MATLAB–Python–Julia cheatsheet

Dependencies and Setup

In the Python code we assume that you have already run import numpy as np

In the Julia, we assume you are using v1.0.2 or later with Compat v1.3.0 or later and have run using LinearAlgebra, Statistics, Compat

Creating Vectors

Operation

MATLAB

Python

Julia

Row vector: size (1, n)

A = [1 2 3]
A = np.array([1, 2, 3]).reshape(1, 3)
A = [1 2 3]

Column vector: size (n, 1)

A = [1; 2; 3]
A = np.array([1, 2, 3]).reshape(3, 1)
A = [1 2 3]'

1d array: size (n, )

Not possible

A = np.array([1, 2, 3])
A = [1; 2; 3]

or

A = [1, 2, 3]

Integers from j to n with step size k

A = j:k:n
A = np.arange(j, n+1, k)
A = j:k:n

Linearly spaced vector of k points

A = linspace(1, 5, k)
A = np.linspace(1, 5, k)
A = range(1, 5,
length = k)

Creating Matrices

Operation

MATLAB

Python

Julia

Create a matrix

A = [1 2; 3 4]
A = np.array([[1, 2], [3, 4]])
A = [1 2; 3 4]

2 x 2 matrix of zeros

A = zeros(2, 2)
A = np.zeros((2, 2))
A = zeros(2, 2)

2 x 2 matrix of ones

A = ones(2, 2)
A = np.ones((2, 2))
A = ones(2, 2)

2 x 2 identity matrix

A = eye(2, 2)
A = np.eye(2)
A = I # will adopt
# 2x2 dims if demanded by
# neighboring matrices

Diagonal matrix

A = diag([1 2 3])
A = np.diag([1, 2, 3])
A = Diagonal([1, 2,
    3])

Uniform random numbers

A = rand(2, 2)
A = np.random.rand(2, 2)
A = rand(2, 2)

Normal random numbers

A = randn(2, 2)
A = np.random.randn(2, 2)
A = randn(2, 2)

Sparse Matrices

A = sparse(2, 2)
A(1, 2) = 4
A(2, 2) = 1
from scipy.sparse import coo_matrix

A = coo_matrix(([4, 1],
                ([0, 1], [1, 1])),
                shape=(2, 2))
using SparseArrays
A = spzeros(2, 2)
A[1, 2] = 4
A[2, 2] = 1

Tridiagonal Matrices

A = [1 2 3 NaN;
     4 5 6 7;
     NaN 8 9 0]
spdiags(A',[-1 0 1], 4, 4)
import sp.sparse as sp
diagonals = [[4, 5, 6, 7], [1, 2, 3], [8, 9, 10]]
sp.diags(diagonals, [0, -1, 2]).toarray()
x = [1, 2, 3]
y = [4, 5, 6, 7]
z = [8, 9, 10]
Tridiagonal(x, y, z)

Manipulating Vectors and Matrices

Operation

MATLAB

Python

Julia

Transpose

A.'
A.T
transpose(A)

Complex conjugate transpose (Adjoint)

A'
A.conj()
A'

Concatenate horizontally

A = [[1 2] [1 2]]

or

A = horzcat([1 2], [1 2])
B = np.array([1, 2])
A = np.hstack((B, B))
A = [[1 2] [1 2]]

or

A = hcat([1 2], [1 2])

Concatenate vertically

A = [[1 2]; [1 2]]

or

A = vertcat([1 2], [1 2])
B = np.array([1, 2])
A = np.vstack((B, B))
A = [[1 2]; [1 2]]

or

A = vcat([1 2], [1 2])

Reshape (to 5 rows, 2 columns)

A = reshape(1:10, 5, 2)
A = A.reshape(5, 2)
A = reshape(1:10, 5, 2)

Convert matrix to vector

A(:)
A = A.flatten()
A[:]

Flip left/right

fliplr(A)
np.fliplr(A)
reverse(A, dims = 2)

Flip up/down

flipud(A)
np.flipud(A)
reverse(A, dims = 1)

Repeat matrix (3 times in the row dimension, 4 times in the column dimension)

repmat(A, 3, 4)
np.tile(A, (4, 3))
repeat(A, 3, 4)

Preallocating/Similar

x = rand(10)
y = zeros(size(x, 1), size(x, 2))

N/A similar type

x = np.random.rand(3, 3)
y = np.empty_like(x)

# new dims
y = np.empty((2, 3))
x = rand(3, 3)
y = similar(x)
# new dims
y = similar(x, 2, 2)

Broadcast a function over a collection/matrix/vector

f = @(x) x.^2
g = @(x, y) x + 2 + y.^2
x = 1:10
y = 2:11
f(x)
g(x, y)

Functions broadcast directly

def f(x):
    return x**2
def g(x, y):
    return x + 2 + y**2
x = np.arange(1, 10, 1)
y = np.arange(2, 11, 1)
f(x)
g(x, y)

Functions broadcast directly

f(x) = x^2
g(x, y) = x + 2 + y^2
x = 1:10
y = 2:11
f.(x)
g.(x, y)

Accessing Vector/Matrix Elements

Operation

MATLAB

Python

Julia

Access one element

A(2, 2)
A[1, 1]
A[2, 2]

Access specific rows

A(1:4, :)
A[0:4, :]
A[1:4, :]

Access specific columns

A(:, 1:4)
A[:, 0:4]
A[:, 1:4]

