# tf.keras.backend.batch_dot

Batchwise dot product.

`batch_dot` is used to compute dot product of `x` and `y` when `x` and `y` are data in batch, i.e. in a shape of `(batch_size, :)`. `batch_dot` results in a tensor or variable with less dimensions than the input. If the number of dimensions is reduced to 1, we use `expand_dims` to make sure that ndim is at least 2.

`x` Keras tensor or variable with `ndim >= 2`.
`y` Keras tensor or variable with `ndim >= 2`.
`axes` Tuple or list of integers with target dimensions, or single integer. The sizes of `x.shape[axes]` and `y.shape[axes]` should be equal.

A tensor with shape equal to the concatenation of `x`'s shape (less the dimension that was summed over) and `y`'s shape (less the batch dimension and the dimension that was summed over). If the final rank is 1, we reshape it to `(batch_size, 1)`.

#### Examples:

Assume `x = [[1, 2], [3, 4]]` and `y = [[5, 6], [7, 8]]` `batch_dot(x, y, axes=1) = [, ]` which is the main diagonal of `x.dot(y.T)`, although we never have to calculate the off-diagonal elements.

• `Pseudocode`: ```inner_products = [] for xi, yi in zip(x, y): inner_products.append(xi.dot(yi)) result = stack(inner_products)```

Shape inference: Let `x`'s shape be `(100, 20)` and `y`'s shape be `(100, 30, 20)`. If `axes` is (1, 2), to find the output shape of resultant tensor, loop through each dimension in `x`'s shape and `y`'s shape:

• `x.shape` : 100 : append to output shape
• `x.shape` : 20 : do not append to output shape, dimension 1 of `x` has been summed over. (`dot_axes` = 1)
• `y.shape` : 100 : do not append to output shape, always ignore first dimension of `y`
• `y.shape` : 30 : append to output shape
• `y.shape` : 20 : do not append to output shape, dimension 2 of `y` has been summed over. (`dot_axes` = 2) `output_shape` = `(100, 30)`
````x_batch = tf.keras.backend.ones(shape=(32, 20, 1))`
`y_batch = tf.keras.backend.ones(shape=(32, 30, 20))`
`xy_batch_dot = tf.keras.backend.batch_dot(x_batch, y_batch, axes=(1, 2))`
`tf.keras.backend.int_shape(xy_batch_dot)`
`(32, 1, 30)`
```
[]
[]