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Up-> cppad_swig library sparse sparse_hes

cppad_swig-> testing swig_xam.i library whats_new_2018

library-> module a_double vector a_fun sparse error xam.m4

sparse-> sparse_rc sparse_rcv jac_sparsity hes_sparsity sparse_jac sparse_hes

sparse_hes-> sparse_hes_xam.cpp sparse_hes_xam.m sparse_hes_xam.pm sparse_hes_xam.py

Headings-> Syntax module_ref Purpose af subset x r pattern work n_sweep Uses Forward Example

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@ Computing Sparse Hessians
Syntax
work = module_ref sparse_hes_work()
n_sweep = af.sparse_hes(subset, x, r, pattern, work)

module_ref
This is the module reference for the particular language.

Purpose
We use @(@ F : \B{R}^n \rightarrow \B{R}^m @)@ to denote the function corresponding to af . Given a vector @(@ r \in \B{R}^m @)@, define @[@ H(x) = (r^\R{T} F)^{(2)} ( x ) @]@ This routine takes advantage of sparsity when computing elements of the Hessian @(@ H(x) @)@.

af
This object has prototype
     ADFun<Base> af
Note that the Taylor coefficients stored in af are affected by this operation; see uses forward below.

subset
This argument has prototype
     sparse_rcv& subset
Its row size and column size is n ; i.e., subset.nr() == n and subset.nc() == n . It specifies which elements of the Hessian are computed. The input value of its value vector subset.val() does not matter. Upon return it contains the value of the corresponding elements of the Jacobian. All of the row, column pairs in subset must also appear in pattern ; i.e., they must be possibly non-zero.

x
This argument has prototype
     const vec_double& x
and its size is n . It specifies the point at which to evaluate the Hessian @(@ H(x) @)@.

r
This argument has prototype
     const vec_double& r
and its size is m . It specifies the multiplier for each component of @(@ F(x) @)@; i.e., @(@ r_i @)@ is the multiplier for @(@ F_i (x) @)@.

pattern
This argument has prototype
     const sparse_rc& pattern
Its row size and column size is n ; i.e., pattern.nr() == n and pattern.nc() == n . It is a sparsity pattern for the Hessian @(@ H(x) @)@. This argument is not used (and need not satisfy any conditions), when work is non-empty.

work
This argument has prototype
     sparse_hes_work& work
We refer to its initial value, and its value after work.clear() , as empty. If it is empty, information is stored in work . This can be used to reduce computation when a future call is for the same object af , and the same subset of the Hessian. If either of these values change, use work.clear() to empty this structure.

n_sweep
The return value n_sweep has prototype
     int n_sweep
It is the number of first order forward sweeps used to compute the requested Hessian values. Each first forward sweep is followed by a second order reverse sweep so it is also the number of reverse sweeps. This is proportional to the total computational work, not counting the zero order forward sweep, or combining multiple columns and rows into a single sweep.

Uses Forward
After each call to a_fun_forward , the object af contains the corresponding Taylor coefficients for all the variables in the operation sequence.. After a call to sparse_hes the zero order coefficients correspond to
     af.forward(0, x)
All the other forward mode coefficients are unspecified.

Example
C++ , Octave , Perl , Python .

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Input File: lib/sparse.cpp