I want to calculate y' * diag(A' * B * A) * y

• y is a N * 1 vector
• A is a m * N matrix where N >> m
• B is a m * m matrix, and B is a symmetric positive definite matrix, the Cholesky decomposition B = L * L' is precomputed if it is needed.

Is it possible to calculate the above expression in O(N*m) complexity?