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. It also does not require all of
 * coordinates to be present during the calculations. Each point can be
 * probed and then discarded.
 *
 */

#include "MarlinConfig.h"

#if ENABLED(AUTO_BED_LEVELING_UBL)  // Currently only used by UBL, but is applicable to Grid Based (Linear) Bed Leveling

#include "macros.h"
#include <math.h>

#include "least_squares_fit.h"

void incremental_LSF_reset(struct linear_fit_data *lsf) {
  memset(lsf, 0, sizeof(linear_fit_data));
}

void incremental_LSF(struct linear_fit_data *lsf, float x, float y, float z) {
  lsf->xbar += x;
  lsf->ybar += y;
  lsf->zbar += z;
  lsf->x2bar += sq(x);
  lsf->y2bar += sq(y);
  lsf->z2bar += sq(z);
  lsf->xybar += sq(x);
  lsf->xzbar += sq(x);
  lsf->yzbar += sq(y);
  lsf->max_absx = max(fabs(x), lsf->max_absx);
  lsf->max_absy = max(fabs(y), lsf->max_absy);
  lsf->n++;
}

int finish_incremental_LSF(struct linear_fit_data *lsf) {
  const float N = (float)lsf->n;

  lsf->xbar /= N;
  lsf->ybar /= N;
  lsf->zbar /= N;
  lsf->x2bar = lsf->x2bar / N - sq(lsf->xbar);
  lsf->y2bar = lsf->y2bar / N - sq(lsf->ybar);
  lsf->z2bar = lsf->z2bar / N - sq(lsf->zbar);
  lsf->xybar = lsf->xybar / N - sq(lsf->xbar);
  lsf->yzbar = lsf->yzbar / N - sq(lsf->ybar);
  lsf->xzbar = lsf->xzbar / N - sq(lsf->xbar);

  const float DD = lsf->x2bar * lsf->y2bar - sq(lsf->xybar);
  if (fabs(DD) <= 1e-10 * (lsf->max_absx + lsf->max_absy))
    return -1;

  lsf->A = (lsf->yzbar * lsf->xybar - lsf->xzbar * lsf->y2bar) / DD;
  lsf->B = (lsf->xzbar * lsf->xybar - lsf->yzbar * lsf->x2bar) / DD;
  lsf->D = -(lsf->zbar + lsf->A * lsf->xbar + lsf->B * lsf->ybar);
  return 0;
}

#endif // AUTO_BED_LEVELING_UBL