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Up-> CppAD ADFun FunEval Sparse ForSparseJac

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

FunEval-> Forward Reverse Sparse

Sparse-> ForSparseJac RevSparseJac RevSparseHes

ForSparseJac-> ForSparseJac.cpp

Headings-> Syntax Purpose f ---..size_forward_bool ---..size_forward_set x q r s VectorSet Entire Sparsity Pattern Example

Jacobian Sparsity Pattern: Forward Mode
Syntax
s = f.ForSparseJac(q, r)

Purpose
We use $\mathit{F}:{\mathit{B}}^{\mathit{n}}\to {\mathit{B}}^{\mathit{m}}$ to denote the AD function corresponding to f . For a fixed $\mathit{n}\times \mathit{q}$ matrix $\mathit{R}$ , the Jacobian of $\mathit{F}[\mathit{x}+\mathit{R}*\mathit{u}]$ with respect to $\mathit{u}$ at $\mathit{u}=0$ is $$\mathit{S}(\mathit{x})={\mathit{F}}^{(1)}(\mathit{x})*\mathit{R}$$ Given a sparsity pattern for $\mathit{R}$ , ForSparseJac returns a sparsity pattern for the $\mathit{S}(\mathit{x})$ .

f
The object f has prototype
     ADFun<Base> f
Note that the ADFun object f is not const. After a call to ForSparseJac, the sparsity pattern for each of the variables in the operation sequence is held in f (for possible later use by RevSparseHes ). These sparsity patterns are stored with elements of type bool or elements of type std::set<size_t> (see VectorSet below).

size_forward_bool
After ForSparseJac, if k is a size_t object,
     k = f.size_forward_bool()
sets k to the amount of memory (in unsigned character units) used to store the sparsity pattern with elements of type bool in the function object f . If the sparsity patterns for the previous ForSparseJac used elements of type bool, the return value for size_forward_bool will be non-zero. Otherwise, its return value will be zero. This sparsity pattern is stored for use by RevSparseHes and when it is not longer needed, it can be deleted (and the corresponding memory freed) using
     f.size_forward_bool(0)
After this call, f.size_forward_bool() will return zero.

size_forward_set
After ForSparseJac, if k is a size_t object,
     k = f.size_forward_set()
sets s to the total number of elements in all the sets corresponding to the sparsity pattern stored in the function object f . If the sparsity patterns for this operation use elements of type bool, the return value for size_forward_set will be zero. Otherwise, its return value will be non-zero (unless the entire sparsity pattern is false). This sparsity pattern is stored for use by RevSparseHes and when it is not longer needed, it can be deleted (and the corresponding memory freed) using
     f.size_forward_set(0)
After this call, f.size_forward_set() will return zero.

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

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

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

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

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 $\mathit{q}=\mathit{n}$ and $\mathit{R}$ is the $\mathit{n}\times \mathit{n}$ identity matrix. In this case, the corresponding value for s is a sparsity pattern for the Jacobian $\mathit{S}(\mathit{x})={\mathit{F}}^{(1)}(\mathit{x})$ .

Example
The file ForSparseJac.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/for_sparse_jac.hpp