Linearize an exponential curve for feeding it in GAMS

I have a set of data that creates an exponential curve. I want to linearize it in order to load it into a gams model.

Any ideas on how I can achieve it?

Thank you for your time!

Answer 1

[John D'Errico]

What do you mean by linearizing a nonlinear curve? I can think of many ways to do that. But no matter what, a nonlinear function is not linear.

For example, one thing you MIGHT be looking to do is to log it. So if your data is

x = -5:5;
y = 2*exp(x/3) + 1;
plot(x,y,'o')

Then we might decide to just take log(y). Of course, that would fail sometimes, because logs of negative numbers will be complex.

plot(x,log(y),'o')

Is that linearized? Not really, because the log of the sum of terms is nothing special.

Or, are you hoping to approximate the relationship using a linear approximation? For example, a truncated Taylor series? Since all you have is the data, that is not really an option. But nothing stops you from using polyfit.

P1 = polyfit(x,y,1)

P1 = 1×2

0.9136 4.3091

So the linear approximation model is just

syms x
vpa(P1(1)*x + P1(2))

ans = 

But while there are many things you MIGHT be thinking about to linearize this model, until you explain more clearly what you mean by the word "linearize" it is impossible to help you more.

You might even post your data, if you want better help yet.

[panagiotis skrempos]

First of all, thank you for your quick response. I want to do something similar to the thing in the picture, in which the red is the curve and the black the linearization. I get the polyfit method, however this one with the log, it makes linear the logy and not y.