bool Erf(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::atan;
using CppAD::exp;
using CppAD::sqrt;
// Construct function object corresponding to erf
CPPAD_TEST_VECTOR< AD<double> > X(1);
CPPAD_TEST_VECTOR< AD<double> > Y(1);
X[0] = 0.;
Independent(X);
Y[0] = erf(X[0]);
ADFun<double> Erf(X, Y);
// vectors to use with function object
CPPAD_TEST_VECTOR<double> x(1);
CPPAD_TEST_VECTOR<double> y(1);
CPPAD_TEST_VECTOR<double> dx(1);
CPPAD_TEST_VECTOR<double> dy(1);
// check value at zero
x[0] = 0.;
y = Erf.Forward(0, x);
ok &= NearEqual(0., y[0], 4e-4, 0.);
// check the derivative of error function
dx[0] = 1.;
double pi = 4. * atan(1.);
double factor = 2. / sqrt( pi );
int i;
for(i = -10; i <= 10; i++)
{ x[0] = i / 4.;
y = Erf.Forward(0, x);
// check derivative
double derf = factor * exp( - x[0] * x[0] );
dy = Erf.Forward(1, dx);
ok &= NearEqual(derf, dy[0], 0., 2e-3);
// test using erf with AD< AD<double> >
AD< AD<double> > X0 = x[0];
AD< AD<double> > Y0 = erf(X0);
ok &= ( y[0] == Value( Value(Y0) ) );
}
return ok;
}
CppAD::ADFun<T>* AtanTestTwoFunc(const std::vector<CppAD::AD<T> >& u) {
using CppAD::atan;
using CppAD::sin;
using CppAD::cos;
using namespace CppAD;
assert(u.size() == 1);
// a temporary values
AD<T> x = sin(u[0]) / cos(u[0]);
// dependent variable vector
std::vector< AD<T> > Z(1);
Z[0] = atan(x); // atan( tan(u) )
// create f: U -> Z and vectors used for derivative calculations
return new ADFun<T > (u, Z);
}
CppAD::ADFun<T>* AtanTestOneFunc(const std::vector<CppAD::AD<T> >& u) {
using CppAD::atan;
using namespace CppAD;
assert(u.size() == 1);
size_t s = 0;
// some temporary values
AD<T> x = cos(u[s]);
AD<T> y = sin(u[s]);
AD<T> z = y / x; // tan(s)
// dependent variable vector and indices
std::vector< AD<T> > Z(1);
size_t a = 0;
// dependent variable values
Z[a] = atan(z); // atan( tan(s) )
// create f: U -> Z and vectors used for derivative calculations
return new ADFun<T > (u, Z);
}
bool VecUnary(void)
{
using namespace CppAD;
using CppAD::abs;
using CppAD::sin;
using CppAD::atan;
using CppAD::cos;
using CppAD::exp;
using CppAD::log;
using CppAD::sqrt;
bool ok = true;
size_t n = 8;
size_t i;
CPPAD_TEST_VECTOR< AD<double> > X(n);
VecAD<double> Y(n);
CPPAD_TEST_VECTOR< AD<double> > Z(n);
for(i = 0; i < n; i++)
X[i] = int(i); // some compilers require the int here
Independent(X);
AD<double> j;
j = 0.;
Y[j] = X[0];
Z[0] = -Y[j];
j = 1.;
Y[j] = X[1];
Z[1] = sin( Y[j] );
j = 2.;
Y[j] = X[2];
Z[2] = abs( Y[j] );
j = 3.;
Y[j] = X[3];
Z[3] = atan( Y[j] );
j = 4.;
Y[j] = X[4];
Z[4] = cos( Y[j] );
j = 5.;
Y[j] = X[5];
Z[5] = exp( Y[j] );
j = 6.;
Y[j] = X[6];
Z[6] = log( Y[j] );
j = 7.;
Y[j] = X[7];
Z[7] = sqrt( Y[j] );
ADFun<double> f(X, Z);
CPPAD_TEST_VECTOR<double> x(n);
CPPAD_TEST_VECTOR<double> z(n);
for(i = 0; i < n; i++)
x[i] = 2. / double(i + 1);
x[7] = abs( x[7] );
z = f.Forward(0, x);
ok &= NearEqual(z[0], - x[0], 1e-10, 1e-10);
ok &= NearEqual(z[1], sin( x[1] ), 1e-10, 1e-10);
ok &= NearEqual(z[2], abs( x[2] ), 1e-10, 1e-10);
ok &= NearEqual(z[3], atan(x[3] ), 1e-10, 1e-10);
ok &= NearEqual(z[4], cos( x[4] ), 1e-10, 1e-10);
ok &= NearEqual(z[5], exp( x[5] ), 1e-10, 1e-10);
ok &= NearEqual(z[6], log( x[6] ), 1e-10, 1e-10);
ok &= NearEqual(z[7], sqrt(x[7] ), 1e-10, 1e-10);
return ok;
}