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@(@\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 .
Sum of the Elements of the Square of a Matrix: Example and Test
# include <vector>
# include <cstddef>
# include <cppad/utility/vector.hpp>
# include <cppad/speed/mat_sum_sq.hpp>

bool mat_sum_sq()
{   bool   ok = true;
    double x_00, x_01, x_10, x_11, check;

    // dimension of the matrices x, y, and the result z
    size_t n = 2;
    CppAD::vector<double> x(n * n), y(n * n), z(1);

    // x = [ 1 2 ; 3 4 ]
    x[0] = x_00 = 1.;
    x[1] = x_01 = 2.;
    x[2] = x_10 = 3.;
    x[3] = x_11 = 4.;

    // compute y = x * x and z = sum of elements in y
    CppAD::mat_sum_sq(n, x, y, z);

    // check y_00
    check = x_00 * x_00 + x_01 * x_10;
    ok   &= (check == y[0]);

    // check y_01
    check = x_00 * x_01 + x_01 * x_11;
    ok   &= (check == y[1]);

    // check y_10
    check = x_10 * x_00 + x_11 * x_10;
    ok   &= (check == y[2]);

    // check y_11
    check = x_10 * x_01 + x_11 * x_11;
    ok   &= (check == y[3]);

    // check z
    check = y[0] + y[1] + y[2] + y[3];
    ok   &= (check == z[0]);

    return ok;
}
Input File: speed/example/mat_sum_sq.cpp