Determinant of a Minor: Example and Test

det_of_minor.cpp

Headings

@(@\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}} }@)@ 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;
     size_t i;

     // dimension of the matrix A
     size_t m = 3;
     // 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(i= 0; i < m; i++)
     {     r[i] = i+1;
          c[i] = i+1;
     }
     r[m] = 0;
     c[m] = 0;
     // values in the matrix A
     double  data[] = {
          1., 2., 3.,
          3., 2., 1.,
          2., 1., 2.
     };
     // construct vector a with the values of the matrix A
     std::vector<double> a(data, data + 9);

     // evaluate the determinant of A
     size_t n   = m; // minor has same dimension as A
     double det = CppAD::det_of_minor(a, m, n, r, c);

     // check the value of the determinant of A
     ok &= (det == (double) (1*(2*2-1*1) - 2*(3*2-1*2) + 3*(3*1-2*2)) );

     // 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
     // evaluate determinant of the minor
     n   = m - 1; // dimension of the minor
     det = CppAD::det_of_minor(a, m, m-1, r, c);

     // check the value of the determinant of the minor
     ok &= (det == (double) (3*2-1*2) );

     return ok;
}

Input File: speed/example/det_of_minor.cpp