Check optimality of computeResidual/computeJacobian

[Derek Gaston]

Try overloading computeResidual / computeJacobian directly and check timings.

Need to understand if computeQpResidual/Jacobian is slowing things down tremendously.

[Derek Gaston]

Also check if Jacobian loop should be reordered for column major access...

[Derek Gaston]

Overriding computeResidual!() and computeJacobian!() directly gives a speedup of 30-40% over overriding computeQpResidual() and computeQpJacobian() for the "manual" case

However - it doesn't seem to effect AD... so maybe the speedup is all in the Jacobian...

[Derek Gaston]

I can confirm... overriding computeJacobian!() directly is the one that makes a big difference.

Now let's look at loop order in computeJacobian!()

[Derek Gaston]

Using @inline actually makes it even slower...

[Derek Gaston]

Let's see if it's the if... try putting it in the loops

[Derek Gaston]

It's not the if... putting it inside the loops doesn't matter.

BTW: doing the jacobian loop "column major" doesn't help

[Derek Gaston]

Specifying the return type of computeQpJacobian() did help some

[Derek Gaston]

Ok... so @inline and specifying the return type means that just overriding computeQpJacobian() is just as optimal as overriding computeJacobian!()

Here is an example of the form that should be used:

@inline function computeQpJacobian(kernel::Diffusion, v::Variable, qp::Int64, i::Int64, j::Int64)::Float64
    u = kernel.u

    if u.id == v.id
        return v.grad_phi[qp][j] ⋅ u.grad_phi[qp][i]
    end

    return 0
end