numpy.ma.inner

ma.inner(a, b) [source]

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

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

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.

Notes

Masked values are replaced by 0.

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)
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]])

An example where b is a scalar:

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