UBL's Grid Based Leveling code

Pretty much...  The code is in place.  Still more work to do.    But it
has a lot of hooks and variables in other code, so commit and merge
before I pick up a million 'Conflicts'.

Marlin/least_squares_fit.cpp

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+/**
+ * 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 algorythm 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 10KB of program memory.
+ *
+ */
+
+#include "MarlinConfig.h"
+
+#if ENABLED(AUTO_BED_LEVELING_UBL)
+  #include <math.h>
+  #include "UBL.h"
+  #include "Marlin.h"
+
+double linear_fit_average(double *, int);
+double linear_fit_average_squared(double *, int);
+double linear_fit_average_mixed_terms(double *, double *, int );
+double linear_fit_average_product(double *matrix1, double *matrix2, int n);
+void   linear_fit_subtract_mean(double *matrix, double bar, int n);
+double linear_fit_max_abs(double *, int);
+
+struct linear_fit linear_fit_results;
+
+struct linear_fit *lsf_linear_fit(double *x, double *y, double *z, int n) {
+	double xbar, ybar, zbar;
+	double x2bar, y2bar;
+	double xybar, xzbar, yzbar;
+	double D;
+	int i;
+
+	linear_fit_results.A = 0.0;
+	linear_fit_results.B = 0.0;
+	linear_fit_results.D = 0.0;
+
+	xbar = linear_fit_average(x, n);
+	ybar = linear_fit_average(y, n);
+	zbar = linear_fit_average(z, n);
+
+	linear_fit_subtract_mean( x, xbar, n);
+	linear_fit_subtract_mean( y, ybar, n);
+	linear_fit_subtract_mean( z, zbar, n);
+
+	x2bar = linear_fit_average_product( x, x, n);
+	y2bar = linear_fit_average_product( y, y, n);
+	xybar =	linear_fit_average_product( x, y, n);
+	xzbar =	linear_fit_average_product( x, z, n);
+	yzbar =	linear_fit_average_product( y, z, n);
+
+	D = x2bar*y2bar - xybar*xybar;
+	for(i=0; i<n; i++) {
+		if (fabs(D) <= 1e-15*( linear_fit_max_abs(x, n) + linear_fit_max_abs(y, n))) {
+			printf( "error: x,y points are collinear at index:%d \n", i );
+			return NULL;
+		}
+	}
+
+	linear_fit_results.A = -(xzbar*y2bar - yzbar*xybar) / D;
+	linear_fit_results.B = -(yzbar*x2bar - xzbar*xybar) / D;
+//	linear_fit_results.D = -(zbar - linear_fit_results->A*xbar - linear_fit_results->B*ybar);
+	linear_fit_results.D = -(zbar + linear_fit_results.A*xbar + linear_fit_results.B*ybar);
+
+	return &linear_fit_results;
+}
+
+
+
+
+double linear_fit_average(double *matrix, int n)
+{
+	int i;
+	double sum=0.0;
+
+	for (i = 0; i < n; i++)
+		sum += matrix[i];
+	return sum / (double) n;
+}
+
+double linear_fit_average_product(double *matrix1, double *matrix2, int n) {
+	int i;
+	double sum = 0.0;
+
+	for (i = 0; i < n; i++)
+		sum += matrix1[i] * matrix2[i];
+	return sum / (double) n;
+}
+
+
+
+void linear_fit_subtract_mean(double *matrix, double bar, int n) {
+	int i;
+
+	for (i = 0; i < n; i++) {
+		matrix[i] -= bar;
+	}
+	return;
+}
+
+double linear_fit_max_abs(double *matrix, int n) {
+	int i;
+	double max_abs = 0.0;
+
+	for(i=0; i<n; i++)
+		if ( max_abs < fabs(matrix[i]))
+			max_abs = fabs(matrix[i]);
+	return max_abs;
+}
+#endif
+
+