- 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.
- a, barray_like
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.
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))
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
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.]])