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Up-> CppAD ADFun FunEval Sparse RevSparseJac

ADFun-> Independent FunConstruct Dependent abort_recording seq_property FunEval Drivers FunCheck optimize

FunEval-> Forward Reverse Sparse

Sparse-> ForSparseJac RevSparseJac RevSparseHes

RevSparseJac-> RevSparseJac.cpp

Headings-> Syntax Purpose f x p s r VectorSet Entire Sparsity Pattern Example

Jacobian Sparsity Pattern: Reverse Mode
Syntax
r = F.RevSparseJac(p, s)

Purpose
We use $\mathit{F}:{\mathbf{R}}^{\mathit{n}}\to {\mathit{R}}^{\mathit{m}}$ to denote the AD function corresponding to f . For a fixed $\mathit{p}\times \mathit{m}$ matrix $\mathit{S}$ , the Jacobian of $\mathit{S}*\mathit{F}(\mathit{x})$ with respect to $\mathit{x}$ is $$\mathit{J}(\mathit{x})=\mathit{S}*{\mathit{F}}^{(1)}(\mathit{x})$$ Given a sparsity pattern for $\mathit{S}$ , RevSparseJac returns a sparsity pattern for the $\mathit{J}(\mathit{x})$ .

f
The object f has prototype
     ADFun<Base> f

x
the sparsity pattern is valid for all values of the independent variables in $\mathit{x}\in {\mathbf{R}}^{\mathit{n}}$ (even if it has CondExp or VecAD operations).

p
The argument p has prototype
     size_t p
It specifies the number of rows in $\mathit{S}\in {\mathbf{R}}^{\mathit{p}\times \mathit{m}}$ and the Jacobian $\mathit{J}(\mathit{x})\in {\mathbf{R}}^{\mathit{p}\times \mathit{n}}$ .

s
The argument s has prototype
     const VectorSet& s
(see VectorSet below). If it has elements of type bool, its size is $\mathit{p}*\mathit{m}$ . If it has elements of type std::set<size_t>, its size is p and all its set elements are between zero and $\mathit{m}-1$ . It specifies a sparsity pattern for the matrix S .

r
The return value r has prototype
     VectorSet r
(see VectorSet below). If it has elements of type bool, its size is $\mathit{p}*\mathit{n}$ . If it has elements of type std::set<size_t>, its size is p . It specifies a sparsity pattern for the matrix $\mathit{J}(\mathit{x})$ .

VectorSet
The type VectorSet must be a SimpleVector class with elements of type bool or std::set<size_t>; see sparsity pattern for a discussion of the difference.

Entire Sparsity Pattern
Suppose that $\mathit{p}=\mathit{m}$ and $\mathit{S}$ is the $\mathit{m}\times \mathit{m}$ identity matrix. In this case, the corresponding value for r is a sparsity pattern for the Jacobian $\mathit{J}(\mathit{x})={\mathit{F}}^{(1)}(\mathit{x})$ .

Example
The file RevSparseJac.cpp contains an example and test of this operation. It returns true if it succeeds and false otherwise.

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Input File: cppad/local/rev_sparse_jac.hpp