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
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
|
// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-24 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin atomic_four_bilinear.cpp}
Bilinear Interpolation Atomic Function: Example and Test
########################################################
See Also
********
:ref:`interp_onetape.cpp-name` .
Define Atomic Function
**********************
{xrst_literal
// BEGIN_DEFINE_ATOMIC_FUNCTION
// END_DEFINE_ATOMIC_FUNCTION
}
Use Atomic Function
*******************
{xrst_literal
// BEGIN_USE_ATOMIC_FUNCTION
// END_USE_ATOMIC_FUNCTION
}
{xrst_end atomic_four_bilinear.cpp}
*/
# include <cppad/cppad.hpp> // CppAD include file
// BEGIN_DEFINE_ATOMIC_FUNCTION
// empty namespace
namespace {
// atomic_bilinear
class atomic_bilinear : public CppAD::atomic_four<double> {
private:
// u_grid_, v_grid_; y_grid_
CppAD::vector<double>& u_grid_;
CppAD::vector<double>& v_grid_;
CppAD::vector<double>& y_grid_;
//
// u_index_, v_index
size_t u_index_;
size_t v_index_;
//
// set_index
void set_index(double u, double v)
{ //
// u_index_
while( u < u_grid_[u_index_] && u_index_ > 0 )
--u_index_;
while( u > u_grid_[u_index_+1] && u_index_ < u_grid_.size() - 2 )
++u_index_;
//
// v_index_
while( v < v_grid_[v_index_] && v_index_ > 0 )
--v_index_;
while( v > v_grid_[v_index_+1] && v_index_ < v_grid_.size() - 2 )
++v_index_;
}
public:
// can use const char* name when calling this constructor
atomic_bilinear(
const std::string& name ,
CppAD::vector<double>& u_grid ,
CppAD::vector<double>& v_grid ,
CppAD::vector<double>& y_grid ) :
CppAD::atomic_four<double>(name) , // inform base class of name
u_grid_(u_grid) ,
v_grid_(v_grid) ,
y_grid_(y_grid) ,
u_index_(0) ,
v_index_(0)
{ assert( u_grid_.size() >= 2 );
assert( v_grid_.size() >= 2 );
assert( y_grid_.size() == u_grid_.size() * v_grid_.size() );
}
private:
// for_type
bool for_type(
size_t call_id ,
const CppAD::vector<CppAD::ad_type_enum>& type_x ,
CppAD::vector<CppAD::ad_type_enum>& type_y ) override
{
assert( call_id == 0 ); // default value
assert( type_x.size() == 2 ); // n
assert( type_y.size() == 1 ); // m
//
type_y[0] = std::max(type_x[0], type_x[1]);
return true;
}
// forward
bool forward(
size_t call_id ,
const CppAD::vector<bool>& select_y ,
size_t order_low ,
size_t order_up ,
const CppAD::vector<double>& taylor_x ,
CppAD::vector<double>& taylor_y ) override
{
// ok
bool ok = order_up <= 1;
if( ! ok )
return ok;
//
// q
size_t q = order_up + 1;
//
# ifndef NDEBUG
size_t n = taylor_x.size() / q;
size_t m = taylor_y.size() / q;
assert( call_id == 0 );
assert( n == 2 );
assert( m == 1 );
assert( m == select_y.size() );
# endif
// u, v
double u = taylor_x[0 * q + 0];
double v = taylor_x[1 * q + 0];
//
// u_index_, v_index_
set_index(u, v);
//
// u_0, u_1, v_0, v_1
double u_0 = u_grid_[ u_index_ + 0 ];
double u_1 = u_grid_[ u_index_ + 1 ];
double v_0 = v_grid_[ v_index_ + 0 ];
double v_1 = v_grid_[ v_index_ + 1 ];
//
// y_00, y_01, y_10, y_11
double y_00 = y_grid_[ (u_index_+0) * v_grid_.size() + v_index_+0 ];
double y_01 = y_grid_[ (u_index_+0) * v_grid_.size() + v_index_+1 ];
double y_10 = y_grid_[ (u_index_+1) * v_grid_.size() + v_index_+0 ];
double y_11 = y_grid_[ (u_index_+1) * v_grid_.size() + v_index_+1 ];
//
// taylor_y
