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