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.

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:

>>> 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.]])

numpy.vdot numpy.outer