向量值多元函数中的插值 [英] Interpolation in vector-valued multi-variate function

问题描述

在Python中，我正在尝试构造一个例程，该例程可以在多维(5+)参数空间中的矢量值数据中进行插值.即我有一个函数，该函数接受多个输入变量并返回多个输出变量.目前，向量的每个元素都有一个调用.数据在一个列文件中，所以我用

In Python, I'm trying to construct a routine that interpolates in vector-valued data in a multi-dimensional (5+) parameter space. i.e. I have a function that takes a number of input variables and returns a number of output variables. At the moment, there is one call for each element of the vector. The data is in a columned file, so I retrieve it with

import numpy
[x_data,y_data,f1_data,f2_data] = numpy.loadtxt('data',unpack=True)

然后，我使用SciPy的函数实例化各个插值器，例如

Then, I instantiate individual interpolators using SciPy's functions, like

from scipy import interpolate
f1 = interpolate.LinearNDInterpolator((x_data,y_data),f1_data)
f2 = interpolate.LinearNDInterpolator((x_data,y_data),f2_data)
...

现在，当我进行插值调用时，我必须为每个值f1，f2等进行插值，即使实际上它应该可以作为一个操作来实现.而且我猜想进行一次插值比进行五次或更多插值要快.

Now, when I make the interpolation call, I have to interpolate for each value f1, f2, etc. even though really it should be achievable as one operation. And I'm guessing that making one interpolation should be faster than making 5 or more.

有没有一种方法可以构造矢量(或数组)值的插值器?

我尝试用构造插值器

f = interpolate.LinearNDInterpolator((x_data,y_data),(f1_data,f2_data,...))

但它返回错误

ValueError:不同数量的值和点

ValueError: different number of values and points

我还阅读了此问题和答案，但这是关于标量的向量值函数的，显然可以由interp1d处理.

I've also read this question and answer but it's about a vector-valued function of a scalar, which can apparently be handled by interp1d.

推荐答案

scipy.interpolate.LinearNDInterpolator 希望以行优先顺序接收其数据:例如，在您的情况下，第一个参数需要是一个成对的数组，而不是一对数组.由于在加载数据时已转置了数据，因此必须将其再次转回，然后再将其传递到LinearNDInterpolator.尝试类似的东西:

scipy.interpolate.LinearNDInterpolator expects to receive its data in row-major order: for example in your case, the first argument needs to be an array of pairs, not a pair of arrays. Since you transposed your data when you loaded it, you'll have to transpose it back again before passing it to LinearNDInterpolator. Try something like:

points = numpy.array((x, y)).T
values = numpy.array((f1, f2)).T
f = interpolate.LinearNDInterpolator(points, values)

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