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Speed Testing Sparse Hessian

Prototype
extern bool link_sparse_hessian(
     size_t                 
repeat    ,
     CppAD::vector<double> &
x         ,
     CppAD::vector<size_t> &
i         ,
     CppAD::vector<size_t> &
j         , 
     CppAD::vector<double> &
hessian
);

f
Given a first index vector  i and a second index vector  j , the corresponding function  f : \R^n \rightarrow \R  is defined by sparse_evaluate and the index vectors i and j . The only non-zero entries in the Hessian of this function have the form  \[
     \DD{f}{x[[k]]}{x[j[k]]}
\] 
for some  k  between zero and  \ell-1  .

repeat
The argument repeat is the number of different functions  f(x) that the Hessian is computed for. Each function corresponds to a randomly chosen index vectors, i.e., for each repetition a random choice is made for  i[k] and  j[k] for  k = 0 , \ldots , \ell-1 .

retape
For this test, the operation sequence changes for each repetition. Thus the argument retape is not present because an AD package can not use one recording of the operation sequence to compute the gradient for all of the repetitions.

x
The argument x has prototype
        CppAD::vector<double> &
x
The size of the vector x determines and is equal to the value of  n . 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.

i
The size of the vector i determines and is equal to the value of  \ell . The input value of the elements of i does not matter. On output, it has been set the first index vector for the last repetition. All the elements of i must are between zero and  n-1 .

j
The argument j is a vector with size  \ell . The input value of its elements does not matter. On output, it has been set the second index vector for the last repetition. All the elements of i must are between zero and  n-1 .

hessian
The argument hessian is a vector with  n \times n elements. The input value of its elements does not matter. The output value of its elements is the Hessian of the function  f(x) that corresponds to output values of i , j , and x . To be more specific, for  k = 0 , \ldots , n-1 ,  m = 0 , \ldots , n-1 ,  \[
     \DD{f}{x[k]}{x[m]} (x) = hessian [ k * n + m ]
\] 


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) (  f^{(2)} (x) is not computed).
Input File: speed/link_sparse_hessian.cpp