Thanks a lot for the detailed answer. I changed a bit your macro,
introducing conj() instead of ' and splicing the Kronecker sum to get a
functional version:
macro M(m,n, ε1,ε2,ε3, X1,X2,X3, A1,A2,A3)
ε = [ε1,ε2,ε3]
X = [X1,X2,X3]
A = [A1,A2,A3]
Asum = {:+}
for q=1:3, t=1:3
if m+q == n+t
push!(Asum, :(conj($(A[q])) * $(A[t])))
end
end
if m == n
:($(ε[m]) + 2*abs2($(X[m])) * $(Expr(:call, Asum...)))
else
:(2 * conj($(X[m])) * $(X[n]) * $(Expr(:call, Asum...)))
end
end
I also defined a macro for the elements of Q:
macro Q(m,n, X1,X2,X3, A1,A2,A3)
X = [X1,X2,X3]
A = [A1,A2,A3]
Asum = {:+}
for q=1:3, t=1:3
if m+n == q+t
push!(Asum, :($(A[q]) * $(A[t])))
end
end
:(conj($(X[m])) * conj($(X[n])) * $(Expr(:call, Asum...)))
end
and now I'm a bit stuck on putting it all together to get the full L
matrix. Im trying to calculated L(i,j) based on M and Q for the 4 separate
blocks. I only implemented the upper left block but I get an error
macro L(i,j, ε1,ε2,ε3, X1,X2,X3, A1,A2,A3)
if i<4
if j<4
@M(i,j, ε1,ε2,ε3, X1,X2,X3, A1,A2,A3)
end
end
end
`+` has no method matching +(::Symbol, ::Int64)
It seems that the @M macro needs a value for the m,n indices for the comparison
if m+q == n+t
Any ideas how to solve this? The end-result I want is a function L(k, A1, A2,
A3, etc) which would return the full 6x6 matrix.
//A
On Thursday, August 28, 2014 10:42:29 PM UTC+2, Steven G. Johnson wrote:
>
> On Thursday, August 28, 2014 6:36:16 AM UTC-4, Andrei Berceanu wrote:
>>
>> Steven, could you detail your macro proposal please? What exactly do you
>> have in mind?
>>
>
> e.g. you could have a macro like (caution: untested):
>
> macro M(m,n, ε1, ε2, ε3, X1,X2,X3, A1,A2,A3)
> ε = [ε1, ε2, ε3]
> X = [X1,X2,X3]
> A = [A1,A2,A3]
> Asum = {:+}
> for q=1:3, t=1:3
> if m+q == n+t
> push!(Asum, :($(A[q])' * $(A[t])))
> end
> end
> if m == n
> :($(ε[m]) + 2*abs2($(X[m])) * $(Expr(:call, Asum)))
> else
> :(2 * $(X[m])' $(X[n]) * $(Expr(:call, Asum)))
> end
> end
>
> Then calling e.g. @M(1,2,ε1, ε2, ε3, X1,X2,X3, A1,A2,A3) would insert a
> hard-coded
> expression for M[1,2] according to your formula, with only the nonzero
> delta terms. Here εm denotes the m'th case of your expression [ε(k_m+k)
> .... ] in brackets, Xm denotes X(k_m+k), and Am denotes Ã_m.
>
> Macros are essentially functions evaluated at parse-time, not at runtime,
> so they are exactly what you want in order to auto-generate fast inlined
> code resulting from some complicated symbolic expression that is known in
> advance, with whatever simplifications you can devise.
>
> You could write another macro for the entries of Q, and another macro to
> put it all together and evaluate the whole matrix if you want.
>
