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MATLAB® and NumPy/SciPy have a lot in common. But there are many differences. NumPy and SciPy were created to do numerical and scientific computing in the most natural way with Python, not to be MATLAB® clones. This page is intended to be a place to collect wisdom about the differences, mostly for the purpose of helping proficient MATLAB® users become proficient NumPy and SciPy users.
Some Key Differences {#1}
In MATLAB®, the basic data type is a multidimensional array of double precision floating point numbers. Most expressions take such arrays and return such arrays. Operations on the 2-D instances of these arrays are designed to act more or less like matrix operations in linear algebra.
In NumPy the basic type is a multidimensional array. Operations on these arrays in all dimensionalities including 2D are element-wise operations. One needs to use specific functions for linear algebra (though for matrix multiplication, one can use the @ operator in python 3.5 and above).
MATLAB® uses 1 (one) based indexing. The initial element of a sequence is found using a(1). See note INDEXING
Python uses 0 (zero) based indexing. The initial element of a sequence is found using a[0].
MATLAB®’s scripting language was created for doing linear algebra. The syntax for basic matrix operations is nice and clean, but the API for adding GUIs and making full-fledged applications is more or less an afterthought.
NumPy is based on Python, which was designed from the outset to be an excellent general-purpose programming language. While Matlab’s syntax for some array manipulations is more compact than NumPy’s, NumPy (by virtue of being an add-on to Python) can do many things that Matlab just cannot, for instance dealing properly with stacks of matrices.
In MATLAB®, arrays have pass-by-value semantics, with a lazy copy-on-write scheme to prevent actually creating copies until they are actually needed. Slice operations copy parts of the array.
In NumPy arrays have pass-by-reference semantics. Slice operations are views into an array.
‘array’ or ‘matrix’? Which should I use?
Historically, NumPy has provided a special matrix type, np.matrix, which is a subclass of ndarray which makes binary operations linear algebra operations. You may see it used in some existing code instead of np.array. So, which one to use?
Short answer
Use arrays.
They are the standard vector/matrix/tensor type of numpy. Many numpy functions return arrays, not matrices.
There is a clear distinction between element-wise operations and linear algebra operations.
You can have standard vectors or row/column vectors if you like.
Until Python 3.5 the only disadvantage of using the array type was that you had to use dot instead of * to multiply (reduce) two tensors (scalar product, matrix vector multiplication etc.). Since Python 3.5 you can use the matrix multiplication @ operator.
Given the above, we intend to deprecate matrix eventually.
Long answer
NumPy contains both an array class and a matrix class. The array class is intended to be a general-purpose n-dimensional array for many kinds of numerical computing, while matrix is intended to facilitate linear algebra computations specifically. In practice there are only a handful of key differences between the two.
Operators * and @, functions dot(), and multiply():
For array, \* means element-wise multiplication, while @ means matrix multiplication; they have associated functions multiply() and dot(). (Before python 3.5, @ did not exist and one had to use dot() for matrix multiplication).
For matrix, \* means matrix multiplication, and for element-wise multiplication one has to use the multiply() function.
Handling of vectors (one-dimensional arrays)
For array, the vector shapes 1xN, Nx1, and N are all different things. Operations like A[:,1] return a one-dimensional array of shape N, not a two-dimensional array of shape Nx1. Transpose on a one-dimensional array does nothing.
For matrix, one-dimensional arrays are always upconverted to 1xN or Nx1 matrices (row or column vectors). A[:,1] returns a two-dimensional matrix of shape Nx1.
Handling of higher-dimensional arrays (ndim > 2)
array objects can have number of dimensions > 2;
matrix objects always have exactly two dimensions.
Convenience attributes
arrayhas a .T attribute, which returns the transpose of the data.
matrixalso has .H, .I, and .A attributes, which return the conjugate transpose, inverse, and asarray() of the matrix, respectively.
Convenience constructor
The array constructor takes (nested) Python sequences as initializers. As in, array([[1,2,3],[4,5,6]]).
The matrix constructor additionally takes a convenient string initializer. As in matrix("[1 2 3; 4 5 6]").
There are pros and cons to using both:
array
:) Element-wise multiplication is easy: A*B.
:( You have to remember that matrix multiplication has its own operator, @.
:) You can treat one-dimensional arrays as either row or column vectors. A @ v treats v as a column vector, while v @ A treats v as a row vector. This can save you having to type a lot of transposes.
:)array is the “default” NumPy type, so it gets the most testing, and is the type most likely to be returned by 3rd party code that uses NumPy.
:) Is quite at home handling data of any number of dimensions.
:) Closer in semantics to tensor algebra, if you are familiar with that.
:)All operations (*, /, +, - etc.) are element-wise.
:( Sparse matrices from scipy.sparse do not interact as well with arrays.
matrix
:\\ Behavior is more like that of MATLAB® matrices.
<:( Maximum of two-dimensional. To hold three-dimensional data you need array or perhaps a Python list of matrix.
<:( Minimum of two-dimensional. You cannot have vectors. They must be cast as single-column or single-row matrices.
<:( Since array is the default in NumPy, some functions may return an array even if you give them a matrix as an argument. This shouldn’t happen with NumPy functions (if it does it’s a bug), but 3rd party code based on NumPy may not honor type preservation like NumPy does.
:)A*B is matrix multiplication, so it looks just like you write it in linear algebra (For Python >= 3.5 plain arrays have the same convenience with the @ operator).
<:( Element-wise multiplication requires calling a function, multiply(A,B).
