Gradient of Determinant Using Expansion by Minors: Example and Test

hes_minor_det.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}} }@)@This is cppad-20221105 documentation. Here is a link to its current documentation . Gradient of Determinant Using Expansion by Minors: Example and Test

// Complex examples should supppress 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 HesMinorDet(void)
{   bool ok = true;

    using namespace CppAD;

    size_t n = 2;

    // object for computing determinants
    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) H( n * n * n * n);
    H = f.Hessian(x, 0);

    /*
    f(x)     = x[0] * x[3] - x[1] * x[2]
    f'(x)    = ( x[3], -x[2], -x[1], x[0] )
    */
    Complex zero(0., 0.);
    Complex one(1., 0.);
    Complex Htrue[]  = {
        zero, zero, zero,  one,
        zero, zero, -one, zero,
        zero, -one, zero, zero,
         one, zero, zero, zero
    };
    for( i = 0; i < n*n*n*n; i++)
        ok &= Htrue[i] == H[i];

    return ok;

}

Input File: example/general/hes_minor_det.cpp