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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
// ----------------------------------------------------------------------------
/*
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace {
double my_discrete(const double& x)
{ return static_cast<int> ( x ); }
CPPAD_DISCRETE_FUNCTION(double, my_discrete)
}
bool forward_order(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
size_t j, k;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 23, m = n;
CPPAD_TESTVECTOR(AD<double>) X(n), Y(m);
for(j = 0; j < n; j++)
X[j] = 0.0;
// declare independent variables and starting recording
CppAD::Independent(X);
// identity function values
size_t i = 0;
size_t identity_begin = i;
Y[i] = cos( acos( X[i] ) ); i++; // AcosOp, CosOp
Y[i] = sin( asin( X[i] ) ); i++; // AsinOp, SinOp
Y[i] = tan( atan( X[i] ) ); i++; // AtanOp, TanOp
Y[i] = CondExpGt(X[i], X[i-1], X[i], X[i-2]); i++; // CExpOp
Y[i] = X[i-1] * X[i] / X[i-1]; i++; // DivvvOp, MulvvOp
Y[i] = X[i] * X[i] * 1.0 / X[i]; i++; // DivpvOp
Y[i] = 5.0 * X[i] / 5.0; i++; // DivvpOp, MulpvOp
Y[i] = exp( log( X[i] ) ); i++; // ExpOp, LogOp
Y[i] = pow( sqrt( X[i] ), 2.0); i++; // PowvpOp, SqrtOp
Y[i] = log( pow( std::exp(1.), X[i] ) ); i++; // PowpvOp
Y[i] = log( pow( X[i], X[i] ) ) / log( X[i]); i++; // PowvvOp
Y[i] = -2. - ((X[i-1] - X[i]) - 2.) + X[i-1]; i++; // Sub*Op: pv, vv, vp
size_t identity_end = i;
// other functions
Y[i] = fabs( X[i] ); i++; // AbsOp
Y[i] = X[i-1] + X[i] + 2.0; i++; // AddvvOp, AddvpOp
Y[i] = cosh( X[i] ); i++; // CoshOp
Y[i] = my_discrete( X[i] ); i++; // DisOp
Y[i] = 4.0; i++; // ParOp
Y[i] = sign( X[i] ); i++; // SignOp
Y[i] = sinh( X[i] ); i++; // SinhOp
Y[i] = tanh(X[i]); i++; // TanhOp
// VecAD operations
CppAD::VecAD<double> V(n);
AD<double> index = 1.;
V[index] = 3.0;
Y[i] = V[index]; i++; // StppOp, LdpOp
V[index] = X[0];
Y[i] = V[index]; i++; // StpvOp, LdpOp
index = double(n) * X[3];
V[index] = X[1];
Y[i] = V[index]; i++; // StvvOp, LdvOp
// create f: X -> Y and stop tape recording
assert( i == m );
CppAD::ADFun<double> f;
f.Dependent(X, Y);
// initially, no values stored in f
ok &= f.size_order() == 0;
// Set X_j (t) = x + t
size_t p = 2, p1 = p+1;
CPPAD_TESTVECTOR(double) x(n), x_p(n * p1), y_p(m * p1);
for(j = 0; j < n; j++)
{ x[j] = double(j) / double(n);
x_p[j * p1 + 0] = x[j]; // order 0
x_p[j * p1 + 1] = 1.; // order 1
x_p[j * p1 + 2] = 0.; // order 2
}
// compute orders 0, 1, 2
y_p = f.Forward(p, x_p);
// identity functions
CPPAD_TESTVECTOR(double) y(p1);
i = 0;
for(j = identity_begin; j != identity_end; j++)
{ y[0] = x[j];
y[1] = 1.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
i++;
}
// y_i = fabs( x_i )
y[0] = fabs( x[i] );
y[1] = CppAD::sign( x[i] );
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = x_[i-1] + x_i + 2
i++;
y[0] = x[i-1] + x[i] + 2.0;
y[1] = 2.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = cosh( x_i )
i++;
y[0] = CppAD::cosh( x[i] );
y[1] = CppAD::sinh( x[i] );
y[2] = CppAD::cosh( x[i] ) / 2.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = my_discrete( x_i )
i++;
y[0] = my_discrete( x[i] );
y[1] = 0.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = 4
i++;
y[0] = 4.0;
y[1] = 0.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = sign( x_i )
i++;
y[0] = CppAD::sign( x[i] );
y[1] = 0.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = sinh( x_i )
i++;
y[0] = CppAD::sinh( x[i] );
y[1] = CppAD::cosh( x[i] );
y[2] = CppAD::sinh( x[i] ) / 2.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = tanh( x_i )
i++;
y[0] = CppAD::tanh( x[i] );
y[1] = 1.0 - y[0] * y[0];
y[2] = - 2.0 * y[0] * y[1] / 2.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = 3.0;
i++;
y[0] = 3.0;
y[1] = 0.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = x_0
i++;
y[0] = x[0];
y[1] = 1.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
// y_i = x_1
i++;
y[0] = x[1];
y[1] = 1.0;
y[2] = 0.0;
for(k = 0; k < p1; k++)
ok &= NearEqual(y[k] , y_p[i * p1 + k], eps, eps);
return ok;
}
// END C++
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