least_squares_fit.h File Reference

#include "../inc/MarlinConfig.h"
#include <math.h>

Go to the source code of this file.

Classes
struct	linear_fit_data

Functions
void	incremental_LSF_reset (struct linear_fit_data *lsf)
void	incremental_WLSF (struct linear_fit_data *lsf, const float &x, const float &y, const float &z, const float &w)
void	incremental_WLSF (struct linear_fit_data *lsf, const xy_pos_t &pos, const float &z, const float &w)
void	incremental_LSF (struct linear_fit_data *lsf, const float &x, const float &y, const float &z)
void	incremental_LSF (struct linear_fit_data *lsf, const xy_pos_t &pos, const float &z)
int	finish_incremental_LSF (struct linear_fit_data *)

Function Documentation

incremental_LSF_reset()

void incremental_LSF_reset

(

struct linear_fit_data *

lsf

)

                                                               {
  memset(lsf, 0, sizeof(linear_fit_data));
}

incremental_WLSF() [1/2]

void 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
  // (analogous to calling inc_LSF twice with same values to weight it by 2X)
  const float wx = w * x, wy = w * y, wz = w * z;
  lsf->xbar  += wx;
  lsf->ybar  += wy;
  lsf->zbar  += wz;
  lsf->x2bar += wx * x;
  lsf->y2bar += wy * y;
  lsf->z2bar += wz * z;
  lsf->xybar += wx * y;
  lsf->xzbar += wx * z;
  lsf->yzbar += wy * z;
  lsf->N     += w;
  lsf->max_absx = _MAX(ABS(wx), lsf->max_absx);
  lsf->max_absy = _MAX(ABS(wy), lsf->max_absy);
}

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incremental_WLSF() [2/2]

void incremental_WLSF	(	struct linear_fit_data *	lsf,
		const xy_pos_t &	pos,
		const float &	z,
		const float &	w
	)

                                                                                                               {
  incremental_WLSF(lsf, pos.x, pos.y, z, w);
}

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incremental_LSF() [1/2]

void 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;
}

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incremental_LSF() [2/2]

void incremental_LSF	(	struct linear_fit_data *	lsf,
		const xy_pos_t &	pos,
		const float &	z
	)

                                                                                              {
  incremental_LSF(lsf, pos.x, pos.y, z);
}

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finish_incremental_LSF()

int finish_incremental_LSF

(

struct linear_fit_data *

lsf

)

Marlin 3D Printer Firmware Copyright (c) 2019 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.

                                                        {
 
  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;
}