Numpy for Matlab user

Ref: http://scipy.github.io/old-wiki/pages/NumPy_for_Matlab_Users

Some Key Differences

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 elementwise operations. However, there is a specialmatrix type for doing linear algebra, which is just a subclass of the array class. Operations on matrix-class arrays are linear algebra operations.

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 subclassing the main array type to do both array and matrix math cleanly.

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.

In MATLAB®, every function must be in a file of the same name, and you can’t define local functions in an ordinary script file or at the command-prompt (inlines are not real functions but macros, like in C).

NumPy code is Python code, so it has no such restrictions. You can define functions wherever you like.

MATLAB® has an active community and there is lots of code available for free. But the vitality of the community is limited by MATLAB®’s cost; your MATLAB® programs can be run by only a few.

!NumPy/!SciPy also has an active community, based right here on this web site! It is smaller, but it is growing very quickly. In contrast, Python programs can be redistributed and used freely. See Topical_Software for a listing of free add-on application software, Mailing_Listsfor discussions, and the rest of this web site for additional community contributions. We encourage your participation!

MATLAB® has an extensive set of optional, domain-specific add-ons (‘toolboxes’) available for purchase, such as for signal processing, optimization, control systems, and the whole SimuLink® system for graphically creating dynamical system models.

There’s no direct equivalent of this in the free software world currently, in terms of range and depth of the add-ons. However the list in Topical_Software certainly shows a growing trend in that direction.

MATLAB® has a sophisticated 2-d and 3-d plotting system, with user interface widgets.

Addon software can be used with Numpy to make comparable plots to MATLAB®. Matplotlib is a mature 2-d plotting library that emulates the MATLAB® interface. PyQwtallows more robust and faster user interfaces than MATLAB®. And mlab, a “matlab-like” API based on Mayavi2, for 3D plotting of Numpy arrays. See the Topical_Software page for more options, links, and details. There is, however, no definitive, all-in-one, easy-to-use, built-in plotting solution for 2-d and 3-d. This is an area where Numpy/Scipy could use some work.

MATLAB® provides a full development environment with command interaction window, integrated editor, and debugger.

Numpy does not have one standard IDE. However, the IPython environment provides a sophisticated command prompt with full completion, help, and debugging support, and interfaces with the Matplotlib library for plotting and the Emacs/XEmacs editors.

MATLAB® itself costs thousands of dollars if you’re not a student. The source code to the main package is not available to ordinary users. You can neither isolate nor fix bugs and performance issues yourself, nor can you directly influence the direction of future development. (If you are really set on Matlab-like syntax, however, there is Octave, another numerical computing environment that allows the use of most Matlab syntax without modification.)

NumPy and SciPy are free (both beer and speech), whoever you are.

‘array’ or ‘matrix’? Which should I use?

Short answer

Use arrays.

  • They are the standard vector/matrix/tensor type of numpy. Many numpy function 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.

The only disadvantage of using the array type is that you will have to use dot instead of * to multiply (reduce) two tensors (scalar product, matrix vector multiplication etc.).

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.

  • Operator *, dot(), and multiply():

    • For array, *‘ means element-wise multiplication, and the dot() function is used for matrix multiplication.

    • For matrix, *‘ means matrix multiplication, and the multiply() function is used for element-wise multiplication.

  • Handling of vectors (rank-1 arrays)
    • For array, the vector shapes 1xN, Nx1, and N are all different things. Operations like A[:,1] return a rank-1 array of shape N, not a rank-2 of shape Nx1. Transpose on a rank-1 array does nothing.

    • For matrix, rank-1 arrays are always upconverted to 1xN or Nx1 matrices (row or column vectors). A[:,1] returns a rank-2 matrix of shape Nx1.

  • Handling of higher-rank arrays (rank > 2)

    • array objects can have rank > 2.

    • matrix objects always have exactly rank 2.

  • Convenience attributes
    • array has a .T attribute, which returns the transpose of the data.

    • matrix also 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]").

General Purpose Equivalents

MATLAB

numpy

Notes

help func

info(func) or help(func) or func? (in Ipython)

get help on the function func

which func

(See note ‘HELP’)

find out where func is defined

type func

source(func) or func?? (in Ipython)

print source for func (if not a native function)

a && b

a and b

short-circuiting logical AND operator (Python native operator); scalar arguments only

a || b

a or b

short-circuiting logical OR operator (Python native operator); scalar arguments only

1*i,1*j,1i,1j

1j

complex numbers

eps

spacing(1)

Distance between 1 and the nearest floating point number

ode45

scipy.integrate.ode(f).set_integrator('dopri5')

integrate an ODE with Runge-Kutta 4,5

ode15s

scipy.integrate.ode(f).\
set_integrator('vode', method='bdf', order=15)

integrate an ODE with BDF

Linear Algebra Equivalents

The notation mat(...) means to use the same expression as array, but convert to matrix with the mat() type converter.

