1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
|
// 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
// ----------------------------------------------------------------------------
/*
{xrst_begin erfc.cpp}
The AD erfc Function: Example and Test
######################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end erfc.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <cmath>
# include <limits>
bool erfc(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) ax(n);
ax[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(ax);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) ay(m);
ay[0] = CppAD::erfc(ax[0]);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
// check relative error
double erfc_x0 = 0.4795001221869534;
ok &= NearEqual(ay[0] , erfc_x0, 0., 4e-4);
double tmp = std::max(1e-15, eps);
ok &= NearEqual(ay[0] , erfc_x0, 0., tmp);
// value of derivative of erfc at x0
double pi = 4. * std::atan(1.);
double factor = 2. / sqrt(pi);
double check = - factor * std::exp(-x0 * x0);
// forward computation of first partial w.r.t. x[0]
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], check, 0., 1e-3);
ok &= NearEqual(dy[0], check, 0., eps);
// reverse computation of derivative of y[0]
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], check, 0., 1e-1);
ok &= NearEqual(dw[0], check, 0., eps);
// use a VecAD<Base>::reference object with erfc
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = x0;
AD<double> result = CppAD::erfc(v[zero]);
ok &= NearEqual(result, ay[0], eps, eps);
// use a double with erfc
ok &= NearEqual(CppAD::erfc(x0), ay[0], eps, eps);
return ok;
}
// END C++
|
