`numpy:inner`

Signature

def inner(a, b, /)

Inner product of two arrays.

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

a, b : array_like: If a and b are nonscalar, their last dimensions must match.

out : ndarray: If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. out.shape = (*a.shape[:-1], *b.shape[:-1])

: ValueError: If both a and b are nonscalar and their last dimensions have different sizes.

For vectors (1-D arrays) it computes the ordinary inner-product

np.inner(a, b) = sum(a[:]*b[:])

More generally, if ndim(a) = r > 0 and ndim(b) = s > 0

np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))

or explicitly

np.inner(a, b)[i0,...,ir-2,j0,...,js-2]
     = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])

In addition a or b may be scalars, in which case

np.inner(a,b) = a*b

Ordinary inner product for vectors:

import numpy as np
a = np.array([1,2,3])
b = np.array([0,1,0])

✓

np.inner(a, b)

✗

np.int64(2)

Some multidimensional examples:

a = np.arange(24).reshape((2,3,4))
b = np.arange(4)
c = np.inner(a, b)
c.shape
c

✓

array([[ 14,  38,  62],
       [ 86, 110, 134]])

a = np.arange(2).reshape((1,1,2))
b = np.arange(6).reshape((3,2))
c = np.inner(a, b)
c.shape
c

✓

array([[[1, 3, 5]]])

An example where `b` is a scalar:

np.inner(np.eye(2), 7)

✓

array([[7., 0.],
       [0., 7.]])