Passing an operation along a specific axis in python

Question

In python, suppose I have a square matrix numpy X of size nxn, and I have a vector numpy a of size n.

Very simple, I want to perform a subtraction in the format X - a , but I want to be able to specify by what dimension so that I can indicate that the subtraction is either along the 0 axis or the 1 axis.

How to specify an axis?

Answer 1

Let arrays with random elements be generated

Inputs

In [62]: X
Out[62]: 
array([[ 0.32322974,  0.50491961,  0.40854442,  0.36908488],
       [ 0.58840196,  0.1696713 ,  0.75428203,  0.01445901],
       [ 0.27728281,  0.33722084,  0.64187916,  0.51361972],
       [ 0.39151808,  0.6883594 ,  0.93848072,  0.48946276]])

In [63]: a
Out[63]: array([ 0.01278876,  0.01854458,  0.16953393,  0.37159562])

I. Subtraction along axis=1

axis=1, .. a X, X . X:

In [64]: X[0] - a
Out[64]: array([ 0.31044099,  0.48637503,  0.23901049, -0.00251074])

, :

X[0,0] - a[0], X[0,1] - a[1], X[0,2] - a[2] , X[0,3] - a[3]

, X a. X 2D, a - 1D, :

X :  n x n
a :      n

, X-a :

In [65]: X-a
Out[65]: 
array([[ 0.31044099,  0.48637503,  0.23901049, -0.00251074],
       [ 0.5756132 ,  0.15112672,  0.5847481 , -0.3571366 ],
       [ 0.26449405,  0.31867625,  0.47234523,  0.1420241 ],
       [ 0.37872932,  0.66981482,  0.76894679,  0.11786714]])

, , , X[0] - a, .

: , a elems , . , , , axis=1, a axis=0.

II. axis=0

, axis=0, .. a X, col X . X:

In [67]: X[:,0]-a
Out[67]: array([ 0.31044099,  0.56985738,  0.10774888,  0.01992247])

, :

X[0,0] - a[0], X[1,0] - a[1], X[2,0] - a[2] , X[3,0] - a[3]

, X a. X 2D, a - 1D, a 2D a[:,None]:

X          :  n x n
a[:,None]  :  n x 1

, X-a[:,None] :

In [68]: X-a[:,None]
Out[68]: 
array([[ 0.31044099,  0.49213085,  0.39575566,  0.35629612],
       [ 0.56985738,  0.15112672,  0.73573745, -0.00408557],
       [ 0.10774888,  0.16768691,  0.47234523,  0.34408579],
       [ 0.01992247,  0.31676379,  0.5668851 ,  0.11786714]])

, , , X[:,0] - a, .

Answer 2

, ( , )

• X shape (n,m)
• a shape (n,)
• b shape (m,)

:

(n,m)-(n,) => (n,m)-(n,1) => (n,m)
X - a[:,None]     

(n,m)-(m,) => (n,m)-(1,m) => (n,m)
X - b[None,:]
X - b      # [None,:] is automatic, if needed.

, numpy , .

2 1d ():

(n,) - (m,) => (n,1)-(1,m) => (n,m)
a[:,None] - b[None,:]
a[:,None] - b

a-b (n,m) (m,n) - .

:

(n,) - (n,) => (n,)
a - a

(n,) - (n,) => (n,1)-(1,n) => (n,n)
a[:,None]-a[None,:]

=============

, axis, np.expand_dims:

In [220]: np.expand_dims([1,2,3],0)
Out[220]: array([[1, 2, 3]])    # like [None,:]
In [221]: np.expand_dims([1,2,3],1)
Out[221]:             # like [:,None]
array([[1],
       [2],
       [3]])

def foo(X, a, axis=0):
    return X - np.expand_dims(a, axis=axis)

:

In [223]: foo(np.eye(3),[1,2,3],axis=0)
Out[223]: 
array([[ 0., -2., -3.],
       [-1., -1., -3.],
       [-1., -2., -2.]])
In [224]: foo(np.eye(3),[1,2,3],axis=1)
Out[224]: 
array([[ 0., -1., -1.],
       [-2., -1., -2.],
       [-3., -3., -2.]])