numpy divide along axis

Question

Is there a numpy function to divide an array along an axis with elements from another array? For example, suppose I have an array a with shape (l,m,n) and an array b with shape (m,); I'm looking for something equivalent to:

def divide_along_axis(a,b,axis=None):     if axis is None:         return a/b     c = a.copy()     for i, x in enumerate(c.swapaxes(0,axis)):         x /= b[i]     return c 

For example, this is useful when normalizing an array of vectors:

>>> a = np.random.randn(4,3) array([[ 1.03116167, -0.60862215, -0.29191449],        [-1.27040355,  1.9943905 ,  1.13515384],        [-0.47916874,  0.05495749, -0.58450632],        [ 2.08792161, -1.35591814, -0.9900364 ]]) >>> np.apply_along_axis(np.linalg.norm,1,a) array([ 1.23244853,  2.62299312,  0.75780647,  2.67919815]) >>> c = divide_along_axis(a,np.apply_along_axis(np.linalg.norm,1,a),0) >>> np.apply_along_axis(np.linalg.norm,1,c) array([ 1.,  1.,  1.,  1.]) 

Answer 1

For the specific example you've given: dividing an (l,m,n) array by (m,) you can use np.newaxis:

a = np.arange(1,61, dtype=float).reshape((3,4,5)) # Create a 3d array  a.shape                                           # (3,4,5)  b = np.array([1.0, 2.0, 3.0, 4.0])                # Create a 1-d array b.shape                                           # (4,)  a / b                                             # Gives a ValueError  a / b[:, np.newaxis]                              # The result you want  

You can read all about the broadcasting rules here. You can also use newaxis more than once if required. (e.g. to divide a shape (3,4,5,6) array by a shape (3,5) array).

From my understanding of the docs, using newaxis + broadcasting avoids also any unecessary array copying.

Indexing, newaxis etc are described more fully here now. (Documentation reorganised since this answer first posted).

Answer 2

I think you can get this behavior with numpy's usual broadcasting behavior:

In [9]: a = np.array([[1., 2.], [3., 4.]])  In [10]: a / np.sum(a, axis=0) Out[10]: array([[ 0.25      ,  0.33333333],        [ 0.75      ,  0.66666667]]) 

If i've interpreted correctly.

If you want the other axis you could transpose everything:

> a = np.random.randn(4,3).transpose() > norms = np.apply_along_axis(np.linalg.norm,0,a) > c = a / norms > np.apply_along_axis(np.linalg.norm,0,c) array([ 1.,  1.,  1.,  1.])