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
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
|
// 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 atomic_four_vector_sub.cpp}
Atomic Vector Subtraction Example
#################################
f(u, v, w)
**********
For this example,
:math:`f : \B{R}^{3m} \rightarrow \B{R}^m`
is defined by :math:`f(u, v, w) = u - (v + w)`.
where *u* , *v* , and *w* are in :math:`\B{R}^m`.
g(u, v, w)
**********
For this example :math:`g : \B{R}^{3m} \rightarrow \B{R}^m`
is defined by :math:`g_i (u, v, w) = \partial_{v[i]} f_i (u, v, w)`
Source
******
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end atomic_four_vector_sub.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <cppad/example/atomic_four/vector/vector.hpp>
bool sub(void)
{ bool ok = true;
using CppAD::NearEqual;
using CppAD::AD;
double eps99 = 99.0 * CppAD::numeric_limits<double>::epsilon();
//
// vec_op
// atomic vector_op object
CppAD::atomic_vector<double> vec_op("atomic_vector");
//
// m
// size of u, v, and w
size_t m = 5;
//
// add_op, sub_op
typedef CppAD::atomic_vector<double>::op_enum_t op_enum_t;
op_enum_t add_op = CppAD::atomic_vector<double>::add_enum;
op_enum_t sub_op = CppAD::atomic_vector<double>::sub_enum;
// -----------------------------------------------------------------------
// Record f(u, v, w) = u - (v + w)
// -----------------------------------------------------------------------
// Independent variable vector
CPPAD_TESTVECTOR( CppAD::AD<double> ) auvw(3 * m);
for(size_t j = 0; j < 3 * m; ++j)
auvw[j] = AD<double>(1 + j);
CppAD::Independent(auvw);
//
// au, av, aw
CPPAD_TESTVECTOR( CppAD::AD<double> ) au(m), av(m), aw(m);
for(size_t i = 0; i < m; ++i)
{ au[i] = auvw[0 * m + i];
av[i] = auvw[1 * m + i];
aw[i] = auvw[2 * m + i];
}
//
// ax = (av, aw)
CPPAD_TESTVECTOR( CppAD::AD<double> ) ax(2 * m);
for(size_t i = 0; i < m; ++i)
{ ax[i] = av[i];
ax[m + i] = aw[i];
}
//
// ay = v + w
CPPAD_TESTVECTOR( CppAD::AD<double> ) ay(m);
vec_op(add_op, ax, ay);
//
// ax = (sub_op, au, ay)
for(size_t i = 0; i < m; ++i)
{ ax[i] = au[i];
ax[m + i] = ay[i];
}
//
// az = au - ay
CPPAD_TESTVECTOR( CppAD::AD<double> ) az(m);
vec_op(sub_op, ax, az);
//
// f
CppAD::ADFun<double> f(auvw, az);
// -----------------------------------------------------------------------
// check forward mode on f
// -----------------------------------------------------------------------
//
// uvw, duvw
CPPAD_TESTVECTOR(double) uvw(3 * m), duvw(3 * m);
for(size_t j = 0; j < 3 * m; ++j)
{ uvw[j] = double(1 + j);
duvw[j] = double(j);
}
//
// z, dz
CPPAD_TESTVECTOR(double) z(m), dz(m);
z = f.Forward(0, uvw);
dz = f.Forward(1, duvw);
//
// ok
for(size_t i = 0; i < m; ++i)
{ double check_z = uvw[0 * m + i] - ( uvw[1 * m + i] + uvw[2 * m + i] );
ok &= NearEqual( z[i] , check_z, eps99, eps99);
double check_dz = double(0 * m + i) - double(1 * m + i + 2 * m + i);
ok &= NearEqual( dz[i] , check_dz, eps99, eps99);
}
// -----------------------------------------------------------------------
// Record g_i (u, v, w) = \partial d/dv[i] f_i (u , v , w)
// -----------------------------------------------------------------------
//
// af
CppAD::ADFun< AD<double>, double > af = f.base2ad();
//
// auvw
CppAD::Independent(auvw);
//
// aduvw
CPPAD_TESTVECTOR( AD<double> ) aduvw(3 * m);
for(size_t i = 0; i < m; ++i)
{ aduvw[0 * m + i] = 0.0; // du[i]
aduvw[1 * m + i] = 1.0; // dv[i]
aduvw[2 * m + i] = 0.0; // dw[i]
}
//
// az
// use the fact that d_v[i] f_k (u, v, w) is zero when i != k
af.Forward(0, auvw);
az = af.Forward(1, aduvw);
CppAD::ADFun<double> g(auvw, az);
// -----------------------------------------------------------------------
// Record h (u, v, w) = sum f_i^(1) (u , v , w)
// -----------------------------------------------------------------------
//
// auvw
CppAD::Independent(auvw);
//
// aweight
CPPAD_TESTVECTOR( AD<double> ) aweight(m);
for(size_t i = 0; i < m; ++i)
aweight[i] = 1.0;
//
// az
CPPAD_TESTVECTOR( AD<double> ) adweight(3 * m);
af.Forward(0, auvw);
az = af.Reverse(1, aweight);
CppAD::ADFun<double> h(auvw, az);
// -----------------------------------------------------------------------
// check forward mode on g
// -----------------------------------------------------------------------
//
// z
z = g.Forward(0, uvw);
//
// ok
for(size_t i = 0; i < m; ++i)
{ double check_z = - 1.0;
ok &= NearEqual( z[i] , check_z, eps99, eps99);
}
return ok;
// -----------------------------------------------------------------------
// check forward mode on h
// -----------------------------------------------------------------------
//
// z
z = h.Forward(0, uvw);
//
// ok
for(size_t i = 0; i < m; ++i)
{ double check_z = 1.0;
ok &= NearEqual( z[0 * m + i] , check_z, eps99, eps99);
check_z = - 1.0;
ok &= NearEqual( z[1 * m + i] , check_z, eps99, eps99);
ok &= NearEqual( z[2 * m + i] , check_z, eps99, eps99);
}
return ok;
}
// END C++
|
