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Are there math programs to do this.

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Patrick

Sun Apr 03 2016, 08:57PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Are there math programs that can take a series of already known X,Y coordinates and turn them into a common f(x) function ?

Bored Chemist

Sun Apr 03 2016, 09:12PM

Registered Member #193 Joined: Fri Feb 17 2006, 07:04AM
Location: sheffield
Posts: 1022

You can do it in excel.
But you need to have some idea what form to use for f(x)
For example, if you tell it to, excel will blindly try to fit a sine wave to a straight line.

What are you trying to achieve?

Patrick

Sun Apr 03 2016, 09:48PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

if I have a concave up trending group of points, id like to derive a f(x). the more points I guess the better, which I can do, but still need a function.

Blackcurrant

Sun Apr 03 2016, 10:10PM

Registered Member #2989 Joined: Sun Jul 11 2010, 12:01AM
Location: UK
Posts: 94

see the bit on software half way down

or try looking for polynomial curve fitting

2Spoons

Mon Apr 04 2016, 12:25AM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

As Bored Chemist said, you still need to have some idea of the underlying function, which should be simple to find if you understand the process thats generating your data points. e.g fitting a polynomial to something fundamentally exponential may be reasonable within the bounds of your measured data, but its likely to be poor near the edges, and hopeless for extrapolation.

Bjørn

Mon Apr 04 2016, 09:58AM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

can fit some types of functions to a data series.

Carbon_Rod

Tue Apr 05 2016, 05:08AM

Registered Member #65 Joined: Thu Feb 09 2006, 06:43AM
Location:
Posts: 1155

Eureqa
"Eureqa is a mathematical software tool originally created by Cornell's Creative Machines Lab and later commercialized by Nutonian, Inc. The software uses symbolic regression to determine mathematical equations that describe sets of data in their simplest form."
(

)

This program did a bit more than simple curve fitting, but now appears to be commercial use only.

... it's likely easier to use iterative curve fitting scripts in octave or Matlab...

flannelhead

Tue Apr 05 2016, 07:04PM

Registered Member #952 Joined: Mon Aug 13 2007, 11:07AM
Location: Finland
Posts: 388

gnuplot can do nonlinear fitting as well, but you'll still need to give the function to fit to the data.

klugesmith

Tue Apr 05 2016, 09:51PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Does your data set have redundant X values?
If not, then you can fit it perfectly with a continuous piecewise linear function.

AKA linear interpolation. Not hard to write from scratch in Excel, and useful in many practical cases.

Dr. Slack

Thu Apr 07 2016, 08:23PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Curve fitting in the general case is an art, not a science.

It's possible to find families of curves that will fit any function. Given the curves, there are efficient ways to get a least squares best fit. Least squares minimises the energy of the errors between the data points and their approximation. Such families include Polynomials (Taylor series), Chebychev functions, sine waves (Fourrier analysis), and any number of others. The art comes from choosing a suitable family, and a suitable order.

Given a curve family to work from, a reasonable way to get to the appropriate order is to fit at several orders starting at the lowest, measuring the error energy for each order. You may see a sudden dip in energy, or you may have a maximum error energy criterion. In any case, an order larger than the square root of the number of data points is unlikely to be a good fit, as it will be likely to be over-fitting, that is fitting the noise.

Any family of curves can approximate any other curve, given sufficient order. However, if the approximating function is a good match for the actual curve, the needed order can be dramatically lower. It is often worth experimentally adding a curve from a different family into the approximation functions to see whether the error improves. A curve might well show a good fit to a.x+b.ln(x)+c.sin(x)+d for instance.

Some curves, a histogram of measurement results, or the intensity of a broadened optical line, can be well fitted by a normal, where the centre position, width and height can be adjusted iteratively.

A program can be written to try combinations of supplied functions. AI to go quickly to the best functions is probably an interesting PhD thesis, one that might perform as well as an experienced mathematician who looks at the data and says 'I reckon a tan plus a couple of normals would look good there!'

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