(A) # Throw error on matrix
# ERROR: MethodError: no method matching sortperm(::Matrix{Float64})

Sort matrix by rows

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`A = rand(4, 3) % sort on first column sortrows(A, 1) % sort on 2nd column sortrows(A, 2) % sort on first column then 3rd column sortrows(A, [1, 3])`	`A = rand(4, 3) # sort on first column sortslices(A, dims=1, lt=(x, y)->isless(x[1], y[1])) # sort on 2nd column sortslices(A, dims=1, lt=(x, y)->isless(x[2], y[2])) # sort on first column then 3rd column sortslices(A, dims=1, lt=(x, y)->(isless(x[1], y[1]) \|\| (isequal(x[1], y[1]) && isless(x[3], y[3]))))`

A = rand(4, 3)

% sort on first column
sortrows(A, 1)

% sort on 2nd column
sortrows(A, 2)

% sort on first column then 3rd column
sortrows(A, [1, 3])

A = rand(4, 3)

# sort on first column
sortslices(A, dims=1, lt=(x, y)->isless(x[1], y[1]))

# sort on 2nd column
sortslices(A, dims=1, lt=(x, y)->isless(x[2], y[2]))

# sort on first column then 3rd column
sortslices(A, dims=1, lt=(x, y)->(isless(x[1], y[1]) || (isequal(x[1], y[1]) && isless(x[3], y[3]))))

Element Wise Operations

Matlab (2020b)	Julia (1.6)	Notes
`+x`	`+x`	unary plus
`-x`	`-x`	element wise negation
`x + y`	`x + y` `x .+ y`	element wise addition. If x and y has the same number of element but different dimension, for example x is row vector and y is column vector, then x + y in Julia gives the same answer in Matlab. Otherwise x + y in Julia throws error and Matlab do auto expansion.
`x - y`	`x - y` `x .- y`	element wise subtraction. Same rule as .+ see above
`x .* y`	`x .* y`	element wise multiplication
`x ./ y`	`x ./ y`	element wise division
`floor(x ./ y)`	`x .÷ y`	element wise integer divide truncated to an integer
`x .\ y`	`x .\ y`	element wise inverse divide equivalent to y / x
`x .^ y`	`x .^ y`	element wise raises x to the yth power
`arrayfun(f, x)`	`f.(x)`	element wise f. Sometimes f(x) in matlab gives the same result when x is array

Element wise operation on function (example)

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`x = rand(4, 1) % works for both x as number or as vector sin(x) arrayfun(@sin, x) a = rand(4, 3) b = rand(4, 3) % works for both x as number or as vector max(a, b) arrayfun(@(x, y) max(x,y), a, b)`	`x = rand(4, 1) sin(x) # ERROR: MethodError: no method matching sin(::Vector{Float64}) sin.(x) # must use element wise operation if x is vector or matrix a = rand(4, 3) b = rand(4, 3) max(a, b) # ERROR: MethodError: no method matching isless(::Matrix{Float64}, ::Matrix{Float64}) max.(a, b) # must use element wise operation if a and b is vector or matrix`

x = rand(4, 1)

% works for both x as number or as vector
sin(x)
arrayfun(@sin, x)

a = rand(4, 3)
b = rand(4, 3)

% works for both x as number or as vector
max(a, b)
arrayfun(@(x, y) max(x,y), a, b)

x = rand(4, 1)

sin(x) # ERROR: MethodError: no method matching sin(::Vector{Float64})
sin.(x) # must use element wise operation if x is vector or matrix

a = rand(4, 3)
b = rand(4, 3)

max(a, b) # ERROR: MethodError: no method matching isless(::Matrix{Float64}, ::Matrix{Float64})
max.(a, b) # must use element wise operation if a and b is vector or matrix

Element wise operation on comparison (example)

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`a = rand(4, 1) a == a % return [true, true, true, true] b = a b(3) = a(3) - 1 a == b % return [true, true, false, true] a > b % return [false, false, true, false]`	`a = rand(4, 1) a == a # return true, equivalent with all(a .== a) a .== a # return [true, true, true, true] b = copy(a) b[3] = a[3] - 1 a == b # return false a .== b # return [true, true, false, true] a > b # ERROR: MethodError: no method matching isless(::Matrix{Float64}, ::Matrix{Float64}) a .> b # return [false, false, true, false]`

a = rand(4, 1)

a == a % return [true, true, true, true]

b = a
b(3) = a(3) - 1

a == b % return [true, true, false, true]

a > b % return [false, false, true, false]

a = rand(4, 1)

a == a # return true, equivalent with all(a .== a)
a .== a # return [true, true, true, true]

b = copy(a)
b[3] = a[3] - 1

a == b # return false
a .== b # return [true, true, false, true]

a > b # ERROR: MethodError: no method matching isless(::Matrix{Float64}, ::Matrix{Float64})
a .> b # return [false, false, true, false]

Comprehension

Sum a series

Matlab (2020b)	Julia (1.6)
`sum(1 ./ ((1:1000) .^ 2))`	`sum(1/n^2 for n=1:1000)`

Weighted average of current element and its left and right neighbor along a 1-d grid

Matlab (2020b)	Julia (1.6)
`x = rand(4, 1) arrayfun(@(x, y, z) 0.25x + 0.5y + 0.25*z, x(1:end-2), x(2:end-1), x(3:end))`	`x = rand(4, 1) [ 0.25x[i-1] + 0.5x[i] + 0.25*x[i+1] for i=2:length(x)-1 ]`

