mxnet.np.inner

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

b (a,) – If a and b are nonscalar, their last dimensions must match.

Returns

out – out.shape = a.shape[:-1] + b.shape[:-1]

Return type

ndarray

Raises

ValueError – If the last dimension of a and b has different size.

See also

tensordot()

Sum products over arbitrary axes.

dot()

Generalised matrix product, using second last dimension of b.

einsum()

Einstein summation convention.

()

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-1,j0,…,js-1] = sum(a[i0,…,ir-1,:]*b[j0,…,js-1,:]) 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)
array(2.)

A multidimensional example:

>>> a = np.arange(24).reshape((2,3,4))
>>> b = np.arange(4)
>>> np.inner(a, b)
array([[ 14.,  38.,  62.],
       [ 86., 110., 134.]])