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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: 2003-24 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
Comprehensive test of Trigonometric and Hyperbolic Sine and Cosine
*/
# include <cppad/cppad.hpp>
# include <cmath>
namespace { // Begin empty namespace
bool Sin(void)
{ bool ok = true;
using CppAD::sin;
using CppAD::cos;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
double x = .5;
double y = .8;
CPPAD_TESTVECTOR(AD<double>) X(2);
X[0] = x;
X[1] = y;
Independent(X);
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
AD<double> U = X[0] * X[1];
Z[0] = sin( U );
// create f: X -> Z and vectors used for derivative calculations
// f(x, y) = sin(x, y)
ADFun<double> f(X, Z);
CPPAD_TESTVECTOR(double) v( 2 );
CPPAD_TESTVECTOR(double) w( 1 );
// check value
double sin_u = sin( Value(U) );
double cos_u = cos( Value(U) );
ok &= NearEqual(sin_u, Value(Z[0]), eps99 , eps99);
// forward computation of partials w.r.t. u
size_t j;
size_t p = 5;
double jfac = 1.;
v[0] = 1.; // differential w.r.t. x
v[1] = 0; // differential w.r.t. y
double yj = 1; // y^j
for(j = 1; j < p; j++)
{ w = f.Forward(j, v);
// compute j-th power of y
yj *= y ;
// compute j-th derivartive of sin function
double sinj;
if( j % 4 == 1 )
sinj = cos_u;
else if( j % 4 == 2 )
sinj = -sin_u;
else if( j % 4 == 3 )
sinj = -cos_u;
else
sinj = sin_u;
jfac *= double(j);
// check j-th derivative of z w.r.t x
ok &= NearEqual(jfac*w[0], sinj * yj, eps99 , eps99);
v[0] = 0.;
}
// reverse computation of partials of Taylor coefficients
CPPAD_TESTVECTOR(double) r( 2 * p);
w[0] = 1.;
r = f.Reverse(p, w);
jfac = 1.;
yj = 1.;
double sinjp = 0.;
for(j = 0; j < p; j++)
{
double sinj = sinjp;
// compute j+1 derivative of sin function
if( j % 4 == 0 )
sinjp = cos_u;
else if( j % 4 == 1 )
sinjp = -sin_u;
else if( j % 4 == 2 )
sinjp = -cos_u;
else
sinjp = sin_u;
// derivative w.r.t x of sin^{(j)} (x * y) * y^j
ok &= NearEqual(jfac*r[0+j], sinjp * yj * y, eps99 , eps99);
// derivative w.r.t y of sin^{(j)} (x * y) * y^j
double value = sinjp * yj * x + double(j) * sinj * yj / y;
ok &= NearEqual(r[p+j], value/jfac, eps99, eps99);
jfac *= double(j + 1);
yj *= y;
}
return ok;
}
bool Cos(void)
{ bool ok = true;
using CppAD::sin;
using CppAD::cos;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
double x = .5;
double y = .8;
CPPAD_TESTVECTOR(AD<double>) X(2);
X[0] = x;
X[1] = y;
Independent(X);
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
AD<double> U = X[0] * X[1];
Z[0] = cos( U );
// create f: X -> Z and vectors used for derivative calculations
// f(x, y) = cos(x, y)
ADFun<double> f(X, Z);
CPPAD_TESTVECTOR(double) v( 2 );
CPPAD_TESTVECTOR(double) w( 1 );
// check value
double sin_u = sin( Value(U) );
double cos_u = cos( Value(U) );
ok &= NearEqual(cos_u, Value(Z[0]), eps99 , eps99);
// forward computation of partials w.r.t. u
size_t j;
size_t p = 5;
double jfac = 1.;
v[0] = 1.; // differential w.r.t. x
v[1] = 0; // differential w.r.t. y
double yj = 1; // y^j
for(j = 1; j < p; j++)
{ w = f.Forward(j, v);
// compute j-th power of y
yj *= y ;
// compute j-th derivartive of cos function
double cosj;
if( j % 4 == 1 )
cosj = -sin_u;
else if( j % 4 == 2 )
cosj = -cos_u;
else if( j % 4 == 3 )
cosj = sin_u;
else
cosj = cos_u;
jfac *= double(j);
// check j-th derivative of z w.r.t x
ok &= NearEqual(jfac*w[0], cosj * yj, eps99 , eps99);
v[0] = 0.;
}
// reverse computation of partials of Taylor coefficients
CPPAD_TESTVECTOR(double) r( 2 * p);
w[0] = 1.;
r = f.Reverse(p, w);
jfac = 1.;
yj = 1.;
double cosjp = 0.;
for(j = 0; j < p; j++)
{
double cosj = cosjp;
// compute j+1 derivative of cos function
if( j % 4 == 0 )
cosjp = -sin_u;
else if( j % 4 == 1 )
cosjp = -cos_u;
else if( j % 4 == 2 )
cosjp = sin_u;
else
cosjp = cos_u;
// derivative w.r.t x of cos^{(j)} (x * y) * y^j
ok &= NearEqual(jfac*r[0+j], cosjp * yj * y, eps99 , eps99);
