Problem 44508. Curve fitting (non-linear functions) & function handles

Created by David Verrelli

Solve Later

In this problem you are provided some raw data. You need to find a way of summarising the data with just a few parameters, so that it can be reconstructed. You then need to provide a handle to your own (generic) custom function that will indeed reproduce the raw data when provided with the parameters that you determine.
Consider a non-linear scalar function y = mˣ + c. Suppose x is the vector [3 2 1 4]. The function would operate elementwise on x; for example, if m=2 and c=3 then y = [11 7 5 19]. You are provided with both the vector x and the vector y. Every number will be provided in some form of an integer data type. The scalar parameters m and c are both whole numbers (although they're not provided directly).
So here you should output two things:
the handle to a generic function that implements the relevant non-linear function (i.e. of the form y = mˣ + c) taking two inputs, namely 1 a set of parameters and 2 the vector x, and outputting the corresponding vector y (in any data type); and
a set of parameter values (m and c) wrapped into a single MATLAB variable (of any data type).
As the parameters will be used in your own function, the data type will be set by you.
So, for the above example, you could return a function handle @myFunc that you have defined, along with the variable param that has two fields such that param.base = 2 and param.translation = 3.
Or, if you have defined your function differently, then you could return the function handle @myFn along with a cell array variable prms that has four elements such that prms{1}='positive', prms{2}=uint8(3), prms{3} = 'positive' and prms{4} = uint8(2).
And so on.
Note 1: the parameter m can be assumed to have values between -30 and +30 (inclusive); the parameter c can be assumed to have values between -10000 and +10000 (inclusive); the elements in x are positive.
Note 2: if the code runs too slowly, then it will also fail the Test Suite.
Note 3: there might not be only one unique pair of the m & c parameter values that is correct — the individual values of m & c are not tested here, only the values of y that they predict are examined.
See also Problem 44507. Curve fitting (linear functions) & function handles — easier.

Solve

Solution Stats

34 Solutions
2 Solvers

Last Solution submitted on Nov 14, 2020

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

Tim on 1 Feb 2018

I think you may need to modify some of the tests to "...ensure both odd and even values of x" in all cases where m might be negative.

David Verrelli on 2 Feb 2018

Hi, Tim. Thanks for your feedback. Actually, from the Player's point of view, m 'could' be negative in any Test. I agree that in some situations there might not be one unique pair of the m & c parameter values that is correct. However, I never apply an assertion to the values of m & c in the Test Suite, rather I check what values of y the user-supplied parameters produce from the user-supplied function(handle). _Any_ valid combination of m & c should be able to REpredict the same values of y provided in the original input, from the same x values (or a subset thereof). There is only one test where I check for prediction of y using x values not included in the original input (extrapolation/interpolation), and for that one test I do have to be careful to ensure there is one unique pair of m & c values that is correct. So I would say this is intentional (I'll add a short note to the Problem Statement). But please let me know if there's a flaw in my logic. —DIV

Tim on 3 Feb 2018

Aha--I see now. To quote Emily Litella: "Never mind."

David Verrelli on 7 Feb 2018

I should clarify one detail for other Players. Given y = mˣ + c (elementwise), suppose x is the vector [7 8 5 6] and y is the vector [123 123 123 123]. Then there are two valid combinations of m & c, namely m=0 & c=123 and m=1 & c=122. So actually there is not just one unique set of m & c values in this case. However, given x>0 (in the Problem Statement), either of these alternatives can be correctly extrapolated or interpolated from.

Solution Comments

Show comments

Problem Recent Solvers2

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!