Fitting an integral
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I'm going to explain my problem with a sample. Assume that i have a function (f(x)=a.*x^2) and i need to calculate its integral indefinitely, lets assume this function doesn't have an indefinite integral. At the end i need to fit this integral to a data set. So I thought this could be achieved by quad function.
ftyp1 = fittype('quad(@(x) a.*x.^2,0,x)','options',ops1,'independent',{'x'},'coefficients',{'a'})
But in this example Matlab gives error. If i create another function to calculate quad function, like this :
function [c ] = myfunction( b ,a)
if length(a)==1, a = a(ones(size(b))); end
if length(b)==1, b = b(ones(size(a))); end
c=NaN(length(b),1);
parfor i=1:length(b)
c(i)=quad(@(x) a(i).*x.^2,0,b(i));
end
end
ftyp1 = fittype('myfunction(x,a)','options',ops1,'independent',{'x'},'coefficients',{'a'})
With using the sample code above, Matlab could find the coefficients. The trick is making it calculate quad function in another function as you can see.So my question is this : how could i implement quad function directly to fittype function without creating extra functions?
0 Kommentare
Antworten (3)
Andrew Newell
am 23 Apr. 2011
If your expression is a linear function of the coefficients, as in your example, you could do something like this:
ftyp1 = fittype('@(x) a.*quad(x.^2,0,x)','independent',{'x'},'coefficients',{'a'})
2 Kommentare
Andrew Newell
am 24 Apr. 2011
I confess I only went as far as creating a fittype object and did not try to fit anything.
Andrew Newell
am 24 Apr. 2011
I think the heart of the problem is that quad only accepts scalars for the lower and upper bounds, so it cannot deal with the vector x. I tried using arrayfun, but it does not accept function handles. Also, fittype does not accept function handles, so solutions involving nested functions are out. Your myfunction is probably the best approach.
Giovanni Ughi
am 17 Okt. 2011
Useful topic. In case I have to fit a model like this: model = b.*x .* quad(a.*x.^2) with a,b parameters and x independent variable?
apparently is not possible to write something like this
for i:1:length(b)
c(i) = @(x) b(i).*x .* quad(@(x) a(i).*x^2,0,d(i))
end
any suggestion?
1 Kommentar
Walter Roberson
am 17 Okt. 2011
c{i} = @(x) b(i).*x .* quad(@(x) a(i).*x^2,0,d(i));
Function handles can not be stored as elements of regular arrays, but can be stored as elements of cell arrays.
What you are going to _do_ with those stored function handles, I do not know.
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