Speed Testing Sparse Hessian
Keywords: speed testing sparse hessian link_sparse_hessian test prototype method size repeat x row col n_sweep double

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Speed Testing Sparse Hessian
Prototype
`extern bool link_sparse_hessian(
size_t size ,
size_t repeat ,
CppAD::vector<double>& x ,
const CppAD::vector<size_t>& row ,
const CppAD::vector<size_t>& col ,
CppAD::vector<double>& hessian ,
size_t n_sweep
);
`
Method
Given a row index vector row and a second column vector col , the corresponding function f : R n → R is defined by sparse_hes_fun . The non-zero entries in the Hessian of this function have one of the following forms: ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ row [ k ] ] , ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ col [ k ] ] , ∂ 2 f ∂ x [ col [ k ] ] ∂ x [ row [ k ] ] , ∂ 2 f ∂ x [ col [ k ] ] ∂ x [ col [ k ] ] for some k between zero and K -1 . All the other terms of the Hessian are zero.
size
The argument `size` , referred to as n below, is the dimension of the domain space for f ( x ) .
repeat
The argument `repeat` is the number of times to repeat the test (with a different value for `x` corresponding to each repetition).
x
The argument `x` has prototype `
CppAD::vector<double>& x
` and its size is n ; i.e., `x.size() == size` . The input value of the elements of `x` does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated. The value of this vector need not change with each repetition.
row
The argument `row` has prototype `
const CppAD::vector<size_t> row
` Its size defines the value K . It contains the row indices for the corresponding function f ( x ) . All the elements of `row` are between zero and n -1 .
col
The argument `col` has prototype `
const CppAD::vector<size_t> col
` Its size must be the same as `row` ; i.e., K . It contains the column indices for the corresponding function f ( x ) . All the elements of `col` are between zero and n -1 . There are no duplicated entries requested, to be specific, if `k1 != k2` then `
( row[k1] , col[k1] ) != ( row[k2] , col[k2] )
`
hessian
The argument `hessian` has prototype `
CppAD::vector<double>& hessian
` and its size is `K` . The input value of its elements does not matter. The output value of its elements is the Hessian of the function f ( x ) . To be more specific, for k = 0 , … , K -1 , ∂ 2 f ∂ x [ row [ k ] ] ∂ x [ col [ k ] ] = hessian [ k ]
n_sweep
The input value of `n_sweep` does not matter. On output, it is the value n_sweep corresponding to the evaluation of `hessian` . This is also the number of colors corresponding to the coloring method , which can be set to colpack , and is otherwise `cppad`.
double
In the case where `package` is `double`, only the first element of `hessian` is used and it is actually the value of f ( x ) (derivatives are not computed).

Input File: speed/src/link_sparse_hessian.cpp