Schmidt decomposition of an operator is a useful tool of quantum information theory nowadays. Let $O$ be an operator acting on the Hilbert space $\mathcal{H}_{d_1} \otimes \mathcal{H}_{d_1}$. $\mathcal{H}_{d_1}$ and $\mathcal{H}_{d_2}$ are Hilbert spaces of dimensions $d_1$ and $d_2$ respectively. $\otimes$ is usual tensor product. Operator Schmidt decomposition of $O$ is $$O = \sum_i s_iA_i \otimes B_i, s_i \ge 0.$$ $A_i$ and $B_i$ are orthonormal operator basis for systems of operators acting on $\mathcal{H}_{d_1}$ and $\mathcal{H}_{d_2}$. My questions are
Is Schmidt decomposition different from singular value decomposition of the matrix $O$?
If they are different how to calculate $s_i$ for a matrix $O$. QUANTLAB, a MATLAB based program has an inbuild function to calculate it. But I want to see a procedure for its step by step calculation.