Prev

Next

Index-> contents reference index search external

Up-> CppAD ADFun sparsity_pattern for_hes_sparsity

CppAD-> Install Introduction AD ADFun preprocessor multi_thread utility ipopt_solve Example speed Appendix

ADFun-> record_adfun drivers Forward Reverse sparsity_pattern sparse_derivative optimize abs_normal FunCheck check_for_nan

sparsity_pattern-> for_jac_sparsity ForSparseJac rev_jac_sparsity RevSparseJac rev_hes_sparsity RevSparseHes for_hes_sparsity ForSparseHes dependency.cpp rc_sparsity.cpp subgraph_sparsity

for_hes_sparsity-> for_hes_sparsity.cpp

Headings-> Syntax Purpose x BoolVector SizeVector f select_domain select_range internal_bool pattern_out Sparsity for Entire Hessian Algorithm Example

@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@Forward Mode Hessian Sparsity Patterns
Syntax
f.for_hes_sparsity(
     select_domain, select_range, internal_bool, pattern_out
)

Purpose
We use @(@ F : \B{R}^n \rightarrow \B{R}^m @)@ to denote the AD function corresponding to the operation sequence stored in f . Fix a diagonal matrix @(@ D \in \B{R}^{n \times n} @)@, a vector @(@ s \in \B{R}^m @)@ and define the function @[@ H(x) = D ( s^\R{T} F )^{(2)} ( x ) D @]@ Given the sparsity for @(@ D @)@ and @(@ s @)@, for_hes_sparsity computes a sparsity pattern for @(@ H(x) @)@.

x
Note that the sparsity pattern @(@ H(x) @)@ corresponds to the operation sequence stored in f and does not depend on the argument x .

BoolVector
The type BoolVector is a SimpleVector class with elements of type bool.

SizeVector
The type SizeVector is a SimpleVector class with elements of type size_t.

f
The object f has prototype
     ADFun<Base> f

select_domain
The argument select_domain has prototype
     const BoolVector& select_domain
It has size @(@ n @)@ and specifies which components of the diagonal of @(@ D @)@ are non-zero; i.e., select_domain[j] is true if and only if @(@ D_{j,j} @)@ is possibly non-zero.

select_range
The argument select_range has prototype
     const BoolVector& select_range
It has size @(@ m @)@ and specifies which components of the vector @(@ s @)@ are non-zero; i.e., select_range[i] is true if and only if @(@ s_i @)@ is possibly non-zero.

internal_bool
If this is true, calculations are done with sets represented by a vector of boolean values. Otherwise, a vector of sets of integers is used.

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 @(@ H(x) @)@.

Sparsity for Entire Hessian
Suppose that @(@ R @)@ is the @(@ n \times n @)@ identity matrix. In this case, pattern_out is a sparsity pattern for @(@ (s^\R{T} F) F^{(2)} ( x ) @)@.

Algorithm
See Algorithm II in Computing sparse Hessians with automatic differentiation by Andrea Walther. Note that s provides the information so that 'dead ends' are not included in the sparsity pattern.

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

---

Input File: cppad/core/for_hes_sparsity.hpp