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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
// ----------------------------------------------------------------------------
# include <cppad/cppad.hpp>
namespace {
// ---------------------------------------------------------------------
bool old_example(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::atan;
using CppAD::exp;
using CppAD::sqrt;
double eps = 100.0 * std::numeric_limits<double>::epsilon();
// Construct function object corresponding to erf
CPPAD_TESTVECTOR(AD<double>) ax(1);
CPPAD_TESTVECTOR(AD<double>) ay(1);
ax[0] = 0.;
Independent(ax);
ay[0] = erf(ax[0]);
ADFun<double> f(ax, ay);
// Construct function object corresponding to derivative of erf
Independent(ax);
double pi = 4.0 * atan(1.0);
ay[0] = exp( - ax[0] * ax[0] ) * 2.0 / sqrt(pi);
ADFun<double> df(ax, ay);
// vectors to use with function object
CPPAD_TESTVECTOR(double) x0(1), y0(1), x1(1), y1(1), check(1);
// check value at zero
x0[0] = 1.5;
y0 = f.Forward(0, x0);
check[0] = 0.96611;
ok &= std::fabs(check[0] - y0[0]) <= 4e-4;
// check the derivative of error function
x1[0] = 1.0;
y1 = f.Forward(1, x1);
check = df.Forward(0, x0);
ok &= NearEqual(check[0], y1[0], 0., 2e-3);
ok &= NearEqual(check[0], y1[0], eps, eps);
// check second derivative
CPPAD_TESTVECTOR(double) x2(1), y2(1);
x2[0] = 0.0;
y2 = f.Forward(2, x2);
check = df.Forward(1, x1);
ok &= NearEqual(check[0] / 2.0, y2[0], 0., 2e-3);
ok &= NearEqual(check[0] / 2.0, y2[0], eps, eps);
// check third derivative
CPPAD_TESTVECTOR(double) x3(1), y3(1);
x3[0] = 0.0;
y3 = f.Forward(3, x3);
check = df.Forward(2, x2);
ok &= NearEqual(check[0] / 3.0, y3[0], 0., 2e-3);
ok &= NearEqual(check[0] / 3.0, y3[0], eps, eps);
// check 4-th order of reverse mode
CPPAD_TESTVECTOR(double) w(1), dy(4), x4(1), y4(1);
x4[0] = 0.0;
w[0] = 1.0;
dy = f.Reverse(4, w);
y4 = f.Forward(4, x4);
//
ok &= NearEqual(dy[0], y1[0], 0., 2e-3);
ok &= NearEqual(dy[0], y1[0], eps, eps);
//
ok &= NearEqual(dy[1], 2.0 * y2[0], 0., 2e-3);
ok &= NearEqual(dy[1], 2.0 * y2[0], eps, eps);
//
ok &= NearEqual(dy[2], 3.0 * y3[0], 0., 2e-3);
ok &= NearEqual(dy[2], 3.0 * y3[0], eps, eps);
//
ok &= NearEqual(dy[3], 4.0 * y4[0], 0., 2e-3);
ok &= NearEqual(dy[3], 4.0 * y4[0], eps, eps);
return ok;
}
// ---------------------------------------------------------------------
bool hessian(void)
{ bool ok = true;
double eps = 1.0 * std::numeric_limits<double>::epsilon();
using CppAD::vector;
using CppAD::AD;
size_t n = 2;
size_t m = 1;
vector<double> x(n), w(m);
w[0] = 1.0;
vector< AD<double> > ax(n), ay(m);
ax[0] = x[0] = 0.5;
ax[1] = x[1] = 0.0;
// construct function
CppAD::Independent(ax);
ay[0] = erf( 2.0 * ax[0] );
CppAD::ADFun<double> f(ax, ay);
// dense hessian
vector<double> dense_hess = f.Hessian(x, 0);
// sparse_hessian
vector<double> sparse_hess = f.SparseHessian(x, w);
