Can Matlab integral2 deal with a non-anonymous function?

Question

I have a user-defined function

function[Rout2] = SSP2(a1,a2,b1,b2,pB)  
if a1/b1>a2/b2
   if pB<=a1-b1*a2/b2
      Rout2 = (a1-pB)/b1; 
   else
       if pB<=a1+a2
          Rout2 = (a1+a2-pB)/(b1+b2); 
       else
          Rout2 = 0;  
       end
   end
else
    if pB<=a2-b2*a1/b1
       Rout2 = (a2-pB)/b2;  
    else
        if pB<=a1+a2
           Rout2 = (a1+a2-pB)/(b1+b2);  
        else
           Rout2 = 0;   
        end
    end     
end
end

b1,b2,pB are all parameters. I want to use Matlab integral2 to integrate this function over a1 in [0,t1] and a2 in [0,t2]. I originally tried

integral2(SSP2,0,t1,0,t2)

But it does not work. Then I guess it is probably I am passing extra parameters. So I did the following modification

function[R] = NumericalIntegration(b1,b2,pB,t1,t2)
function[Rout2] = SSP2(a1,a2)  
if a1/b1>a2/b2
   if pB<=a1-b1*a2/b2
      Rout2 = (a1-pB)/b1; 
   else
       if pB<=a1+a2
          Rout2 = (a1+a2-pB)/(b1+b2); 
       else
          Rout2 = 0;  
       end
   end
else
    if pB<=a2-b2*a1/b1
       Rout2 = (a2-pB)/b2;  
    else
        if pB<=a1+a2
           Rout2 = (a1+a2-pB)/(b1+b2);  
        else
           Rout2 = 0;   
        end
    end     
end
end
R = integral2(@SSP2,0,t1,0,t2);
end

Now, inside the function NumericalIntegration, the function SSP2 can have access to the parameters b1,b2,pB. I thought it should work. But it does not. And when I call the function NumericalIntegration in my main program, it generates error "Not enough input arguments". I was wondering is that because the Matlab integral2 can only work with those one-line anonymous function?

Answer 1

The problem here is the way you defined your function. To do a double integration using the built-in functions, the integrand should be properly vectorized.

One way to do it is to rewrite your function using for loops to treat the cases where a1 and a2 are 2D-arrays of dimensions [m,n]. But you can use MATLAB element-wise multiplication and the logical operators to define your function as:

function[Rout2] = SSP2(a1,a2,b1,b2,pB)
    Rout2 = 0*a1;

    Rout2 = Rout2 + ((a1-pB)/b1).*(a1/b1>a2/b2).*(pB<=a1-b1*a2/b2) + &
        ((a2-pB)/b2).*(a1/b1<=a2/b2).*(pB<=a2-b2*a1/b1);
end

And then create the anonymous function and call it as:

b1 = rand;
b2 = rand;
pB = rand;

fun = @(a1,a2) SSP2(a1,a2,b1,b2,pB);

t1 = rand;
t2 = rand;
I = integral2(fun,0,t1,0,t2)

Just define your parameters b1, b2 and pB and integration limits t1 and t2 accordingly.