text: /**
   * 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/>.
   *
   */
  
  /**
   * Incremental 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.   And even better...  the data
   * fed into the algorithm does not need to all be present at the same time.
   * A point can be probed and its values fed into the algorithm and then discarded.
   *
   */
  
  #include "MarlinConfig.h"
  
  #if ENABLED(AUTO_BED_LEVELING_UBL) || ENABLED(AUTO_BED_LEVELING_LINEAR)
  
  #include "Marlin.h"
  #include "macros.h"
  #include <math.h>
  
  struct linear_fit_data {
    float xbar, ybar, zbar,
          x2bar, y2bar, z2bar,
          xybar, xzbar, yzbar,
          max_absx, max_absy,
          A, B, D, N;
  };
  
  void inline incremental_LSF_reset(struct linear_fit_data *lsf) {
    memset(lsf, 0, sizeof(linear_fit_data));
  }
  
  void inline incremental_WLSF(struct linear_fit_data *lsf, const float &x, const float &y, const float &z, const float &w) {
    // weight each accumulator by factor w, including the "number" of samples
    // (analagous to calling inc_LSF twice with same values to weight it by 2X)
    lsf->xbar  += w * x;
    lsf->ybar  += w * y;
    lsf->zbar  += w * z;
    lsf->x2bar += w * x * x;  // don't use sq(x) -- let compiler re-use w*x four times
    lsf->y2bar += w * y * y;
    lsf->z2bar += w * z * z;
    lsf->xybar += w * x * y;
    lsf->xzbar += w * x * z;
    lsf->yzbar += w * y * z;
    lsf->N     += w;
    lsf->max_absx = MAX(ABS(w * x), lsf->max_absx);
    lsf->max_absy = MAX(ABS(w * y), lsf->max_absy);
  }
  
  void inline incremental_LSF(struct linear_fit_data *lsf, const float &x, const float &y, const 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 += x * y;
    lsf->xzbar += x * z;
    lsf->yzbar += y * z;
    lsf->max_absx = MAX(ABS(x), lsf->max_absx);
    lsf->max_absy = MAX(ABS(y), lsf->max_absy);
    lsf->N += 1.0;
  }
  
  int finish_incremental_LSF(struct linear_fit_data *);
  
  #endif
  