numpy.gradient

numpy.gradient(f, *varargs)

Return the gradient of an N-dimensional array.

The gradient is computed using second order accurate central differences in the interior and 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` : scalars

0, 1, or N scalars specifying the sample distances in each direction, that is: dx, dy, dz, ... The default distance is 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 = gradient(x)
>>> y = x**2
>>> gradient(y,dx)
array([0.,  2.,  4.,  6.,  8.])