# xorbits.numpy.inner#

xorbits.numpy.inner(a, b, /)[source]#

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 (array_like) – If a and b are nonscalar, their last dimensions must match.

• b (array_like) – If a and b are nonscalar, their last dimensions must match.

Returns

out – 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])`

Return type

ndarray

Raises

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

`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.]])
```

This docstring was copied from numpy.