numpy.inner¶

numpy.inner(a,b)¶

Inner product of two arrays.

Ordinary inner product of vectors for 1-D arrays (without complexconjugation), in higher dimensions a sum product over the last axes.

Parameters:	a, b : array_like Ifa andb are nonscalar, their last dimensions must match.
Returns:	out : ndarray out.shape = a.shape[:-1] + b.shape[:-1]
Raises:	ValueError If the last dimension ofa andb has different size.

See also

tensordot

Sum products over arbitrary axes.

dot

Generalised matrix product, using second last dimension ofb.

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, ifndim(a) = r > 0 andndim(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 additiona orb 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 whereb is a scalar:

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