The notation asarray(...) means to use the same expression as matrix, but convert to array with the asarray() type converter.

MATLAB

numpy.array

numpy.matrix

Notes

ndims(a)

ndim(a) or a.ndim

get the number of dimensions of a (tensor rank)

numel(a)

size(a) or a.size

get the number of elements of an array

size(a)

shape(a) or a.shape

get the “size” of the matrix

size(a,n)

a.shape[n-1]

get the number of elements of the nth dimension of array a. (Note that MATLAB® uses 1 based indexing while Python uses 0 based indexing, See note ‘INDEXING’)

[ 1 2 3; 4 5 6 ]

array([[1.,2.,3.],
[4.,5.,6.]])

mat([[1.,2.,3.],
[4.,5.,6.]]) or
mat("1 2 3; 4 5 6")

2×3 matrix literal

[ a b; c d ]

vstack([hstack([a,b]),
        hstack([c,d])])

bmat('a b; c d')

construct a matrix from blocks a,b,c, and d

a(end)

a[-1]

a[:,-1][0,0]

access last element in the 1xn matrix a

a(2,5)

a[1,4]

access element in second row, fifth column

a(2,:)

a[1] or a[1,:]

entire second row of a

a(1:5,:)

a[0:5] or a[:5] or a[0:5,:]

the first five rows of a

a(end-4:end,:)

a[-5:]

the last five rows of a

a(1:3,5:9)

a[0:3][:,4:9]

rows one to three and columns five to nine of a. This gives read-only access.

a([2,4,5],[1,3])

a[ix_([1,3,4],[0,2])]

rows 2,4 and 5 and columns 1 and 3. This allows the matrix to be modified, and doesn’t require a regular slice.

a(3:2:21,:)

a[ 2:21:2,:]

every other row of a, starting with the third and going to the twenty-first

a(1:2:end,:)

a[ ::2,:]

every other row of a, starting with the first

a(end:-1:1,:) orflipud(a)

a[ ::-1,:]

a with rows in reverse order

a([1:end 1],:)

a[r_[:len(a),0]]

a with copy of the first row appended to the end

a.'

a.transpose() or a.T

transpose of a

a'

a.conj().transpose() ora.conj().T

a.H

conjugate transpose of a

a * b

dot(a,b)

a * b

matrix multiply

a .* b

a * b

multiply(a,b)

element-wise multiply

a./b

a/b

element-wise divide

a.^3

a**3

power(a,3)

element-wise exponentiation

(a>0.5)

(a>0.5)

matrix whose i,jth element is (a_ij > 0.5)

find(a>0.5)

nonzero(a>0.5)

find the indices where (a > 0.5)

a(:,find(v>0.5))

a[:,nonzero(v>0.5)[0]]

a[:,nonzero(v.A>0.5)[0]]

extract the columms of a where vector v > 0.5

a(:,find(v>0.5))

a[:,v.T>0.5]

a[:,v.T>0.5)]

extract the columms of a where column vector v > 0.5

a(a<0.5)=0

a[a<0.5]=0

a with elements less than 0.5 zeroed out

a .* (a>0.5)

a * (a>0.5)

mat(a.A * (a>0.5).A)

a with elements less than 0.5 zeroed out

a(:) = 3

a[:] = 3

set all values to the same scalar value

y=x

y = x.copy()

numpy assigns by reference

y=x(2,:)

y = x[1,:].copy()

numpy slices are by reference

y=x(:)

y = x.flatten(1)

turn array into vector (note that this forces a copy)

1:10

arange(1.,11.) or
r_[1.:11.] or
r_[1:10:10j]

mat(arange(1.,11.))or
r_[1.:11.,'r']

create an increasing vector see note ‘RANGES’

0:9

arange(10.) or
r_[:10.] or
r_[:9:10j]

mat(arange(10.)) or
r_[:10.,'r']

create an increasing vector see note ‘RANGES’

[1:10]'

arange(1.,11.)[:, newaxis]

r_[1.:11.,'c']

create a column vector

zeros(3,4)

zeros((3,4))

mat(...)

3×4 rank-2 array full of 64-bit floating point zeros

zeros(3,4,5)

zeros((3,4,5))

mat(...)

3x4x5 rank-3 array full of 64-bit floating point zeros

ones(3,4)

ones((3,4))

mat(...)

