taylor.h

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#ifndef THEORETICA_TAYLOR_H
#define THEORETICA_TAYLOR_H
 
#include "../polynomial/polynomial.h"
#include "../autodiff/dual.h"
#include "../autodiff/dual2.h"
 
 
namespace theoretica {
 
    namespace taylor {
 
 
        template<typename DualFunction>
        inline polynomial<real> expand_linear(DualFunction f, real x0 = 0) {
 
            const dual d = f(dual(x0, 1));
            const real fx = d.Re();
            const real dfx = d.Dual();
 
            polynomial<real> P = {fx, 0.0};
            P += polynomial<>({-x0, 1}) * dfx;
            
            return P;
        }
 
 
        template<typename Dual2Function>
        inline polynomial<real> expand_quadratic(Dual2Function f, real x0 = 0) {
 
            const dual2 d = f(dual2(x0, 1, 0));
            const real fx = d.Re();
            const real dfx = d.Dual1();
            const real d2fx = d.Dual2();
 
            polynomial<real> P = {fx, 0.0, 0.0};
            P += polynomial<>({-x0, 1}) * dfx;
            P += polynomial<>({square(x0), -2 * x0, 1}) * (d2fx / 2.0);
 
            return P;
        }
 
    }
 
}
 
 
#endif