迭代插值:首先插值网格，然后插值 [英] Iterated Interpolation: First interpolate grids, then interpolate value
本文介绍了迭代插值:首先插值网格，然后插值的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
我想从x插值到z.但有一个警告:
根据状态y，我有一个不同的xGrid -我需要进行插值.
我有一个y，yGrid的网格.说yGrid=[0,1].而xGrid由
1 10
2 20
3 30
对应的zGrid是
100 1000
200 2000
300 3000
这意味着对于y=0，[1,2,3]是x的正确网格，对于y = 1，[10,20,30]是正确的网格.和z类似.
一切都是线性的，并且是均匀分布的，以证明问题所在，但实际数据中却没有.
换句话说
- 如果
y=0，x=1.5，z是[1,2,3]在1.5上的[100, 200, 300]到150的插值. - 如果
y=1，x=10，z=1000
这是问题所在:如果y=0.5是什么?在这种简单的情况下，我希望插值的网格为[5.5, 11, 33/2]和[550, 1100, 1650]，所以x=10将接近1000.
在我看来，我需要进行3次插值:
- 两次获得正确的
xGrid和zGrid，以及 - 一次插值
xGrid->xGrid
这是瓶颈的一部分，效率至关重要.如何最有效地编写代码?
这是我效率很低的代码:
xGrid = np.array([[1, 10], [2, 20], [3, 30]])
zGrid = np.array([[100, 1000], [200, 2000], [300, 3000]])
yGrid = np.array([0, 1])
yValue = 0.5
xInterpolated = np.zeros(xGrid.shape[0])
zInterpolated = np.zeros(zGrid.shape[0])
for i in np.arange(xGrid.shape[0]):
f1 = interpolate.interp1d(pGrid, xGrid[i,:])
f2 = interpolate.interp1d(pGrid, zGrid[i,:])
xInterpolated[i] = f1(yValue)
zInterpolated[i] = f2(yValue)
f3 = interpolate.interp1d(xInterpolated, zInterpolated)
输出为
In[73]: xInterpolated, zInterpolated
Out[73]: (array([ 5.5, 11. , 16.5]), array([ 550., 1100., 1650.]))
In[75]: f3(10)
Out[75]: array(1000.0)
实际用例数据
xGrid:
array([[ 0.30213582, 0.42091889, 0.48596506, 0.55045007,
0.61479495, 0.67906768, 0.74328653, 0.8074641 ,
0.8716093 , 0.93572867, 0.99982708, 1.06390825,
1.12797508, 1.19202984, 1.25607435, 1.32011008,
1.38413823, 1.44815978, 1.51217558, 1.57618631],
[ 1.09945362, 1.17100971, 1.23588956, 1.30034354,
1.36467675, 1.42894086, 1.49315319, 1.55732567,
1.62146685, 1.68558297, 1.74967873, 1.8137577 ,
1.87782269, 1.94187589, 2.00591907, 2.06995365,
2.1339808 , 2.1980015 , 2.26201653, 2.32602659],
[ 1.96474476, 2.03281806, 2.09757883, 2.16200519,
2.22632562, 2.29058026, 2.35478537, 2.41895223,
2.48308893, 2.54720144, 2.61129424, 2.67537076,
2.73943368, 2.80348513, 2.86752681, 2.93156011,
2.99558615, 3.05960586, 3.12362004, 3.18762935],
[ 2.97271432, 3.03917779, 3.10382629, 3.16822546,
3.23253177, 3.29677589, 3.36097295, 3.42513351,
3.48926519, 3.55337363, 3.61746308, 3.68153682,
3.74559741, 3.80964688, 3.87368686, 3.93771869,
4.00174345, 4.06576206, 4.12977526, 4.1937837 ],
[ 4.17324037, 4.23880534, 4.30336811, 4.36773934,
4.43202986, 4.49626215, 4.56045011, 4.62460351,
4.68872947, 4.75283326, 4.81691888, 4.88098942,
4.94504732, 5.0090945 , 5.07313252, 5.13716266,
5.20118595, 5.26520326, 5.32921533, 5.39322276],
[ 5.64337535, 5.70841895, 5.77290336, 5.83724805,
5.90152063, 5.96573939, 6.02991687, 6.094062 ,
6.15818132, 6.22227969, 6.28636083, 6.35042763,
6.41448236, 6.47852685, 6.54256256, 6.60659069,
6.67061223, 6.73462802, 6.79863874, 6.86264497],
[ 7.51378714, 7.57851747, 7.6429358 , 7.70725236,
7.77150412, 7.83570702, 7.89987216, 7.9640075 ,
