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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 sqrt examples now used just for validation testing.
*/
# include <cppad/cppad.hpp>
# include <cmath>
namespace { // BEGIN empty namespace
bool SqrtTestOne(void)
{ bool ok = true;
using CppAD::sqrt;
using CppAD::pow;
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] = 4.;
Independent(U);
// dependent variable vector, indices, and values
CPPAD_TESTVECTOR(AD<double>) Z(2);
size_t x = 0;
size_t y = 1;
Z[x] = sqrt(U[s]);
Z[y] = sqrt(Z[x]);
// define f : U -> Z and vectors for derivative calculations
ADFun<double> f(U, Z);
CPPAD_TESTVECTOR(double) v( f.Domain() );
CPPAD_TESTVECTOR(double) w( f.Range() );
// check values
ok &= NearEqual(Z[x] , 2., eps99 , eps99);
ok &= NearEqual(Z[y] , sqrt(2.), eps99 , eps99);
// forward computation of partials w.r.t. s
v[s] = 1.;
w = f.Forward(1, v);
ok &= NearEqual(w[x], .5 * pow(4., -.5), eps99 , eps99); // dx/ds
ok &= NearEqual(w[y], .25 * pow(4., -.75), eps99 , eps99); // dy/ds
// reverse computation of partials of y
w[x] = 0.;
w[y] = 1.;
v = f.Reverse(1,w);
ok &= NearEqual(v[s], .25 * pow(4., -.75), eps99 , eps99); // dy/ds
// forward computation of second partials w.r.t s
v[s] = 1.;
w = f.Forward(1, v);
v[s] = 0.;
w = f.Forward(2, v);
ok &= NearEqual( // d^2 y / (ds ds)
2. * w[y] ,
-.75 * .25 * pow(4., -1.75),
eps99 ,
eps99
);
// reverse computation of second partials of y
CPPAD_TESTVECTOR(double) r( f.Domain() * 2 );
w[x] = 0.;
w[y] = 1.;
r = f.Reverse(2, w);
ok &= NearEqual( // d^2 y / (ds ds)
r[2 * s + 1] ,
-.75 * .25 * pow(4., -1.75),
eps99 ,
eps99
);
return ok;
}
bool SqrtTestTwo(void)
{ bool ok = true;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
CPPAD_TESTVECTOR(AD<double>) U(1);
U[0] = 2.;
Independent(U);
// a temporary values
AD<double> x = U[0] * U[0];
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
Z[0] = sqrt( x ); // z = sqrt( u * 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;
}
bool SqrtTestThree(void)
{ bool ok = true;
using CppAD::sqrt;
using CppAD::exp;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector, indices, values, and declaration
double x = 4.;
CPPAD_TESTVECTOR(AD<double>) X(1);
X[0] = x;
Independent(X);
// dependent variable vector, indices, and values
CPPAD_TESTVECTOR(AD<double>) Y(1);
Y[0] = sqrt( exp(X[0]) );
// define f : X -> Y and vectors for derivative calculations
ADFun<double> f(X, Y);
// forward computation of first Taylor coefficient
CPPAD_TESTVECTOR(double) x1( f.Domain() );
CPPAD_TESTVECTOR(double) y1( f.Range() );
x1[0] = 1.;
y1 = f.Forward(1, x1);
ok &= NearEqual(y1[0], exp(x/2.)/2., eps99 , eps99);
// forward computation of second Taylor coefficient
CPPAD_TESTVECTOR(double) x2( f.Domain() );
CPPAD_TESTVECTOR(double) y2( f.Range() );
x2[0] = 0.;
y2 = f.Forward(2, x2);
ok &= NearEqual(2.*y2[0] , exp(x/2.)/4., eps99 , eps99 );
// forward computation of third Taylor coefficient
CPPAD_TESTVECTOR(double) x3( f.Domain() );
CPPAD_TESTVECTOR(double) y3( f.Range() );
x3[0] = 0.;
y3 = f.Forward(3, x3);
ok &= NearEqual(6.*y3[0] , exp(x/2.)/8., eps99 , eps99 );
// reverse computation of deritavitve of Taylor coefficients
CPPAD_TESTVECTOR(double) r( f.Domain() * 4 );
CPPAD_TESTVECTOR(double) w(1);
w[0] = 1.;
r = f.Reverse(4, w);
ok &= NearEqual(r[0], exp(x/2.)/2., eps99 , eps99);
ok &= NearEqual(r[1], exp(x/2.)/4., eps99 , eps99 );
ok &= NearEqual(2.*r[2], exp(x/2.)/8., eps99 , eps99 );
ok &= NearEqual(6.*r[3], exp(x/2.)/16., eps99 , eps99 );
return ok;
}
} // END empty namespace
bool Sqrt(void)
{ bool ok = true;
ok &= SqrtTestOne();
ok &= SqrtTestTwo();
ok &= SqrtTestThree();
return ok;
}
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