Remove a row

A([1 2 4], :)
A[[0, 1, 3], :]
A[[1, 2, 4], :]

Diagonals of matrix

diag(A)
np.diag(A)
diag(A)

Get dimensions of matrix

[nrow ncol] = size(A)
nrow, ncol = np.shape(A)
nrow, ncol = size(A)

Mathematical Operations

Operation

MATLAB

Python

Julia

Dot product

dot(A, B)
np.dot(A, B) or A @ B
dot(A, B)

A  B # \cdot<TAB>

Matrix multiplication

A * B
A @ B
A * B

Inplace matrix multiplication

Not possible

x = np.array([1, 2]).reshape(2, 1)
A = np.array(([1, 2], [3, 4]))
y = np.empty_like(x)
np.matmul(A, x, y)
x = [1, 2]
A = [1 2; 3 4]
y = similar(x)
mul!(y, A, x)

Element-wise multiplication

A .* B
A * B
A .* B

Matrix to a power

A^2
np.linalg.matrix_power(A, 2)
A^2

Matrix to a power, elementwise

A.^2
A**2
A.^2

Inverse

inv(A)

or

A^(-1)
np.linalg.inv(A)
inv(A)

or

A^(-1)

Determinant

det(A)
np.linalg.det(A)
det(A)

Eigenvalues and eigenvectors

[vec, val] = eig(A)
val, vec = np.linalg.eig(A)
val, vec = eigen(A)

Euclidean norm

norm(A)
np.linalg.norm(A)
norm(A)

Solve linear system \(Ax=b\) (when \(A\) is square)

A\b
np.linalg.solve(A, b)
A\b

Solve least squares problem \(Ax=b\) (when \(A\) is rectangular)

A\b
np.linalg.lstsq(A, b)
A\b

Sum / max / min

Operation

MATLAB

Python

Julia

Sum / max / min of each column

sum(A, 1)
max(A, [], 1)
min(A, [], 1)
sum(A, 0)
np.amax(A, 0)
np.amin(A, 0)
sum(A, dims = 1)
maximum(A, dims = 1)
minimum(A, dims = 1)

Sum / max / min of each row

sum(A, 2)
max(A, [], 2)
min(A, [], 2)
sum(A, 1)
np.amax(A, 1)
np.amin(A, 1)
sum(A, dims = 2)
maximum(A, dims = 2)
minimum(A, dims = 2)

Sum / max / min of entire matrix

sum(A(:))
max(A(:))
min(A(:))
np.sum(A)
np.amax(A)
np.amin(A)
sum(A)
maximum(A)
minimum(A)

Cumulative sum / max / min by row

cumsum(A, 1)
cummax(A, 1)
cummin(A, 1)
np.cumsum(A, 0)
np.maximum.accumulate(A, 0)
np.minimum.accumulate(A, 0)
cumsum(A, dims = 1)
accumulate(max, A, dims = 1)
accumulate(min, A, dims = 1)

Cumulative sum / max / min by column

cumsum(A, 2)
cummax(A, 2)
cummin(A, 2)
np.cumsum(A, 1)
np.maximum.accumulate(A, 1)
np.minimum.accumulate(A, 1)
cumsum(A, dims = 2)
accumulate(max, A, dims = 2)
accumulate(min, A, dims = 2)

Programming

Operation

MATLAB

Python

Julia

Comment one line

% This is a comment
# This is a comment
# This is a comment

Comment block

%{
Comment block
%}
# Block
# comment
# following PEP8
#=
Comment block
=#

For loop

for i = 1:N
   % do something
end
for i in range(n):
    # do something
for i in 1:N
   # do something
end

While loop

while i <= N
   % do something
end
while i <= N:
    # do something
while i <= N
   # do something
end

If

if i <= N
   % do something
end
if i <= N:
   # do something
if i <= N
   # do something
end

If / else

if i <= N
   % do something
else
   % do something else
end
if i <= N:
    # do something
else:
    # so something else
if i <= N
   # do something
else
   # do something else
end

Print text and variable

x = 10
fprintf('x = %d \n', x)
x = 10
print(f'x = {x}')
x = 10
println("x = $x")

Function: anonymous

f = @(x) x^2
f = lambda x: x**2
f = x -> x^2
# can be rebound

Function

function out  = f(x)
   out = x^2
end
def f(x):
    return x**2
function f(x)
   return x^2
end

f(x) = x^2 # not anon!

Tuples

t = {1 2.0 "test"}
t{1}

Can use cells but watch performance

t = (1, 2.0, "test")
t[0]
t = (1, 2.0, "test")
t[1]

Named Tuples/ Anonymous Structures

m.x = 1
m.y = 2

m.x
from collections import namedtuple

mdef = namedtuple('m', 'x y')
m = mdef(1, 2)

m.x
# vanilla
m = (x = 1, y = 2)
m.x

# constructor
using Parameters
mdef = @with_kw (x=1, y=2)
m = mdef() # same as above
m = mdef(x = 3)

Closures

a = 2.0
f = @(x) a + x
f(1.0)
a = 2.0
def f(x):
    return a + x
f(1.0)
a = 2.0
f(x) = a + x
f(1.0)

Inplace Modification

function f(out, x)
     out = x.^2
end
x = rand(10)
y = zeros(length(x), 1)
f(y, x)
def f(x):
    x **=2
    return

x = np.random.rand(10)
f(x)
function f!(out, x)
    out .= x.^2
end
x = rand(10)
y = similar(x)
f!(y, x)