Non-linear curvefitting in MATLAB

Hey guys! I'm some given some huge set of data. I am trying to fit a set of data into a model of functional form as described below:

z(x, y) = c0. * x^0 * y^2 + c1. * x^1 * y^1 + c2. * x^2 *y^1

where c0, c1, c2 are the coefficients to be found.

My attempt is to use the nlinfit function to solve it.

So far I have tried:

% i have just added a small portion of my data

a= [ 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001,0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011];

x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

y = x.* a;

z = [ -.304860225, .170315374, .343019354, .370114906, .373180536, .36719579, .363397853, .363417755, .366962504, .379710865, -.304860225, .170315374, .343019354, .370114906, .373180536, .36719579, .363397853, .363417755, .366962504, .379710865];

model= c0.* (x(:).^0).* (y(:).^2) + c1.* (x(:).^1).* (y(:).^1) + c2.* (x(:).^2).* (y(:).^0)

[c0 c1 c2] = [0.001 0.007 0.788]

C= nlinfit( [x,y], z, 'model', [0.001 0.007 0.788])

% Here x,y are independent variables and z is dependent variable.

How can one set these initial values for the coefficients? I'm not getting how to pass the arguments. I'm getting this error "??? Undefined function or variable 'c0' ". Please help!!!

Thanks in advance, Syeda

Answer 1

[Greg Heath]

The solution is trivial because you have a linear system of equations for the 3 coefficients

 A*c = b;

c = A\b

Hope this helps

Thank you for formally accepting my answer

Greg

[Syeda]

Thankyou Greg! Now, if I put these three co-efficients back into my proposed model. and re-check for random x,y values again. It gives error:

x=1;
y=0.001;
z =  0 * x^0 * y^2 + 0.0000 * x^1 * y^1 + 0.0056 * x^0 * y^2

Any advice?

[Matt J]

It's really not ideal to fit polynomials bluntly using backslash. That's why MATLAB offers the more robust POLYFIT and why the File Exchange offers a variety of polynomial fitters.

[Syeda]

yes!! My results are not accurate by using this method.

Answer 2

[Matt J]

Using a nonlinear solver for a linear fitting problem seems like the wrong way to go. A better option might be

http://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

[Syeda]

Thankyou for replying Matt.

I tried John D'Errico's polyfitn()as well. But, how can I fit my proposed model in this function?

model = [ ( x(:).^0 ).*( y(:).^2 ), ( x(:).^1 ).*( y(:).^1 ), ( x(:).^2 ).*( y(:).^0 ) ]

p = polyfitn([x,y], z, 'model');

It gives an error:

??? Error using ==> polyfitn at 137 indepvar and depvar are of inconsistent sizes.

[Matt J]

I've never used the tool myself. Perhaps you need to columnize z,

 p = polyfitn([x,y], z(:), 'model');

[Syeda]

It still gives the same error.

Anyways, thankyou for replying!!

[Matt J]

Maybe this

 p = polyfitn([x(:),y(:)], z(:),  {'y', 'x*y', 'x^2*y'});

[Syeda]

This works for me

p = polyfitn([x(:),y(:)], z(:), 'model')

But, it is giving only one coefficient. I want 3 coefficients..

[Syeda]

I tried both equations, but it gives error!

p = polyfitn([x(:),y(:)], z(:),  {'y', 'x*y', 'x^2*y'});

p = polyfitn([x(:),y(:)], z(:),  {'x*y^2', 'x*y', 'x^2*y'});

??? Error using ==> polyfitn>parsemodel at 319 Variable is not a valid name: '2'

Error in ==> polyfitn at 151 [modelterms,varlist] = parsemodel(modelterms,p);

[Matt J]

I can't see why the syntax

p = polyfitn([x(:),y(:)], z(:), 'model')

would work. And it is obviously not working, since it gives you the wrong number of coefficients.

[Syeda]

yes! it is not working as well. I guess there is some syntax problem in my code.

[Matt J]

Dunno. Instead of 'x^2*y' maybe you should try either 'x*x*y' or 'y*x^2'.

[Syeda]

No, it still gives error.

??? Undefined function or method 'polyfitn' for input arguments of type 'cell'