/NumPy 1.17

# numpy.diff

`numpy.diff(a, n=1, axis=-1, prepend=<no value>, append=<no value>)` [source]

Calculate the n-th discrete difference along the given axis.

The first difference is given by `out[i] = a[i+1] - a[i]` along the given axis, higher differences are calculated by using `diff` recursively.

Parameters: `a : array_like` Input array `n : int, optional` The number of times values are differenced. If zero, the input is returned as-is. `axis : int, optional` The axis along which the difference is taken, default is the last axis. `prepend, append : array_like, optional` Values to prepend or append to “a” along axis prior to performing the difference. Scalar values are expanded to arrays with length 1 in the direction of axis and the shape of the input array in along all other axes. Otherwise the dimension and shape must match “a” except along axis. `diff : ndarray` The n-th differences. The shape of the output is the same as `a` except along `axis` where the dimension is smaller by `n`. The type of the output is the same as the type of the difference between any two elements of `a`. This is the same as the type of `a` in most cases. A notable exception is `datetime64`, which results in a `timedelta64` output array.

#### Notes

Type is preserved for boolean arrays, so the result will contain `False` when consecutive elements are the same and `True` when they differ.

For unsigned integer arrays, the results will also be unsigned. This should not be surprising, as the result is consistent with calculating the difference directly:

```>>> u8_arr = np.array([1, 0], dtype=np.uint8)
>>> np.diff(u8_arr)
array([255], dtype=uint8)
>>> u8_arr[1,...] - u8_arr[0,...]
255
```

If this is not desirable, then the array should be cast to a larger integer type first:

```>>> i16_arr = u8_arr.astype(np.int16)
>>> np.diff(i16_arr)
array([-1], dtype=int16)
```

#### Examples

```>>> x = np.array([1, 2, 4, 7, 0])
>>> np.diff(x)
array([ 1,  2,  3, -7])
>>> np.diff(x, n=2)
array([  1,   1, -10])
```
```>>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])
>>> np.diff(x)
array([[2, 3, 4],
[5, 1, 2]])
>>> np.diff(x, axis=0)
array([[-1,  2,  0, -2]])
```
```>>> x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64)
>>> np.diff(x)
array([1, 1], dtype='timedelta64[D]')
```