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# numpy.inner

`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 of 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

  `tensordot`
    Sum products over arbitrary axes.
  `dot`
    Generalised matrix product, using second last dimension of b.

  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:

      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.]])

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