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s = f.ForSparseJac(q, r)
s = f.ForSparseJac(q, r, transpose)
F : B^n \rightarrow B^m
to denote the
AD function
corresponding to
f
.
For a fixed
n \times q
matrix
R
,
the Jacobian of
F[ x + R * u ]
with respect to
u
at
u = 0
is
\[
S(x) = F^{(1)} ( x ) * R
\]
Given a
sparsity pattern
for
R
,
ForSparseJac returns a sparsity pattern for the
S(x)
.
f
has prototype
ADFun<Base> f
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).
ForSparseJac, if
k
is a size_t object,
k = f.size_forward_bool()
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)
f.size_forward_bool()
will return zero.
ForSparseJac, if
k
is a size_t object,
k = f.size_forward_set()
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)
f.size_forward_set()
will return zero.
x \in B^n
(even if it has CondExp
or VecAD
operations).
q
has prototype
size_t q
R \in B^{n \times q}
and the Jacobian
S(x) \in B^{m \times q}
.
transpose
has prototype
bool transpose
false is used when
transpose
is not present.
r
has prototype
const VectorSet& r
r
has elements of type bool,
its size is
n * q
.
If it has elements of type std::set<size_t>,
its size is
n
and all the set elements must be between
zero and
q-1
inclusive.
It specifies a
sparsity pattern
for the matrix
R in B^{n times q}
.
r
has elements of type bool,
its size is
q * n
.
If it has elements of type std::set<size_t>,
its size is
q
and all the set elements must be between
zero and
n-1
inclusive.
It specifies a
sparsity pattern
for the matrix
R^R{T} in B^{q times n}
.
s
has prototype
VectorSet s
s
has elements of type bool,
its size is
m * q
.
If it has elements of type std::set<size_t>,
its size is
m
and all its set elements are between
zero and
q-1
inclusive.
It specifies a
sparsity pattern
for the matrix
S(x) \in B^{m \times q}
.
s
has elements of type bool,
its size is
q * m
.
If it has elements of type std::set<size_t>,
its size is
q
and all its set elements are between
zero and
m-1
inclusive.
It specifies a
sparsity pattern
for the matrix
S(x)^\R{T} \in B^{q \times m}
.
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.
q = n
and
R
is the
n \times n
identity matrix.
In this case,
the corresponding value for
s
is a
sparsity pattern for the Jacobian
S(x) = F^{(1)} ( x )
.