Integral doesn't work

I'm supposed to implement a program which, for a given partition xi and a continuous fonction on [a,b], computes the solution of the linear system Au=r, where , (for which I have computated formulas) and , .

My problem is that my function r does not run. The integral function is apparently not happy with my definition of my bj's and I really don't have much ideas how to solve the problem. I'd much appreciate some help.

Edit: Errors in the command window:

Error using integralCalc/finalInputChecks (line 526)

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);

Here's my code:

%{

The function b takes as arguments: an index j, a real number x between

a=x_0 and b=x_{n+1}, and the vector of the points x_i of the partition g.

b computes bj(x).

%}

function bj=b(j,x,xi)

n=size(xi,2)-2; %There are n+2 points in the partition

switch j

case 1

if (x>=xi(1) & x<=xi(2))

bj=(xi(2)-x)./(xi(2)-x(1));

else

bj=0;

end

case n

if (x>=xi(n+1) & x<=xi(n+2))

bj=(x-xi(n+1))./(xi(n+2)-xi(n+1));

else

bj=0;

end

otherwise

if (x>=xi(j-1) & x<=xi(j))

bj=(x-xi(j-1))./(xi(j)-xi(j-1));

elseif (x>=xi(j) & x<=xi(j+1))

bj=(xi(j+1)-x)./(xi(j+1)-xi(j));

else

bj=0;

end

end

end

%{

The function A computes the matrix A defined as in the exercise 5.1.a

%}

function mat=A(xi)

n=size(xi,2)-2;

mat=zeros(n,n);

h=zeros(n,1);

for k=1:n+1

h(k)=xi(k+1)-xi(k);

end

for i=1:n

for j=i:n

if i==j

switch i

case 1

mat(i,j)=1/h(1);

case n

mat(i,j)=1/h(n+1);

otherwise

mat(i,j)=(h(i)+h(i+1))*(h(i)*h(i+1)+3)/(3*h(i)*h(i+1));

end

elseif i==j-1

mat(i,j)=(h(i)+h(i+1))/3;

mat(j,i)=mat(i,j);

else

mat(i,j)=0;

mat(j,i)=0;

end

end

end

end

%{

The function r takes a continuous function f and the partion as arguments,

and computes the rj's (and hence r) with the bj's

%}

function int_r=r(f,xi)

n=size(xi,2);

int_r=zeros(1,n);

for j=1:n

g=@(x)f(x).*b(j,x,xi);

int_r(j)=integral(g,0,1);

end

end

Answer 1

[Star Strider]

I have no idea what the arguments are, or what ‘doesn’t work’ means.

However, since the integrand is apparently an array, see if:

int_r(j)=integral(g,0,1, 'ArrayValued',true);

produces the correct result.

NOTE — The ‘int_r’ variable may also need to be defined as an array for this to work correctly.

.

[Florian Spicher]

I mean it produces an error, and we’ve learnt to call arguments the objects inserted into the function.

Thanks, I’ll try this when I’ve got my computer!

[Star Strider]

Please share the full text of the error message (all the red text from the Command Window).

[Florian Spicher]

Well, strange thing is, I tried to run in on my phone with the app to show you and… it works… I’ll try to reinstall Matlab on my computer I guess. I’ll show you the errors when I can though. Thanks for the help!

[Star Strider]

My pleasure!

The online Run app is R2021b, so if your computer is running an earliler version, the version differences could be the problem.

.

[Florian Spicher]

Mine is R2021a, so maybe that's why. However, using your "ArrayValued",true corrected the errors (which I'm going to publish, for the record) and now not only have I a result, but also it is coherent!

Thanks a lot, you saved me!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.