numpy.inner#

numpy.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.

Parameters:

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

Returns:

outndarray: 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])

Raises:

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

See also

tensordot: Sum products over arbitrary axes.
dot: Generalised matrix product, using second last dimension of b.
vecdot: Vector dot product of two arrays.
einsum: Einstein summation convention.

Notes

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

Examples

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)
2

Some multidimensional examples:

>>> a = np.arange(24).reshape((2,3,4))
>>> b = np.arange(4)
>>> c = np.inner(a, b)
>>> c.shape
(2, 3)
>>> 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
(1, 1, 3)
>>> c
array([[[1, 3, 5]]])

An example where b is a scalar:

>>> np.inner(np.eye(2), 7)
array([[7., 0.],
       [0., 7.]])