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/*---------------------------------------------------------------------------*\
FILE........: linreg.c
AUTHOR......: David Rowe
DATE CREATED: April 2015
Linear regression C module based on:
http://stackoverflow.com/questions/5083465/fast-efficient-least-squares-fit-algorithm-in-c
Use:
$ gcc linreg.c -o linreg -D__UNITTEST__ -Wall
$ ./linreg
Then compare yfit results with octave/tlinreg.m
\*---------------------------------------------------------------------------*/
/*
Copyright (C) 2015 David Rowe
All rights reserved.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License version 2.1, as
published by the Free Software Foundation. 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 Lesser General Public License
along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
#include "linreg.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "comp_prim.h"
void linreg(COMP *m, COMP *b, float x[], COMP y[], int n) {
float sumx = 0.0; /* sum of x */
float sumx2 = 0.0; /* sum of x^2 */
COMP sumxy = {0.0, 0.0}; /* sum of x * y */
COMP sumy = {0.0, 0.0}; /* sum of y */
COMP sumy2 = {0.0, 0.0}; /* sum of y**2 */
float denom;
COMP zero;
int i;
for (i = 0; i < n; i++) {
sumx += x[i];
sumx2 += x[i] * x[i];
sumxy = cadd(sumxy, fcmult(x[i], y[i]));
sumy = cadd(sumy, y[i]);
sumy2 = cadd(sumy2, cmult(y[i], y[i]));
}
denom = (n * sumx2 - sumx * sumx);
if (denom == 0) {
/* singular matrix. can't solve the problem */
zero.real = 0.0;
zero.imag = 0.0;
*m = zero;
*b = zero;
} else {
*m = fcmult(1.0 / denom, cadd(fcmult(n, sumxy), cneg(fcmult(sumx, sumy))));
*b = fcmult(1.0 / denom,
cadd(fcmult(sumx2, sumy), cneg(fcmult(sumx, sumxy))));
}
}
#ifdef __UNITTEST__
static float x[] = {1, 2, 7, 8};
static COMP y[] = {{-0.70702, 0.70708},
{-0.77314, 0.63442},
{-0.98083, 0.19511},
{-0.99508, 0.09799}};
int main(void) {
float x1;
COMP m, b, yfit;
linreg(&m, &b, x, y, sizeof(x) / sizeof(float));
for (x1 = 1; x1 <= 8; x1++) {
yfit = cadd(fcmult(x1, m), b);
printf("%f %f\n", yfit.real, yfit.imag);
}
return 0;
}
#endif
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