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link_sparse_jacobian

Headings-> Prototype f repeat x i j jacobian ---..double

Speed Testing Sparse Jacobian
Prototype
extern bool link_sparse_jacobian(
     size_t                 repeat    ,
     CppAD::vector<double> &x         ,
     CppAD::vector<size_t> &i         ,
     CppAD::vector<size_t> &j         , 
     CppAD::vector<double> &jacobian
);

f
Given a first index vector $\mathit{i}$ and a second index vector $\mathit{j}$ , the corresponding function $\mathit{g}:{\mathbf{R}}^{\mathit{n}}\to {\mathbf{R}}^{\ell }$ is defined by sparse_evaluate and the index vectors i and j . The function $\mathit{g}(\mathit{x})$ is defined by $${\mathit{g}}_{\mathit{k}}(\mathit{x})=\frac{\partial \mathit{f}}{\partial {\mathit{x}}_{\mathit{i}[\mathit{k}]}}$$ The non-zero entries in the Jacobian of this function have the form $$\frac{\partial {\mathit{g}}_{\mathit{k}}}{\partial \mathit{x}[\mathit{j}[\mathit{k}]]}$$ or $$\frac{\partial {\mathit{g}}_{\mathit{k}}}{\partial \mathit{x}[\mathit{i}[\mathit{k}]]}$$ for some $\mathit{k}$ between zero and $\ell -1$ . All the other terms of the Jacobian are zero.

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

x
The argument x has prototype
        CppAD::vector<double> &x
The size of the vector x determines and is equal to the value of $\mathit{n}$ . 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 $\mathit{n}-1$ .

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 $\mathit{n}-1$ .

jacobian
The argument jacobian is a vector with $\ell \times \mathit{n}$ elements. The input value of its elements does not matter. The output value of its elements is the Jacobian of the function $\mathit{g}(\mathit{x})$ that corresponds to output values of i , j , and x . To be more specific, for $\mathit{k}=0,\dots ,\ell -1$ , $\mathit{m}=0,\dots ,\mathit{n}-1$ , $$\frac{\partial {\mathit{g}}_{\mathit{k}}}{\partial \mathit{x}[\mathit{m}]}(\mathit{x})=\mathit{jacobian}[\mathit{k}*\ell +\mathit{m}]$$
double
In the case where package is double, only the first $\ell$ elements of jacobian are used and they are set to the value of $\mathit{g}(\mathit{x})$ ( $\mathit{g}\text{'}(\mathit{x})$ is not computed).

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Input File: speed/src/link_sparse_jacobian.cpp