Curve fitting: Getting very poor results on seemingly simple data set ("fit" function)

Hello everyone,

I will be the first to admit I am a complete newbie with the "fit" function and "cfun" data type, and find the documentation available on it much less than user friendly, so please refrain from directing me to it - I have been through it front to back and have not found a solution.

I am going through a dataset in which I am analyzing hundreds of discrete blocks, each of which has an essentially periodic behaviour. I need to find the amplitude of this periodic behaviour. I have included an example.

My problem is this. I used a very clear sample dataset containing 13 samples (one of the best I have) with a very obvious cosine behaviour. I set the fit function up and ran it, and got parameters that give me almost a straight line. I tried using repmat thinking maybe it was my sample size, and this does almost nothing.

I manually solved the periodic fit and have included the plot with the original data, the empirically derived fit, and the results from the 'fit' function below. I have also provided what I believe to be the relevant chunk of code, but I could be wrong. Please let me know what else if anything I need to include. As I have to perform this operation on literally hundreds or thousands of these blocks, this is not something I can feasibly do manually, so if someone can direct me as to what I'm doing wrong, I would be infinitely grateful.

Thank you kindly for your time.

My image should be available here: http://i42.tinypic.com/jf7oud.jpg

Here is what cfun spits out:

cfun =

     General model Sin1:
       cfun(x) =  a1*sin(b1*x+c1)
     Coefficients (with 95% confidence bounds):
       a1 =      0.8323  (-22.99, 24.66)
       b1 =    0.004459  (-0.9294, 0.9383)
       c1 =       1.936  (-72.97, 76.84)

And here is the relevant snippet:

%%%%%%%%%%%%%%%%%
% CURVE FITTING %
%%%%%%%%%%%%%%%%%

x = 2*pi.*((0:num_phases-1)./(num_phases-1));

num_phases2 = num_phases*10;
x2 = 2*pi.*((0:num_phases2-1)./(num_phases2-1));

x = x';
x2 = x2';

y = results(working_block*num_phases+1:working_block*num_phases+num_phases,1);
y2 = repmat(y,10,1);

cfun = fit(x,y,'sin1');

test = 0.025*cos(2*pi.*((0:num_phases-1)./(num_phases-1)))+0.775;

figure(1);
plot(2*pi.*((0:num_phases-1)./(num_phases-1)),results(working_block*num_phases+1:working_block*num_phases+num_phases,1)); hold on;
plot(2*pi.*((0:num_phases-1)./(num_phases-1)),test,'-r');
plot(cfun,'-g');

xlabel('Block');
ylabel('Correlation');
legend('Original Data','0.025cos(2pi*x)+0.775','Fitted Data');

[bym]

please include your data!

[Matthew]

My data is several thousand images so I don't know how to field this request?

Answer 1

[dpb]

Your model without an intercept term doesn't fit the data pattern worth a hoot...

With no intercept there's no offset to shift an initial zero value of sin(0) and the amplitude of the sin/cos has to be about +/-0.025 to fit the range of the data.

Try something more like

g = fittype( @(a,b,c,d,x) a.*sin(b.*x+c)+d )

With that I get a reasonable fit. Of course, w/ four parameters and only 13 data points you're using up a sizable fraction of the available DOF...

ADDENDUM:

Came to see if had been any followup and noticed what hadn't actually seen before...

I see in your legend text you don't have a phase angle in the equation--altho you don't show it, in that case you mis-specified the model. As the tool showed you, the model you fitted was

cfun(x) =  a1*sin(b1*x+c1)

whereas you wanted (apparently)

    cfun(x) =  a1*sin(b1*x)+c1

based on the text in

legend('Original Data','0.025cos(2pi*x)+0.775','Fitted Data');

IOW, you had a misplaced ')' in the function definition...

[Matthew]

Thank you, that definitely makes much more sense. However, 0.025*cos(2*pi.*((0:num_phases-1)./(num_phases-1)))+0.775; will not always be the appropriate parameters. I assume that @(a,b,c,d,x) are function handlers to find the appropriate values?

Additionally, when I try that snippet, I get this error:

??? Error using ==> fittype.fittype>fittype.fittype at 201
First input argument must be a string or cell array.

    Error in ==> Results_Analysis_working_copy at 95
    g = fittype( @(a,b,c,d,x) 'a.*sin(b.*x+c)+d' )

Could you provide an extended snippet of how you utilized this code to get a reasonable fit?

[Matthew]

My ignorance, it works now.

Per your ADDENDUM, that I was using the 'sin1' model, which would be a.*sin(b.*x+c) model. I tried using the 'a.*sin(b.*x+c)+d' model as well, and it works. Thank you kindly.