8.0281189 , 8.09221078, 8.15628654, 8.22034883,
8.28439974, 8.34844097, 8.41247386, 8.47649955,
8.54051897, 8.60453289, 8.66854195, 8.73254673],
[ 10.03324294, 10.09777483, 10.162134 , 10.22641722,
10.29064401, 10.35482771, 10.41897777, 10.48310105,
10.54720264, 10.61128646, 10.67535549, 10.73941211,
10.80345821, 10.8674953 , 10.93152463, 10.99554722,
11.05956392, 11.12357544, 11.1875824 , 11.25158529],
[ 13.77079831, 13.83519161, 13.89949459, 13.96373623,
14.02793138, 14.09209044, 14.15622093, 14.2203284 ,
14.28441705, 14.34849012, 14.41255015, 14.47659914,
14.54063872, 14.6046702 , 14.66869465, 14.73271299,
14.79672596, 14.86073419, 14.92473821, 14.9887385 ],
[ 20.60440125, 20.66868421, 20.7329108 , 20.79709436,
20.8612443 , 20.92536747, 20.98946899, 21.05355274,
21.11762172, 21.1816783 , 21.24572435, 21.30976141,
21.37379071, 21.43781328, 21.50182995, 21.56584146,
21.6298484 , 21.69385127, 21.75785053, 21.82184654]])
zGrid:
array([[ 0.30213582, 0.42091889, 0.48596506, 0.55045007, 0.61479495,
0.67906768, 0.74328653, 0.8074641 , 0.8716093 , 0.93572867,
0.99982708, 1.06390825, 1.12797508, 1.19202984, 1.25607435,
1.32011008, 1.38413823, 1.44815978, 1.51217558, 1.57618631],
[ 0.35871288, 0.43026897, 0.49514882, 0.5596028 , 0.62393601,
0.68820012, 0.75241245, 0.81658493, 0.88072611, 0.94484223,
1.00893799, 1.07301696, 1.13708195, 1.20113515, 1.26517833,
1.32921291, 1.39324006, 1.45726076, 1.52127579, 1.58528585],
[ 0.37285697, 0.44093027, 0.50569104, 0.5701174 , 0.63443782,
0.69869247, 0.76289758, 0.82706444, 0.89120114, 0.95531365,
1.01940644, 1.08348296, 1.14754589, 1.21159734, 1.27563902,
1.33967232, 1.40369835, 1.46771807, 1.53173225, 1.59574155],
[ 0.38688189, 0.45334537, 0.51799386, 0.58239303, 0.64669934,
0.71094347, 0.77514053, 0.83930108, 0.90343277, 0.96754121,
1.03163066, 1.0957044 , 1.15976498, 1.22381445, 1.28785443,
1.35188626, 1.41591103, 1.47992963, 1.54394284, 1.60795127],
[ 0.40252392, 0.46808889, 0.53265166, 0.59702289, 0.66131341,
0.7255457 , 0.78973366, 0.85388706, 0.91801302, 0.98211681,
1.04620243, 1.11027297, 1.17433087, 1.23837805, 1.30241607,
1.36644621, 1.4304695 , 1.49448681, 1.55849888, 1.62250631],
[ 0.42106765, 0.48611125, 0.55059566, 0.61494035, 0.67921293,
0.74343169, 0.80760917, 0.87175431, 0.93587362, 0.99997199,
1.06405313, 1.12811993, 1.19217466, 1.25621915, 1.32025486,
1.38428299, 1.44830454, 1.51232032, 1.57633104, 1.64033728],
[ 0.4442679 , 0.50899823, 0.57341657, 0.63773312, 0.70198488,
0.76618779, 0.83035293, 0.89448826, 0.95859966, 1.02269154,
1.08676731, 1.15082959, 1.21488051, 1.27892173, 1.34295463,
1.40698032, 1.47099973, 1.53501365, 1.59902272, 1.66302749],
[ 0.47525152, 0.53978341, 0.60414258, 0.6684258 , 0.73265259,
0.79683629, 0.86098635, 0.92510963, 0.98921122, 1.05329504,
1.11736407, 1.18142069, 1.24546679, 1.30950388, 1.37353321,
