numpy.vdot

numpy.outer

# 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, barray_like

If a and b are nonscalar, their last dimensions must match.

Returns
outndarray

out.shape = a.shape[:-1] + b.shape[:-1]

Raises
ValueError

If the last dimension of a and b has different size.

`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-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.]])
```