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")

2x3 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,:) or flipud(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() or a.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(...)

3x4 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(...)

3x4 rank-2 array full of 64-bit floating point ones

eye(3)

eye(3)

mat(...)

3x3 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 3x4 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()

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