反转一系列数据，就像使用MATLAB反转函数一样 [英] Invert a series of data as if inverting a function using MATLAB

问题描述

是否可以像反转函数一样反转"一系列数据?

Is it possible to "invert" a series of data like when a function is inverted?

让我解释一下.如果我有一个可以在MATLAB中绘制的函数，我总是(几乎)可以通过finverse找到该函数的逆函数，并且该图将提供以下信息:

Let me explain. If I have a function that I can plot in MATLAB, I can always (almost) find the inverse of such function with the finverse and the plot would provide this:

但是我没有用于数据的函数，我仍然想找到这类数据系列的逆函数，例如y=f(x) where

But I do not have the a function for my data, and I would still like to find a sort of inverse of such series of data, like for example y=f(x) where

x=[0.0050879   0.0056528   0.0062176   0.0067822   0.0073467   0.0079111   0.0084752   0.0090392   0.0096030   0.0101666   0.0107299   0.0112930   0.0118558   0.0124184   0.0129807   0.0135428   0.0141045   0.0146659   0.0152270   0.0157877   0.0163481];

和

y=[0.0000e+00   0.0000e+00   0.0000e+00   0.0000e+00   0.0000e+00   0.0000e+00   0.0000e+00   0.0000e+00   0.0000e+00   0.0000e+00   4.4901e-05   4.4901e-05   8.9801e-05   1.3470e-04   1.7960e-04   2.2450e-04   2.6940e-04   3.5920e-04   4.0411e-04   4.9391e-04   5.8371e-04];

在MATLAB中可以对一系列数据进行这种操作吗?是否有可以解决这个问题的技术/方法/功能?

Is this kind of operation on a series of data possible in MATLAB? Is there a technique/method/function that handles this?

注意:我以前尝试通过polyfit函数使用多项式对数据序列进行拟合"，然后通过finverse函数对其进行求逆；但是会导致同时依赖x和y的f^-1函数.而且由于x的间距甚至不均匀，我什至都不知道如何绘制...

NOTE: I previously tried to "fit" the series of data with a polynomial via the polyfit function and then invert it via the finverse function; but it results in an f^-1 function that is dependent on both x and y at the same time. And because x is not even spaced homogeneously, I do not even know how to plot it...

推荐答案

通过更改x和y:(y, x)的位置，可以反转由一系列(x, y)数据点表示的函数.可以在Matlab中将其可视化，如下所示:

Inverting a function represented by a series of (x, y) data points is done by changing the position of x and y: (y, x). This can be visualised in Matlab as follows:

figure
hold on
plot(x, y, 'red')
plot(y, x, 'blue')
from = min(min(x), min(y));
to = max(max(x), max(y));
plot([from to], [from to], 'k--')
legend('Original', 'Inverted')

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