Почему scipy.interpolate.griddata и scipy.interpolate.RectBivariateSpline возвращают разные значения?

Question

Я хочу нарисовать поверхность в заданных точках. И я хочу получить координату z для произвольной точки. Я не могу понять, почему scipy.interpolate.griddata и scipy.interpolate.RectBivariateSpline возвращают разные значения для тех же координат x и y. Где я неправ?

import numpy as np 
from scipy.interpolate import griddata, RectBivariateSpline 
from mpl_toolkits.mplot3d import Axes3D 
import matplotlib.pyplot as plt 


x_list = np.array([ 10.0, 10.0, 0.0, 0.0]) 
y_list = np.array([ 0.0, 10.0, 10.0, 0.0]) 
z_list = np.array([103.95, 105.5, 104.85, 104.6]) 

xi = np.linspace(min(x_list), max(x_list),11) 
yi = np.linspace(min(y_list), max(y_list),11) 

grid_x, grid_y = np.meshgrid(xi, yi) 

grid_z1 = griddata((x_list, y_list), z_list, (grid_x, grid_y), method='nearest') 
grid_z2 = griddata((x_list, y_list), z_list, (grid_x, grid_y), method='linear') 
grid_z3 = griddata((x_list, y_list), z_list, (grid_x, grid_y), method='cubic') 

z = RectBivariateSpline(xi, yi, grid_z2, kx=1, ky=1, s=0) 

print z(10.0, 0.0)[0,0] #return 104.85!!! Must be 103.95. 

fig = plt.figure() 
ax1 = fig.add_subplot(221, projection='3d') 
surf = ax1.plot_surface(grid_x, grid_y, grid_z1) 
ax1.set_xlabel(u'X') 
ax1.set_ylabel(u'Y') 
ax1.set_zlabel(u'Z') 

ax2 = fig.add_subplot(222, projection='3d') 
surf = ax2.plot_surface(grid_x, grid_y, grid_z2) 
ax2.set_xlabel(u'X') 
ax2.set_ylabel(u'Y') 
ax2.set_zlabel(u'Z') 

ax3 = fig.add_subplot(223, projection='3d') 
surf = ax3.plot_surface(grid_x, grid_y, grid_z3) 
ax3.set_xlabel(u'X') 
ax3.set_ylabel(u'Y') 
ax3.set_zlabel(u'Z') 

plt.show() 

Answer 1

Я использую параметр indexing = 'ij', и мой код работает правильно.

import numpy as np 
from scipy.interpolate import griddata, RectBivariateSpline 
from mpl_toolkits.mplot3d import Axes3D 
import matplotlib.pyplot as plt 

x_list = np.array([ 10.0, 10.0, 0.0, 0.0]) 
y_list = np.array([ 0.0, 10.0, 10.0, 0.0]) 
z_list = np.array([103.95, 105.5, 104.85, 104.6]) 

xi = np.linspace(min(x_list), max(x_list),11) 
yi = np.linspace(min(y_list), max(y_list),11) 

grid_x, grid_y = np.meshgrid(xi, yi, indexing = 'ij') 

grid_z1 = griddata((x_list, y_list), z_list, (grid_x, grid_y), method='nearest') 
grid_z2 = griddata((x_list, y_list), z_list, (grid_x, grid_y), method='linear') 
grid_z3 = griddata((x_list, y_list), z_list, (grid_x, grid_y), method='cubic') 

z = RectBivariateSpline(xi, yi, grid_z2, kx=1, ky=1, s=0) 

print z(10.0, 0.0)[0,0] #return 103.95))) 

fig = plt.figure() 
ax1 = fig.add_subplot(221, projection='3d') 
surf = ax1.plot_surface(grid_x, grid_y, grid_z1) 
ax1.set_xlabel(u'X') 
ax1.set_ylabel(u'Y') 
ax1.set_zlabel(u'Z') 

ax2 = fig.add_subplot(222, projection='3d') 
surf = ax2.plot_surface(grid_x, grid_y, grid_z2) 
ax2.set_xlabel(u'X') 
ax2.set_ylabel(u'Y') 
ax2.set_zlabel(u'Z') 

ax3 = fig.add_subplot(223, projection='3d') 
surf = ax3.plot_surface(grid_x, grid_y, grid_z3) 
ax3.set_xlabel(u'X') 
ax3.set_ylabel(u'Y') 
ax3.set_zlabel(u'Z') 

plt.show()