Reducing the number of AD passes for computing a sparse Jacobian matrix

A reduction in the computational work is possible if we do not require that the nonzeros of a Jacobian matrix be determined directly. If a column or row partition is available, the proposed substitution technique can be used to reduce the number of groups in the partition further. In this chapter, we present a substitution method to determine the structure of sparse Jacobian matrices efficiently using forward, reverse, or a combination of forward and reverse modes of AD. Specifically, if it is true that the difference between the maximum number of nonzeros in a column or row and the number of groups in the corresponding partition is large, then the proposed method can save many AD passes. This assertion is supported by numerical examples.

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