Prev Next Index-> contents reference index search external Up-> CppAD utility pow_int pow_int.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 pow_int-> pow_int.cpp pow_int.cpp Headings

$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
The Pow Integer Exponent: Example and Test
 # include <cppad/cppad.hpp> # include <cmath> bool pow_int(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits<double>::epsilon(); // declare independent variables and start tape recording size_t n = 1; double x0 = -0.5; CPPAD_TESTVECTOR(AD<double>) x(n); x[0] = x0; CppAD::Independent(x); // dependent variable vector size_t m = 7; CPPAD_TESTVECTOR(AD<double>) y(m); int i; for(i = 0; i < int(m); i++) y[i] = CppAD::pow(x[0], i - 3); // create f: x -> y and stop tape recording CppAD::ADFun<double> f(x, y); // check value double check; for(i = 0; i < int(m); i++) { check = std::pow(x0, double(i - 3)); ok &= NearEqual(y[i] , check, eps99 , eps99); } // forward computation of first partial w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); for(i = 0; i < int(m); i++) { check = double(i-3) * std::pow(x0, double(i - 4)); ok &= NearEqual(dy[i] , check, eps99 , eps99); } // reverse computation of derivative of y[i] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); for(i = 0; i < int(m); i++) w[i] = 0.; for(i = 0; i < int(m); i++) { w[i] = 1.; dw = f.Reverse(1, w); check = double(i-3) * std::pow(x0, double(i - 4)); ok &= NearEqual(dw[0] , check, eps99 , eps99); w[i] = 0.; } return ok; } 
Input File: example/general/pow_int.cpp