| Prev | Next |  |  |  |  |  |  |

Compute Sparse Jacobians Using Subgraphs
Syntax
`f.subgraph_jac_rev(x, subset)
` `f.subgraph_jac_rev(
select_domain, select_range, x, matrix_out
)`
Purpose
We use F : R n → R m to denote the function corresponding to `f` . Here `n` is the domain size, and `m` is the range size, or `f` . The syntax above takes advantage of sparsity when computing the Jacobian J ( x ) = F ( 1 ) ( x ) The first syntax computes the sparsity pattern and the value of the Jacobian at the same time. If one only wants the sparsity pattern, it should be faster to use subgraph_sparsity .
Method
This routine uses a subgraph technique. To be specific, for each dependent variable, it creates a subgraph of the operation sequence containing the variables that affect the dependent variable. This avoids the overhead of performing set operations that is inherent in other methods for computing sparsity patterns.
BaseVector
The type `BaseVector` is a SimpleVector class with elements of type `Base` .
SizeVector
The type `SizeVector` is a SimpleVector class with elements of type `size_t`.
BoolVector
The type `BoolVector` is a SimpleVector class with elements of type `bool`.
f
This object has prototype `
ADFun<Base> f
` Note that the Taylor coefficients stored in `f` are affected by this operation; see uses forward below.
x
This argument has prototype `
const BaseVector& x
` It is the value of `x` at which we are computing the Jacobian.
Uses Forward
After each call to Forward , the object `f` contains the corresponding Taylor coefficients . After a call to `sparse_jac_forward` or `sparse_jac_rev`, the zero order coefficients correspond to `
f.Forward(0, x)
` All the other forward mode coefficients are unspecified.
subset
This argument has prototype `
sparse_rcv<SizeVector, BaseVector>& subset
` Its row size is `subset.nr() == m` , and its column size is `subset.nc() == n` . It specifies which elements of the Jacobian are computed. The input elements in its value vector `subset.val()` do not matter. Upon return it contains the value of the corresponding elements of the Jacobian.
select_domain
The argument `select_domain` has prototype `
const BoolVector& select_domain
` It has size n and specifies which independent variables to include.
select_range
The argument `select_range` has prototype `
const BoolVector& select_range
` It has size m and specifies which components of the range to include in the calculation. A subgraph is built for each dependent variable and the selected set of independent variables.
matrix_out
This argument has prototype `
sparse_rcv<SizeVector, BaseVector>& matrix_out
` This input value of `matrix_out` does not matter. Upon return `matrix_out` is sparse matrix representation of F ( 1 ) ( x ) . The matrix has m rows, n columns. If `select_domain[j]` is true, `select_range[i]` is true, and F i ( x ) depends on x j , then the pair ( i , j ) is in `matrix_out` . For each `k = 0 , ..., matrix_out.nnz()` , let `
i = matrix_out.row()[k]
j = matrix_out.col()[k]
v = matrix_out.val()[k]
` It follows that the partial of F i ( x ) with respect to x j is equal to v .
Example
The files subgraph_jac_rev.cpp and subgraph_hes2jac.cpp are examples and tests using `subgraph_jac_rev`. They returns `true` for success and `false` for failure.

Input File: cppad/core/subgraph_jac_rev.hpp