// function value
if( order_low <= 0 )
{ double sum = 0.0;
sum += y_00 * (u_1 - u) * (v_1 - v);
sum += y_01 * (u_1 - u) * (v - v_0);
sum += y_10 * (u - u_0) * (v_1 - v);
sum += y_11 * (u - u_0) * (v - v_0);
taylor_y[0] = sum / ( (u_1 - u_0) * (v_1 - v_0) );
}
//
// taylor_y
// first order derivatives
if( order_low <= 1 && 1 <= order_up )
{ //
// du, dv
double du = taylor_x[0 * q + 1];
double dv = taylor_x[1 * q + 1];
double dsum = 0.0;
//
dsum -= y_00 * du * (v_1 - v);
dsum -= y_01 * du * (v - v_0);
dsum += y_10 * du * (v_1 - v);
dsum += y_11 * du * (v - v_0);
dsum -= y_00 * (u_1 - u) * dv;
dsum += y_01 * (u_1 - u) * dv;
dsum -= y_10 * (u - u_0) * dv;
dsum += y_11 * (u - u_0) * dv;
taylor_y[1] = dsum / ( (u_1 - u_0) * (v_1 - v_0) );
}
//
return ok;
}
};
}
// END_DEFINE_ATOMIC_FUNCTION
// BEGIN_USE_ATOMIC_FUNCTION
bool bilinear(void)
{ //
// ok, eps
bool ok = true;
double eps = 10. * CppAD::numeric_limits<double>::epsilon();
//
// nu, u_grid
size_t nu = 4;
CppAD::vector<double> u_grid(nu);
for(size_t i = 0; i < nu; ++i)
u_grid[i] = double(i) * 2.0;
//
// nv, v_grid
size_t nv = 5;
CppAD::vector<double> v_grid(nv);
for(size_t j = 0; j < nv; ++j)
v_grid[j] = double(j) * 3.0;
//
// y_grid
CppAD::vector<double> y_grid( u_grid.size() * v_grid.size() );
for(size_t i = 0; i < nu; ++i)
{ for(size_t j = 0; j < nv; ++j)
{ double u = u_grid[i];
double v = v_grid[j];
y_grid[i * v_grid.size() + j] = u * u + v * v;
}
}
//
// afun
std::string name = "atomic_bilinear";
atomic_bilinear afun(name, u_grid, v_grid, y_grid);
//
// n, m
size_t n = 2;
size_t m = 1;
//
// ax
CPPAD_TESTVECTOR( CppAD::AD<double> ) ax(n);
ax[0] = 0.0;
ax[1] = 0.0;
CppAD::Independent(ax);
//
// ay
// call atomic function and store result in ay
CPPAD_TESTVECTOR( CppAD::AD<double> ) ay(m);
afun(ax, ay);
//
// f
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(ax, ay);
//
// y
CPPAD_TESTVECTOR( double ) x(n), y(m);
x[0] = 1.0;
x[1] = 3.5;
y = f.Forward(0, x);
//
// u_0, u_1
double u_0 = u_grid[0];
double u_1 = u_grid[1];
assert( u_0 < x[0] && x[0] < u_1 );
//
// v_0, v_1
double v_0 = v_grid[1];
double v_1 = v_grid[2];
assert( v_0 < x[1] && x[1] < v_1 );
//
// y_00, y_01, y_10, y_11
double y_00 = y_grid[ 0 * v_grid.size() + 1 ];
double y_01 = y_grid[ 0 * v_grid.size() + 2 ];
double y_10 = y_grid[ 1 * v_grid.size() + 1 ];
double y_11 = y_grid[ 1 * v_grid.size() + 2 ];
//
// check, ok
double sum = 0.0;
sum += y_00 * (u_1 - x[0]) * (v_1 - x[1]);
sum += y_01 * (u_1 - x[0]) * (x[1] - v_0);
sum += y_10 * (x[0] - u_0) * (v_1 - x[1]);
sum += y_11 * (x[0] - u_0) * (x[1] - v_0);
double check = sum / ( (u_1 - u_0) * (v_1 - v_0) );
ok &= CppAD::NearEqual(y[0] , check, eps, eps);
//
// dy
CPPAD_TESTVECTOR( double ) dx(n), dy(m);
dx[0] = 1.0;
dx[1] = 0.0;
dy = f.Forward(1, dx);
//
// check
sum = 0.0;
sum -= y_00 * (v_1 - x[1]);
sum -= y_01 * (x[1] - v_0);
sum += y_10 * (v_1 - x[1]);
sum += y_11 * (x[1] - v_0);
check = sum / ( (u_1 - u_0) * (v_1 - v_0) );
ok &= CppAD::NearEqual(dy[0] , check, eps, eps);
//
// dy
dx[0] = 0.0;
dx[1] = 1.0;
dy = f.Forward(1, dx);
//
// check
sum = 0.0;
sum -= y_00 * (u_1 - x[0]);
sum += y_01 * (u_1 - x[0]);
sum -= y_10 * (x[0] - u_0);
sum += y_11 * (x[0] - u_0);
check = sum / ( (u_1 - u_0) * (v_1 - v_0) );
ok &= CppAD::NearEqual(dy[0] , check, eps, eps);
//
return ok;
}
// END_USE_ATOMIC_FUNCTION
|
