rev_jac_sparsity

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Reverse Mode Jacobian Sparsity Patterns

Syntax

f . rev_jac_sparsity (
      pattern_in , transpose , dependency , internal_bool , pattern_out
)

Purpose

We use \(F : \B{R}^n \rightarrow \B{R}^m\) to denote the AD Function corresponding to the operation sequence stored in f . Fix \(R \in \B{R}^{\ell \times m}\) and define the function

\[J(x) = R * F^{(1)} ( x )\]

Given the Sparsity Pattern for \(R\), rev_jac_sparsity computes a sparsity pattern for \(J(x)\).

x

Note that the sparsity pattern \(J(x)\) corresponds to the operation sequence stored in f and does not depend on the argument x . (The operation sequence may contain CondExp and VecAD operations.)

SizeVector

The type SizeVector is a SimpleVector class with elements of type size_t .

f

The object f has prototype

ADFun < Base > f

pattern_in

The argument pattern_in has prototype

const sparse_rc < SizeVector >& pattern_in

see sparse_rc . If transpose it is false (true), pattern_in is a sparsity pattern for \(R\) (\(R^\R{T}\)).

transpose

This argument has prototype

bool transpose

See pattern_in above and pattern_out below.

dependency

This argument has prototype

bool dependency

see pattern_out below.

internal_bool

If this is true, calculations are done with sets represented by a vector of boolean values. Otherwise, a vector of sets of integers is used.

pattern_out

This argument has prototype

sparse_rc < SizeVector >& pattern_out

This input value of pattern_out does not matter. If transpose it is false (true), upon return pattern_out is a sparsity pattern for \(J(x)\) (\(J(x)^\R{T}\)). If dependency is true, pattern_out is a Dependency Pattern instead of sparsity pattern.

Sparsity for Entire Jacobian

Suppose that \(R\) is the \(m \times m\) identity matrix. In this case, pattern_out is a sparsity pattern for \(F^{(1)} ( x )\) ( \(F^{(1)} (x)^\R{T}\) ) if transpose is false (true).

Example

The file rev_jac_sparsity.cpp contains an example and test of this operation.