--- /dev/null
+// leastsqs.c -- Implements a simple linear least squares best fit routine
+//
+// Written by Curtis Olson, started September 1997.
+//
+// Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
+//
+// 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 2 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, write to the Free Software
+// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+//
+// $Id$
+// (Log is kept at end of this file)
+//
+
+
+#include <stdio.h>
+
+#include "leastsqs.hxx"
+
+
+/*
+Least squares fit:
+
+y = b0 + b1x
+
+ n*sum(xi*yi) - (sum(xi)*sum(yi))
+b1 = --------------------------------
+ n*sum(xi^2) - (sum(xi))^2
+
+
+b0 = sum(yi)/n - b1*(sum(xi)/n)
+*/
+
+double sum_xi, sum_yi, sum_xi_2, sum_xi_yi;
+int sum_n;
+
+void least_squares(double *x, double *y, int n, double *m, double *b) {
+ int i;
+
+ sum_xi = sum_yi = sum_xi_2 = sum_xi_yi = 0.0;
+ sum_n = n;
+
+ for ( i = 0; i < n; i++ ) {
+ sum_xi += x[i];
+ sum_yi += y[i];
+ sum_xi_2 += x[i] * x[i];
+ sum_xi_yi += x[i] * y[i];
+ }
+
+ /* printf("sum(xi)=%.2f sum(yi)=%.2f sum(xi^2)=%.2f sum(xi*yi)=%.2f\n",
+ sum_xi, sum_yi, sum_xi_2, sum_xi_yi); */
+
+ *m = ( (double)sum_n * sum_xi_yi - sum_xi * sum_yi ) /
+ ( (double)sum_n * sum_xi_2 - sum_xi * sum_xi );
+ *b = (sum_yi / (double)sum_n) - (*m) * (sum_xi / (double)sum_n);
+
+ /* printf("slope = %.2f intercept = %.2f\n", *m, *b); */
+}
+
+
+/* incrimentally update existing values with a new data point */
+void least_squares_update(double x, double y, double *m, double *b) {
+ ++sum_n;
+
+ sum_xi += x;
+ sum_yi += y;
+ sum_xi_2 += x * x;
+ sum_xi_yi += x * y;
+
+ /* printf("sum(xi)=%.2f sum(yi)=%.2f sum(xi^2)=%.2f sum(xi*yi)=%.2f\n",
+ sum_xi, sum_yi, sum_xi_2, sum_xi_yi); */
+
+ *m = ( (double)sum_n * sum_xi_yi - sum_xi * sum_yi ) /
+ ( (double)sum_n * sum_xi_2 - sum_xi * sum_xi );
+ *b = (sum_yi / (double)sum_n) - (*m) * (sum_xi / (double)sum_n);
+
+ /* printf("slope = %.2f intercept = %.2f\n", *m, *b); */
+}
+
+
+/*
+ return the least squares error:
+
+ (y[i] - y_hat[i])^2
+ -------------------
+ n
+ */
+double least_squares_error(double *x, double *y, int n, double m, double b) {
+ int i;
+ double error, sum;
+
+ sum = 0.0;
+
+ for ( i = 0; i < n; i++ ) {
+ error = y[i] - (m * x[i] + b);
+ sum += error * error;
+ // printf("%.2f %.2f\n", error, sum);
+ }
+
+ return ( sum / (double)n );
+}
+
+
+/*
+ return the maximum least squares error:
+
+ (y[i] - y_hat[i])^2
+ */
+double least_squares_max_error(double *x, double *y, int n, double m, double b){
+ int i;
+ double error, max_error;
+
+ max_error = 0.0;
+
+ for ( i = 0; i < n; i++ ) {
+ error = y[i] - (m * x[i] + b);
+ error = error * error;
+ if ( error > max_error ) {
+ max_error = error;
+ }
+ }
+
+ return ( max_error );
+}
+
+
+// $Log$
+// Revision 1.1 1999/03/13 17:34:45 curt
+// Moved to math subdirectory.
+//
+// Revision 1.2 1998/04/21 17:03:41 curt
+// Prepairing for C++ integration.
+//
+// Revision 1.1 1998/04/08 22:57:24 curt
+// Adopted Gnu automake/autoconf system.
+//
+// Revision 1.1 1998/03/19 02:54:47 curt
+// Reorganized into a class lib called fgDEM.
+//
+// Revision 1.1 1997/10/13 17:02:35 curt
+// Initial revision.
+//
--- /dev/null
+// leastsqs.h -- Implements a simple linear least squares best fit routine
+//
+// Written by Curtis Olson, started September 1997.
+//
+// Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
+//
+// 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 2 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, write to the Free Software
+// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+//
+// $Id$
+// (Log is kept at end of this file)
+///
+
+
+#ifndef _LEASTSQS_H
+#define _LEASTSQS_H
+
+
+#ifndef __cplusplus
+# error This library requires C++
+#endif
+
+
+/*
+Least squares fit:
+
+y = b0 + b1x
+
+ n*sum(xi*yi) - (sum(xi)*sum(yi))
+b1 = --------------------------------
+ n*sum(xi^2) - (sum(xi))^2
+
+
+b0 = sum(yi)/n - b1*(sum(xi)/n)
+*/
+
+void least_squares(double *x, double *y, int n, double *m, double *b);
+
+/* incrimentally update existing values with a new data point */
+void least_squares_update(double x, double y, double *m, double *b);
+
+
+/*
+ return the least squares error:
+
+ (y[i] - y_hat[i])^2
+ -------------------
+ n
+*/
+double least_squares_error(double *x, double *y, int n, double m, double b);
+
+
+/*
+ return the maximum least squares error:
+
+ (y[i] - y_hat[i])^2
+*/
+double least_squares_max_error(double *x, double *y, int n, double m, double b);
+
+
+#endif // _LEASTSQS_H
+
+
+// $Log$
+// Revision 1.1 1999/03/13 17:34:45 curt
+// Moved to math subdirectory.
+//
+// Revision 1.2 1998/04/21 17:03:42 curt
+// Prepairing for C++ integration.
+//
+// Revision 1.1 1998/04/08 22:57:25 curt
+// Adopted Gnu automake/autoconf system.
+//
+// Revision 1.1 1998/03/19 02:54:48 curt
+// Reorganized into a class lib called fgDEM.
+//
+// Revision 1.1 1997/10/13 17:02:35 curt
+// Initial revision.
+//
projects / flightgear.git / commitdiff