Atomic Matrix Multiply Jacobian Sparsity Pattern: Example Implementation

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atomic_four_mat_mul_hes_sparsity.hpp

@(@\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 . Atomic Matrix Multiply Jacobian Sparsity Pattern: Example Implementation
Purpose
The hes_sparsity routine overrides the virtual functions used by the atomic_four base class for Jacobian sparsity calculations; see hes_sparsity .

Example
The file atomic_four_mat_mul_sparsity.cpp contains an example and test using this operator.

Source


# include <cppad/example/atomic_four/mat_mul/mat_mul.hpp>

namespace CppAD { // BEGIN_CPPAD_NAMESPACE
//
// hes_sparsity override
template <class Base>
bool atomic_mat_mul<Base>::hes_sparsity(
    size_t                                         call_id      ,
    const CppAD::vector<bool>&                     ident_zero_x ,
    const CppAD::vector<bool>&                     select_x     ,
    const CppAD::vector<bool>&                     select_y     ,
    CppAD::sparse_rc< CppAD::vector<size_t> >&     pattern_out  )
{
    // n_left, n_middle, n_right
    size_t n_left, n_middle, n_right;
    get(call_id, n_left, n_middle, n_right);
    //
    // n
    size_t n     = select_x.size();
    //
    // check sizes
# ifndef NDEBUG
    size_t m     = select_y.size();
    assert( n == n_middle * ( n_left +  n_right ) );
    assert( m == n_left * n_right );
# endif
    //
    // offset
    size_t offset = n_left * n_middle;
    //
    // pattern_out
    pattern_out.resize(n, n, 0);
    for(size_t i = 0; i < n_left; ++i)
    {   for(size_t j = 0; j < n_right; ++j)
        {   size_t ij = i * n_right + j;               // C_{i,j} = y[ij]
            if( select_y[ij] ) for(size_t k = 0; k < n_middle; ++k)
            {   size_t ik = i * n_middle + k;          // A_{i,k} = x[ik]
                size_t kj = offset + k * n_right + j;  // B_{k,j} = x[kj]
                if( select_x[ik] & select_x[kj] )
                {   // an (ik, kj) pair can only occur once in this loop
                    pattern_out.push_back(ik, kj);
                    pattern_out.push_back(kj, ik);
                }
            }
        }
    }
# ifndef NDEBUG
    // sorting checks hat there are no duplicate entries
    pattern_out.row_major();
# endif
    //
    return true;
}
} // END_CPPAD_NAMESPACE

Input File: include/cppad/example/atomic_four/mat_mul/hes_sparsity.hpp