lincorr.c File Reference

Functions for computing linear correlation coefficients and their significance. More...

#include "mdb.h"

Go to the source code of this file.

Functions
double	linearCorrelationCoefficient (double *data1, double *data2, short *accept1, short *accept2, long rows, long *count)
	Compute the linear correlation coefficient for two data sets.
double	linearCorrelationSignificance (double r, long rows)
	Compute the statistical significance of a linear correlation coefficient.
double	shiftedLinearCorrelationCoefficient (double *data1, double *data2, short *accept1, short *accept2, long rows, long *count, long shift)
	Compute the linear correlation coefficient between two data sets with a given shift.

Detailed Description

Functions for computing linear correlation coefficients and their significance.

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, R. Soliday

Definition in file lincorr.c.

Function Documentation

linearCorrelationCoefficient()

double linearCorrelationCoefficient	(	double *	data1,
		double *	data2,
		short *	accept1,
		short *	accept2,
		long	rows,
		long *	count )

Compute the linear correlation coefficient for two data sets.

Given two arrays of data and optional acceptance arrays, this function calculates the linear correlation coefficient (r) between the two data sets. Invalid values (NaN or Inf) and unaccepted entries are skipped.

Parameters

data1	First data array.
data2	Second data array.
accept1	Optional acceptance array for data1, may be NULL.
accept2	Optional acceptance array for data2, may be NULL.
rows	Number of elements in each data array.
count	Pointer to a long to store the number of valid paired samples used.

Returns

The linear correlation coefficient (between -1 and 1).

Definition at line 32 of file lincorr.c.

                                                            {
  double sum1[2] = {0, 0}, sum2[2] = {0, 0}, sum12 = 0;
  double d1, d2, r;
  long i;
  long count1;
 
  count1 = 0;
  for (i = 0; i < rows; i++) {
    if (isnan(data1[i]) || isnan(data2[i]) || isinf(data1[i]) || isinf(data2[i]))
      continue;
    if ((accept1 && !accept1[i]) || (accept2 && !accept2[i]))
      continue;
    count1 += 1;
    sum1[0] += data1[i];
    sum1[1] += data1[i] * data1[i];
    sum2[0] += data2[i];
    sum2[1] += data2[i] * data2[i];
    sum12 += data1[i] * data2[i];
  }
  if (count)
    *count = count1;
  d1 = count1 * sum1[1] - sum1[0] * sum1[0];
  d2 = count1 * sum2[1] - sum2[0] * sum2[0];
  if (d1 <= 0 || d2 <= 0)
    return 0.0;
  if ((d1 *= d2) <= 0)
    return 0.0;
  r = (count1 * sum12 - sum1[0] * sum2[0]) / sqrt(d1);
  if (r < -1)
    r = -1;
  else if (r > 1)
    r = 1;
  return r;
}

linearCorrelationSignificance()

double linearCorrelationSignificance	(	double	r,
		long	rows )

Compute the statistical significance of a linear correlation coefficient.

Given a correlation coefficient and the sample size, this function returns the significance level, i.e., the probability of observing such a correlation by chance.

Parameters

r	The linear correlation coefficient.
rows	The number of samples used to compute r.

Returns

The significance level as a probability (0 to 1).

Definition at line 79 of file lincorr.c.

                                                          {
  if (rows < 2)
    return 1.0;
  if ((r = fabs(r)) > 1)
    r = 1;
  return rSigLevel(r, rows - 2);
}

shiftedLinearCorrelationCoefficient()

double shiftedLinearCorrelationCoefficient	(	double *	data1,
		double *	data2,
		short *	accept1,
		short *	accept2,
		long	rows,
		long *	count,
		long	shift )

Compute the linear correlation coefficient between two data sets with a given shift.

Similar to linearCorrelationCoefficient(), but applies a time shift (lag) between the data sets. One array is shifted relative to the other, and only overlapping values are considered.

Parameters

data1	First data array.
data2	Second data array.
accept1	Optional acceptance array for data1, may be NULL.
accept2	Optional acceptance array for data2, may be NULL.
rows	Number of elements in each data array.
count	Pointer to a long to store the number of valid paired samples used after shifting.
shift	The integer shift to apply (positive or negative).

Returns

The linear correlation coefficient (between -1 and 1) for the shifted data.

Definition at line 102 of file lincorr.c.

                                                                               {
  double sum1[2] = {0, 0}, sum2[2] = {0, 0}, sum12 = 0;
  double d1, d2, r;
  long i, i1, i2, is;
 
  if (shift > 0) {
    i1 = shift;
    i2 = rows;
  } else {
    i1 = 0;
    i2 = rows + shift;
  }
  *count = 0;
  for (i = i1; i < i2; i++) {
    is = i - shift;
    if (is < 0 || is >= rows) {
      fprintf(stderr, "shift limits set incorrectly\n");
      exit(1);
    }
    if (isnan(data1[i]) || isnan(data2[is]) || isinf(data1[i]) || isinf(data2[is]))
      continue;
    if ((accept1 && !accept1[i]) || (accept2 && !accept2[is]))
      continue;
    *count += 1;
    sum1[0] += data1[i];
    sum1[1] += data1[i] * data1[i];
    sum2[0] += data2[is];
    sum2[1] += data2[is] * data2[is];
    sum12 += data1[i] * data2[is];
  }
  if (!*count)
    return 0.0;
  d1 = (*count) * sum1[1] - sum1[0] * sum1[0];
  d2 = (*count) * sum2[1] - sum2[0] * sum2[0];
  if (d1 <= 0 || d2 <= 0)
    return 0.0;
  if ((d1 *= d2) <= 0)
    return 0.0;
  r = ((*count) * sum12 - sum1[0] * sum2[0]) / sqrt(d1);
  if (r < -1)
    r = -1;
  else if (r > 1)
    r = 1;
  return r;
}