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?
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답변 (3개)
Andrew Newell
2011년 4월 23일
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'})
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Andrew Newell
2011년 4월 24일
I confess I only went as far as creating a fittype object and did not try to fit anything.
Andrew Newell
2011년 4월 24일
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
2011년 10월 17일
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?
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Walter Roberson
2011년 10월 17일
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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