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//
// 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>
#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 */
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