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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
Test higher order derivatives for tan(x) function.
*/
# include <cppad/cppad.hpp>
namespace {
bool tan_two(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = 0.5;
// declare independent variables and starting recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = tan( ax[0] );
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// first order Taylor coefficient
CPPAD_TESTVECTOR(double) x1(n), y1;
x1[0] = 2.0;
y1 = f.Forward(1, x1);
ok &= size_t( y1.size() ) == m;
// secondorder Taylor coefficients
CPPAD_TESTVECTOR(double) x2(n), y2;
x2[0] = 0.0;
y2 = f.Forward(2, x2);
ok &= size_t( y2.size() ) == m;
//
// Y (t) = F[X_0(t)]
// = tan(0.5 + 2t )
// Y' (t) = 2 * cos(0.5 + 2t )^(-2)
double sec_sq = 1.0 / ( cos(0.5) * cos(0.5) );
double check = 2.0 * sec_sq;
ok &= NearEqual(y1[0] , check, eps, eps);
//
// Y''(0) = 8*cos(0.5)^(-3)*sin(0.5)
check = 8.0 * tan(0.5) * sec_sq / 2.0;
ok &= NearEqual(y2[0] , check, eps, eps);
//
return ok;
}
bool tan_case(bool tan_first)
{ bool ok = true;
double eps = 100. * std::numeric_limits<double>::epsilon();
using CppAD::AD;
using CppAD::NearEqual;
// independent variable vector, indices, values, and declaration
size_t n = 1;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = .7;
Independent(ax);
// dependent variable vector and indices
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
if( tan_first )
ay[0] = atan( tan( ax[0] ) );
else
ay[0] = tan( atan( ax[0] ) );
// check value
ok &= NearEqual(ax[0] , ay[0], eps, eps);
// create f: x -> y and vectors used for derivative calculations
CppAD::ADFun<double> f(ax, ay);
CPPAD_TESTVECTOR(double) dx(n), dy(m);
// forward computation of partials w.r.t. x
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 1e0, eps, eps);
size_t p, order = 5;
dx[0] = 0.;
for(p = 2; p < order; p++)
{ dy = f.Forward(p, dx);
ok &= NearEqual(dy[0], 0e0, eps, eps);
}
// reverse computation of order partial
CPPAD_TESTVECTOR(double) w(m), dw(n * order);
w[0] = 1.;
dw = f.Reverse(order, w);
ok &= NearEqual(dw[0], 1e0, eps, eps);
for(p = 1; p < order; p++)
ok &= NearEqual(dw[p], 0e0, eps, eps);
return ok;
}
bool tanh_case(bool tanh_first)
{ bool ok = true;
double eps = 100. * std::numeric_limits<double>::epsilon();
using CppAD::AD;
using CppAD::NearEqual;
// independent variable vector, indices, values, and declaration
size_t n = 1;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = .5;
Independent(ax);
// dependent variable vector and indices
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
AD<double> z;
if( tanh_first )
{ z = tanh( ax[0] );
ay[0] = .5 * log( (1. + z) / (1. - z) );
}
else
{ z = .5 * log( (1. + ax[0]) / (1. - ax[0]) );
ay[0] = tanh(z);
}
// check value
ok &= NearEqual(ax[0] , ay[0], eps, eps);
// create f: x -> y and vectors used for derivative calculations
CppAD::ADFun<double> f(ax, ay);
CPPAD_TESTVECTOR(double) dx(n), dy(m);
// forward computation of partials w.r.t. x
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], 1e0, eps, eps);
size_t p, order = 5;
dx[0] = 0.;
for(p = 2; p < order; p++)
{ dy = f.Forward(p, dx);
ok &= NearEqual(dy[0], 0e0, eps, eps);
}
// reverse computation of order partial
CPPAD_TESTVECTOR(double) w(m), dw(n * order);
w[0] = 1.;
dw = f.Reverse(order, w);
ok &= NearEqual(dw[0], 1e0, eps, eps);
for(p = 1; p < order; p++)
ok &= NearEqual(dw[p], 0e0, eps, eps);
return ok;
}
}
bool tan(void)
{ bool ok = true;
//
ok &= tan_case(true);
ok &= tan_case(false);
ok &= tanh_case(true);
ok &= tanh_case(false);
//
ok &= tan_two();
return ok;
}
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