What is "lobpcg"

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric positive definite generalized eigenvalue problem

Ax = λBx, 

for a given pair (A, B) of complex Hermitian or real symmetric matrices, where the matrix B is also assumed positive-definite.