使用RegularGridInterpolator时如何仅在边界外使用最近邻插值

Question

Using RegularGridInterpolator for obtaining values outside of the hull (bounds) of the input data one can choose between extrapolation or fixed values. How can I get linear interpolation inside the hull and nearest neighbor interpolation outside of the hull?

Answer 1

The following class uses two interpolators. The first sets all values outside the hull to np.nan . The second interpolator does nearest neighbor interpolation only on those nan values.

class RegularGridInterpolatorNNextrapol:
    def __init__( self, points, values, method='linear' ):
        self.interp = RegularGridInterpolator(points, values, method=method,
                                              bounds_error=False, fill_value=np.nan)
        self.nearest = RegularGridInterpolator(points, values, method='nearest',
                                           bounds_error=False, fill_value=None)

    def __call__( self, xi ):
        vals = self.interp( xi )
        idxs = np.isnan( vals )
        vals[idxs] = self.nearest( xi[idxs] )
        return vals

Here is an example which results in the image below:

x = np.linspace( -0.5, 0.5, 5 )
y = np.linspace( -0.5, 0.5, 5 )
X1, Y1 = np.meshgrid(x, y)
z = np.hypot(X1, Y1)

interp = RegularGridInterpolatorNNextrapol((x,y), z)

X = np.linspace(min(x)-0.2, max(x)+0.2,40)
Y = np.linspace(min(y)-0.2, max(y)+0.2,40)
X, Y = np.meshgrid(X, Y)  # 2D grid for interpolation

pts = np.column_stack((X.flatten(),Y.flatten()))
Z = interp( pts )

plt.pcolormesh(X, Y, Z.reshape(X.shape), shading='auto')
plt.plot(X1, Y1, "ok" )
plt.legend()
plt.colorbar()
plt.axis("equal")
plt.show()