diff2

arrayfire.diff2(array: Array, /, axis: int = 0) → Array

Computes the second-order differences of an ArrayFire array along a specified dimension.

The second-order difference is calculated as array[i+2] - 2*array[i+1] + array[i] along the specified axis, which is analogous to the second derivative in continuous functions.

Parameters

arrayArray

The input ArrayFire array to compute second-order differences on.

axisint, optional, default: 0

The dimension along which the second-order differences are calculated. For a 2D array, axis=0 computes the difference between consecutive rows (down each column), while axis=1 computes the difference between consecutive columns (across each row).

Returns

Array

An ArrayFire array of second-order differences. The size of this array along the specified axis is two less than the input array, as the operation effectively reduces the dimension size by two.

Examples

>>> import arrayfire as af
>>> a = af.Array([1, 2, 4, 7, 11])
>>> af.diff2(a)
[3 1 1 1]
    1.0000
    1.0000
    1.0000

Note

The operation requires that the array has at least three elements along the specified axis to compute the second-order differences. For arrays with fewer than three elements along the axis, the result will be an empty array.