Personal fit using lsq

Hi every one. I have a couple of data "t,y" file

i need to fit them by using this function

where a,b,c are parameters that I must get by the fit.

I wrote:

A=load('D:/datifit.txt')
  t=A(:,1);
  y=A(:,2);
  plot(t,y,'ro');
  title('Data');

to plot the data and I get the plot...later, to fit, I wrote:

F=@(x,xdata)(xdata/15+0.964)*(xdata/15+0.964)*x(1)+2*(xdata/15+0.964)*(xdata*xdata/15-0.36*xdata)*x(2)+(xdata*xdata/15-0.36*xdata)*(xdata*xdata/15-0.36*xdata)*x(3)
x0=[1 1 1];
[x,resnorm,~,exitflag,output] = lsqcurvefit(F,x0,t,y)

but I get this error

Error using  * 
Inner matrix dimensions must agree.

Error in
@(x,xdata)(xdata/15+0.964)*(xdata/15+0.964)*x(1)+2*(xdata/15+0.964)*(xdata*xdata/15-0.36*xdata)*x(2)+(xdata*xdata/15-0.36*xdata)*(xdata*xdata/15-0.36*xdata)*x(3)

Error in lsqcurvefit (line 202)
            initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Caused by:
    Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

Can someone help me please?

[Image Analyst]

Here I was getting all ready to help you and then I found out you forgot to attach 'D:/datifit.txt'. I'll check back later in the day. http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

Answer 1

[Image Analyst]

Since you didn't supply your actual data, I just made up some. Here is my program for you:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format short g;
format compact;
fontSize = 25;

% Define function that the X values obey.
X = sort(rand(1, 50));
a = 10 % Arbitrary sample values I picked.
b = 1
c = 1
% Get a vector.  No noise in this Y yet.
Y = (X/15+0.964)*a + 2*(X/15+0.964).*(X.^2/15-0.36*X)*b+(X.^2/15-0.36).^2*c;
plot(X, Y, 'bd-');
grid on;

% Add noise to Y.
Y = Y + 0.001 * randn(1, length(Y));
% Now we have noisy training data that we can send to fitnlm().
% Plot the noisy initial data.
plot(X, Y, 'b*', 'LineWidth', 2, 'MarkerSize', 15);
grid on;

% Convert X and Y into a table, which is the form fitnlm() likes the input data to be in.
tbl = table(X', Y');
% Define the model as Y = (X/15+0.964)*a + 2*(X/15+0.964).*(X.^2/15-0.36*X)*b+(X.^2/15-0.36).^2*c
% Note how this "x" of modelfun is related to big X and big Y.
% x((:, 1) is actually X and x(:, 2) is actually Y - the first and second columns of the table.
modelfun = @(b,x) (x(:, 1)/15+0.964)*b(1) + 2*(x(:, 1)/15+0.964).*(x(:, 1).^2/15-0.36*x(:, 1))*b(2)+(x(:, 1).^2/15-0.36).^2*b(3);
beta0 = [10, .8, 1.2]; % Guess values to start with.  Just make your best guess.
% Now the next line is where the actual model computation is done.
mdl = fitnlm(tbl, modelfun, beta0);
% Now the model creation is done and the coefficients have been determined.
% YAY!!!!

% Extract the coefficient values from the the model object.
% The actual coefficients are in the "Estimate" column of the "Coefficients" table that's part of the mode.
coefficients = mdl.Coefficients{:, 'Estimate'}
% Create smoothed/regressed data using the model:
a = coefficients(1)
b = coefficients(2)
c = coefficients(3)
yFitted = (X/15+0.964)*a + 2*(X/15+0.964).*(X.^2/15-0.36*X)*b+(X.^2/15-0.36).^2*c;
% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.
hold on;
plot(X, yFitted, 'r-', 'LineWidth', 2);
grid on;
title('Non-Linear Regression with fitnlm()', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
legendHandle = legend('Noisy Y', 'Fitted Y', 'Location', 'north');
legendHandle.FontSize = 25;

message = sprintf('Coefficients : \n  a = %8.5f\n  b = %8.5f\n  c = %8.5f',...
coefficients(1), coefficients(2), coefficients(3));
text(0.1, 9.778, message, 'FontSize', 23, 'Color', 'r', 'FontWeight', 'bold', 'Interpreter', 'none');
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')

and here is the result:

[Stephan]

This is insane - i like it ;-)

[Image Analyst]

Stephan, do you like it enough to "Accept this Answer" and "Vote" for it?

