NUMPY for matlab users

NumPy for MATLAB users

Help

MATLAB/OctavePythonDescription
doc
help -i % browse with Info
help()Browse help interactively
help help or doc dochelpHelp on using help
help plothelp(plot) or ?plotHelp for a function
help splines or doc splineshelp(pylab)Help for a toolbox/library package
demo
Demonstration examples

Searching available documentation

MATLAB/OctavePythonDescription
lookfor plot
Search help files
helphelp(); modules [Numeric]List available packages
which plothelp(plot)Locate functions

Using interactively

MATLAB/OctavePythonDescription
octave -qipython -pylabStart session
TAB or M-?TABAuto completion
foo(.m)execfile('foo.py') or run foo.pyRun code from file
historyhist -nCommand history
diary on [..] diary off
Save command history
exit or quitCTRL-D
CTRL-Z # windows
sys.exit()
End session

Operators

MATLAB/OctavePythonDescription
help -
Help on operator syntax

Arithmetic operators

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

Relational operators

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

Logical operators

MATLAB/OctavePythonDescription
a && ba and bShort-circuit logical AND
a || ba or bShort-circuit logical OR
a & b or and(a,b)logical_and(a,b) or a and bElement-wise logical AND
a | b or or(a,b)logical_or(a,b) or a or bElement-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 aLogical NOT
any(a)
True if any element is nonzero
all(a)
True if all elements are nonzero

root and logarithm

MATLAB/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
pimath.pi$\pi=3.141592$
exp(1)math.e or math.exp(1)$e=2.718281$

Missing values; IEEE-754 floating point status flags

MATLAB/OctavePythonDescription
NaNnanNot a Number
InfinfInfinity, $\infty$

plus_infInfinity, $+\infty$

minus_infInfinity, $-\infty$

plus_zeroPlus zero, $+0$

minus_zeroMinus zero, $-0$

Complex numbers

MATLAB/OctavePythonDescription
iz = 1jImaginary unit
z = 3+4iz = 3+4j or z = complex(3,4)A complex number, $3+4i$
abs(z)abs(3+4j)Absolute value (modulus)
real(z)z.realReal part
imag(z)z.imagImaginary part
arg(z)
Argument
conj(z)z.conj(); z.conjugate()Complex conjugate

Trigonometry

MATLAB/OctavePythonDescription
atan(a,b)atan2(b,a)Arctangent, $\arctan(b/a)$

hypot(x,y)Hypotenus; Euclidean distance

Generate random numbers

MATLAB/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
1:10arange(1,11, dtype=Float)
range(1,11)
1,2,3, ... ,10
0:9arange(10.)0.0,1.0,2.0, ... ,9.0
1:3:10arange(1,11,3)1,4,7,10
10:-1:1arange(10,0,-1)10,9,8, ... ,1
10:-3:1arange(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(:) = 3a.fill(3), a[:] = 3Set all values to same scalar value

Concatenation (vectors)

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

Repeating

MATLAB/OctavePythonDescription
[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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
a.*aa*aMultiply two vectors
dot(u,v)dot(u,v)Vector dot product, $u \cdot v$

Matrices

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

Concatenation (matrices); rbind and cbind

MATLAB/OctavePythonDescription
[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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
b = ab = a.copy()Copy of a

Indexing and accessing elements (Python: slicing)

MATLAB/OctavePythonDescription
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/OctavePythonDescription
a(:,1) = 99a[:,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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
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.ndimNumber of dimensions

a.nbytesNumber of bytes used in memory

Matrix- and elementwise- multiplication

MATLAB/OctavePythonDescription
a .* ba * b or multiply(a,b)Elementwise operations
a * bmatrixmultiply(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 \ blinalg.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/OctavePythonDescription
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/OctavePythonDescription
a = cat(3, [1 2; 1 2],[3 4; 3 4]);a = array([[[1,2],[1,2]], [[3,4],[3,4]]])Define a 3-way array
a(1,:,:)a[0,...]

File input and output

MATLAB/OctavePythonDescription
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 fsave('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/OctavePythonDescription
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/OctavePythonDescription
grid ongrid()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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
hist(randn(1000,1))

hist(randn(1000,1), -4:4)

plot(sort(a))

3d data

Contour and image plots

MATLAB/OctavePythonDescription
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 aboveImage with contours
quiver()quiver()Direction field vectors

Perspective plots of surfaces over the x-y plane

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

Save plot to a graphics file

MATLAB/OctavePythonDescription
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.pngsavefig('foo.png')PNG (raster graphics)

Data analysis

Set membership operators

MATLAB/OctavePythonDescription
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/OctavePythonDescription
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/OctavePythonDescription
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\ylinalg.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/OctavePythonDescription

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/OctavePythonDescription
diff(a)diff(x, n=1, axis=0)Discrete difference function and approximate derivative


Solve differential equations

Fourier analysis

MATLAB/OctavePythonDescription
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/OctavePythonDescription
factor()
Factorization

Programming

MATLAB/OctavePythonDescription
.m.pyScript 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/OctavePythonDescription
for i=1:5; disp(i); endfor 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/OctavePythonDescription
if 1>0 a=100; endif 1>0: a=100if-statement
if 1>0 a=100; else a=0; end
if-else-statement

Debugging

MATLAB/OctavePythonDescription
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 aPrint

Working directory and OS

MATLAB/OctavePythonDescription
dir or lsos.listdir(".")List files in directory
whatgrep.grep("*.py")List script files in directory
pwdos.getcwd()Displays the current working directory
cd fooos.chdir('foo')Change working directory
!notepad
system("notepad")
os.system('notepad')
os.popen('notepad')
Invoke a System Command
Time-stamp: "2007-11-09T16:46:36 vidar"
©2006 Vidar Bronken Gundersen, /mathesaurus.sf.net
Permission is granted to copy, distribute and/or modify this document as long as the above attribution is retained.