如果输入"值"包含 nan，为什么 scipy.griddata 会用"立方体"插值返回 nan？

Question

我想使用scipy.griddata对包含一些nan值的数组执行三次插值。但是，只要values参数中存在单个nan，返回的插值将仅填充nan。使用"最近"或"线性"插值方法时，情况并非如此。

这种行为的原因是什么，有没有一种简单的方法可以忽略values输入中的nan？

这是一个最小的工作示例，改编自 griddata scipy 插值不起作用(给出 nan(：

import numpy as np
def func(x, y):
return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2
grid_x, grid_y = np.mgrid[0:1:10j, 0:1:10j]
points = np.random.rand(100, 2)
values = func(points[:,0], points[:,1])
values[0]=np.nan # now add a single nan value to the array
from scipy.interpolate import griddata
grid_z0 = griddata(points, values, (grid_x, grid_y), method='nearest') # no nans here
grid_z1 = griddata(points, values, (grid_x, grid_y), method='linear') # this has nans on the edges (as expected)
grid_z2 = griddata(points, values, (grid_x, grid_y), method='cubic') # this is filled only with nans.

Answer 1

解决方案是在插值数据之前从points和values输入数组中删除所有nan。numpy可以有效地用于执行此操作：

import numpy as np
def func(x, y):
return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2
grid_x, grid_y = np.mgrid[0:1:10j, 0:1:10j]
points = np.random.rand(100, 2)
values = func(points[:,0], points[:,1])
values[0]=np.nan # now add a single nan value to the array
#Find all the indexes where there is no nan neither in values nor in points.
nonanindex=np.invert(np.isnan(points[:,0]))*np.invert(np.isnan(points[:,1]))*np.invert(np.isnan(values))
#Remove the nan using fancy indexing. griddata can now properly interpolate. The result will have nan only on the edges of the array
from scipy.interpolate import griddata
grid_z2 = riddata(np.stack((points[nonanindex,0],points[nonanindex,1]),axis=1), values[nonanindex], (grid_x, grid_y), method='cubic')

虽然这解决了问题，但我还没有回答为什么 griddata 函数的这个问题只出现在三次插值中。