numpy.inner — NumPy v1.11 Manual (original) (raw)
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, b : array_like If a and b are nonscalar, their last dimensions must match. |
|---|---|
| Returns: | out : ndarray out.shape = a.shape[:-1] + b.shape[:-1] |
| Raises: | ValueError If the last dimension of a and b has different size. |
See also
Sum products over arbitrary axes.
Generalised matrix product, using second last dimension of b.
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-1,j0,...,js-1] = sum(a[i0,...,ir-1,:]*b[j0,...,js-1,:])
In addition a or b may be scalars, in which case:
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.]])