1.4375558 , 1.5015725 , 1.56558403, 1.62959098, 1.69359387],
[ 0.52099935, 0.58539265, 0.64969564, 0.71393728, 0.77813242,
0.84229149, 0.90642197, 0.97052944, 1.03461809, 1.09869116,
1.16275119, 1.22680018, 1.29083976, 1.35487124, 1.4188957 ,
1.48291403, 1.546927 , 1.61093523, 1.67493926, 1.73893954],
[ 0.60440125, 0.66868421, 0.7329108 , 0.79709436, 0.8612443 ,
0.92536747, 0.98946899, 1.05355274, 1.11762172, 1.1816783 ,
1.24572435, 1.30976141, 1.37379071, 1.43781328, 1.50182995,
1.56584146, 1.6298484 , 1.69385127, 1.75785053, 1.82184654]])
yGrid:
array([ 1. , 6.21052632, 11.42105263, 16.63157895,
21.84210526, 27.05263158, 32.26315789, 37.47368421,
42.68421053, 47.89473684, 53.10526316, 58.31578947,
63.52631579, 68.73684211, 73.94736842, 79.15789474,
84.36842105, 89.57894737, 94.78947368, 100. ])
我已经按照给定的答案创建了插值器，然后插值了一些点:
yGrid = yGrid + np.zeros(xGrid.shape)
f3 = interpolate.interp2d(xGrid,yGrid,zGrid,kind='linear')
import matplotlib.pyplot as plt
plt.plot(np.linspace(0.001, 5, 100), [f3(y, 2) for y in np.linspace(0.001, 5, 100)])
plt.plot(xGrid[:, 1], zGrid[:, 1])
plt.plot(xGrid[:, 0], zGrid[:, 0])
这是输出:
蓝线是内插的.我担心对于非常小的x值，它应该 稍微向下倾斜(遵循两个函数的加权平均值)，但根本不是.
解决方案
您实际上正在查看2d插值:您需要z(x,y)且插值值为x和y.唯一的妙处是，您需要广播yGrid使其具有与x和z数据相同的形状:
import scipy.interpolate as interpolate
xGrid = np.array([[1, 10], [2, 20], [3, 30]])
zGrid = np.array([[100, 1000], [200, 2000], [300, 3000]])
yGrid = np.array([0, 1]) + np.zeros(xGrid.shape)
yValue = 0.5
f3 = interpolate.interp2d(xGrid,yGrid,zGrid,kind='linear')
这是一个双变量函数，您可以将其称为
In [372]: f3(10,yValue)
Out[372]: array([ 1000.])
您可以使用lambda将其转换为返回标量的单变量函数:
f4 = lambda x,y=yValue: f3(x,y)[0]
这将为您的(假定)单个y值返回一个单个值，该值在lambda定义时设置为yValue.像这样使用它:
In [376]: f4(10)
Out[376]: 1000.0
但是，常规的f3函数可能更适合您的问题，因为您可以根据需要动态更改y的值，并可以使用数组输入获取z的数组输出. /p>
更新
对于形状奇怪的x,y数据，interp2d可能会给出不令人满意的结果，尤其是在网格边界处.因此，另一种方法是使用 interpolate.LinearNDInterpolator ，它基于输入数据的三角剖分，固有地给出了局部分段线性逼近
f4 = interpolate.LinearNDInterpolator((xGrid.flatten(),yGrid.flatten()),zGrid.flatten())
设置了更新数据:
plt.figure()
plt.plot(np.linspace(0.001, 5, 100), f4(np.linspace(0.001, 5, 100), 2))
plt.plot(xGrid[:, 0], zGrid[:, 0])
plt.plot(xGrid[:, 1], zGrid[:, 1])
请注意，这种插值法也有其缺点.我建议将两个插值函数绘制为一个曲面，并查看它们与原始数据相比如何失真:
from mpl_toolkits.mplot3d import Axes3D
xx,yy=(np.linspace(0,10,20),np.linspace(0,20,40))
xxs,yys=np.meshgrid(xx,yy)
zz3=f3(xx,yy) #from interp2d
zz4=f4(xxs,yys) #from LinearNDInterpolator
#plot raw data
hf=plt.figure()
ax=hf.add_subplot(111,projection='3d')
ax.plot_surface(xGrid,yGrid,zGrid,rstride=1,cstride=1)
plt.draw()
#plot interp2d case
hf=plt.figure()
ax=hf.add_subplot(111,projection='3d')
ax.plot_surface(xxs,yys,zz3,rstride=1,cstride=1)
plt.draw()
#plot LinearNDInterpolator case
hf=plt.figure()
ax=hf.add_subplot(111,projection='3d')
ax.plot_surface(xxs,yys,f4(xxs,yys),rstride=1,cstride=1)
plt.draw()
这将使您能够旋转曲面，并查看它们包含哪些工件(具有适当的后端).
