[eigen] Efficient syntax for Ax=b where A is diagonal/Toeplitz

[Manoj Rajagopalan <rmanoj@xxxxxxxxx>]

Hi eigen-users,

    I come across cases where my physics generates different types of 
matrices, sometimes diagonal, sometimes Toeplitz depending on the simulation 
region. My PDE solution code requires me to solve systems of the form AX=B 
where A takes such different patterns. For readability it would be nice to 
introduce code that looks likes B = A.solve(X).

   The Eigen tutorial mentions A.lu().solve(X) for dense matrices but I 
couldn't locate similar info for diagonal matrices for which the solution 
procedure is very simple. I could explicitly code this in a few lines but I 
am just wondering if the above syntactic-sugar is possible with Eigen.

   When B,X are dense, column-major, the procedure, in slightly-abused MATLAB 
notation, is X[:,j]=B[:,j] ./ A.diagonal()[:]. When B,X are row-major, the 
fast procedure is X[i,:] = B[i,:] / A[i,i]. We may be more efficient if A is 
triangular or diagonal.

   If the convenient syntax doesn't exist, would it be possible to add this? I 
don't see any solve() or solveInPlace() methods on classes DiagonalMatrix or 
DiagonalWrapper.

   Also, efficient storage, arithmetic and linear-system solution (O(n^2)) 
algorithms are possible when A is (symmetric) Toeplitz (occur frequently in 
signal-processing and Fourier-series solution of ODE/PDE). Does the roadmap 
consider this case?

Thanks,
Manoj