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Reverse Mode Jacobian Sparsity Patterns

Syntax
f.rev_jac_sparsity(
     
pattern_intransposedependencyinternal_boolpattern_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<
Basef

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. It returns true if it succeeds and false otherwise.
Input File: cppad/core/rev_jac_sparsity.hpp