Use of 'ArrayValued' in Matlab numerical integration

Why in Matlab numerical integration

f = @(x) 5;
integral(f,0,2,'ArrayValued',true)

needs 'ArrayValued',true ... while

f = @(x) x;
integral(f,0,2)

don't need it?

Answer 1

[Davide Masiello]

Let's take a look at the error message

f = @(x) 5;
integral(f,0,2)

Error using integralCalc/finalInputChecks
Output of the function must be the same size as the input. If FUN is an array-valued integrand, set the 'ArrayValued' option to true.

Error in integralCalc/iterateScalarValued (line 315)
finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

The important line here is "Output of the function must be the same size as the input".

I believe this could be due to the fact that integral passes a whole array of x-values in the attempt to integrate the function within the default tolerances.

If your functions does not depend on x, then the ouput would be a single scalar and therefore different from the input.

Specifing 'ArrayValued' as true, you tell the solver that the output must be an array the same size as the x passed to it.

In fact, you could try to integrate an equivalent function where the dependance on x is explicit, and it would work without specifying 'ArrayValued' as true.

f = @(x) 5*(x-x+1);
integral(f,0,2)

10

[Renzo Del Fabbro]

Thank you for your help Davide.

Answer 2

[Torsten]

f = @(x) 5*ones(size(x));
integral(f,0,2)

ans = 10