// derivative w.r.t y of cos^{(j)} (x * y) * y^j
double value = cosjp * yj * x + double(j) * cosj * yj / y;
ok &= NearEqual(r[p+j], value/jfac, eps99, eps99);
jfac *= double(j + 1);
yj *= y;
}
return ok;
}
bool Cosh(void)
{ bool ok = true;
using CppAD::sinh;
using CppAD::cosh;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
double x = .5;
double y = .8;
CPPAD_TESTVECTOR(AD<double>) X(2);
X[0] = x;
X[1] = y;
Independent(X);
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
AD<double> U = X[0] * X[1];
Z[0] = cosh( U );
// create f: X -> Z and vectors used for derivative calculations
// f(x, y) = cosh(x, y)
ADFun<double> f(X, Z);
CPPAD_TESTVECTOR(double) v( 2 );
CPPAD_TESTVECTOR(double) w( 1 );
// check value
double sinh_u = sinh( Value(U) );
double cosh_u = cosh( Value(U) );
ok &= NearEqual(cosh_u, Value(Z[0]), eps99 , eps99);
// forward computation of partials w.r.t. u
size_t j;
size_t p = 5;
double jfac = 1.;
v[0] = 1.; // differential w.r.t. x
v[1] = 0; // differential w.r.t. y
double yj = 1; // y^j
for(j = 1; j < p; j++)
{ w = f.Forward(j, v);
// compute j-th power of y
yj *= y ;
// compute j-th derivartive of cosh function
double coshj;
if( j % 2 == 1 )
coshj = sinh_u;
else
coshj = cosh_u;
jfac *= double(j);
// check j-th derivative of z w.r.t x
ok &= NearEqual(jfac*w[0], coshj * yj, eps99 , eps99);
v[0] = 0.;
}
// reverse computation of partials of Taylor coefficients
CPPAD_TESTVECTOR(double) r( 2 * p);
w[0] = 1.;
r = f.Reverse(p, w);
jfac = 1.;
yj = 1.;
double coshjp = 0.;
for(j = 0; j < p; j++)
{
double coshj = coshjp;
// compute j+1 derivative of cosh function
if( j % 2 == 0 )
coshjp = sinh_u;
else
coshjp = cosh_u;
// derivative w.r.t x of cosh^{(j)} (x * y) * y^j
ok &= NearEqual(jfac*r[0+j], coshjp * yj * y, eps99 , eps99);
// derivative w.r.t y of cosh^{(j)} (x * y) * y^j
double value = coshjp * yj * x + double(j) * coshj * yj / y;
ok &= NearEqual(r[p+j], value/jfac, eps99, eps99);
jfac *= double(j + 1);
yj *= y;
}
return ok;
}
bool Sinh(void)
{ bool ok = true;
using CppAD::sinh;
using CppAD::cosh;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
double x = .5;
double y = .8;
CPPAD_TESTVECTOR(AD<double>) X(2);
X[0] = x;
X[1] = y;
Independent(X);
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
AD<double> U = X[0] * X[1];
Z[0] = sinh( U );
// create f: X -> Z and vectors used for derivative calculations
// f(x, y) = sinh(x, y)
ADFun<double> f(X, Z);
CPPAD_TESTVECTOR(double) v( 2 );
CPPAD_TESTVECTOR(double) w( 1 );
// check value
double sinh_u = sinh( Value(U) );
double cosh_u = cosh( Value(U) );
ok &= NearEqual(sinh_u, Value(Z[0]), eps99 , eps99);
// forward computation of partials w.r.t. u
size_t j;
size_t p = 5;
double jfac = 1.;
v[0] = 1.; // differential w.r.t. x
v[1] = 0; // differential w.r.t. y
double yj = 1; // y^j
for(j = 1; j < p; j++)
{ w = f.Forward(j, v);
// compute j-th power of y
yj *= y ;
// compute j-th derivartive of sinh function
double sinhj;
if( j % 2 == 1 )
sinhj = cosh_u;
else
sinhj = sinh_u;
jfac *= double(j);
// check j-th derivative of z w.r.t x
ok &= NearEqual(jfac*w[0], sinhj * yj, eps99 , eps99);
v[0] = 0.;
}
// reverse computation of partials of Taylor coefficients
CPPAD_TESTVECTOR(double) r( 2 * p);
w[0] = 1.;
r = f.Reverse(p, w);
jfac = 1.;
yj = 1.;
double sinhjp = 0.;
for(j = 0; j < p; j++)
{
double sinhj = sinhjp;
// compute j+1 derivative of sinh function
if( j % 2 == 0 )
sinhjp = cosh_u;
else
sinhjp = sinh_u;
// derivative w.r.t x of sinh^{(j)} (x * y) * y^j
ok &= NearEqual(jfac*r[0+j], sinhjp * yj * y, eps99 , eps99);
// derivative w.r.t y of sinh^{(j)} (x * y) * y^j
double value = sinhjp * yj * x + double(j) * sinhj * yj / y;
ok &= NearEqual(r[p+j], value/jfac, eps99, eps99);
jfac *= double(j + 1);
yj *= y;
}
return ok;
}
} // End empty namespace
bool SinCos(void)
{ bool ok = Sin() && Cos() && Cosh() && Sinh();
return ok;
}
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