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

jac_minor_det.cpp

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Gradient of Determinant Using Expansion by Minors: Example and Test

// Complex examples should suppress conversion warnings
# include <cppad/wno_conversion.hpp>

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <complex>


typedef std::complex<double>     Complex;
typedef CppAD::AD<Complex>       ADComplex;
typedef CPPAD_TESTVECTOR(ADComplex)   ADVector;

// ----------------------------------------------------------------------------

bool JacMinorDet(void)
{   bool ok = true;

    using namespace CppAD;

    size_t n = 2;

    // object for computing determinant
    det_by_minor<ADComplex> Det(n);

    // independent and dependent variable vectors
    CPPAD_TESTVECTOR(ADComplex)  X(n * n);
    CPPAD_TESTVECTOR(ADComplex)  D(1);

    // value of the independent variable
    size_t i;
    for(i = 0; i < n * n; i++)
        X[i] = Complex( double(i), -double(i) );

    // set the independent variables
    Independent(X);

    // comupute the determinant
    D[0] = Det(X);

    // create the function object
    ADFun<Complex> f(X, D);

    // argument value
    CPPAD_TESTVECTOR(Complex)     x( n * n );
    for(i = 0; i < n * n; i++)
        x[i] = Complex( double(2 * i) , double(i) );

    // first derivative of the determinant
    CPPAD_TESTVECTOR(Complex) J( n * n );
    J = f.Jacobian(x);

    /*
    f(x)     = x[0] * x[3] - x[1] * x[2]
    f'(x)    = ( x[3], -x[2], -x[1], x[0] )
    */
    Complex Jtrue[] = { x[3], -x[2], -x[1], x[0] };
    for(i = 0; i < n * n; i++)
        ok &= Jtrue[i] == J[i];

    return ok;

}