122 lines
2.8 KiB
C
122 lines
2.8 KiB
C
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/* leastsqs.c -- Implements a simple linear least squares best fit routine
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*
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* Written by Curtis Olson, started September 1997.
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*
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* Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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*
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* $Id$
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* (Log is kept at end of this file)
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*/
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#include <stdio.h>
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#include "leastsqs.h"
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/*
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Least squares fit:
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y = b0 + b1x
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n*sum(xi*yi) - (sum(xi)*sum(yi))
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b1 = --------------------------------
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n*sum(xi^2) - (sum(xi))^2
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b0 = sum(yi)/n - b1*(sum(xi)/n)
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*/
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void least_squares(double *x, double *y, int n, double *m, double *b) {
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double sum_xi, sum_yi, sum_xi_2, sum_xi_yi;
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int i;
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sum_xi = sum_yi = sum_xi_2 = sum_xi_yi = 0.0;
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for ( i = 0; i < n; i++ ) {
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sum_xi += x[i];
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sum_yi += y[i];
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sum_xi_2 += x[i] * x[i];
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sum_xi_yi += x[i] * y[i];
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}
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/* printf("sum(xi)=%.2f sum(yi)=%.2f sum(xi^2)=%.2f sum(xi*yi)=%.2f\n",
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sum_xi, sum_yi, sum_xi_2, sum_xi_yi); */
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*m = ( (double)n * sum_xi_yi - sum_xi * sum_yi ) /
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( (double)n * sum_xi_2 - sum_xi * sum_xi );
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*b = (sum_yi / (double)n) - (*m) * (sum_xi / (double)n);
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/* printf("slope = %.2f intercept = %.2f\n", *m, *b); */
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}
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/*
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return the least squares error:
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(y[i] - y_hat[i])^2
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-------------------
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n
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*/
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double least_squares_error(double *x, double *y, int n, double m, double b) {
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int i;
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double error, sum;
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sum = 0.0;
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for ( i = 0; i < n; i++ ) {
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error = y[i] - (m * x[i] + b);
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sum += error * error;
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/* printf("%.2f %.2f\n", error, sum); */
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}
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return ( sum / (double)n );
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}
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/*
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return the maximum least squares error:
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(y[i] - y_hat[i])^2
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*/
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double least_squares_max_error(double *x, double *y, int n, double m, double b){
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int i;
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double error, max_error;
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max_error = 0.0;
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for ( i = 0; i < n; i++ ) {
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error = y[i] - (m * x[i] + b);
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error = error * error;
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if ( error > max_error ) {
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max_error = error;
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}
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}
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return ( max_error );
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}
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/* $Log$
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/* Revision 1.1 1998/03/19 02:54:47 curt
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/* Reorganized into a class lib called fgDEM.
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/*
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* Revision 1.1 1997/10/13 17:02:35 curt
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* Initial revision.
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*
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*/
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