3×4 rank-2 array full of 64-bit floating point ones

eye(3)

eye(3)

mat(...)

3×3 identity matrix

diag(a)

diag(a)

mat(...)

vector of diagonal elements of a

diag(a,0)

diag(a,0)

mat(...)

square diagonal matrix whose nonzero values are the elements of a

rand(3,4)

random.rand(3,4)

mat(...)

random 3×4 matrix

linspace(1,3,4)

linspace(1,3,4)

mat(...)

4 equally spaced samples between 1 and 3, inclusive

[x,y]=meshgrid(0:8,0:5)

mgrid[0:9.,0:6.] or
meshgrid(r_[0:9.],r_[0:6.]

mat(...)

two 2D arrays: one of x values, the other of y values

ogrid[0:9.,0:6.] or
ix_(r_[0:9.],r_[0:6.]

mat(...)

the best way to eval functions on a grid

[x,y]=meshgrid([1,2,4],[2,4,5])

meshgrid([1,2,4],[2,4,5])

mat(...)

ix_([1,2,4],[2,4,5])

mat(...)

the best way to eval functions on a grid

repmat(a, m, n)

tile(a, (m, n))

mat(...)

create m by n copies of a

[a b]

concatenate((a,b),1) or
hstack((a,b)) or
column_stack((a,b)) or
c_[a,b]

concatenate((a,b),1)

concatenate columns of a and b

[a; b]

concatenate((a,b)) or
vstack((a,b)) or
r_[a,b]

concatenate((a,b))

concatenate rows of a and b

max(max(a))

a.max()

maximum element of a (with ndims(a)<=2 for matlab)

max(a)

a.max(0)

maximum element of each column of matrix a

max(a,[],2)

a.max(1)

maximum element of each row of matrix a

max(a,b)

maximum(a, b)

compares a and b element-wise, and returns the maximum value from each pair

norm(v)

sqrt(dot(v,v)) or
Sci.linalg.norm(v) or
linalg.norm(v)

sqrt(dot(v.A,v.A))or
Sci.linalg.norm(v)or
linalg.norm(v)

L2 norm of vector v

a & b

logical_and(a,b)

element-by-element AND operator (Numpy ufunc) see note ‘LOGICOPS’

a | b

logical_or(a,b)

element-by-element OR operator (Numpy ufunc) see note ‘LOGICOPS’

bitand(a,b)

a & b

bitwise AND operator (Python native and Numpy ufunc)

bitor(a,b)

a | b

bitwise OR operator (Python native and Numpy ufunc)

inv(a)

linalg.inv(a)

inverse of square matrix a

pinv(a)

linalg.pinv(a)

pseudo-inverse of matrix a

rank(a)

linalg.matrix_rank(a)

rank of a matrix a

a\b

linalg.solve(a,b) if a is square
linalg.lstsq(a,b) otherwise

solution of a x = b for x

b/a

Solve a.T x.T = b.T instead

solution of x a = b for x

[U,S,V]=svd(a)

U, S, Vh = linalg.svd(a), V = Vh.T

singular value decomposition of a

chol(a)

linalg.cholesky(a).T

cholesky factorization of a matrix (chol(a) in matlab returns an upper triangular matrix, but linalg.cholesky(a) returns a lower triangular matrix)

[V,D]=eig(a)

D,V = linalg.eig(a)

eigenvalues and eigenvectors of a

[V,D]=eig(a,b)

V,D = Sci.linalg.eig(a,b)

eigenvalues and eigenvectors of a,b

[V,D]=eigs(a,k)

find the k largest eigenvalues and eigenvectors of a

[Q,R,P]=qr(a,0)

Q,R = Sci.linalg.qr(a)

mat(...)

QR decomposition

[L,U,P]=lu(a)

L,U = Sci.linalg.lu(a) or
LU,P=Sci.linalg.lu_factor(a)

mat(...)

LU decomposition (note: P(Matlab) == transpose(P(numpy)) )

conjgrad

Sci.linalg.cg

mat(...)

Conjugate gradients solver

fft(a)

fft(a)

mat(...)

Fourier transform of a

ifft(a)

ifft(a)

mat(...)

inverse Fourier transform of a

sort(a)

sort(a) or a.sort()

mat(...)

sort the matrix

[b,I] = sortrows(a,i)

I = argsort(a[:,i]), b=a[I,:]

sort the rows of the matrix

regress(y,X)

linalg.lstsq(X,y)

multilinear regression

decimate(x, q)

Sci.signal.resample(x, len(x)/q)

downsample with low-pass filtering

unique(a)

unique(a)

squeeze(a)

a.squeeze()

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