I want to interpolate from x onto z. But there's a caveat:
Depending on a state y, I have a different xGrid - which i need to interpolate.
I have a grid for y, yGrid. Say yGrid=[0,1]. And xGrid is given by
1 10
2 20
3 30
The corresponding zGrid, is
100 1000
200 2000
300 3000
This means that for y=0, [1,2,3] is the proper grid for x, and for y=1, [10,20,30] is the proper grid. And similar for z.
Everything is linear and even-spaced for demonstration of the problem, but it is not in the actual data.
In words,
- if
y=0,x=1.5,zis the interpolation of[1,2,3]onto[100, 200, 300]at1.5- which is150. - If
y=1,x=10,z=1000
Here's the problem: What if is y=0.5? In this simple case, I want the interpolated grids to be [5.5, 11, 33/2] and [550, 1100, 1650], so x=10 would be something close to 1000.
It appears to me, that I need to interpolate 3 times:
- twice to get the correct
xGrid, andzGrid, and - once to interpolate
xGrid->xGrid
This is part of a bottleneck and efficiency is vital. How do I code this most efficiently?
Here is how I can code it quite inefficiently:
xGrid = np.array([[1, 10], [2, 20], [3, 30]])
zGrid = np.array([[100, 1000], [200, 2000], [300, 3000]])
yGrid = np.array([0, 1])
yValue = 0.5
xInterpolated = np.zeros(xGrid.shape[0])
zInterpolated = np.zeros(zGrid.shape[0])
for i in np.arange(xGrid.shape[0]):
f1 = interpolate.interp1d(pGrid, xGrid[i,:])
f2 = interpolate.interp1d(pGrid, zGrid[i,:])
xInterpolated[i] = f1(yValue)
zInterpolated[i] = f2(yValue)
f3 = interpolate.interp1d(xInterpolated, zInterpolated)
And the output is
In[73]: xInterpolated, zInterpolated
Out[73]: (array([ 5.5, 11. , 16.5]), array([ 550., 1100., 1650.]))
In[75]: f3(10)
Out[75]: array(1000.0)
Actual use-case data
xGrid:
array([[ 0.30213582, 0.42091889, 0.48596506, 0.55045007,
0.61479495, 0.67906768, 0.74328653, 0.8074641 ,
0.8716093 , 0.93572867, 0.99982708, 1.06390825,
1.12797508, 1.19202984, 1.25607435, 1.32011008,
1.38413823, 1.44815978, 1.51217558, 1.57618631],
[ 1.09945362, 1.17100971, 1.23588956, 1.30034354,
1.36467675, 1.42894086, 1.49315319, 1.55732567,
1.62146685, 1.68558297, 1.74967873, 1.8137577 ,
1.87782269, 1.94187589, 2.00591907, 2.06995365,
2.1339808 , 2.1980015 , 2.26201653, 2.32602659],
[ 1.96474476, 2.03281806, 2.09757883, 2.16200519,
2.22632562, 2.29058026, 2.35478537, 2.41895223,
2.48308893, 2.54720144, 2.61129424, 2.67537076,
2.73943368, 2.80348513, 2.86752681, 2.93156011,
2.99558615, 3.05960586, 3.12362004, 3.18762935],
[ 2.97271432, 3.03917779, 3.10382629, 3.16822546,
3.23253177, 3.29677589, 3.36097295, 3.42513351,
3.48926519, 3.55337363, 3.61746308, 3.68153682,
3.74559741, 3.80964688, 3.87368686, 3.93771869,
4.00174345, 4.06576206, 4.12977526, 4.1937837 ],
[ 4.17324037, 4.23880534, 4.30336811, 4.36773934,
4.43202986, 4.49626215, 4.56045011, 4.62460351,
4.68872947, 4.75283326, 4.81691888, 4.88098942,
4.94504732, 5.0090945 , 5.07313252, 5.13716266,
5.20118595, 5.26520326, 5.32921533, 5.39322276],
[ 5.64337535, 5.70841895, 5.77290336, 5.83724805,
5.90152063, 5.96573939, 6.02991687, 6.094062 ,
6.15818132, 6.22227969, 6.28636083, 6.35042763,
6.41448236, 6.47852685, 6.54256256, 6.60659069,
6.67061223, 6.73462802, 6.79863874, 6.86264497],
[ 7.51378714, 7.57851747, 7.6429358 , 7.70725236,
7.77150412, 7.83570702, 7.89987216, 7.9640075 ,
8.0281189 , 8.09221078, 8.15628654, 8.22034883,
8.28439974, 8.34844097, 8.41247386, 8.47649955,
