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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 Div examples now used just for valiadation testing
*/
# include <cppad/cppad.hpp>
namespace { // BEGIN empty namespace
bool DivTestOne(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// assign some parameters
AD<double> zero = 0.;
AD<double> one = 1.;
// independent variable vector, indices, values, and declaration
CPPAD_TESTVECTOR(AD<double>) U(2);
size_t s = 0;
size_t t = 1;
U[s] = 2.;
U[t] = 3.;
Independent(U);
// dependent variable vector and indices
CPPAD_TESTVECTOR(AD<double>) Z(6);
size_t x = 0;
size_t y = 1;
size_t z = 2;
size_t u = 3;
size_t v = 4;
size_t w = 5;
// dependent variables
Z[x] = U[s] / U[t]; // AD<double> / AD<double>
Z[y] = Z[x] / 4.; // AD<double> / double
Z[z] = 5. / Z[y]; // double / AD<double>
Z[u] = Z[z] / one; // division by a parameter equal to one
Z[v] = Z[z] / 1.; // division by a double equal to one
Z[w] = zero / Z[z]; // division into a parameter equal to zero
// check division into a zero valued parameter results in a parameter
// (must do this before creating f because it erases the tape)
ok &= Parameter(Z[w]);
// create f : U -> Z and vectors used for derivative calculations
ADFun<double> f(U, Z);
CPPAD_TESTVECTOR(double) q( f.Domain() );
CPPAD_TESTVECTOR(double) r( f.Range() );
// check parameter flag
ok &= f.Parameter(w);
// check values
ok &= NearEqual( Z[x] , 2. / 3. , eps99, eps99);
ok &= NearEqual( Z[y] , 2. / ( 3. * 4. ) , eps99, eps99);
ok &= NearEqual( Z[z] , 5. * 3. * 4. / 2. , eps99, eps99);
ok &= ( Z[w] == 0. );
ok &= ( Z[u] == Z[z] );
// forward computation of partials w.r.t. s
q[s] = 1.;
q[t] = 0.;
r = f.Forward(1, q);
ok &= NearEqual(r[x], 1./U[t], eps99, eps99); // dx/ds
ok &= NearEqual(r[y], 1./(U[t]*4.), eps99, eps99); // dy/ds
ok &= NearEqual(r[z], -5.*U[t]*4./(U[s]*U[s]), eps99, eps99); // dz/ds
ok &= ( r[u] == r[z] ); // du/ds
ok &= ( r[v] == r[z] ); // dv/ds
ok &= ( r[w] == 0. ); // dw/ds
// forward computation in the direction (1, 1)
q[s] = 1.;
q[t] = 1.;
r = f.Forward(1, q);
ok &= NearEqual(r[x], 1./U[t] - U[s]/(U[t] * U[t]), eps99, eps99);
// second order reverse mode computation
CPPAD_TESTVECTOR(double) Q( f.Domain() * 2 );
r[x] = 1.;
r[y] = r[z] = r[u] = r[v] = r[w] = 0.;
Q = f.Reverse(2, r);
ok &= NearEqual(
Q[s * f.Domain() + 1],
- 1. / (U[t] * U[t]),
eps99,
eps99
);
return ok;
}
bool DivTestTwo(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// independent variable vector
double u0 = .5;
CPPAD_TESTVECTOR(AD<double>) U(1);
U[0] = u0;
Independent(U);
AD<double> a = U[0] / 1.; // AD<double> / double
AD<double> b = a / 2; // AD<double> / int
AD<double> c = 3. / b; // double / AD<double>
AD<double> d = 4 / c; // int / AD<double>
// dependent variable vector
CPPAD_TESTVECTOR(AD<double>) Z(1);
Z[0] = U[0] * U[0] / d; // AD<double> / AD<double>
// 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(Value(Z[0]) , u0*u0/(4/(3/(u0/2))), eps99, eps99);
// forward computation of partials w.r.t. u
size_t j;
size_t p = 5;
double jfac = 1.;
v[0] = 1.;
double value = 6. / 4.;
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 = 6. / 4.;
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 DivTestThree(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// more testing of variable / variable case
double x0 = 2.;
double x1 = 3.;
size_t n = 2;
CPPAD_TESTVECTOR(AD<double>) X(n);
X[0] = x0;
X[1] = x1;
Independent(X);
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = X[0] / X[1];
ADFun<double> f(X, Y);
CPPAD_TESTVECTOR(double) dx(n), dy(m);
double check;
dx[0] = 1.;
dx[1] = 1.;
dy = f.Forward(1, dx);
check = 1. / x1 - x0 / (x1 * x1);
ok &= NearEqual(dy[0], check, eps99, eps99);
CPPAD_TESTVECTOR(double) w(m), dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
check = 1. / x1;
ok &= NearEqual(dw[0], check, eps99, eps99);
check = - x0 / (x1 * x1);
ok &= NearEqual(dw[1], check, eps99, eps99);
return ok;
}
} // END empty namespace
bool Div(void)
{ bool ok = true;
ok &= DivTestOne();
ok &= DivTestTwo();
ok &= DivTestThree();
return ok;
}
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