llsqwt.c File Reference

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "include/llsqwt.h"


Functions
int	_medianline_cmp (const void e1, const void e2)
int	llsqwt (double x, double y, int n, double wx, double wy, double tol, double w, double ic, double slope, double nwss, double sic, double sslope, double cx, double cy)
int	best_llsqwt (double x, double y, double wx, double wy, int nr, int min_nr, int mode, double slope, double ic, double nwss, double sslope, double sic, double cx, double cy, int bnr)
int	llsqperp (double x, double y, int nr, double slope, double ic, double *ssd)
int	llsqperp3 (double x, double y, int nr, double slope, double ic, double *ssd)
int	quadratic (double a, double b, double c, double m1, double m2)
int	medianline (double x, double y, int nr, double slope, double ic)

Function Documentation

int _medianline_cmp ( const void * e1,

const void * e2

)

int best_llsqwt ( double * x,

double * y,

double * wx,

double * wy,

int nr,

int min_nr,

int mode,

double * slope,

double * ic,

double * nwss,

double * sslope,

double * sic,

double * cx,

double * cy,

int * bnr

)

Finds the best least-squares line to (x,y)-data, leaving points out either from the beginning (mode=0) or from the end (mode=1).
Returns:
Returns 0, if ok.

Parameters:

x Plot x axis values

y Plot y axis values

wx Weighting factors for x

wy Weighting factors for y

nr Nr of plot data points

min_nr Min nr of points to use in the fit; must be >=4

mode Leave out points from beginning (0) or from end (1)

slope Slope is returned in here

ic Y axis intercept is returned in here

nwss sqrt(WSS)/wsum is returned here

sslope Expected sd of slope at calculated points

sic Expected sd of intercept at calculated points

cx Calculated x data points

cy Calculated y data points

bnr Number of points in the best fit (incl data with w=0)

int llsqperp ( double * x,

double * y,

int nr,

double * slope,

double * ic,

double * ssd

)

Simple non-iterative perpendicular line fitting. This function is fully based on the article [1].
References: 1. Varga J & Szabo Z. Modified regression model for the Logan plot. J Cereb Blood Flow Metab 2002; 22:240-244.

Returns:
If successful, function returns value 0.

Parameters:

x Coordinates of data points (dimension nr)

y Coordinates of data points (dimension nr)

nr Number of data points

slope Estimated slope

ic Estimated intercept

ssd Sum of squared distances / nr

int llsqperp3 ( double * x,

double * y,

int nr,

double * slope,

double * ic,

double * ssd

)

See llsqperp(). This function accepts data that contains NA's.

int llsqwt ( double * x,

double * y,

int n,

double * wx,

double * wy,

double tol,

double * w,

double * ic,

double * slope,

double * nwss,

double * sic,

double * sslope,

double * cx,

double * cy

)

Iterative method for linear least-squares fit with errors in both coordinates. This function is fully based on article [3].
For n data-point pairs (x[i], y[i]) each point has its own weighting factors in (wx[i], wy[i]). This routine finds the values of the parameters m (slope) and c (intercept, ic) that yield the "best-fit" of the model equation Y = mX + c to the data, where X and Y are the predicted or calculated values of the data points.
Weighting factors wx and wy must be assigned as the inverses of the variances or squares of the measurement uncertainties (SDs), i.e. w[i]=1/(sd[i])^2
If true weights are unknown but yet the relative weights are correct, the slope, intercept and residuals (WSS) will be correct. The applied term S/(N-2) makes also the estimate of sigma (sd) of slope less dependent on the scaling of weights. The sigmas are not exact, since only the lowest-order terms in Taylor-series expansion are incorporated; anyhow sigmas are more accurate than the ones based on York algorithm.
One or more data points can be excluded from the fit by setting either x or y weight to 0.
References: 1. York, D. Linear-squares fitting of a straight line. Can. J. Phys. 1966;44:1079-1086. 2. Lybanon, M. A better least squares method when both variables have uncertainties. Am. J. Phys. 1984;52:22-26 and 276-278. 3. Reed BC. Linear least-squares fits with errors in both coordinates. II: Comments on parameter variances. Am. J. Phys. 1992;60:59-62.

Returns:
If successful, function returns value 0.

Parameters:

x coordinates of data points (of dimension n)

y coordinates of data points (of dimension n)

n number of data points

wx weighting factors in x

wy weighting factors in y

tol allowed tolerance in slope estimation

w work vector (of dimension n); effective weights w[i] are returned in it.

ic Estimated intercept

slope Estimated slope

nwss sqrt(WSS)/wsum of the residuals

sic expected sd of intercept at calculated points; If NULL, then not calculated and variable is left unchanged

sslope Expected sd of slope at calculated points; If NULL, then not calculated and variable is left unchanged

cx Estimated data points (X,y); If NULL, then not calculated and variable is left unchanged

cy Estimated data points (x,Y); If NULL, then not calculated and variable is left unchanged

int medianline ( double * x,

double * y,

int nr,

double * slope,

double * ic

)

Median-based distribution-free estimation of slope and intercept. This method has no need for weighting and is insensitive to outliers. Note that this is not LMS !
Reference (containing reference to the original idea): 1. Siegel AF. Robust regression using repeated medians. Biometrika 1982; 69(1):242-244.

Returns:
If successful, function returns value 0.

Parameters:

x Coordinates of data points (dimension nr)

y Coordinates of data points (dimension nr)

nr Number of data points

slope Estimated slope

ic Estimated intercept

int quadratic ( double a,

double b,

double c,

double * m1,

double * m2

)

Finds the real roots of a*x^2 + b*x + c = 0
Returns:
Returns the nr of roots, and the roots in m1 and m2.

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llsqwt.c File Reference

Functions

Function Documentation