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MATLAB / Python (NumPy) Translation

by Josh Kaplan, Sep 12, 2017

Disclaimer: Most of the content here comes from mathesaurus.sf.net, reproduced here within the limitations of the copyright. The reproduced content is © 2006 Vidar Bronken Gundersen, mathesaurus.sf.net.

Some of the content below is modified and/or new content added. I will continue to add to this document as necessary.

Help

MATLAB/Octave Python Description
doc
help -i % browse with Info
help() Browse help interactively
help help or doc doc help Help on using help
help plot help(plot) or ?plot Help for a function
help splines or doc splines help(pylab) Help for a toolbox/library package
demo Demonstration examples

Searching available documentation

MATLAB/Octave Python Description
lookfor plot Search help files
help help(); modules [Numeric] List available packages
which plot help(plot) Locate functions

Using interactively

MATLAB/Octave Python Description
octave -q ipython -pylab Start session
TAB or M-? TAB Auto completion
foo(.m) execfile('foo.py') or run foo.py Run code from file
history hist -n Command history
diary on [..] diary off Save command history
exit or quit CTRL-D
CTRL-Z # windows
sys.exit()
End session

Operators

MATLAB/Octave Python Description
help - Help on operator syntax

Arithmetic operators

MATLAB/Octave Python Description
a=1; b=2; a=1; b=1 Assignment; defining a number
a + b a + b or add(a,b) Addition
a - b a - b or subtract(a,b) Subtraction
a * b a * b or multiply(a,b) Multiplication
a / b a / b or divide(a,b) Division
a .^ b a ** b
power(a,b)
pow(a,b)
Power, $a^b$
rem(a,b) a % b
remainder(a,b)
fmod(a,b)
Remainder
a+=1 a+=b or add(a,b,a) In place operation to save array creation overhead
factorial(a) Factorial, $n!$

Relational operators

MATLAB/Octave Python Description
a == b a == b or equal(a,b) Equal
a < b a < b or less(a,b) Less than
a > b a > b or greater(a,b) Greater than
a <= b a <= b or less_equal(a,b) Less than or equal
a >= b a >= b or greater_equal(a,b) Greater than or equal
a ~= b a != b or not_equal(a,b) Not Equal

Logical operators

MATLAB/Octave Python Description
a && b a and b Short-circuit logical AND
a || b a or b Short-circuit logical OR
a & b or and(a,b) logical_and(a,b) or a and b Element-wise logical AND
a | b or or(a,b) logical_or(a,b) or a or b Element-wise logical OR
xor(a, b) logical_xor(a,b) Logical EXCLUSIVE OR
~a or not(a)
~a or !a
logical_not(a) or not a Logical NOT
any(a) True if any element is nonzero
all(a) True if all elements are nonzero

root and logarithm

MATLAB/Octave Python Description
sqrt(a) math.sqrt(a) Square root
log(a) math.log(a) Logarithm, base $e$ (natural)
log10(a) math.log10(a) Logarithm, base 10
log2(a) math.log(a, 2) Logarithm, base 2 (binary)
exp(a) math.exp(a) Exponential function

Round off

MATLAB/Octave Python Description
round(a) around(a) or math.round(a) Round
ceil(a) ceil(a) Round up
floor(a) floor(a) Round down
fix(a) fix(a) Round towards zero

Mathematical constants

MATLAB/Octave Python Description
pi math.pi $\pi=3.141592$
exp(1) math.e or math.exp(1) $e=2.718281$

Missing values; IEEE-754 floating point status flags

MATLAB/Octave Python Description
NaN nan Not a Number
Inf inf Infinity, $\infty$
plus_inf Infinity, $+\infty$
minus_inf Infinity, $-\infty$
plus_zero Plus zero, $+0$
minus_zero Minus zero, $-0$

Complex numbers

MATLAB/Octave Python Description
i z = 1j Imaginary unit
z = 3+4i z = 3+4j or z = complex(3,4) A complex number, $3+4i$
abs(z) abs(3+4j) Absolute value (modulus)
real(z) z.real Real part
imag(z) z.imag Imaginary part
arg(z) Argument
conj(z) z.conj(); z.conjugate() Complex conjugate

Trigonometry

MATLAB/Octave Python Description
atan(a,b) atan2(b,a) Arctangent, $\arctan(b/a)$
hypot(x,y) Hypotenus; Euclidean distance

