*Last updated: 2023-03-16.*
# tf_quant_finance.math.diff
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Computes the difference between elements of an array at a regular interval.
```python
tf_quant_finance.math.diff(
x, order=1, exclusive=False, axis=-1, dtype=None, name=None
)
```
For a difference along the final axis, if exclusive is True, then computes:
```
result[..., i] = x[..., i+order] - x[..., i] for i < size(x) - order
```
This is the same as doing `x[..., order:] - x[..., :-order]`. Note that in
this case the result `Tensor` is smaller in size than the input `Tensor`.
If exclusive is False, then computes:
```
result[..., i] = x[..., i] - x[..., i-order] for i >= order
result[..., i] = x[..., i] for 0 <= i < order
```
#### Example
```python
x = tf.constant([1, 2, 3, 4, 5])
dx = diff(x, order=1, exclusive=False) # Returns [1, 1, 1, 1, 1]
dx1 = diff(x, order=1, exclusive=True) # Returns [1, 1, 1, 1]
dx2 = diff(x, order=2, exclusive=False) # Returns [1, 2, 2, 2, 2]
```
#### Args:
* `x`: A `Tensor` of shape `batch_shape + [n]` and of any dtype for which
arithmetic operations are permitted.
* `order`: Positive Python int. The order of the difference to compute. `order =
1` corresponds to the difference between successive elements.
Default value: 1
* `exclusive`: Python bool. See description above.
Default value: False
* `axis`: Python int. The axis of `x` along which to difference.
Default value: -1 (the final axis).
* `dtype`: Optional `tf.DType`. If supplied, the dtype for `x` to use when
converting to `Tensor`.
Default value: None which maps to the default dtype inferred by TF.
* `name`: Python `str` name prefixed to Ops created by this class.
Default value: None which is mapped to the default name 'diff'.
#### Returns:
* `diffs`: A `Tensor` of the same dtype as `x`. If `exclusive` is True,
then the shape is `batch_shape + [n-min(order, n)]`, otherwise it is
`batch_shape + [n]`. The final dimension of which contains the differences
of the requested order.