Eigen efficient type for dense symmetric matrix

Question

Does Eigen have efficient type for store dense, fixed-size, symmetric matrix? (hey, they are ubiquitous!)

I.e. for N=9, it should store only (1+9)*9/2==45 elements and it has appropriate operations. For instance there should be efficient addition of two symmetric matrices, which returns simmilar symmetric matrix.

If there is no such thing, which actions (looks like this) I should make to introduce such type to Eigen? Does it has concepts of "Views"? Can I write something like "matrix view" for my own type, which would make it Eigen-friednly?

P.S. Probably I can treat plain array as 1xN matrix using map, and do operations on it. But it is not the cleanest solution.

Answer 1

Packed storage of symmetric matrices is a big enemy of vectorized code, i.e. of speed. Standard practice is to store the relevant N*(N+1)/2 coefficients in the upper or lower triangular part of a full dense NxN matrix and leave the remaining (N-1)*N/2 unreferenced. All operations on the symmetric matrix are then defined by taking into account this peculiar storage. In eigen you have the concept of triangular and self-adjoint views for obtaining this.

From the eigen reference: (for real matrices selfadjoint==symmetric).

Just as for triangular matrix, you can reference any triangular part of a square matrix to see it as a selfadjoint matrix and perform special and optimized operations. Again the opposite triangular part is never referenced and can be used to store other information.

Unless memory is a big problem, I would suggest to leave the unreferenced part of the matrix empty. (More readable code, no performance problems.)