Sparsity Patterns For a Subset of Variables: Example and Test

sparsity_sub.cpp

@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@This is cppad-20221105 documentation. Here is a link to its current documentation . Sparsity Patterns For a Subset of Variables: Example and Test
See Also
sparse_sub_hes.cpp , sub_sparse_hes.cpp .

ForSparseJac
The routine ForSparseJac is used to compute the sparsity for both the full Jacobian (see s ) and a subset of the Jacobian (see s2 ).

RevSparseHes
The routine RevSparseHes is used to compute both sparsity for both the full Hessian (see h ) and a subset of the Hessian (see h2 ).

# include <cppad/cppad.hpp>

bool sparsity_sub(void)
{   // C++ source code
    bool ok = true;
    //
    using std::cout;
    using CppAD::vector;
    using CppAD::AD;
    using CppAD::vectorBool;

    size_t n = 4;
    size_t m = n-1;
    vector< AD<double> > ax(n), ay(m);
    for(size_t j = 0; j < n; j++)
        ax[j] = double(j+1);
    CppAD::Independent(ax);
    for(size_t i = 0; i < m; i++)
        ay[i] = (ax[i+1] - ax[i]) * (ax[i+1] - ax[i]);
    CppAD::ADFun<double> f(ax, ay);

    // Evaluate the full Jacobian sparsity pattern for f
    vectorBool r(n * n), s(m * n);
    for(size_t j = 0 ; j < n; j++)
    {   for(size_t i = 0; i < n; i++)
            r[i * n + j] = (i == j);
    }
    s = f.ForSparseJac(n, r);

    // evaluate the sparsity for the Hessian of f_0 + ... + f_{m-1}
    vectorBool t(m), h(n * n);
    for(size_t i = 0; i < m; i++)
        t[i] = true;
    h = f.RevSparseHes(n, t);

    // evaluate the Jacobian sparsity pattern for first n/2 components of x
    size_t n2 = n / 2;
    vectorBool r2(n * n2), s2(m * n2);
    for(size_t j = 0 ; j < n2; j++)
    {   for(size_t i = 0; i < n; i++)
            r2[i * n2 + j] = (i == j);
    }
    s2 = f.ForSparseJac(n2, r2);

    // evaluate the sparsity for the subset of Hessian of
    // f_0 + ... + f_{m-1} where first partial has only first n/2 components
    vectorBool h2(n2 * n);
    h2 = f.RevSparseHes(n2, t);

    // check sparsity pattern for Jacobian
    for(size_t i = 0; i < m; i++)
    {   for(size_t j = 0; j < n2; j++)
            ok &= s2[i * n2 + j] == s[i * n + j];
    }

    // check sparsity pattern for Hessian
    for(size_t i = 0; i < n2; i++)
    {   for(size_t j = 0; j < n; j++)
            ok &= h2[i * n + j] == h[i * n + j];
    }
    return ok;
}

Input File: example/sparse/sparsity_sub.cpp