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
|
/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: ext_diff_func.cpp
Revision: $Id: ext_diff_func.cpp 370 2012-11-22 13:18:52Z kulshres $
Contents: example for external differentiated functions
Copyright (c) Andrea Walther
This file is part of ADOL-C. This software is provided as open source.
Any use, reproduction, or distribution of the software constitutes
recipient's acceptance of the terms of the accompanying license file.
---------------------------------------------------------------------------*/
#include <math.h>
#include <adolc/adolc.h>
#define h 0.01
#define steps 100
// time step function
// double version
int euler_step(int n, double *yin, int m, double *yout);
// adouble version
void euler_step_act(int n, adouble *yin, int m, adouble *yout);
// versions for usage as external differentiated function
ADOLC_ext_fct zos_for_euler_step;
ADOLC_ext_fct_fos_reverse fos_rev_euler_step;
ext_diff_fct *edf;
int tag_full, tag_part, tag_ext_fct;
int main()
{
// time interval
double t0, tf;
// state, double and adouble version
adouble y[2];
adouble ynew[2];
int n, m;
// control, double and adouble version
adouble con[2];
double conp[2];
// target value;
double f;
//variables for derivative caluclation
double yp[2], ynewp[2];
double u[2], z[2];
double grad[2];
int i,j;
// tape identifiers
tag_full = 1;
tag_part = 2;
tag_ext_fct = 3;
// two input variables for external differentiated function
n = 2;
// two output variables for external differentiated function
m = 2;
// time interval
t0 = 0.0;
tf = 1.0;
//control
conp[0] = 1.0;
conp[1] = 1.0;
trace_on(tag_full);
con[0] <<= conp[0];
con[1] <<= conp[1];
y[0] = con[0];
y[1] = con[1];
for(i=0;i<steps;i++)
{
euler_step_act(n,y,m,ynew);
for(j=0;j<2;j++)
y[j] = ynew[j];
}
y[0] + y[1] >>= f;
trace_off(1);
gradient(tag_full,2,conp,grad);
printf(" full taping:\n gradient=( %f, %f)\n\n",grad[0],grad[1]);
// Now using external function facilities
// tape external differentiated function
trace_on(tag_ext_fct);
y[0] <<= conp[0];
y[1] <<= conp[1];
euler_step_act(2,y,2,ynew);
ynew[0] >>= f;
ynew[1] >>= f;
trace_off(1);
// register external function
edf = reg_ext_fct(euler_step);
// information for Zero-Order-Scalar (=zos) forward
// yp = new double[2];
// ynewp = new double[2];
edf->zos_forward = zos_for_euler_step;
edf->dp_x = yp;
edf->dp_y = ynewp;
// information for First-Order-Scalar (=fos) reverse
edf->fos_reverse = fos_rev_euler_step;
edf->dp_U = u;
edf->dp_Z = z;
trace_on(tag_part);
con[0] <<= conp[0];
con[1] <<= conp[1];
y[0] = con[0];
y[1] = con[1];
for(i=0;i<steps;i++)
{
call_ext_fct(edf, 2, yp, y, 2, ynewp, ynew);
for(j=0;j<2;j++)
y[j] = ynew[j];
}
y[0] + y[1] >>= f;
trace_off(1);
gradient(tag_part,2,conp,grad);
printf(" taping with external function facility:\n gradient=( %f, %f)\n\n",grad[0],grad[1]);
return 0;
}
void euler_step_act(int n, adouble *yin, int m, adouble *yout)
{
// Euler step, adouble version
yout[0] = yin[0]+h*yin[0];
yout[1] = yin[1]+h*2*yin[1];
}
int euler_step(int n, double *yin, int m, double *yout)
{
// Euler step, double version
yout[0] = yin[0]+h*yin[0];
yout[1] = yin[1]+h*2*yin[1];
return 1;
}
int zos_for_euler_step(int n, double *yin, int m, double *yout)
{
int rc;
rc = zos_forward(tag_ext_fct, 2, 2, 0, yin, yout);
return rc;
}
int fos_rev_euler_step(int n, double *u, int m, double *z, double */* unused */, double */*unused*/)
{
int rc;
zos_forward(tag_ext_fct, 2, 2, 1, edf->dp_x, edf->dp_y);
rc = fos_reverse(tag_ext_fct, 2, 2, u, z);
return rc;
}
|
