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@ -21,13 +21,13 @@
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*/
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/**
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* Least Squares Best Fit By Roxy and Ed Williams
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* Least Squares Best Fit by Roxy and Ed Williams
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*
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* This algorithm is high speed and has a very small code footprint.
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* Its results are identical to both the Iterative Least-Squares published
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* earlier by Roxy and the QR_SOLVE solution. If used in place of QR_SOLVE
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* it saves roughly 10K of program memory. It also does not require all of
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* coordinates to be present during the calculations. Each point can be
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* it saves roughly 10K of program memory. It also does not require all of
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* coordinates to be present during the calculations. Each point can be
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* probed and then discarded.
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*
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*/
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@ -41,56 +41,44 @@
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#include "least_squares_fit.h"
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void incremental_LSF_reset(struct linear_fit_data *lsf) {
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lsf->n = 0;
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lsf->A = 0.0; // probably a memset() can be done to zero
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lsf->B = 0.0; // this whole structure
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lsf->D = 0.0;
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lsf->xbar = lsf->ybar = lsf->zbar = 0.0;
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lsf->x2bar = lsf->y2bar = lsf->z2bar = 0.0;
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lsf->xybar = lsf->xzbar = lsf->yzbar = 0.0;
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lsf->max_absx = lsf->max_absy = 0.0;
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}
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void incremental_LSF_reset(struct linear_fit_data *lsf) { ZERO(lsf); }
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void incremental_LSF(struct linear_fit_data *lsf, float x, float y, float z) {
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lsf->xbar += x;
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lsf->ybar += y;
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lsf->zbar += z;
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lsf->x2bar += x*x;
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lsf->y2bar += y*y;
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lsf->z2bar += z*z;
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lsf->xybar += x*y;
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lsf->xzbar += x*z;
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lsf->yzbar += y*z;
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lsf->max_absx = (fabs(x) > lsf->max_absx) ? fabs(x) : lsf->max_absx;
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lsf->max_absy = (fabs(y) > lsf->max_absy) ? fabs(y) : lsf->max_absy;
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lsf->n++;
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return;
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}
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lsf->xbar += x;
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lsf->ybar += y;
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lsf->zbar += z;
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lsf->x2bar += sq(x);
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lsf->y2bar += sq(y);
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lsf->z2bar += sq(z);
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lsf->xybar += sq(x);
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lsf->xzbar += sq(x);
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lsf->yzbar += sq(y);
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lsf->max_absx = max(fabs(x), lsf->max_absx);
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lsf->max_absy = max(fabs(y), lsf->max_absy);
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lsf->n++;
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}
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int finish_incremental_LSF(struct linear_fit_data *lsf) {
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float DD, N;
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const float N = (float)lsf->n;
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N = (float) lsf->n;
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lsf->xbar /= N;
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lsf->ybar /= N;
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lsf->zbar /= N;
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lsf->x2bar = lsf->x2bar/N - lsf->xbar*lsf->xbar;
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lsf->y2bar = lsf->y2bar/N - lsf->ybar*lsf->ybar;
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lsf->z2bar = lsf->z2bar/N - lsf->zbar*lsf->zbar;
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lsf->xybar = lsf->xybar/N - lsf->xbar*lsf->ybar;
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lsf->yzbar = lsf->yzbar/N - lsf->ybar*lsf->zbar;
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lsf->xzbar = lsf->xzbar/N - lsf->xbar*lsf->zbar;
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lsf->xbar /= N;
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lsf->ybar /= N;
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lsf->zbar /= N;
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lsf->x2bar = lsf->x2bar / N - lsf->xbar * lsf->xbar;
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lsf->y2bar = lsf->y2bar / N - lsf->ybar * lsf->ybar;
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lsf->z2bar = lsf->z2bar / N - lsf->zbar * lsf->zbar;
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lsf->xybar = lsf->xybar / N - lsf->xbar * lsf->ybar;
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lsf->yzbar = lsf->yzbar / N - lsf->ybar * lsf->zbar;
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lsf->xzbar = lsf->xzbar / N - lsf->xbar * lsf->zbar;
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DD = lsf->x2bar*lsf->y2bar - lsf->xybar*lsf->xybar;
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if (fabs(DD) <= 1e-10*(lsf->max_absx+lsf->max_absy))
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return -1;
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const float DD = lsf->x2bar * lsf->y2bar - sq(lsf->xybar);
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if (fabs(DD) <= 1e-10 * (lsf->max_absx + lsf->max_absy))
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return -1;
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lsf->A = (lsf->yzbar*lsf->xybar - lsf->xzbar*lsf->y2bar) / DD;
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lsf->B = (lsf->xzbar*lsf->xybar - lsf->yzbar*lsf->x2bar) / DD;
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lsf->D = -(lsf->zbar + lsf->A*lsf->xbar + lsf->B*lsf->ybar);
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return 0;
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lsf->A = (lsf->yzbar * lsf->xybar - lsf->xzbar * lsf->y2bar) / DD;
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lsf->B = (lsf->xzbar * lsf->xybar - lsf->yzbar * lsf->x2bar) / DD;
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lsf->D = -(lsf->zbar + lsf->A * lsf->xbar + lsf->B * lsf->ybar);
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return 0;
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}
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#endif
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#endif // AUTO_BED_LEVELING_UBL
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