Generate random numbers

MATLAB/Octave Python Description
rand(1,10) random.random((10,))
random.uniform((10,))
Uniform distribution
2+5*rand(1,10) random.uniform(2,7,(10,))
Uniform: Numbers between 2 and 7
rand(6) random.uniform(0,1,(6,6))
Uniform: 6,6 array
randn(1,10) random.standard_normal((10,))
Normal distribution

Vectors

MATLAB/Octave Python Description
a=[2 3 4 5]; a=array([2,3,4,5]) Row vector, $1 \times n$-matrix
adash=[2 3 4 5]'; array([2,3,4,5])[:,NewAxis]
array([2,3,4,5]).reshape(-1,1)
r_[1:10,'c']
Column vector, $m \times 1$-matrix

Sequences

MATLAB/Octave Python Description
1:10 arange(1,11, dtype=Float)
range(1,11)
1,2,3, ... ,10
0:9 arange(10.) 0.0,1.0,2.0, ... ,9.0
1:3:10 arange(1,11,3) 1,4,7,10
10:-1:1 arange(10,0,-1) 10,9,8, ... ,1
10:-3:1 arange(10,0,-3) 10,7,4,1
linspace(1,10,7) linspace(1,10,7) Linearly spaced vector of n=7 points
reverse(a) a[::-1] or Reverse
a(:) = 3 a.fill(3), a[:] = 3 Set all values to same scalar value

Concatenation (vectors)

MATLAB/Octave Python Description
[a a] concatenate((a,a)) Concatenate two vectors
[1:4 a] concatenate((range(1,5),a), axis=1)

Repeating

MATLAB/Octave Python Description
[a a] concatenate((a,a)) 1 2 3, 1 2 3
a.repeat(3) or 1 1 1, 2 2 2, 3 3 3
a.repeat(a) or 1, 2 2, 3 3 3

Miss those elements out

MATLAB/Octave Python Description
a(2:end) a[1:] miss the first element
a([1:9]) miss the tenth element
a(end) a[-1] last element
a(end-1:end) a[-2:] last two elements

Maximum and minimum

MATLAB/Octave Python Description
max(a,b) maximum(a,b) pairwise max
max([a b]) concatenate((a,b)).max() max of all values in two vectors
[v,i] = max(a) v,i = a.max(0),a.argmax(0)

Vector multiplication

MATLAB/Octave Python Description
a.*a a*a Multiply two vectors
dot(u,v) dot(u,v) Vector dot product, $u \cdot v$

Matrices

MATLAB/Octave Python Description
a = [2 3;4 5] a = array([[2,3],[4,5]]) Define a matrix

Concatenation (matrices); rbind and cbind

MATLAB/Octave Python Description
[a ; b] concatenate((a,b), axis=0)
vstack((a,b))
Bind rows
[a , b] concatenate((a,b), axis=1)
hstack((a,b))
Bind columns
concatenate((a,b), axis=2)
dstack((a,b))
Bind slices (three-way arrays)
[a(:), b(:)] concatenate((a,b), axis=None) Concatenate matrices into one vector
[1:4 ; 1:4] concatenate((r_[1:5],r_[1:5])).reshape(2,-1)
vstack((r_[1:5],r_[1:5]))
Bind rows (from vectors)
[1:4 ; 1:4]' Bind columns (from vectors)

Array creation

MATLAB/Octave Python Description
zeros(3,5) zeros((3,5),Float) 0 filled array
zeros((3,5)) 0 filled array of integers
ones(3,5) ones((3,5),Float) 1 filled array
ones(3,5)*9 Any number filled array
eye(3) identity(3) Identity matrix
diag([4 5 6]) diag((4,5,6)) Diagonal
magic(3) Magic squares; Lo Shu
a = empty((3,3)) Empty array

Reshape and flatten matrices

MATLAB/Octave Python Description
reshape(1:6,3,2)'; arange(1,7).reshape(2,-1)
a.setshape(2,3)
Reshaping (rows first)
reshape(1:6,2,3); arange(1,7).reshape(-1,2).transpose() Reshaping (columns first)
a'(:) a.flatten() or Flatten to vector (by rows, like comics)
a(:) a.flatten(1)
Flatten to vector (by columns)
vech(a) Flatten upper triangle (by columns)

Shared data (slicing)

MATLAB/Octave Python Description
b = a b = a.copy() Copy of a

Indexing and accessing elements (Python: slicing)

