MATLAB: How to Sum functions

sum

Hi,
I have an ugly function which I want to integrate it with respect to θ1 and θ2 in a function handle. X and Y are two n*1 arrays. I wonder how can I do the summation so that at the end (before integration) I have the result as sum square of n functions in terms θ1 and θ2? That is, this sum should take values of X and Y from the arrays simultanouesly and plug into y and y^ respectively.
Thanks
σ_f^2≡∫(y-y ̂ )^2 *pdf(θ)dθ
pdf(θ)=exp⁡(-1/(2σ^2 ) *∑(y-y ̂ )^2 )
y=C1-θ1*f(x)-θ2g(x)
y ̂ =Y

Best Answer

Uff!!!. I think I finally found a solution to this. I will not assure this is the best way to do it.
clear all;
%initialize global variables
global X;
global Y;
global n;
global var2; %this provide Y(k)
global var1; %this provides X(k)
global c;
% get the inputs
X=[0;5;10;20;30;50;100;200;300;400;500;600;700;800;1000;1200];
Y=[0.96;0.88;0.85;0.82;0.8;0.78;0.73;0.69;0.65;0.61;0.57;0.54;0.51;0.48;0.39;0.21];
c=[.961 .04 .868 1204.2 1.996e-4];
%find the length of X
n = length(X);
err=2.8929e-05;
% define Sigma_f2
Sigma_f2 = zeros(n,1);
This above part is only for initialization. The next part is used for calculation. I have defined the function names as per their function. Previously defined global variables are used in the functions below.
% this creates a function handle for (Y-y^)^2
Square = @Calculate_ydiff_square;
% this is the part where you got stuck. I created a different handle for this purpose. you can look at the working below
Sum = @Summation;
%similar function handle to calculate pdf
Pdf = @(te1,te2)(2*exp(-(1/(2*err^2)))* Sum(te1,te2));
%here we multiply and two functioan handles and prepare it for integration!
IntegralProduct = @(te1,te2)(Square(te1,te2).*Pdf(te1,te2));
for k =1:n
    %get the value of X and Y required for calculation
    var1 = X(k);
    var2 = Y(k);
    %Intergrate it!!
    Sigma_f2(k)=integral2(IntegralProduct,3.76E-02,4.19E-02,1.72E-04,2.25E-04)/((2*pi*err)^(n/2));
end
%calculate the (y-y^)^2
function y_diff_square = Calculate_ydiff_square(te1,te2)
% define the glovbbal variable used here
    global var2;
    global c;
    global var1;
    y = (c(1)-te1*asinh((c(3)^2*var1) / (1-var1/c(4))) - te2*var1);
   % return the required value
    y_diff_square = (y - var2).^2;
end
% the Mystery box of this function!:)
function SumVal = Summation(te1,te2)
    SumVal = 0;
    global X;
    global Y;
    global n;
    global c;
    % re-iterate the values for all values of x and Y and then Add it
    for k=1:n
       var1 = X(k);
       var2 = Y(k);
       %Here function cannot be called as the  var1 and var2 is different for this case and hence cannot be made global
       SumVal = SumVal + ((c(1)-te1*asinh((c(3)^2*var1) / (1-var1/c(4))) - te2*var1) - var2).^2;
    end
end
I am still not sure with the solution. please let me know if this works fine
The reason why matrix cannot be used in integration is during integration Matlab makes its own matrix for all the values in the range of the integrals!. So having a Input matrix of different size cannot be processed,
:)
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