@(@\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
.
Subset of Second Order Partials: Example and Test
# include <cppad/cppad.hpp>
namespace { // -----------------------------------------------------// define the template function in empty namespace// bool ForTwoCases<BaseVector, SizeVector_t>(void)template <class BaseVector, class SizeVector_t>
bool ForTwoCases()
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
using CppAD::exp;
using CppAD::sin;
using CppAD::cos;
// domain space vector
size_t n = 2;
CPPAD_TESTVECTOR(AD<double>) X(n);
X[0] = 1.;
X[1] = 2.;
// declare independent variables and starting recording
CppAD::Independent(X);
// a calculation between the domain and range values
AD<double> Square = X[0] * X[0];
// range space vector
size_t m = 3;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = Square * exp( X[1] );
Y[1] = Square * sin( X[1] );
Y[2] = Square * cos( X[1] );
// create f: X -> Y and stop tape recording
CppAD::ADFun<double> f(X, Y);
// new value for the independent variable vector
BaseVector x(n);
x[0] = 2.;
x[1] = 1.;
// set j and k to compute specific second partials of y
size_t p = 2;
SizeVector_t j(p);
SizeVector_t k(p);
j[0] = 0; k[0] = 0; // for second partial w.r.t. x[0] and x[0]
j[1] = 0; k[1] = 1; // for second partial w.r.t x[0] and x[1]// compute the second partials
BaseVector ddy(m * p);
ddy = f.ForTwo(x, j, k);
/* partial of y w.r.t x[0] is [ 2 * x[0] * exp(x[1]) ] [ 2 * x[0] * sin(x[1]) ] [ 2 * x[0] * cos(x[1]) ] */// second partial of y w.r.t x[0] and x[1]
ok &= NearEqual( 2.*exp(x[1]), ddy[0*p+0], eps99, eps99);
ok &= NearEqual( 2.*sin(x[1]), ddy[1*p+0], eps99, eps99);
ok &= NearEqual( 2.*cos(x[1]), ddy[2*p+0], eps99, eps99);
// second partial of F w.r.t x[0] and x[1]
ok &= NearEqual( 2.*x[0]*exp(x[1]), ddy[0*p+1], eps99, eps99);
ok &= NearEqual( 2.*x[0]*cos(x[1]), ddy[1*p+1], eps99, eps99);
ok &= NearEqual(-2.*x[0]*sin(x[1]), ddy[2*p+1], eps99, eps99);
return ok;
}
} // End empty namespace# include <vector>
# include <valarray>
bool ForTwo(void)
{ bool ok = true;
// Run with BaseVector equal to three different cases// all of which are Simple Vectors with elements of type double.
ok &= ForTwoCases< CppAD::vector <double>, std::vector<size_t> >();
ok &= ForTwoCases< std::vector <double>, std::vector<size_t> >();
ok &= ForTwoCases< std::valarray <double>, std::vector<size_t> >();
// Run with SizeVector_t equal to two other cases// which are Simple Vectors with elements of type size_t.
ok &= ForTwoCases< std::vector <double>, CppAD::vector<size_t> >();
ok &= ForTwoCases< std::vector <double>, std::valarray<size_t> >();
return ok;
}
