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
|
/* Copyright 2018-2023. Martin Uecker.
* All rights reserved. Use of this source code is governed by
* a BSD-style license which can be found in the LICENSE file.
*/
#include <math.h>
#include "misc/nested.h"
#include "num/ode.h"
#include "utest.h"
#if 0
static void lorenz(float out[3], const float in[3], float sigma, float rho, float beta)
{
out[0] = sigma * (in[1] - in[0]);
out[1] = in[0] * (rho - in[2]) - in[1];
out[2] = in[0] * in[1] - beta * in[2];
}
static void lorenz_fun(void* data, float* out, float t, const float* in)
{
(void)data; (void)t;
lorenz(out, in, 10., 28., 8. / 3.);
}
#endif
static bool test_ode_matrix(void)
{
float mat[2][2] = { { 0., +1. }, { -1., 0. } };
float x[2] = { 1., 0. };
float h = 10.;
float tol = 1.E-4;
ode_matrix_interval(h, tol, 2, x, 0., M_PI, mat);
float err = pow(fabs(x[0] + 1.), 2.) + pow(fabs(x[1] - 0.), 2.);
return (sqrtf(err) < 1.E-3);
}
UT_REGISTER_TEST(test_ode_matrix);
static bool test_ode_adjoint(void)
{
float r1 = 1.;
float r2 = 0.5;
float x0[2] = { 1., 1. };
float h = 0.1;
float tol = 1.E-3;
int N = 10;
float t[N + 1];
for (int i = 0; i <= N; i++)
t[i] = i * (1. / N);
float x[N + 1][2];
float z[N + 1][2];
NESTED(void, sys, (float out[2], float t, const float in[2]))
{
(void)t;
out[0] = -r1 * in[0];
out[1] = -r2 * in[1];
};
NESTED(void, cost, (float out[2], float t))
{
(void)t;
for (int l = 0; l < 2; l++)
out[l] = 1.;
};
ode_adjoint_sa(h, tol, N, t, 2, x, z, x0, sys, sys, cost);
if (1.E-3 < powf(fabs(x[N][0] - expf(-r1)), 2.))
return false;
if (1.E-3 < powf(fabs(x[N][1] - expf(-r2)), 2.))
return false;
float d1 = -1.;
float d2 = -3.;
float dp[2][2][2] = { 0 };
dp[0][0][0] = d1;
dp[1][1][1] = d2;
float dj[2] = { 0., 0. };
ode_adjoint_sa_eq_eval(N, 2, 2, dj, x, z, dp);
int N2 = 1000;
float djX = 0.;
for (int i = 0; i < N2; i++)
djX += ((d1 * i) / N2) * expf(i * (-(r1) / N2)) / N2;
if (5.E-4 < fabs(dj[0] - djX))
return false;
float djY = 0.;
for (int i = 0; i < N2; i++)
djY += ((d2 * i) / N2) * expf(i * (-(r2) / N2)) / N2;
if (1.E-3 < fabs(dj[1] - djY))
return false;
return true;
}
UT_REGISTER_TEST(test_ode_adjoint);
static bool test_ode_matrix_adjoint(void)
{
float r1 = 1.;
float r2 = 0.5;
float mat[2][2] = { { -r1, 0. }, { 0., -r2 } };
float x0[2] = { 1., 1. };
float h = 0.1;
float tol = 1.E-3;
int N = 35; // 10 is ok for equal_eq
float t[N + 1];
for (int i = 0; i <= N; i++)
t[i] = i * (1. / N);
float x[N + 1][2];
float z[N + 1][2];
float sys[N][2][2];
for (int i = 0; i < N; i++)
for (int l = 0; l < 2; l++)
for (int k = 0; k < 2; k++)
sys[i][l][k] = mat[l][k];
float cost[N][2];
for (int i = 0; i < N; i++)
for (int l = 0; l < 2; l++)
cost[i][l] = 1.;
ode_matrix_adjoint_sa(h, tol, N, t, 2, x, z, x0, sys, cost);
if (1.E-3 < powf(fabs(x[N][0] - expf(-r1)), 2.))
return false;
if (1.E-3 < powf(fabs(x[N][1] - expf(-r2)), 2.))
return false;
float d1 = -1.;
float d2 = -3.;
float dp[2][2][2] = { 0 };
dp[0][0][0] = d1;
dp[1][1][1] = d2;
float dj[2] = { 0., 0. };
ode_adjoint_sa_eq_eval(N, 2, 2, dj, x, z, dp);
float dj2[2] = { 0., 0. };
ode_adjoint_sa_eval(N, t, 2, 2, dj2, x, z, dp);
int N2 = 1000;
float djX = 0.;
for (int i = 0; i < N2; i++)
djX += ((d1 * i) / N2) * expf(i * (-(r1) / N2)) / N2;
if (5.E-4 < fabs(dj[0] - djX))
return false;
if (1.E-2 < fabs(dj2[0] - djX))
return false;
float djY = 0.;
for (int i = 0; i < N2; i++)
djY += ((d2 * i) / N2) * expf(i * (-(r2) / N2)) / N2;
if (1.E-3 < fabs(dj[1] - djY))
return false;
if (5.E-2 < fabs(dj2[1] - djY))
return false;
return true;
}
UT_REGISTER_TEST(test_ode_matrix_adjoint);
|
