Multiple Variable Non Linear Regression OR Curve Fitting Matlab

Question

I have a set of noisy data and want to fit a custom equation though it in MATLAB. Next I would take the values of the coefficients and utilize them in my algorithm. However I am stuck and I cant figure out why. I use a non linear equation a+b*log10(x1-dcos(alpha-x2)) where x1,x2 and the response value are known. First problem is the coefficients of a ,b, and alpha must be bounded. alpha here being in degrees can only vary from 0 to 360 for example.I dont know how to achieve this using curve fitting toolbox.

I have also tried other options like non linear regression techniques in MATLAB( fitnlm,lsqcurvefit etc) which proved to be disappointing as i cant have bounds over these variables. So in spite of fit being quite good, the coefficients are way too bad.

So, Question 1 : How do I fit multiple variables using curve fitting ? Question 2 : If thats not possible then what other techiniques can I use except non linear regression .

Many thnaks in advance ! Have a great day !

Configure your problem in cftool until you get it right, then use the "export code" function to learn how to do it programmatically. — Dev-iL
@Sayantan Roy Did you try the answer? Or please clarify your question — anquegi
@anquegi Sorry for the late reply. Yes I saw your answer and thank you for the effort. My problem is the fitting that I get gives a weird alpha value which can only be between 0 and 360. I used your function and added a bound. However, the fitting doesnot meet my needs. I feel that a set of data may have different number of solutions since cos(theta) = cos(-theta). So as matlab computes the angle alpha it generates a value, however this alpha can be another value too which would satisfy the same equation and data set. I dont know how to get multiples values for alpha . — Sayantan Roy
@Sayantan Roy, maybe you can use the tirgonmetic identities that I added later to the response, with this will we easy to find that value, also we carefull that x2 is also angle — anquegi
and be carefully about cos(alfa), it is true cos(alfa) = cos(-alfa), but in this case is cos(-alfa+X2). so in my opinion alfa can only be alfa + n*360 being n from 0 to infinity, so is the same angle, be carefull with the range for X2 — anquegi

anquegi anquegi · Accepted Answer · 2016-07-11T16:32:10

Well If I get your problem you have a set of data, for the variables x1 and x2 and thre result y, and you want to model it with this equation:

y =  a + b * log10(x1 - cosd(alpha - x2)) % I suppose that dcos = cosd, I do not really known this functions

First I will create the data for this values:

function y = getting_data(x1,x2)

a = 3;
b = 5;
alpha = 120;

y =  a + b * log10(x1 - cosd(alpha - x2));

Now let's generate de datasets

>> % generate the data sets
>> x1 = 9 .* rand(1000,1) + 1; % random values [1,10]
>> x2 = 360 .* rand(1000,1); % random values [0,360]
>> y = getting_data(x1,x2); % the values for the function

create a function that use curve fitting for your model

function myfit = fitting_data(x1,x2,y)

myfittype = fittype('a + b * log10(x1 - cosd(alpha - x2))',...
    'dependent',{'y'},'independent',{'x1','x2'},...
    'coefficients',{'a','b','alpha'})

myfit = fit([x1 x2],y,myfittype)

be carefull with the input vector it should be nx1 to the fit function

and finally we get the coefficients:

>> fitting_data(x1,x2,y)

myfittype = 

     General model:
     myfittype(a,b,alpha,x1,x2) = a + b * log10(x1 - cosd(alpha - x2))
Warning: Start point not provided, choosing random start point. 
> In curvefit.attention.Warning/throw (line 30)
  In fit>iFit (line 299)
  In fit (line 108)
  In fitting_data (line 7) 

     General model:
     myfit(x1,x2) = a + b * log10(x1 - cosd(alpha - x2))
     Coefficients (with 95% confidence bounds):
       a =           3  (3, 3)
       b =           5  (5, 5)
       alpha =         120  (120, 120)


     General model:
     ans(x1,x2) = a + b * log10(x1 - cosd(alpha - x2))
     Coefficients (with 95% confidence bounds):
       a =           3  (3, 3)
       b =           5  (5, 5)
       alpha =         120  (120, 120)

wich represent the values that we guess

Also it will be usefull to separe de con(A - B) like this:

and also remember that

Multiple Variable Non Linear Regression OR Curve Fitting Matlab

1 Answers