MATLAB/Octave Python Description
a = [ 11 12 13 14 ...
21 22 23 24 ...
31 32 33 34 ]
a = array([[ 11, 12, 13, 14 ],
[ 21, 22, 23, 24 ],
[ 31, 32, 33, 34 ]])
Input is a 3,4 array
a(2,3) a[1,2] Element 2,3 (row,col)
a(1,:) a[0,] First row
a(:,1) a[:,0] First column
a([1 3],[1 4]); a.take([0,2]).take([0,3], axis=1)
Array as indices
a(2:end,:) a[1:,] All, except first row
a(end-1:end,:) a[-2:,] Last two rows
a(1:2:end,:) a[::2,:] Strides: Every other row
a[...,2] Third in last dimension (axis)
a(:,[1 3 4]) a.take([0,2,3],axis=1)
Remove one column
a.diagonal(offset=0) Diagonal

Assignment

MATLAB/Octave Python Description
a(:,1) = 99 a[:,0] = 99
a(:,1) = [99 98 97]' a[:,0] = array([99,98,97])
a(a>90) = 90; (a>90).choose(a,90)
a.clip(min=None, max=90)
Clipping: Replace all elements over 90
a.clip(min=2, max=5)
Clip upper and lower values

Transpose and inverse

MATLAB/Octave Python Description
a' a.conj().transpose()
Transpose
a.' or transpose(a) a.transpose() Non-conjugate transpose
det(a) linalg.det(a) or Determinant
inv(a) linalg.inv(a) or Inverse
pinv(a) linalg.pinv(a) Pseudo-inverse
norm(a) norm(a) Norms
eig(a) linalg.eig(a)[0]
Eigenvalues
svd(a) linalg.svd(a)
Singular values
chol(a) linalg.cholesky(a) Cholesky factorization
[v,l] = eig(a) linalg.eig(a)[1]
Eigenvectors
rank(a) rank(a) Rank

Sum

MATLAB/Octave Python Description
sum(a) a.sum(axis=0) Sum of each column
sum(a') a.sum(axis=1) Sum of each row
sum(sum(a)) a.sum() Sum of all elements
a.trace(offset=0) Sum along diagonal
cumsum(a) a.cumsum(axis=0) Cumulative sum (columns)

Sorting

MATLAB/Octave Python Description
a = [ 4 3 2 ; 2 8 6 ; 1 4 7 ] a = array([[4,3,2],[2,8,6],[1,4,7]]) Example data
sort(a(:)) a.ravel().sort() or Flat and sorted
sort(a) a.sort(axis=0) or msort(a) Sort each column
sort(a')' a.sort(axis=1) Sort each row
sortrows(a,1) a[a[:,0].argsort(),] Sort rows (by first row)
a.ravel().argsort() Sort, return indices
a.argsort(axis=0) Sort each column, return indices
a.argsort(axis=1) Sort each row, return indices

Maximum and minimum

MATLAB/Octave Python Description
max(a) a.max(0) or amax(a [,axis=0]) max in each column
max(a') a.max(1) or amax(a, axis=1) max in each row
max(max(a)) a.max() or max in array
[v i] = max(a) return indices, i
max(b,c) maximum(b,c) pairwise max
cummax(a)
a.ptp(); a.ptp(0) max-to-min range

Matrix manipulation

MATLAB/Octave Python Description
fliplr(a) fliplr(a) or a[:,::-1] Flip left-right
flipud(a) flipud(a) or a[::-1,] Flip up-down
rot90(a) rot90(a) Rotate 90 degrees
repmat(a,2,3)
kron(ones(2,3),a)
kron(ones((2,3)),a) Repeat matrix: [ a a a ; a a a ]
triu(a) triu(a) Triangular, upper
tril(a) tril(a) Triangular, lower

Equivalents to "size"

MATLAB/Octave Python Description
size(a) a.shape or a.getshape() Matrix dimensions
size(a,2) or length(a) a.shape[1] or size(a, axis=1) Number of columns
length(a(:)) a.size or size(a[, axis=None]) Number of elements
ndims(a) a.ndim Number of dimensions
a.nbytes Number of bytes used in memory

Matrix- and elementwise- multiplication

MATLAB/Octave Python Description
a .* b a * b or multiply(a,b) Elementwise operations
a * b matrixmultiply(a,b) Matrix product (dot product)
inner(a,b) or Inner matrix vector multiplication $a\cdot b'$
outer(a,b) or Outer product
kron(a,b) kron(a,b) Kronecker product
a / b Matrix division, $b{\cdot}a^{-1}$
a \ b linalg.solve(a,b)
Left matrix division, $b^{-1}{\cdot}a$ \newline (solve linear equations)
vdot(a,b) Vector dot product
cross(a,b) Cross product

