MarlinFirmware/Marlin/src/libs/least_squares_fit.cpp

/**
 * Marlin 3D Printer Firmware
 * Copyright (c) 2020 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 <https://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 "../inc/MarlinConfig.h"

#if ANY(AUTO_BED_LEVELING_UBL, AUTO_BED_LEVELING_LINEAR, Z_STEPPER_ALIGN_KNOWN_STEPPER_POSITIONS)

#include "least_squares_fit.h"

#include <math.h>

int finish_incremental_LSF(struct linear_fit_data *lsf) {

  const float N = lsf->N;

  if (N == 0.0)
    return 1;

  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 - lsf->xbar * lsf->ybar;
  lsf->yzbar = lsf->yzbar / N - lsf->ybar * lsf->zbar;
  lsf->xzbar = lsf->xzbar / N - lsf->xbar * lsf->zbar;
  const float DD = lsf->x2bar * lsf->y2bar - sq(lsf->xybar);

  if (ABS(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 || ENABLED(AUTO_BED_LEVELING_LINEAR)