Purpose
We use @(@
F : \B{R}^n \rightarrow \B{R}^m
@)@ to denote the
function corresponding to the operation sequence stored in
af
.
for_jac_sparsity
Fix @(@
R \in \B{R}^{n \times \ell}
@)@ and define the function
@[@
J(x) = F^{(1)} ( x ) * R
@]@
Given a sparsity pattern for @(@
R
@)@,
for_jac_sparsity computes a sparsity pattern for @(@
J(x)
@)@.
rev_jac_sparsity
Fix @(@
R \in \B{R}^{\ell \times m}
@)@ and define the function
@[@
J(x) = R * F^{(1)} ( x )
@]@
Given a sparsity pattern for @(@
R
@)@,
rev_jac_sparsity computes a sparsity pattern for @(@
J(x)
@)@.
x
Note that a sparsity pattern for @(@
J(x)
@)@ corresponds to the
operation sequence stored in
af
and does not depend on
the argument
x
.
af
The object
af
has prototype
a_fun af
The object
af
is not const when using
for_jac_sparsity.
After a call to for_jac_sparsity, a sparsity pattern
for each of the variables in the operation sequence
is held in
af
for possible later use during
reverse Hessian sparsity calculations.
pattern_in
The argument
pattern_in
has prototype
const sparse_rc& pattern_in
see sparse_rc
.
This is a sparsity pattern for @(@
R
@)@.
pattern_out
This argument has prototype
sparse_rc<SizeVector>& pattern_out
This input value of
pattern_out
does not matter.
Upon return
pattern_out
is a sparsity pattern for
@(@
J(x)
@)@.
Sparsity for Entire Jacobian
Suppose that @(@
R
@)@ is the identity matrix.
In this case,
pattern_out
is a sparsity pattern for
@(@
F^{(1)} ( x )
@)@.
