numpy.gradient

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

Return the gradient of an N-dimensional array.

计算梯度：内部使用二阶精确中心差，边界处使用一阶差或二阶精确单边（向前或向后）差。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 : scalar or list of scalar, optional

N个标量，其指定每个维度的样本距离，即dx、dy、dz等。默认距离：1。只有一个标量表示所有维度的样本距离。如果给定axis，则varargs的数量必须等于轴的数量。

edge_order : {1, 2}, optional

边界处使用的N^th阶精度差来计算梯度。Default: 1.

New in version 1.9.1.

axis：None、整数或整数元组，可选

仅沿给定轴计算梯度。默认值（axis = None）用于计算输入数组的所有轴的梯度。axis may be negative, in which case it counts from the last to the first axis.

New in version 1.11.0.

Returns:

gradient : ndarray列表

Each element of list has 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 ])

对于二维数组，返回将是按轴排序的两个数组。In this example the first array stands for the gradient in rows and the second one in columns direction:

>>> 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.])

axis关键字可用于指定轴的一个子集来计算梯度

>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float), axis=0)
array([[ 2., 2., -1.], [ 2., 2., -1.]]