Batched DGEMM Operations in Density Matrix Renormalization Group

The Lanczos algorithm for computing the lowest eigenvector of the Hamiltonian matrix is a computational kernel in DMRG (Density Matrix Renormalization Group) for modeling correlated materials. This matrix is block partitioned where each submatrix is a sum of  Kronecker products of various sizes. The Kronecker products (vec(Y) = kron(A,B)*vec(X) = B*X*A^t) can be implemented as DGEMM operations. This is a use case for batch DGEMM of different matrix sizes on GPU and multi-core CPUs.