How to make the linear function

first of all, on the simulation condition

pf(pf>0.06) =1;

pf(pf<0.05) =1e3;

the value of f are decrease from 1 to 0, but once the value f<0.05 then become 1e4 times

but this condition make the trasition value changed was high ( the ranges is 1-10K ) how to makes the condition (f<0.05) as linear function, so the trasition will smoothly decrease.

[Sam Chak]

Best is to sketch out what the desired function looks like, and we can suggest how to build the math for it.

Some MATLAB functions do not require the input of math, only need to specify the critical points and then connect the dots to draw the line. This approach is more effective if you don't require the math for rigorous proof later.

[Agung Putra]

please kindly find the attached file

Answer 1

[Walter Roberson]

In order for it to be a linear function as you asked for, then you should take a list of all of the (x, y) coordinates that you want to preserve, and you should use polyfit() or equivalent to fit a polynomial to the points. It will probably end up having to be a high degree polynomial in order to fit the constant stretches on both ends. Once you fit a polynomial to your satisfaction, use polyval() to create new points.

If you have the Curve Fitting Toolbox, you may want to use cftool() to help with the fitting.

[Walter Roberson]

If I were doing this, I would not require a that a linear function be used.

[Agung Putra]

do you have any idea?

[Walter Roberson]

I already told you how to do it: fit a polynomial to the points you want to preserve. That will ensure that you satisfy the condition that it is a linear function.

[Sam Chak]

Hi @Agung Putra

Perhaps you need to clarify if the data points come from

1. the solution from a dynamical system such as , or
2. a static function such as , or
3. a set of data in an observational study (cannot be expressed in an analytical equation).

MATLAB has different tools to handle different cases.

From spreadsheet on the image, the plot appears to be generated from a data set in a table. If this is Case #3, then read this article:

https://www.mathworks.com/help/curvefit/smoothing-data.html

Answer 2

[Sam Chak]

Aha, I see... If you want to get rid of spikes and want a smooth transition, but not strictly linear, then you can consider adding a low-pass filter (signal terminology), or a 1st-order dynamics (just need to design the time constant to ensure that the transition is fast enough).