I am doing triple integration by matlab and some error displayed.

Error using  ^  (line 51)

Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To perform elementwise matrix powers, use '.^'.

Error in integral3>@(y,z)FUN(x(1)*ones(size(z)),y,z) (line 138)

@(y,z)FUN(x(1)*ones(size(z)),y,z), ...

Error in integral2Calc>integral2t/tensor (line 237)

Z1 = FUN(X(VTSTIDX),Y(VTSTIDX)); NFE = NFE + 1;

Error in integral2Calc>integral2t (line 55)

[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)

[q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral3/innerintegral (line 137)

Q1 = integral2Calc( ...

Error in integralCalc/iterateScalarValued (line 314)

fx = FUN(t);

Error in integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)

[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral3 (line 121)

Q = integralCalc(@innerintegral,xmin,xmax,integralOptions);

I believe the frist error is caused by my constant setting, how to change the type of the constant type?

For me, I just input k=50 to do it. any advice to me?

[LA Leung]

Also, if I input a very complicated formula when will the .* and ./ be used?

Answer 1

[Steven Lord]

Use the ^ operator when you want to perform matrix multiplication in raising the matrix to a power.

Use the .^ operator when you want to perform element-wise multiplication in raising each element in the array to a power.

A = [1 2; 3 4]
A^2 % equivalent of A * A, using matrix multiplication
A.^2 % equivalent of A .* A, using element-wise multiplication

Since integral3 is going to call your function with an array of data, you probably want to use the element-wise operators rather than the matrix operators in your function.

[LA Leung]

Also, I want to ask if y is the first integrartion variable, how to let the computer knows that I am going to integrate with y first, if the integral order is y>x>z, is integral3(f,zmin,zmax,xmin,xmax,ymin,ymax) right input?

[LA Leung]

if the function is like this cos(x*(2-(c*y-0.5*y^2))*(z^2-x^2)^0.5, where should I place these pot operators in my function? cos(x.*(2-(c.*y-0.5.*y.^2)).*(z.^2-x.^2).^0.5, is that a right way? here, x,y,z are variable, c is constant.

[Steven Lord]

Re: ordering

The integral3 function doesn't really care what variable names you use as the inputs for your integrand function so long as the first set of limits corresponds to the limits of the first input argument to your integrand, the second to the second, and the third to the third. So if your integrand computes f(y, x, z) then the first set of limits are the limits of the integral over y, the second the limits over x, and the third the limits over z.

See the "4-D Integral of Sphere" example on the integral3 documentation page and note that the integral3 call in the function handle Q integrates over theta, then phi, then xi.

Re: vectorizing

The only multiplication or power operator in that integrand that doesn't need to be element-wise is the one between c and y, and it doesn't really matter whether that's matrix or element-wise multiplication. If one or both of a and b in the expression a*b is scalar it's equivalent to a.*b and I'm assuming your statement "c is constant" means that it's a scalar constant.

[LA Leung]

If I want to see the shape of function after second integral, how can I plot it? the integration order of f(y,x,z) is (y>x>z), can I do that f(z)=@(z) integral2(f,ymin,ymax,xmin,xmax)? because I try this and I can't plot it.