Wrote

are data provided by the producers of materials or devices whose characteristics are not determined by analytical mathematical formulas, but only by measurements in the laboratories of the respective manufacturers.

That what I'm trying to explain: collected data are not true, they are just data.
They carry the noise from digitizing the measurements, hysteresis ... and manipulations
from the Lab(s). You can only interpolate pure or considered pure data.
What's the point to interpolate between noisy data ?

Matlab has "Spline smooth" [gadget] => That's why they never did carbon 12 alpha.
Please attach a vector of your data, just to check and keep going ahead, and
orient towards some interpolation method [there are quite a lot !].

At the point you are, the sole methods that will clean and interpolate are
polynomials methods. Not necessarily successful for any kind of profile.

Isn't an objective to model the data set by a function ?

Waiting for a vector of data ...

Wrote

Waiting for a vector of data ...

Three tings here: from very quick
1. a polynomial fit
2. Grow2 model
3. power model

One way or another, you have to do for each column
then populate for more data points, compose the matrix,
from the smmoothed matrices, proceed like before to interpolate
within the matrices ...

Not a big job for me, please do not hesitate: YES/NO

Jean

Wrote

Three tings here: from very quick

Page3 Nicolas.sm (29 KiB) downloaded 40 time(s).

Hello Nicolas,

This is as far as can do from your data. They aren't so nicely collected
as you pretended. Some models will do as well but can fit "Genfit" Smath.

Please: comment ... Jean

Page19 Nicolas Interpolation.sm (50 KiB) downloaded 47 time(s).

... you may prefer this polyfit model ?

Page22 Nicolas Other Fit_Interpolate.sm (27 KiB) downloaded 43 time(s).

Best regards Jean Giraud.
There are many ways to approach engineering. There are researchers in engineering issues, who usually do projects that have input data, vectors or data matrix results directly from lab measurements. These data are smoothed even by the project that these researchers accomplish and are then collected and edited in special books, called engineering design guidelines. There are then design engineers who use those design guidelines with readily smoothed data. Their project input data will then be processed by interpolation from the existing tables in these design guidelines. There are then applicant engineers, who read the projects made by designers and translate them into engineering products in the process of technological processing. The list can continue. I did not work in research, but I'm part of the second category. So let's clear the problem. All the arrays in my examples represent the magnetization curves of some magnetic materials, with certain preset parameters. The graphs provided by you are not relevant, as I have used interpolation, linear interpolation. At the same time, to simplify the vectors and data matrix used for interpolation, they were introduced into the project as discrete values ​​having intervals (where the curve has a more linear shape) where the data is more distant from each other than in the curvilinear portions. Cumulating the effects of how matrix values ​​are entered with the fact that I used a linear interpolation rather than a non-linear (cubic, logarithmic, etc.) resulted in those portions you presented that give the apparent appearance of some curves that were not smoothed. I hope the problem is understood and we will not discuss in the future the issue.
All the best.

The project is still in limbo, as long as you won't provide raw data from the Lab.

Spline2XV6 is world top for processing raw data.
The public version is freeware, somehow not as
powerful as the Mathcad coded version.

Best regards Jean Giraud.
Thanks for your lessons about data smoothing. As I was saying, I use the data from the already-smoothed design guidelines. Besides, there is no guarantee that if we smooth a graphic curve, just to look good, we have solved the problem of precision. In engineering there is a saying: any calculation is better than none. So I've used my designing guides all over my career and I never wrong. That's why I am grateful to the researchers who design guides, and I have stored the fruit of there research in my library. This does not mean that I do not take into account the process of smoothing the data, when necessary. Otherwise, I joined your forum to learn the basics of using SMath Studio, and not for any other reason. The math I know is enough for me until my age of 62. If I still feel the need to learn new things, I will ask on this forum.
All the best.

Wrote

until my age of 62

Oh ! my friend, you are a spring chicken vs Jean.
Smoothing is a rescue tool when no fitting method
is productive [model global, model piece wise ...].
1000's of data sets got well done Mathsoft Collaboratory.
I'm just addict to data.

Cheers, all the best.

Best regards Jean Giraud.

Wrote

... Oh ! my friend, you are a spring chicken vs Jean ...

... I understand. I just wanted to clarify why I'm here. As I have already said, mathematics is just a tool for me but not an object of study. I add new math knowledge only if I have something new to add to my engineering knowledge. You must however know that I already used in my work data smoothing techniques. MathCAD is well-equipped for this. Your tips above will remain for me a "just in case" guide.
All the best.