For the others, don't be afraid that the code looks long and complicated. It's not. Most of the code is just comment lines, lines to create a sample data set, and code to make a fancy plot. The actual code that does the fit/regressions and get the coefficients is only 3 lines!

modelfun = @(b,x) (x(:, 1)/15+0.964)*b(1) + 2*(x(:, 1)/15+0.964).*(x(:, 1).^2/15-0.36*x(:, 1))*b(2)+(x(:, 1).^2/15-0.36).^2*b(3);
beta0 = [10, .8, 1.2];
mdl = fitnlm(tbl, modelfun, beta0);

[Stephan]

Hi,

I already voted for this answer. If i could i would accept this answer but i was not the one who asked the question. Im only the guy which tried to answer this question in a convetional way.

Best regards

Stephan

Answer 2

[Stephan]

Hi,

try this:

F = @(x,xdata)x(1).*(xdata.*(1.0./1.5e1)+2.41e2./2.5e2).^2+x(3).*(xdata.*(9.0./2.5e1)-xdata.^2.*(1.0./1.5e1)).^2-x(2).*(xdata.*(2.0./1.5e1)+2.41e2./1.25e2).*(xdata.*(9.0./2.5e1)-xdata.^2.*(1.0./1.5e1))

do not worry - matlab symbolic toolbox has reshaped your equation slightly. But this should work.

Best regards

Stephan

Answer 3

[Fc Fc]

Hi, thank you to the both.

1) @Stefan Jung. By your code I get a,b,c values, but when I add the code

hold on
plot(t,F(x,t))
hold off

to plot also the fit function, it changes all the graph...What I mean is that first I've this plot

Lastly I get this one

2) @ImageAnalyst: I changed your code to get x,y values by my datafile... First I wrote:

A=load('D:/Datifit.txt');

then I replaced this line X = sort(rand(1, 50));

with this one

X = A(:,1);

and this line:

Y = Y + 0.001 * randn(1, length(Y));

with this one

Y = A(:,2);

but I get this error

Error using nlinfit (line 211)
MODELFUN must be a function that returns a vector of fitted values the same size as Y (1-by-15).  The model function you provided
returned a result that was 1-by-1.

One common reason for a size mismatch is using matrix operators (*, /, ^) in your function instead of the corresponding elementwise
operators (.*, ./, .^).
Error in NonLinearModel/fitter (line 1123)
                    nlinfit(X,y,F,b0,opts,wtargs{:},errormodelargs{:});
Error in classreg.regr.FitObject/doFit (line 94)
            model = fitter(model);
Error in NonLinearModel.fit (line 1430)
            model = doFit(model);
Error in fitnlm (line 94)
model = NonLinearModel.fit(X,varargin{:});
Error in personal_fit (line 32)
mdl = fitnlm(tbl, modelfun, beta0);

[Stephan]

Hi,

the change of the graph when adding the fitted line is resulting from a bad fit, if i assume that xdata only has the 15 values shown in your plot. The y-axis changes from an upper value of 8x10^-10 to 8x10^-09 which is a result of the used function.

If you were free to choose the function im sure you could reach better results. For example if you would use a polynom with degree of 3:

fun1 = @(x,xdata)x(4)+x(3).*xdata+x(1).*xdata.^3+x(2).*xdata.^2

Now you have to find out 4 values for a,b,c and d - but i guess that will be a pretty nice fit.

Best regards

Stephan

[Fc Fc]

Thank you stephan, but I'm not free to choose the fit function! I've to fit using that function!

[Stephan]

Ok. So my part is done for this question. Im going to unfollow this question.

Best regards

Stephan

[Fc Fc]

Thank you for your help !

[Image Analyst]

"I'm not free to choose the..." -- does this mean it's your homework?

[Fc Fc]

No...it isn't matlab homework! I'm just writing a laboratory report!