surface fitting

I am using MATLAB 2007. I want to do surface fitting. Any help will be appreciated.

Thanks.

Answer 1

[Grzegorz Knor]

See:

http://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit

You can also write your own function e.g. by using the Optimization Toolbox.

Answer 2

[smp]

Thanks.

I have downloaded the files on my Desktop of my Linux machine. What to do next i.e. how to incorporate gridfit in MATLAB 2007?

smp

Answer 3

[Grzegorz Knor]

Add folder which contains this function to search path, and type:

help gridfit

Answer 4

[smp]

I did as you said.

Then I used this command:

zgrid = gridfit(x,y,z,xi,yi)

where

x= experimental x co-ordinates 
y= experimental y co-ordinates
z= experimental values for each pair (x,y)

and 

xi = linspace(-0.8,0.8,50)
yi=  linspace(-0.8,0.8,50)

But where and when I will provide my "model surface" to be fitted to experimental data (x,y,z(x,y))?

My model surface is z(x,y)= c*( 2*(x^2+y^2)-1 )

And more important for me : How to obtain fitted coefficient c?

Thanks & Regards,

smp

Answer 5

[Grzegorz Knor]

Gridfit produce only smooth surface that approximates your data.

If you want to calculate the coefficient c from your model look at the example:

[x y] = meshgrid(-1:.1:1);
c = sqrt(2);
z = c*( 2*(x.^2+y.^2)-1 );
z = z + randn(size(z))/5;
plot3(x,y,z,'r.')

f = @(c)norm(z-c*( 2*(x.^2+y.^2)-1));

c1 = fminsearch(f,1);

z1 = c1*( 2*(x.^2+y.^2)-1 );

hold on
surf(x,y,z1,'FaceColor','none')

Answer 6

[smp]

I worked out your example in my machine. It worked well. But I have some problems when I tried to do similar thing to my data:

I did this:

[x,y]=meshgrid(-0.707107:0.141421:0.707107)
c=1.0
f = @(c)norm(z-c*(2*(x^2+y^2)-1))

where z is a vector of experimental values (which I had loaded earlier by command "load z.txt")

Then I gave this command:

c1=fminsearch(f,0.1)

Then I got this message:

??? Error using ==> minus
Matrix dimensions must agree.

Error in ==> @(c)norm(z-c*(2*(x^2+y^2)-1))

Error in ==> fminsearch at 205
fv(:,1) = funfcn(x,varargin{:});

So what's my mistake?

Thanks & Regards,

smp

[Grzegorz Knor]

If z is a vector, then x and y should be vectors too.

BTW: add dots to this line before ^:

f = @(c)norm(z-c*(2*(x.^2+y.^2)-1))

Answer 7

[smp]

I started afresh:

>> load x.txt

>> load y.txt

>> load z.txt

Here x,y,z are vectors each containing 121 entries. Basically I have array of 11x11 x values, array of 11x11 y values, and corresponding array of 11x11 z values. But for some reason I want x,y,z in vector forms.

Then I gave these commands:

>> c=1.0
>> f = @(c)norm(z-c* (2*(x.^2+y.^2)-1 ) )
>> c1=fminsearch(f,0.1)

(why dots are needed for x & y in 'f' ?)

I got c1 = 1.4958

But when I changed c to 5, still I got c1=1.4958

Obviously this is wrong.

Thanks & Regards,

smp

[Walter Roberson]

See the reference material for mpower ("^") and power (".^") to see when to use one or the other.

Changing the initial value of c to 5 has no effect on the code. The anonymous function f does not use the existing value of c in any way. The anonymous function uses c as a "dummy argument". Nothing would change if you were to instead use

f = @(ThisC)norm(z-ThisC* (2*(x.^2+y.^2)-1 ) )

[smp]

Ok. thanks. But then what is the way to find fitted coefficient c?

Regards,

smp

Answer 8

[smp]

To Walter Roberson (regarding your comment): Ok. thanks. But then what is the way to find fitted coefficient c?

Regards, smp