8.54051897, 8.60453289, 8.66854195, 8.73254673],
[ 10.03324294, 10.09777483, 10.162134 , 10.22641722,
10.29064401, 10.35482771, 10.41897777, 10.48310105,
10.54720264, 10.61128646, 10.67535549, 10.73941211,
10.80345821, 10.8674953 , 10.93152463, 10.99554722,
11.05956392, 11.12357544, 11.1875824 , 11.25158529],
[ 13.77079831, 13.83519161, 13.89949459, 13.96373623,
14.02793138, 14.09209044, 14.15622093, 14.2203284 ,
14.28441705, 14.34849012, 14.41255015, 14.47659914,
14.54063872, 14.6046702 , 14.66869465, 14.73271299,
14.79672596, 14.86073419, 14.92473821, 14.9887385 ],
[ 20.60440125, 20.66868421, 20.7329108 , 20.79709436,
20.8612443 , 20.92536747, 20.98946899, 21.05355274,
21.11762172, 21.1816783 , 21.24572435, 21.30976141,
21.37379071, 21.43781328, 21.50182995, 21.56584146,
21.6298484 , 21.69385127, 21.75785053, 21.82184654]])
zGrid:
array([[ 0.30213582, 0.42091889, 0.48596506, 0.55045007, 0.61479495,
0.67906768, 0.74328653, 0.8074641 , 0.8716093 , 0.93572867,
0.99982708, 1.06390825, 1.12797508, 1.19202984, 1.25607435,
1.32011008, 1.38413823, 1.44815978, 1.51217558, 1.57618631],
[ 0.35871288, 0.43026897, 0.49514882, 0.5596028 , 0.62393601,
0.68820012, 0.75241245, 0.81658493, 0.88072611, 0.94484223,
1.00893799, 1.07301696, 1.13708195, 1.20113515, 1.26517833,
1.32921291, 1.39324006, 1.45726076, 1.52127579, 1.58528585],
[ 0.37285697, 0.44093027, 0.50569104, 0.5701174 , 0.63443782,
0.69869247, 0.76289758, 0.82706444, 0.89120114, 0.95531365,
1.01940644, 1.08348296, 1.14754589, 1.21159734, 1.27563902,
1.33967232, 1.40369835, 1.46771807, 1.53173225, 1.59574155],
[ 0.38688189, 0.45334537, 0.51799386, 0.58239303, 0.64669934,
0.71094347, 0.77514053, 0.83930108, 0.90343277, 0.96754121,
1.03163066, 1.0957044 , 1.15976498, 1.22381445, 1.28785443,
1.35188626, 1.41591103, 1.47992963, 1.54394284, 1.60795127],
[ 0.40252392, 0.46808889, 0.53265166, 0.59702289, 0.66131341,
0.7255457 , 0.78973366, 0.85388706, 0.91801302, 0.98211681,
1.04620243, 1.11027297, 1.17433087, 1.23837805, 1.30241607,
1.36644621, 1.4304695 , 1.49448681, 1.55849888, 1.62250631],
[ 0.42106765, 0.48611125, 0.55059566, 0.61494035, 0.67921293,
0.74343169, 0.80760917, 0.87175431, 0.93587362, 0.99997199,
1.06405313, 1.12811993, 1.19217466, 1.25621915, 1.32025486,
1.38428299, 1.44830454, 1.51232032, 1.57633104, 1.64033728],
[ 0.4442679 , 0.50899823, 0.57341657, 0.63773312, 0.70198488,
0.76618779, 0.83035293, 0.89448826, 0.95859966, 1.02269154,
1.08676731, 1.15082959, 1.21488051, 1.27892173, 1.34295463,
1.40698032, 1.47099973, 1.53501365, 1.59902272, 1.66302749],
[ 0.47525152, 0.53978341, 0.60414258, 0.6684258 , 0.73265259,
0.79683629, 0.86098635, 0.92510963, 0.98921122, 1.05329504,
1.11736407, 1.18142069, 1.24546679, 1.30950388, 1.37353321,
1.4375558 , 1.5015725 , 1.56558403, 1.62959098, 1.69359387],
[ 0.52099935, 0.58539265, 0.64969564, 0.71393728, 0.77813242,
0.84229149, 0.90642197, 0.97052944, 1.03461809, 1.09869116,
1.16275119, 1.22680018, 1.29083976, 1.35487124, 1.4188957 ,
1.48291403, 1.546927 , 1.61093523, 1.67493926, 1.73893954],
[ 0.60440125, 0.66868421, 0.7329108 , 0.79709436, 0.8612443 ,
0.92536747, 0.98946899, 1.05355274, 1.11762172, 1.1816783 ,
1.24572435, 1.30976141, 1.37379071, 1.43781328, 1.50182995,
1.56584146, 1.6298484 , 1.69385127, 1.75785053, 1.82184654]])
yGrid:
array([ 1. , 6.21052632, 11.42105263, 16.63157895,
21.84210526, 27.05263158, 32.26315789, 37.47368421,
