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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
// ----------------------------------------------------------------------------
/*
Two old atan examples now used just for validation testing.
*/
# include <cppad/cppad.hpp>
namespace { // BEGIN empty namespace
bool AtanTestOne(void)
{ bool ok = true;
using CppAD::atan;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector, indices, values, and declaration
CPPAD_TESTVECTOR(AD<double>) U(1);
size_t s = 0;
U[s] = 1.;
Independent(U);
// some temporary values
AD<double> x = cos(U[s]);
AD<double> y = sin(U[s]);
AD<double> z = y / x; // tan(s)
// dependent variable vector and indices
CPPAD_TESTVECTOR(AD<double>) Z(1);
size_t a = 0;
// dependent variable values
Z[a] = atan(z); // atan( tan(s) )
// create f: U -> Z and vectors used for dierivative calculations
ADFun<double> f(U, Z);
CPPAD_TESTVECTOR(double) v( f.Domain() );
CPPAD_TESTVECTOR(double) w( f.Range() );
// check value
ok &= NearEqual(U[s] , Z[a], eps99 , eps99);
// forward computation of partials w.r.t. s
v[s] = 1.;
w = f.Forward(1, v);
ok &= NearEqual(w[a], 1e0, eps99 , eps99); // da/ds
// reverse computation of first order partial of a
w[a] = 1.;
v = f.Reverse(1, w);
ok &= NearEqual(v[s], 1e0, eps99 , eps99); // da/ds
// forward computation of second partials w.r.t. s and s
v[s] = 1.;
f.Forward(1, v);
v[s] = 0.;
w = f.Forward(2, v);
ok &= NearEqual(2. * w[a], 0e0, eps99 , eps99); // d^2 a / (ds ds)
// reverse computation of second partials of a
CPPAD_TESTVECTOR(double) r( f.Domain() * 2 );
w[a] = 1.;
r = f.Reverse(2, w);
ok &= NearEqual(r[2 * s + 1] ,0e0, eps99 , eps99 ); // d^2 a / (ds ds)
return ok;
}
bool AtanTestTwo(void)
{ bool ok = true;
using CppAD::atan;
using CppAD::sin;
using CppAD::cos;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
CPPAD_TESTVECTOR(AD<double>) U(1);
U[0] = 1.;
Independent(U);
// a temporary values
AD<double> x = sin(U[0]) / cos(U[0]);
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
Z[0] = atan(x); // atan( tan(u) )
// create f: U -> Z and vectors used for derivative calculations
ADFun<double> f(U, Z);
CPPAD_TESTVECTOR(double) v(1);
CPPAD_TESTVECTOR(double) w(1);
// check value
ok &= NearEqual(U[0] , Z[0], eps99 , eps99);
// forward computation of partials w.r.t. u
size_t j;
size_t p = 5;
double jfac = 1.;
double value = 1.;
v[0] = 1.;
for(j = 1; j < p; j++)
{ jfac *= double(j);
w = f.Forward(j, v);
ok &= NearEqual(w[0], value/jfac, eps99, eps99);// d^jz/du^j
v[0] = 0.;
value = 0.;
}
// reverse computation of partials of Taylor coefficients
CPPAD_TESTVECTOR(double) r(p);
w[0] = 1.;
r = f.Reverse(p, w);
jfac = 1.;
value = 1.;
for(j = 0; j < p; j++)
{ ok &= NearEqual(r[j], value/jfac, eps99, eps99);// d^jz/du^j
jfac *= double(j + 1);
value = 0.;
}
return ok;
}
} // END empty namespace
bool atan(void)
{ bool ok = true;
ok &= AtanTestOne();
ok &= AtanTestTwo();
return ok;
}
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