numpy.gradient

numpy.gradient(f, *varargs, **kwargs)

Return the gradient of an N-dimensional array.

The gradient is computed using second order accurate central differences in the interior and either first differences or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.

Parameters:

f : array_like

An N-dimensional array containing samples of a scalar function.

varargs : list of scalar, optional

N scalars specifying the sample distances for each dimension, i.e. dx, dy, dz, ... Default distance: 1.

edge_order : {1, 2}, optional

Gradient is calculated using N^th order accurate differences at the boundaries. Default: 1.

New in version 1.9.1.

Returns:

gradient : ndarray

N arrays of the same shape as f giving the derivative of f with respect to each dimension.

Examples

>>> x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float)
>>> np.gradient(x)
array([ 1. ,  1.5,  2.5,  3.5,  4.5,  5. ])
>>> np.gradient(x, 2)
array([ 0.5 ,  0.75,  1.25,  1.75,  2.25,  2.5 ])

>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float))
[array([[ 2.,  2., -1.],
        [ 2.,  2., -1.]]), array([[ 1. ,  2.5,  4. ],
        [ 1. ,  1. ,  1. ]])]

>>> x = np.array([0, 1, 2, 3, 4])
>>> dx = np.gradient(x)
>>> y = x**2
>>> np.gradient(y, dx, edge_order=2)
array([-0.,  2.,  4.,  6.,  8.])