# 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 must match.

  Returns
    out ndarray

      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])`

  Raises
    ValueError

      If both a and b are nonscalar and their last dimensions have different sizes.

  See also

  `tensordot`

    Sum products over arbitrary axes.

  `dot`

    Generalised matrix product, using second last dimension of b.

  `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, 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-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

  Examples

  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.]])

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