\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

det_of_minor.cpp

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Determinant of a Minor: Example and Test

# include <vector>
# include <cstddef>
# include <cppad/speed/det_of_minor.hpp>

bool det_of_minor()
{   bool   ok = true;
    //
    // a
    // values in the matrix A in row major order
    std::vector<double> a = {
        1., 2., 3.,
        4., 5., 6.,
        7., 8., 10.
    };
    //
    // m
    // dimension of the matrix A
    size_t m = 3;
    assert( m * m == a.size() );
    //
    // r, c
    // index vectors set so minor is the entire matrix A
    std::vector<size_t> r(m + 1);
    std::vector<size_t> c(m + 1);
    for(size_t i= 0; i < m; i++)
    {   r[i] = i+1;
        c[i] = i+1;
    }
    r[m] = 0;
    c[m] = 0;
    //
    // n
    // size of minor that is the entire matrix A
    size_t n = m;
    //
    // det
    // evaluate the determinant of A
    double det = CppAD::det_of_minor(a, m, n, r, c);
    //
    // ok
    // check the value of the determinant of A
    ok &= (det == (double) (1*(5*10-6*8) - 2*(4*10-6*7) + 3*(4*8-5*7)) );
    //
    // M
    // minor where row 0 and column 1 are removed
    r[m] = 1;     // skip row index 0 by starting at row index 1
    c[0] = 2;     // skip column index 1 by pointing from index 0 to index 2
    n    = m - 1; // dimension of the minor M
    //
    // det
    // evaluate determinant of the minor
    det = CppAD::det_of_minor(a, m, m-1, r, c);
    //
    // ok
    // check the value of the determinant of the minor
    ok &= (det == (double) (4*10-6*7) );
    //
    return ok;
}