迭代插值：首先插入网格，然后插值

Question

我想从x插入z。但有一点需要注意：

根据州y，我有一个不同的xGrid - 我需要进行插值。

我有y，yGrid的网格。说yGrid=[0,1]。 <{1}}由

提供

xGrid

相应的1 10 2 20 3 30 ，是

zGrid

这意味着对于100 1000 200 2000 300 3000 ，y=0是x的正确网格，而对于y = 1，[1,2,3]是正确的网格。和z相似。

所有内容都是线性的，均匀间隔以显示问题，但它不在实际数据中。

用语言说，

• 如果[10,20,30]，y=0，x=1.5是z在[1,2,3]上[100, 200, 300]的插值 - 1.5 。
• 如果150，y=1，x=10

问题在于：z=1000怎么办？在这个简单的例子中，我希望插值网格为y=0.5和[5.5, 11, 33/2]，因此[550, 1100, 1650]将接近1000。

在我看来，我需要插补3次：

• 两次以获得正确的x=10和xGrid以及
• 一次插入zGrid - ＆gt; xGrid

这是瓶颈的一部分，效率至关重要。我如何最有效地编码？

以下是我可以非常低效地编写代码的方法：

xGrid

输出

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)

实际用例数据

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) ：

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

我按照给定的答案创建了插值器，然后插入了一些点：

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.        ])

这是输出：

蓝线是插值线。我担心，对于非常小的x值，应向下倾斜一点（遵循两个函数的加权平均值），但它根本不是。

Answer 1

您实际上在查看二维插值：您需要z(x,y)，其内插值为x和y。唯一的细微之处在于，您需要广播yGrid，使其与x和z数据具有相同的形状：

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.])

您可以将其转换为使用lambda：

返回标量的单变量函数

f4 = lambda x,y=yValue: f3(x,y)[0]

这将为您的（假定的）单y值返回单个值，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，一般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来获取{的数组输出{1}}。

更新

对于形状奇特的z数据，x,y可能会产生令人不满意的结果，尤其是在网格的边界处。所以另一种方法是使用interpolate.LinearNDInterpolator代替，它基于输入数据的三角测量，固有地给出局部分段线性逼近

interp2d

使用您的更新数据集：

f4 = interpolate.LinearNDInterpolator((xGrid.flatten(),yGrid.flatten()),zGrid.flatten())

请注意，这种插值也有其缺点。我建议将插值函数绘制为曲面，并查看它们与原始数据相比如何失真：

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])

这将允许您旋转表面并查看它们包含的工件类型（使用适当的后端）。