42.68421053, 47.89473684, 53.10526316, 58.31578947,
63.52631579, 68.73684211, 73.94736842, 79.15789474,
84.36842105, 89.57894737, 94.78947368, 100. ])
I've created the interpolater following the given answer, and then interpolated some points:
yGrid = yGrid + np.zeros(xGrid.shape)
f3 = interpolate.interp2d(xGrid,yGrid,zGrid,kind='linear')
import matplotlib.pyplot as plt
plt.plot(np.linspace(0.001, 5, 100), [f3(y, 2) for y in np.linspace(0.001, 5, 100)])
plt.plot(xGrid[:, 1], zGrid[:, 1])
plt.plot(xGrid[:, 0], zGrid[:, 0])
And here's the output:
The blue line is the interpolated one. I am worried that for very small values of x, it should be tilted downwards a bit (following the weighted average of the two functions), but it is not at all.
解决方案
You're actually looking at 2d interpolation: you need z(x,y) with interpolated values of x and y. The only subtlety is that you need to broadcast yGrid to have the same shape as the x and z data:
import scipy.interpolate as interpolate
xGrid = np.array([[1, 10], [2, 20], [3, 30]])
zGrid = np.array([[100, 1000], [200, 2000], [300, 3000]])
yGrid = np.array([0, 1]) + np.zeros(xGrid.shape)
yValue = 0.5
f3 = interpolate.interp2d(xGrid,yGrid,zGrid,kind='linear')
This is a bivariate function, you can call it as
In [372]: f3(10,yValue)
Out[372]: array([ 1000.])
You can turn it into a univariate function returning a scalar by using a lambda:
f4 = lambda x,y=yValue: f3(x,y)[0]
this will return a single value for your (assumedly) single y value, which is set to be yValue at the moment of the lambda definition. Use it like so:
In [376]: f4(10)
Out[376]: 1000.0
However, the general f3 function might be more suited to your problem, as you can dynamically change the value of y according to your needs, and can use array input to obtain array output for z.
Update
For oddly shaped x,y data, interp2d might give unsatisfactory results, especially at the borders of the grid. So another approach is using interpolate.LinearNDInterpolator instead, which is based on a triangulation of your input data, inherently giving a local piecewise linear approximation
f4 = interpolate.LinearNDInterpolator((xGrid.flatten(),yGrid.flatten()),zGrid.flatten())
With your update data set:
plt.figure()
plt.plot(np.linspace(0.001, 5, 100), f4(np.linspace(0.001, 5, 100), 2))
plt.plot(xGrid[:, 0], zGrid[:, 0])
plt.plot(xGrid[:, 1], zGrid[:, 1])
Note that this interpolation also has its drawbacks. I suggest plotting both interpolated functions as a surface and looking at how they are distorted compared to your original data:
from mpl_toolkits.mplot3d import Axes3D
xx,yy=(np.linspace(0,10,20),np.linspace(0,20,40))
xxs,yys=np.meshgrid(xx,yy)
zz3=f3(xx,yy) #from interp2d
zz4=f4(xxs,yys) #from LinearNDInterpolator
#plot raw data
hf=plt.figure()
ax=hf.add_subplot(111,projection='3d')
ax.plot_surface(xGrid,yGrid,zGrid,rstride=1,cstride=1)
plt.draw()
#plot interp2d case
hf=plt.figure()
ax=hf.add_subplot(111,projection='3d')
ax.plot_surface(xxs,yys,zz3,rstride=1,cstride=1)
plt.draw()
#plot LinearNDInterpolator case
hf=plt.figure()
ax=hf.add_subplot(111,projection='3d')
ax.plot_surface(xxs,yys,f4(xxs,yys),rstride=1,cstride=1)
plt.draw()
This will allow you to rotate the surfaces around and see what kind of artifacts they contain (with an appropriate backend).
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