linfit.c File Reference

Provides routines for performing simple linear fits. More...

#include "mdb.h"

Go to the source code of this file.

Functions
long	unweightedLinearFit (double *xData, double *yData, long nData, double *slope, double *intercept, double *variance)
	Performs an unweighted linear fit on the provided data.
long	unweightedLinearFitSelect (double *xData, double *yData, short *select, long nData, double *slope, double *intercept, double *variance)
	Performs an unweighted linear fit on the provided data with optional data point selection.

Detailed Description

Provides routines for performing simple linear fits.

This file contains functions to perform unweighted linear regression on datasets. It includes functions to compute the slope, intercept, and variance of the best-fit line.

Copyright

• (c) 2002 The University of Chicago, as Operator of Argonne National Laboratory.
• (c) 2002 The Regents of the University of California, as Operator of Los Alamos National Laboratory.

License

This file is distributed under the terms of the Software License Agreement found in the file LICENSE included with this distribution.

Author

M. Borland, C. Saunders, R. Soliday

Definition in file linfit.c.

Function Documentation

unweightedLinearFit()

long unweightedLinearFit	(	double *	xData,
		double *	yData,
		long	nData,
		double *	slope,
		double *	intercept,
		double *	variance )

Performs an unweighted linear fit on the provided data.

This function computes the slope and intercept of the best-fit line for the given x and y data by invoking the select-based linear fit function without selecting specific data points.

Parameters

xData	Pointer to the array of x-values.
yData	Pointer to the array of y-values.
nData	Number of data points in the arrays.
slope	Pointer to store the computed slope of the best-fit line.
intercept	Pointer to store the computed intercept of the best-fit line.
variance	Pointer to store the computed variance of the fit.

Returns

1 on successful fit,

0 if the fit could not be performed (e.g., insufficient data).

Definition at line 37 of file linfit.c.

                                                                             {
  return unweightedLinearFitSelect(xData, yData, NULL, nData, slope, intercept, variance);
}

unweightedLinearFitSelect()

long unweightedLinearFitSelect	(	double *	xData,
		double *	yData,
		short *	select,
		long	nData,
		double *	slope,
		double *	intercept,
		double *	variance )

Performs an unweighted linear fit on the provided data with optional data point selection.

This function computes the slope and intercept of the best-fit line for the given x and y data, optionally considering only selected data points as indicated by the select array. It also calculates the variance of the residuals from the fit.

Parameters

xData	Pointer to the array of x-values.
yData	Pointer to the array of y-values.
select	Pointer to an array of selection flags (non-zero to include the data point). Can be NULL to include all points.
nData	Number of data points in the arrays.
slope	Pointer to store the computed slope of the best-fit line.
intercept	Pointer to store the computed intercept of the best-fit line.
variance	Pointer to store the computed variance of the fit.

Returns

1 on successful fit,

0 if the fit could not be performed (e.g., insufficient data or no variation in x-data).

Definition at line 60 of file linfit.c.

                                                                                   {
  long i;
  double x, y, sum_x2, sum_x, sum_xy, sum_y, D, residual1, nUsed;
 
  if (nData < 2)
    return 0;
 
  /* compute linear fit and associated parameters */
  /* linear fit to y = a + bx:
     a = (S x^2 Sy - S x S xy)/D
     b = (N S xy  - Sx Sy)/D
     D = N S x^2 - (S x)^2
     */
  sum_x = sum_x2 = sum_y = sum_xy = 0;
  nUsed = 0;
  for (i = 0; i < nData; i++) {
    if (!select || select[i]) {
      nUsed++;
      sum_x += (x = xData[i]);
      sum_x2 += x * x;
      sum_y += (y = yData[i]);
      sum_xy += x * y;
    }
  }
  if (nUsed < 2)
    return 0;
 
  if ((D = nUsed * sum_x2 - sum_x * sum_x)) {
    *slope = (nUsed * sum_xy - sum_x * sum_y) / D;
    *intercept = (sum_x2 * sum_y - sum_x * sum_xy) / D;
    *variance = 0;
    for (i = 0; i < nData; i++) {
      if (!select || select[i]) {
        residual1 = (yData[i] - (xData[i] * (*slope) + (*intercept)));
        *variance += residual1 * residual1;
      }
    }
    if (nUsed > 2)
      *variance /= (nUsed - 2);
    else
      *variance = DBL_MAX;
    return 1;
  } else
    return 0;
}