Loop and filter

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`% use for loop output = []; for i = 1:3 for j = 1:i if i+j == 4 output = [output; i, j]; end end end`	`# use list comprehension [(i,j) for i=1:3 for j=1:i if i+j == 4] # 2-element Vector{Tuple{Int64, Int64}}: # (2, 2) # (3, 1)`

% use for loop
output = [];
for i = 1:3
  for j = 1:i
    if i+j == 4
      output = [output; i, j];
    end
  end
end

# use list comprehension
[(i,j) for i=1:3 for j=1:i if i+j == 4]
# 2-element Vector{Tuple{Int64, Int64}}:
#  (2, 2)
#  (3, 1)

Functional programming

Matlab (2020b)	Julia (1.6)
	`map(tuple, (1/(i+j) for i=1:2, j=1:2), [1 3; 2 4]) # 2×2 Matrix{Tuple{Float64, Int64}}: # (0.5, 1) (0.333333, 3) # (0.333333, 2) (0.25, 4)`

Broadcasting

Expansion of matrix of different column size

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`a = rand(2,1) A = rand(2,3) a + A % matlab perform auto expansion % a = % % 0.7757 % 0.4868 % % % A = % % 0.4359 0.3063 0.5108 % 0.4468 0.5085 0.8176 % % % ans = % % 1.2116 1.0821 1.2865 % 0.9336 0.9953 1.3044`	`a = rand(2,1) A = rand(2,3) broadcast(+, a, A) # needs explicit broadcast # 2×1 Matrix{Float64}: # 0.4355140727705087 # 0.3300976619630358 # # 2×3 Matrix{Float64}: # 0.180913 0.490403 0.523406 # 0.786117 0.438144 0.310452 # # 2×3 Matrix{Float64}: # 0.616427 0.925917 0.95892 # 1.11622 0.768242 0.64055`

a = rand(2,1)
A = rand(2,3)

a + A % matlab perform auto expansion
% a =
% 
%     0.7757
%     0.4868
% 
% 
% A =
% 
%     0.4359    0.3063    0.5108
%     0.4468    0.5085    0.8176
% 
% 
% ans =
% 
%     1.2116    1.0821    1.2865
%     0.9336    0.9953    1.3044

a = rand(2,1)
A = rand(2,3)

broadcast(+, a, A) # needs explicit broadcast
# 2×1 Matrix{Float64}:
#  0.4355140727705087
#  0.3300976619630358
# 
# 2×3 Matrix{Float64}:
#  0.180913  0.490403  0.523406
#  0.786117  0.438144  0.310452
# 
# 2×3 Matrix{Float64}:
#  0.616427  0.925917  0.95892
#  1.11622   0.768242  0.64055

Expansion of matrix of different size

Matlab (2020b) Julia (1.6)

Matlab (2020b)	Julia (1.6)
`a = rand(2,1) b = rand(1,2) a + b % matlab perform auto expansion % a = % % 0.7948 % 0.6443 % % % b = % % 0.3786 0.8116 % % % ans = % % 1.1734 1.6064 % 1.0229 1.4559`	`a = rand(2,1) b = rand(1,2) broadcast(+, a, b) # needs explicit broadcast # 2×1 Matrix{Float64}: # 0.7805359041834159 # 0.21249440551207988 # # 1×2 Matrix{Float64}: # 0.986313 0.57324 # # 2×2 Matrix{Float64}: # 1.76685 1.35378 # 1.19881 0.785735`

a = rand(2,1)
b = rand(1,2)

a + b % matlab perform auto expansion
% a =
% 
%     0.7948
%     0.6443
% 
% 
% b =
% 
%     0.3786    0.8116
% 
% 
% ans =
% 
%     1.1734    1.6064
%     1.0229    1.4559

a = rand(2,1)
b = rand(1,2)

broadcast(+, a, b) # needs explicit broadcast
# 2×1 Matrix{Float64}:
#  0.7805359041834159
#  0.21249440551207988
# 
# 1×2 Matrix{Float64}:
#  0.986313  0.57324
# 
# 2×2 Matrix{Float64}:
#  1.76685  1.35378
#  1.19881  0.785735

Main Page

Contents

Vector and Matrix

Creation

Empty vector

Row vector

Column vector

Assignment

Range of numbers

Explicit range of numbers

NaN and Inf

Built in functions

Combination

Horizontal concatenation

Vertical concatenation

Horizontal concatenation of column vectors

Concatenating range

Expand matrix

Removal

Remove single row

Remove single column

Remove multiple rows

Remove multiple rows and column

Remove dimension

Indexing

Indexing bracket

Multi dimension indexing using range

Select a few rows and a few columns

Index with 'end' keyword

Select no element

Select specific row

Select specific column

Vectorizing matrix

Indexing by boolean

Assigning parts of matrix

Size and Shape

Finding element type

Number of element, dimension, shape

Testing matrix

Functions not available in Matlab

Resize and Reshape

Sort

Sorting vector and matrix

Outputing index of the sorted matrix

Sort matrix by rows

Element Wise Operations

Element wise operation on function (example)

Element wise operation on comparison (example)

Comprehension

Sum a series

Weighted average of current element and its left and right neighbor along a 1-d grid

Loop and filter

Functional programming

Broadcasting

Expansion of matrix of different column size

Expansion of matrix of different size