// Define g(u) = erf(2 * u)
// g'(u) = 2 * erf'(2 * u)
// = 2 * exp( - 2 * u * 2 * u ) * 2 / sqrt(pi)
// = exp( - 4 * u * u ) * 4 / sqrt(pi)
// g''(u) = - exp( - 4 * u * u ) * 32 * u / sqrt(pi)
double root_pi = std::sqrt( 4.0 * atan(1.0) );
double check = -std::exp(-4.0 * x[0] * x[0]) * 32.0 * x[0] / root_pi;
ok &= CppAD::NearEqual(dense_hess[0], check, eps, eps);
ok &= CppAD::NearEqual(sparse_hess[0], check, eps, eps);
for(size_t k = 1; k < n * n; k++)
{ ok &= CppAD::NearEqual(dense_hess[k], 0.0, eps, eps);
ok &= CppAD::NearEqual(sparse_hess[k], 0.0, eps, eps);
}
return ok;
}
// ---------------------------------------------------------------------
bool mul_dir(void)
{ bool ok = true;
using namespace CppAD;
using CppAD::atan;
using CppAD::exp;
using CppAD::sqrt;
double eps = 100.0 * std::numeric_limits<double>::epsilon();
// Construct function object corresponding to erf
CPPAD_TESTVECTOR(AD<double>) ax(1);
CPPAD_TESTVECTOR(AD<double>) ay(1);
ax[0] = 0.;
Independent(ax);
ay[0] = erf(ax[0]);
ADFun<double> f(ax, ay);
// Construct function object corresponding to derivative of erf
Independent(ax);
double pi = 4.0 * atan(1.0);
ay[0] = exp( - ax[0] * ax[0] ) * 2.0 / sqrt(pi);
ADFun<double> df(ax, ay);
// number of directions
size_t r = 1;
// vectors to use with objects
CPPAD_TESTVECTOR(double) x0(1), y0(1), x1(1), y1(1), y2(1), y3(1);
CPPAD_TESTVECTOR(double) zero(1), check(1);
CPPAD_TESTVECTOR(double) xq(r), yq(r), checkq(r), zeroq(r);
// check function value
x0[0] = 1.5;
y0 = f.Forward(0, x0);
check[0] = 0.9661051464753108;
double tmp = std::max(1e-15, eps);
ok &= NearEqual(check[0], y0[0], 0.0, tmp);
// check first order derivative
x1[0] = 1.0;
y1 = f.Forward(1, x1);
check = df.Forward(0, x0);
ok &= NearEqual(check[0], y1[0], eps, eps);
for(size_t ell = 0; ell < r; ell++)
{ xq[ell] = x1[ell] / double(ell + 1);
zeroq[ell] = 0.0;
}
yq = f.Forward(1, r, xq);
for(size_t ell = 0; ell < r; ell++)
{ checkq[ell] = check[0] * xq[ell];
ok &= NearEqual(checkq[ell], yq[ell], eps, eps);
}
// check second order derivative
zero[0] = 0.0;
y2 = f.Forward(2, zero);
check = df.Forward(1, x1);
check[0] /= 2.0;
ok &= NearEqual(check[0], y2[0], eps, eps);
yq = f.Forward(2, r, zeroq);
for(size_t ell = 0; ell < r; ell++)
{ checkq[ell] = check[0] * xq[ell];
ok &= NearEqual(checkq[ell], yq[ell], eps, eps);
}
// check third order derivative
zero[0] = 0.0;
y3 = f.Forward(3, zero);
check = df.Forward(2, zero);
check[0] /= 3.0;
ok &= NearEqual(check[0], y3[0], eps, eps);
yq = f.Forward(3, r, zeroq);
for(size_t ell = 0; ell < r; ell++)
{ checkq[ell] = check[0] * xq[ell];
ok &= NearEqual(checkq[ell], yq[ell], eps, eps);
}
return ok;
}
// -------------------------------------------------------------------
}
bool erf(void)
{ bool ok = true;
ok &= old_example();
ok &= hessian();
ok &= mul_dir();
return ok;
}
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