<:( The use of operator overloading is a bit illogical: * does not work element-wise but / does.
Interaction with scipy.sparse is a bit cleaner.
The array is thus much more advisable to use. Indeed, we intend to deprecate matrix eventually.
Table of Rough MATLAB-NumPy Equivalents
The table below gives rough equivalents for some common MATLAB® expressions. These are not exact equivalents, but rather should be taken as hints to get you going in the right direction. For more detail read the built-in documentation on the NumPy functions.
In the table below, it is assumed that you have executed the following commands in Python:
from numpy import *
import scipy.linalg
Also assume below that if the Notes talk about “matrix” that the arguments are two-dimensional entities.
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 asetmember1d(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)ormedian(a [,axis=0])
Median
std(a)
a.std(axis=0)orstd(a [,axis=0])
Standard deviation
var(a)
a.var(axis=0)orvar(a)
Variance
corr(x,y)
correlate(x,y)orcorrcoef(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=1:5disp(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
whosorwho
List variables loaded into memory
clear xorclear [all]
Clear variable $x$ from memory
disp(a)
print a
Print
Working directory and OS
MATLAB/Octave
Python
Description
dirorls
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
!notepadsystem("notepad")
os.system('notepad')os.popen('notepad')
Invoke a System Command
Notes
Submatrix: Assignment to a submatrix can be done with lists of indexes using the ix_ command. E.g., for 2d array a, one might do: ind=[1,3]; a[np.ix_(ind,ind)]+=100.
HELP: There is no direct equivalent of MATLAB’s which command, but the commands help and source will usually list the filename where the function is located. Python also has an inspect module (do import inspect) which provides a getfile that often works.
INDEXING: MATLAB® uses one based indexing, so the initial element of a sequence has index 1. Python uses zero based indexing, so the initial element of a sequence has index 0. Confusion and flamewars arise because each has advantages and disadvantages. One based indexing is consistent with common human language usage, where the “first” element of a sequence has index 1. Zero based indexing simplifies indexing. See also a text by prof.dr. Edsger W. Dijkstra.
RANGES: In MATLAB®, 0:5 can be used as both a range literal and a ‘slice’ index (inside parentheses); however, in Python, constructs like 0:5 can only be used as a slice index (inside square brackets). Thus the somewhat quirky r_ object was created to allow numpy to have a similarly terse range construction mechanism. Note that r_ is not called like a function or a constructor, but rather indexed using square brackets, which allows the use of Python’s slice syntax in the arguments.
LOGICOPS: & or | in NumPy is bitwise AND/OR, while in Matlab & and | are logical AND/OR. The difference should be clear to anyone with significant programming experience. The two can appear to work the same, but there are important differences. If you would have used Matlab’s & or | operators, you should use the NumPy ufuncs logical_and/logical_or. The notable differences between Matlab’s and NumPy’s & and | operators are:
Non-logical {0,1} inputs: NumPy’s output is the bitwise AND of the inputs. Matlab treats any non-zero value as 1 and returns the logical AND. For example (3 & 4) in NumPy is 0, while in Matlab both 3 and 4 are considered logical true and (3 & 4) returns 1.
Precedence: NumPy’s & operator is higher precedence than logical operators like < and >; Matlab’s is the reverse.
If you know you have boolean arguments, you can get away with using NumPy’s bitwise operators, but be careful with parentheses, like this: z = (x > 1) & (x < 2). The absence of NumPy operator forms of logical_and and logical_or is an unfortunate consequence of Python’s design.
RESHAPE and LINEAR INDEXING: Matlab always allows multi-dimensional arrays to be accessed using scalar or linear indices, NumPy does not. Linear indices are common in Matlab programs, e.g. find() on a matrix returns them, whereas NumPy’s find behaves differently. When converting Matlab code it might be necessary to first reshape a matrix to a linear sequence, perform some indexing operations and then reshape back. As reshape (usually) produces views onto the same storage, it should be possible to do this fairly efficiently. Note that the scan order used by reshape in NumPy defaults to the ‘C’ order, whereas Matlab uses the Fortran order. If you are simply converting to a linear sequence and back this doesn’t matter. But if you are converting reshapes from Matlab code which relies on the scan order, then this Matlab code: z = reshape(x,3,4); should become z = x.reshape(3,4,order=’F’).copy() in NumPy.
Customizing Your Environment
In MATLAB® the main tool available to you for customizing the environment is to modify the search path with the locations of your favorite functions. You can put such customizations into a startup script that MATLAB will run on startup.
NumPy, or rather Python, has similar facilities.
To modify your Python search path to include the locations of your own modules, define the PYTHONPATH environment variable.
To have a particular script file executed when the interactive Python interpreter is started, define the PYTHONSTARTUP environment variable to contain the name of your startup script.
Unlike MATLAB®, where anything on your path can be called immediately, with Python you need to first do an ‘import’ statement to make functions in a particular file accessible.
For example you might make a startup script that looks like this (Note: this is just an example, not a statement of “best practices”):
# Make all numpy available via shorter 'np' prefix
import numpy as np
# Make all matlib functions accessible at the top level via M.func()
import numpy.matlib as M
# Make some matlib functions accessible directly at the top level via, e.g. rand(3,3)
from numpy.matlib import rand,zeros,ones,empty,eye
# Define a Hermitian function
def hermitian(A, **kwargs):
return np.transpose(A,**kwargs).conj()
# Make some shortcuts for transpose,hermitian:
# np.transpose(A) --> T(A)
# hermitian(A) --> H(A)
T = np.transpose
H = hermitian