Firmware2/Marlin/least_squares_fit.cpp

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/**
* Marlin 3D Printer Firmware
* Copyright (C) 2016 MarlinFirmware [https://github.com/MarlinFirmware/Marlin]
*
* Based on Sprinter and grbl.
* Copyright (C) 2011 Camiel Gubbels / Erik van der Zalm
*
* 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/>.
*
*/
/**
* Least Squares Best Fit By Roxy and Ed Williams
*
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* This algorithm is high speed and has a very small code footprint.
* Its results are identical to both the Iterative Least-Squares published
* earlier by Roxy and the QR_SOLVE solution. If used in place of QR_SOLVE
* it saves roughly 10K of program memory.
*
*/
#include "MarlinConfig.h"
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#if ENABLED(AUTO_BED_LEVELING_UBL) // Currently only used by UBL, but is applicable to Grid Based (Linear) Bed Leveling
#include "ubl.h"
#include "Marlin.h"
#include "macros.h"
#include <math.h>
double linear_fit_average(double m[], const int);
//double linear_fit_average_squared(double m[], const int);
//double linear_fit_average_mixed_terms(double m1[], double m2[], const int);
double linear_fit_average_product(double matrix1[], double matrix2[], const int n);
void linear_fit_subtract_mean(double matrix[], double bar, const int n);
double linear_fit_max_abs(double m[], const int);
linear_fit linear_fit_results;
linear_fit* lsf_linear_fit(double x[], double y[], double z[], const int n) {
double xbar, ybar, zbar,
x2bar, y2bar,
xybar, xzbar, yzbar,
D;
linear_fit_results.A = 0.0;
linear_fit_results.B = 0.0;
linear_fit_results.D = 0.0;
xbar = linear_fit_average(x, n);
ybar = linear_fit_average(y, n);
zbar = linear_fit_average(z, n);
linear_fit_subtract_mean(x, xbar, n);
linear_fit_subtract_mean(y, ybar, n);
linear_fit_subtract_mean(z, zbar, n);
x2bar = linear_fit_average_product(x, x, n);
y2bar = linear_fit_average_product(y, y, n);
xybar = linear_fit_average_product(x, y, n);
xzbar = linear_fit_average_product(x, z, n);
yzbar = linear_fit_average_product(y, z, n);
D = x2bar * y2bar - xybar * xybar;
for (int i = 0; i < n; i++) {
if (fabs(D) <= 1e-15 * (linear_fit_max_abs(x, n) + linear_fit_max_abs(y, n))) {
printf("error: x,y points are collinear at index:%d\n", i);
return NULL;
}
}
linear_fit_results.A = -(xzbar * y2bar - yzbar * xybar) / D;
linear_fit_results.B = -(yzbar * x2bar - xzbar * xybar) / D;
// linear_fit_results.D = -(zbar - linear_fit_results->A * xbar - linear_fit_results->B * ybar);
linear_fit_results.D = -(zbar + linear_fit_results.A * xbar + linear_fit_results.B * ybar);
return &linear_fit_results;
}
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double linear_fit_average(double *matrix, const int n) {
double sum = 0.0;
for (int i = 0; i < n; i++)
sum += matrix[i];
return sum / (double)n;
}
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double linear_fit_average_product(double *matrix1, double *matrix2, const int n) {
double sum = 0.0;
for (int i = 0; i < n; i++)
sum += matrix1[i] * matrix2[i];
return sum / (double)n;
}
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void linear_fit_subtract_mean(double *matrix, double bar, const int n) {
for (int i = 0; i < n; i++)
matrix[i] -= bar;
}
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double linear_fit_max_abs(double *matrix, const int n) {
double max_abs = 0.0;
for (int i = 0; i < n; i++)
NOLESS(max_abs, fabs(matrix[i]));
return max_abs;
}
#endif