Atomic Matrix Multiply Identical Zero: Example and Test

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atomic_four_mat_mul_identical_zero.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 . Atomic Matrix Multiply Identical Zero: Example and Test
Purpose
This example demonstrates how the atomic_four_mat_mul_for_type.hpp routine uses the identical_zero_enum type to reduce the number of variables.

Zero
The first case computes the following matrix product @[@ \left( \begin{array}{ccc} u_0 & 0 & 0 \\ 0 & u_1 & 0 \\ 0 & 0 & u_2 \end{array} \right) \left( \begin{array}{ccc} u_3 & 0 & 0 \\ 0 & u_4 & 0 \\ 0 & 0 & u_5 \end{array} \right) = \left( \begin{array}{ccc} u_0 u_3 & 0 & 0 \\ 0 & u_1 u_4 & 0 \\ 0 & 0 & u_2 u_5 \end{array} \right) @]@ The result matrix for this case has three variables, one for each product on the diagonal.

One
The second case computes the following matrix product @[@ \left( \begin{array}{ccc} u_0 & 1 & 1 \\ 1 & u_1 & 1 \\ 1 & 1 & u_2 \end{array} \right) \left( \begin{array}{ccc} u_3 & 1 & 1 \\ 1 & u_4 & 1 \\ 1 & 1 & u_5 \end{array} \right) = \left( \begin{array}{ccc} u_0 u_3 + 2 & u_0 + u_3 + 1 & u_0 + u_5 + 1 \\ u_1 + u_3 + 1 & u_1 u_4 + 2 & u_1 + u_5 + 1 \\ u_2 + u_3 + 1 & u_2 + u_4 + 1 & u_2 u_5 + 2 \end{array} \right) @]@ The result matrix for this case has nine variables, one for each of its elements.

Source


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

bool identical_zero(void)
{   // ok, eps
    bool ok = true;
    //
    // AD, NearEqual
    using CppAD::AD;
    using CppAD::NearEqual;
    // -----------------------------------------------------------------------
    // Record f
    // -----------------------------------------------------------------------
    //
    // afun
    CppAD::atomic_mat_mul<double> afun("atomic_mat_mul");
    //
    // nleft
    size_t size = 3;
    //
    // size_var
    size_t size_var[2];
    //
    // zero_one
    for(size_t zero_one = 0; zero_one < 2; ++zero_one)
    {   //
        // n_right, n_middle
        size_t n_left = size, n_middle = size, n_right = size;
        //
        // nu, au
        size_t nu = 2 * size;
        CPPAD_TESTVECTOR( AD<double> ) au(nu);
        for(size_t j = 0; j < nu; ++j)
            au[j] = AD<double>(j + 2);
        CppAD::Independent(au);
        //
        // offset
        size_t offset = size * size;
        //
        // nx, ax
        size_t nx = size * (size + size);
        CPPAD_TESTVECTOR( AD<double> ) ax(nx);
        for(size_t i = 0; i < size; ++i)
        {   for(size_t j = 0; j < size; ++j)
            {   // left
                size_t ij = i * size + j;
                if( i == j )
                    ax[ij] = au[j];
                else
                    ax[ij] = AD<double>(zero_one);
                // right
                ij = offset + i * n_right + j;
                if( i == j )
                    ax[ij] = au[i];
                else
                    ax[ij] = AD<double>(zero_one);
            }
        }
        //
        // ay
        size_t ny = size * size;
        CPPAD_TESTVECTOR( AD<double> ) ay(ny);
        size_t call_id = afun.set(n_left, n_middle, n_right);
        afun(call_id, ax, ay);
        //
        // av
        size_t nv = size;
        CPPAD_TESTVECTOR( AD<double> ) av(nv);
        for(size_t i = 0; i < nv; ++i)
            av[i] += ay[i * size + i];
        //
        // f
        CppAD::ADFun<double> f(au, av);
        //
        // size_var
        size_var[zero_one] = f.size_var();
    }
    // ok
    ok = size_var[1] - size_var[0] == size * size - size;
    //
    return ok;
}

Input File: example/atomic_four/mat_mul/identical_zero.cpp