Find; conditional indexing

MATLAB/Octave Python Description
find(a) a.ravel().nonzero()
Non-zero elements, indices
[i j] = find(a) (i,j) = a.nonzero()
(i,j) = where(a!=0)
Non-zero elements, array indices
[i j v] = find(a) v = a.compress((a!=0).flat)
v = extract(a!=0,a)
Vector of non-zero values
find(a>5.5) (a>5.5).nonzero()
Condition, indices
a.compress((a>5.5).flat)
Return values
a .* (a>5.5) where(a>5.5,0,a) or a * (a>5.5) Zero out elements above 5.5
a.put(2,indices) Replace values

Multi-way arrays

MATLAB/Octave Python Description
a = cat(3, [1 2; 1 2],[3 4; 3 4]); a = array([[[1,2],[1,2]], [[3,4],[3,4]]]) Definpe a 3-way array
a(1,:,:) a[0,...]

File input and output

MATLAB/Octave Python Description
f = load('data.txt') f = fromfile("data.txt")
f = load("data.txt")
Reading from a file (2d)
f = load('data.txt') f = load("data.txt") Reading from a file (2d)
x = dlmread('data.csv', ';') f = load('data.csv', delimiter=';') Reading fram a CSV file (2d)
save -ascii data.txt f save('data.csv', f, fmt='%.6f', delimiter=';') Writing to a file (2d)
f.tofile(file='data.csv', format='%.6f', sep=';') Writing to a file (1d)
f = fromfile(file='data.csv', sep=';') Reading from a file (1d)

Plotting

Basic x-y plots

MATLAB/Octave Python Description
plot(a) plot(a) 1d line plot
plot(x(:,1),x(:,2),'o') plot(x[:,0],x[:,1],'o') 2d scatter plot
plot(x1,y1, x2,y2) plot(x1,y1,'bo', x2,y2,'go') Two graphs in one plot
plot(x1,y1)
hold on
plot(x2,y2)
plot(x1,y1,'o')
plot(x2,y2,'o')
show() # as normal
Overplotting: Add new plots to current
subplot(211) subplot(211) subplots
plot(x,y,'ro-') plot(x,y,'ro-') Plotting symbols and color

Axes and titles

MATLAB/Octave Python Description
grid on grid() Turn on grid lines
axis equal
axis('equal')
replot
figure(figsize=(6,6)) 1:1 aspect ratio
axis([ 0 10 0 5 ]) axis([ 0, 10, 0, 5 ]) Set axes manually
title('title')
xlabel('x-axis')
ylabel('y-axis')
Axis labels and titles
text(2,25,'hello') Insert text

Log plots

MATLAB/Octave Python Description
semilogy(a) semilogy(a) logarithmic y-axis
semilogx(a) semilogx(a) logarithmic x-axis
loglog(a) loglog(a) logarithmic x and y axes

Filled plots and bar plots

MATLAB/Octave Python Description
fill(t,s,'b', t,c,'g')
% fill has a bug?
fill(t,s,'b', t,c,'g', alpha=0.2) Filled plot

Functions

MATLAB/Octave Python Description
f = inline('sin(x/3) - cos(x/5)') Defining functions
ezplot(f,[0,40])
fplot('sin(x/3) - cos(x/5)',[0,40])
% no ezplot
x = arrayrange(0,40,.5)
y = sin(x/3) - cos(x/5)
plot(x,y, 'o')
Plot a function for given range

Polar plots

MATLAB/Octave Python Description
theta = 0:.001:2*pi;
r = sin(2*theta);
theta = arange(0,2*pi,0.001)
r = sin(2*theta)
polar(theta, rho) polar(theta, rho)

Histogram plots

MATLAB/Octave Python Description
hist(randn(1000,1))
hist(randn(1000,1), -4:4)
plot(sort(a))

3d data

Contour and image plots

MATLAB/Octave Python Description
contour(z) levels, colls = contour(Z, V,
origin='lower', extent=(-3,3,-3,3))
clabel(colls, levels, inline=1,
fmt='%1.1f', fontsize=10)
Contour plot
contourf(z); colormap(gray) contourf(Z, V,
cmap=cm.gray,
origin='lower',
extent=(-3,3,-3,3))
Filled contour plot
image(z)
colormap(gray)
im = imshow(Z,
interpolation='bilinear',
origin='lower',
extent=(-3,3,-3,3))
Plot image data
# imshow() and contour() as above Image with contours
quiver() quiver() Direction field vectors

Perspective plots of surfaces over the x-y plane

MATLAB/Octave Python Description
n=-2:.1:2;
[x,y] = meshgrid(n,n);
z=x.*exp(-x.^2-y.^2);
n=arrayrange(-2,2,.1)
[x,y] = meshgrid(n,n)
z = x*power(math.e,-x**2-y**2)
mesh(z) Mesh plot
surf(x,y,z) or surfl(x,y,z)
% no surfl()
Surface plot

