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
|
//
// Copyright 2016 Ettus Research
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
//
#ifndef INCLUDED_UHD_INTERPOLATION_IPP
#define INCLUDED_UHD_INTERPOLATION_IPP
#include "interpolation.hpp"
#include <uhd/utils/log.hpp>
// This is a bugfix for Boost 1.64, maybe future Boosts won't need this
#if BOOST_VERSION >= 106400
# include <boost/serialization/array_wrapper.hpp>
#endif // end of bugfix
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/lu.hpp>
using namespace boost::numeric;
namespace uhd {
namespace cal {
#define CAL_INTERP_METHOD(return_type, method, args, ...) \
template<typename in_type, typename out_type> \
return_type interp<in_type, out_type>::\
method(args, __VA_ARGS__)
#define ARGS_T typename interp<in_type, out_type>::args_t
#define CONTAINER_T typename interp<in_type, out_type>::container_t
CAL_INTERP_METHOD(in_type, calc_dist, const ARGS_T &a, const ARGS_T &b)
{
in_type dist = 0;
for (size_t i = 0; i < std::min(a.size(), b.size()); i++)
{
dist += std::abs(a[i] - b[i]);
}
return dist;
}
CAL_INTERP_METHOD(const out_type, nn_interp, CONTAINER_T &data, const ARGS_T &args)
{
// Check the cache for the output
if (data.find(args) != data.end()) {
return data[args];
}
out_type output = 0;
in_type min_dist = 0;
typename container_t::const_iterator citer;
for (citer = data.begin(); citer != data.end(); citer++)
{
in_type dist = calc_dist(citer->first, args);
if (citer == data.begin() || dist < min_dist) {
min_dist = dist;
output = data[citer->first];
}
}
return output;
}
CAL_INTERP_METHOD(const out_type, bl_interp, CONTAINER_T &data, const ARGS_T &args)
{
if (args.size() != 2) {
throw uhd::assertion_error(str(boost::format(
"Bilinear interpolation expects 2D values. Received %d.")
% args.size()
));
}
if (data.size() < 4) {
throw uhd::assertion_error(str(boost::format(
"Bilinear interpolation requires at least 4 input points. Found %d.")
% data.size()
));
}
// Locate the nearest 4 points
typedef std::pair<interp<in_type, out_type>::args_t, out_type> cal_pair_t;
typename std::vector<cal_pair_t> nearest;
// Initialize the resulting pair to something
cal_pair_t pair = *data.begin();
for (size_t i = 0; i < 4; i++) {
bool init = true;
in_type min_dist = 0;
typename container_t::const_iterator citer;
for (citer = data.begin(); citer != data.end(); citer++)
{
cal_pair_t temp = *citer;
if (std::find(nearest.begin(), nearest.end(), temp) == nearest.end())
{
in_type dist = calc_dist(citer->first, args);
if (dist < min_dist || init)
{
min_dist = dist;
pair = temp;
init = false;
}
}
}
// Push back the nearest pair
nearest.push_back(pair);
}
//
// Since these points are not grid aligned,
// we perform irregular bilinear interpolation.
// This math involves finding our interpolation
// function using lagrange multipliers:
//
// f(x, y) = ax^2 + bxy + cy^2 + dx + ey + f
//
// The solution is to solve the following system:
//
// A x b
// | E X' | | s | - | 0 |
// | X 0 | | l | - | z |
//
// where s is a vector of the above coefficients.
//
typename ublas::matrix<in_type> A(10, 10, 0.0);
// E
A(0, 0) = 1.0; A(1, 1) = 1.0; A(2, 2) = 1.0;
in_type x1, x2, x3, x4;
in_type y1, y2, y3, y4;
x1 = nearest[0].first[0]; y1 = nearest[0].first[1];
x2 = nearest[1].first[0]; y2 = nearest[1].first[1];
x3 = nearest[2].first[0]; y3 = nearest[2].first[1];
x4 = nearest[3].first[0]; y4 = nearest[3].first[1];
// X
A(0, 6) = x1*x1; A(1, 6) = x1*y1; A(2, 6) = y1*y1; A(3, 6) = x1; A(4, 6) = y1; A(5, 6) = 1.0;
A(0, 7) = x2*x2; A(1, 7) = x2*y2; A(2, 7) = y2*y2; A(3, 7) = x2; A(4, 7) = y2; A(5, 7) = 1.0;
A(0, 8) = x3*x3; A(1, 8) = x3*y3; A(2, 8) = y3*y3; A(3, 8) = x3; A(4, 8) = y3; A(5, 8) = 1.0;
A(0, 9) = x4*x4; A(1, 9) = x4*y4; A(2, 9) = y4*y4; A(3, 9) = x4; A(4, 9) = y4; A(5, 9) = 1.0;
// X'
A(6, 0) = x1*x1; A(6, 1) = x1*y1; A(6, 2) = y1*y1; A(6, 3) = x1; A(6, 4) = y1; A(6, 5) = 1.0;
A(7, 0) = x2*x2; A(7, 1) = x2*y2; A(7, 2) = y2*y2; A(7, 3) = x2; A(7, 4) = y2; A(7, 5) = 1.0;
A(8, 0) = x3*x3; A(8, 1) = x3*y3; A(8, 2) = y3*y3; A(8, 3) = x3; A(8, 4) = y3; A(8, 5) = 1.0;
A(9, 0) = x4*x4; A(9, 1) = x4*y4; A(9, 2) = y4*y4; A(9, 3) = x4; A(9, 4) = y4; A(9, 5) = 1.0;
// z
typename ublas::vector<in_type> b(10, 0.0);
b(6) = nearest[0].second;
b(7) = nearest[1].second;
b(8) = nearest[2].second;
b(9) = nearest[3].second;
typename ublas::matrix<in_type> A_t = A;
typename ublas::vector<in_type> s = b;
typename ublas::permutation_matrix<in_type> P(A_t.size1());
// Use LUP factorization to solve for the coefficients
// We're solving the problem in the form of Ax = b
bool is_singular = ublas::lu_factorize(A_t, P);
out_type output = 0;
// Fall back to 1D interpolation if the matrix is singular
if (is_singular) {
// Warn the user that the A matrix is singular
UHD_LOGGER_WARNING("CAL") << "Bilinear interpolation: singular matrix detected. "
<< "Performing 1D linear interpolation against the nearest measurements. "
<< "Provide calibration data with more measurements";
output = (b[7] - b[6]) / 2.0;
output += b[6];
return output;
}
ublas::lu_substitute(A_t, P, s);
in_type x = args[0];
in_type y = args[1];
// Utilize the solution to calculate the interpolation function
output = s[0]*x*x + s[1]*x*y + s[2]*y*y + s[3]*x + s[4]*y + s[5];
return output;
}
} // namespace cal
} // namespace uhd
#endif /* INCLUDED_UHD_INTERPOLATION_IPP */
|
