TMBad::Decomp2< ADFun > Struct Template Reference

Decomposition of computational graph. More...

#include <TMBad.hpp>

Public Member Functions
Decomp3< ADFun >	HesFun (std::vector< bool > keep_rc=std::vector< bool >(0), bool sparse_1=true, bool sparse_2=true, bool sparse_3=true)
	Calculate a sparse plus low rank representation of the Hessian. More...

Detailed Description

template<class ADFun>
struct TMBad::Decomp2< ADFun >

Decomposition of computational graph.

This structure holds a decomposition (f,g) of a computational graph of the form x -> f(x, g(x)) mapping R^n to R^m.

• The member first represents the mapping g:R^n -> R^k
• The member second represents the mapping f:R^(n+k) -> R^m

Definition at line 13 of file TMBad.hpp.

Member Function Documentation

HesFun()

template<class ADFun>

Decomp3<ADFun> TMBad::Decomp2< ADFun >::HesFun ( std::vector< bool >  keep_rc = std::vector<bool>(0), bool  sparse_1 = true, bool  sparse_2 = true, bool  sparse_3 = true  )

inline

Calculate a sparse plus low rank representation of the Hessian.

Recall that the present object represents a composition f(x, g(x)). Its Hessian is a sum of five terms:

\[ \nabla_x^2 f(x, g(x)) = f''_{xx}(x, g(x)) + f''_{xy}(x, g(x)) g'(x) + g'(x) f''_{yx}(x, g(x)) + f'_y(x, g(x)) g''(x) + g'(x) f''_{yy}(x, g(x)) g'(x) \]

The result is a structure of three components

1. The first four terms are represented by a sparse matrix H
2. The g' of the last term represented by a sparse matrix
3. f''_{yy} represented by a sparse matrix

Parameters

keep_rc	Rows/cols to keep. If used this mask selects a subset of x.
sparse_1	Return sparse first component
sparse_2	Return sparse second component
sparse_3	Return sparse third component

Note

This function preserves the inner/outer parameter categories if in use.

Definition at line 1285 of file TMBad.hpp.

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The documentation for this struct was generated from the following file:

• TMBad.hpp