如果输入 'values' 包含 nan，为什么 scipy.griddata return nans 带有 'cubic' 插值？

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，一旦 values 参数中出现单个 nan，返回的插值将仅填充 nan。使用 'nearest' 或 'linear' 插值方法时情况并非如此。

这种行为的原因是什么？是否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 interpolation not working (giving 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

一种解决方案是在插入数据之前从 points 和 values 输入数组中删除所有 nan。 numpy 可以有效地用于这样做：

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上。

如果输入 'values' 包含 nan，为什么 scipy.griddata return nans 带有 'cubic' 插值？

Why does scipy.griddata return nans with 'cubic' interpolation if input 'values' contains nan?

python

scipy

interpolation

nan

cubic