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Numerical method

The minimization of L in Equation 6 and Equation 10 is achieved by employing a conjugate gradient solver. A direct gradient is computed from the augmented cost function L by using a discrete positional derivative for the individual elements of B at each iteration, and is updated according to the conjugate gradient method for optimization. The algorithm uses fast sparse matrix routines and a quadratic minimization subproblem to determine the optimal step length α, producing a fast and efficient optimizer. Subroutines for computationally intense calculations such as the sparse matrix-vector products have been threaded with OpenMP and so can be executed in parallel. The number of threads utilized in this is determined by the NCORES input parameter.