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Marlin-Artillery-M600/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
*
* This algorythm 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 10KB 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 <math.h>
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#include "ubl.h"
#include "Marlin.h"
double linear_fit_average(double *, int);
double linear_fit_average_squared(double *, int);
double linear_fit_average_mixed_terms(double *, double *, int );
double linear_fit_average_product(double *matrix1, double *matrix2, int n);
void linear_fit_subtract_mean(double *matrix, double bar, int n);
double linear_fit_max_abs(double *, int);
struct linear_fit linear_fit_results;
struct linear_fit *lsf_linear_fit(double *x, double *y, double *z, int n) {
double xbar, ybar, zbar;
double x2bar, y2bar;
double xybar, xzbar, yzbar;
double D;
int i;
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(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;
}
double linear_fit_average(double *matrix, int n)
{
int i;
double sum=0.0;
for (i = 0; i < n; i++)
sum += matrix[i];
return sum / (double) n;
}
double linear_fit_average_product(double *matrix1, double *matrix2, int n) {
int i;
double sum = 0.0;
for (i = 0; i < n; i++)
sum += matrix1[i] * matrix2[i];
return sum / (double) n;
}
void linear_fit_subtract_mean(double *matrix, double bar, int n) {
int i;
for (i = 0; i < n; i++) {
matrix[i] -= bar;
}
return;
}
double linear_fit_max_abs(double *matrix, int n) {
int i;
double max_abs = 0.0;
for(i=0; i<n; i++)
if ( max_abs < fabs(matrix[i]))
max_abs = fabs(matrix[i]);
return max_abs;
}
#endif