marlin/Marlin/least_squares_fit.cpp

/**
 * 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 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"

#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;
}

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;
}

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;
}

void linear_fit_subtract_mean(double *matrix, double bar, const int n) {
  for (int i = 0; i < n; i++)
    matrix[i] -= bar;
}

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