Prev Next Index-> contents reference index search external Up-> CppAD utility OdeGearControl ode_gear_control.cpp CppAD-> Install Introduction AD ADFun preprocessor multi_thread utility ipopt_solve Example speed Appendix utility-> ErrorHandler NearEqual speed_test SpeedTest time_test test_boolofvoid NumericType CheckNumericType SimpleVector CheckSimpleVector nan pow_int Poly LuDetAndSolve RombergOne RombergMul Runge45 Rosen34 OdeErrControl OdeGear OdeGearControl CppAD_vector thread_alloc index_sort to_string set_union sparse_rc sparse_rcv OdeGearControl-> ode_gear_control.cpp ode_gear_control.cpp Headings

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OdeGearControl: Example and Test
Define $X : \B{R} \rightarrow \B{R}^2$ by $$\begin{array}{rcl} X_0 (t) & = & - \exp ( - w_0 t ) \\ X_1 (t) & = & \frac{w_0}{w_1 - w_0} [ \exp ( - w_0 t ) - \exp( - w_1 t )] \end{array}$$ It follows that $X_0 (0) = 1$, $X_1 (0) = 0$ and $$\begin{array}{rcl} X_0^{(1)} (t) & = & - w_0 X_0 (t) \\ X_1^{(1)} (t) & = & + w_0 X_0 (t) - w_1 X_1 (t) \end{array}$$ The example tests OdeGearControl using the relations above:  # include <cppad/cppad.hpp> # include <cppad/utility/ode_gear_control.hpp> // CppAD::OdeGearControl namespace { // -------------------------------------------------------------- class Fun { private: CPPAD_TESTVECTOR(double) w; public: // constructor Fun(const CPPAD_TESTVECTOR(double) &w_) : w(w_) { } // set f = x'(t) template <typename Scalar> void Ode( const Scalar &t, const CPPAD_TESTVECTOR(Scalar) &x, CPPAD_TESTVECTOR(Scalar) &f) { f[0] = - w[0] * x[0]; f[1] = + w[0] * x[0] - w[1] * x[1]; } void Ode_dep( const double &t, const CPPAD_TESTVECTOR(double) &x, CPPAD_TESTVECTOR(double) &f_x) { using namespace CppAD; size_t n = x.size(); CPPAD_TESTVECTOR(AD<double>) T(1); CPPAD_TESTVECTOR(AD<double>) X(n); CPPAD_TESTVECTOR(AD<double>) F(n); // set argument values T[0] = t; size_t i, j; for(i = 0; i < n; i++) X[i] = x[i]; // declare independent variables Independent(X); // compute f(t, x) this->Ode(T[0], X, F); // define AD function object ADFun<double> fun(X, F); // compute partial of f w.r.t x CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) df(n); for(j = 0; j < n; j++) dx[j] = 0.; for(j = 0; j < n; j++) { dx[j] = 1.; df = fun.Forward(1, dx); for(i = 0; i < n; i++) f_x [i * n + j] = df[i]; dx[j] = 0.; } } }; } bool OdeGearControl(void) { bool ok = true; // initial return value using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits<double>::epsilon(); CPPAD_TESTVECTOR(double) w(2); w[0] = 10.; w[1] = 1.; Fun F(w); CPPAD_TESTVECTOR(double) xi(2); xi[0] = 1.; xi[1] = 0.; CPPAD_TESTVECTOR(double) eabs(2); eabs[0] = 1e-4; eabs[1] = 1e-4; // return values CPPAD_TESTVECTOR(double) ef(2); CPPAD_TESTVECTOR(double) maxabs(2); CPPAD_TESTVECTOR(double) xf(2); size_t nstep; // input values size_t M = 5; double ti = 0.; double tf = 1.; double smin = 1e-8; double smax = 1.; double sini = eps99; double erel = 0.; xf = CppAD::OdeGearControl(F, M, ti, tf, xi, smin, smax, sini, eabs, erel, ef, maxabs, nstep); double x0 = exp(-w[0]*tf); ok &= NearEqual(x0, xf[0], 1e-4, 1e-4); ok &= NearEqual(0., ef[0], 1e-4, 1e-4); double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]); ok &= NearEqual(x1, xf[1], 1e-4, 1e-4); ok &= NearEqual(0., ef[1], 1e-4, 1e-4); return ok; } 
Input File: example/utility/ode_gear_control.cpp