Scatter (cloud) plots

MATLAB/Octave Python Description
plot3(x,y,z,'k+') 3d scatter plot

Save plot to a graphics file

MATLAB/Octave Python Description
plot(1:10)
print -depsc2 foo.eps
gset output "foo.eps"
gset terminal postscript eps
plot(1:10)
savefig('foo.eps') PostScript
savefig('foo.pdf') PDF
savefig('foo.svg') SVG (vector graphics for www)
print -dpng foo.png savefig('foo.png') PNG (raster graphics)

Data analysis

Set membership operators

MATLAB/Octave Python Description
a = [ 1 2 2 5 2 ];
b = [ 2 3 4 ];
a = array([1,2,2,5,2])
b = array([2,3,4])
a = set([1,2,2,5,2])
b = set([2,3,4])
Create sets
unique(a) unique1d(a)
unique(a)
set(a)
Set unique
union(a,b) union1d(a,b)
a.union(b)
Set union
intersect(a,b) intersect1d(a)
a.intersection(b)
Set intersection
setdiff(a,b) setdiff1d(a,b)
a.difference(b)
Set difference
setxor(a,b) setxor1d(a,b)
a.symmetric_difference(b)
Set exclusion
ismember(2,a) 2 in a
setmember1d(2,a)
contains(a,2)
True for set member

Statistics

MATLAB/Octave Python Description
mean(a) a.mean(axis=0)
mean(a [,axis=0])
Average
median(a) median(a) or median(a [,axis=0]) Median
std(a) a.std(axis=0) or std(a [,axis=0]) Standard deviation
var(a) a.var(axis=0) or var(a) Variance
corr(x,y) correlate(x,y) or corrcoef(x,y) Correlation coefficient
cov(x,y) cov(x,y) Covariance

Interpolation and regression

MATLAB/Octave Python Description
z = polyval(polyfit(x,y,1),x)
plot(x,y,'o', x,z ,'-')
(a,b) = polyfit(x,y,1)
plot(x,y,'o', x,a*x+b,'-')
Straight line fit
a = x\y linalg.lstsq(x,y)
Linear least squares $y = ax + b$
polyfit(x,y,3) polyfit(x,y,3) Polynomial fit

Non-linear methods

Polynomials, root finding

MATLAB/Octave Python Description
poly() Polynomial
roots([1 -1 -1]) roots() Find zeros of polynomial
f = inline('1/x - (x-1)')
fzero(f,1)
Find a zero near $x = 1$
solve('1/x = x-1') Solve symbolic equations
polyval([1 2 1 2],1:10) polyval(array([1,2,1,2]),arange(1,11)) Evaluate polynomial

Differential equations

MATLAB/Octave Python Description
diff(a) diff(x, n=1, axis=0) Discrete difference function and approximate derivative
Solve differential equations

Fourier analysis

MATLAB/Octave Python Description
fft(a) fft(a) or Fast fourier transform
ifft(a) ifft(a) or Inverse fourier transform
convolve(x,y) Linear convolution

Symbolic algebra; calculus

MATLAB/Octave Python Description
factor() Factorization

Programming

MATLAB/Octave Python Description
.m .py Script file extension
%
% or #
# Comment symbol (rest of line)
% must be in MATLABPATH
% must be in LOADPATH
from pylab import * Import library functions
string='a=234';
eval(string)
string="a=234"
eval(string)
Eval

Loops

MATLAB/Octave Python Description
for i=1:5; disp(i); end for i in range(1,6): print(i) for-statement
for i=1:5
disp(i)
disp(i*2)
end
for i in range(1,6):
print(i)
print(i*2)
Multiline for statements

Conditionals

MATLAB/Octave Python Description
if 1>0 a=100; end if 1>0: a=100 if-statement
if 1>0 a=100; else a=0; end if-else-statement

Debugging

MATLAB/Octave Python Description
ans Most recent evaluated expression
whos or who List variables loaded into memory
clear x or clear [all] Clear variable $x$ from memory
disp(a) print a Print

Working directory and OS

MATLAB/Octave Python Description
dir or ls os.listdir(".") List files in directory
what grep.grep("*.py") List script files in directory
pwd os.getcwd() Displays the current working directory
cd foo os.chdir('foo') Change working directory
!notepad
system("notepad")
os.system('notepad')
os.popen('notepad')
Invoke a System Command