difference between numpy dot() and inner()

Question

What is the difference between

import numpy as np np.dot(a,b) 

and

import numpy as np np.inner(a,b) 

all examples I tried returned the same result. Wikipedia has the same article for both?! In the description of inner() it says, that its behavior is different in higher dimensions, but I couldn't produce any different output. Which one should I use?

Answer 1

numpy.dot:

For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of a and the second-to-last of b:

numpy.inner:

Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes.

(Emphasis mine.)

As an example, consider this example with 2D arrays:

>>> a=np.array([[1,2],[3,4]]) >>> b=np.array([[11,12],[13,14]]) >>> np.dot(a,b) array([[37, 40],        [85, 92]]) >>> np.inner(a,b) array([[35, 41],        [81, 95]]) 

Thus, the one you should use is the one that gives the correct behaviour for your application.

---

Performance testing

(Note that I am testing only the 1D case, since that is the only situation where .dot and .inner give the same result.)

>>> import timeit >>> setup = 'import numpy as np; a=np.random.random(1000); b = np.random.random(1000)'  >>> [timeit.timeit('np.dot(a,b)',setup,number=1000000) for _ in range(3)] [2.6920320987701416, 2.676928997039795, 2.633111000061035]  >>> [timeit.timeit('np.inner(a,b)',setup,number=1000000) for _ in range(3)] [2.588860034942627, 2.5845699310302734, 2.6556360721588135] 

So maybe .inner is faster, but my machine is fairly loaded at the moment, so the timings are not consistent nor are they necessarily very accurate.

Answer 2

np.dot and np.inner are identical for 1-dimensions arrays, so that is probably why you aren't noticing any differences. For N-dimension arrays, they correspond to common tensor operations.

np.inner is sometimes called a "vector product" between a higher and lower order tensor, particularly a tensor times a vector, and often leads to "tensor contraction". It includes matrix-vector multiplication.

np.dot corresponds to a "tensor product", and includes the case mentioned at the bottom of the Wikipedia page. It is generally used for multiplication of two similar tensors to produce a new tensor. It includes matrix-matrix multiplication.

If you're not using tensors, then you don't need to worry about these cases and they behave identically.