median.c File Reference

Calculation of median value. More...

#include "libtpcmodel.h"

Go to the source code of this file.

Functions
double	d_kth_smallest (double *data, int n, int k)
double	dmedian (double *data, int n)
double	dmean (double *data, int n, double *sd)
double	dmean_nan (double *data, int n, double *sd, int *vn)

Detailed Description

Calculation of median value.

Author

Vesa Oikonen

Definition in file median.c.

Function Documentation

d_kth_smallest()

double d_kth_smallest	(	double *	data,
		int	n,
		int	k )

Returns the kth smallest value in data[0..n-1]. Array is partially sorted. Algorithm is based on the book Wirth N. Algorithms + data structures = programs. Englewood Cliffs, Prentice-Hall, 1976.

Returns

Returns the kth smallest value in data[0..n-1].

Parameters

data	Pointer to data; array is partially sorted.
n	Length of data array.
k	kth smallest value will be returned.

Definition at line 15 of file median.c.

  {
  int i, j, l, m;
  double x, s;
 
  l=0; m=n-1;
  while(l<m) {
    x=data[k]; i=l; j=m;
    do {
      while(data[i]<x) i++;
      while(x<data[j]) j--;
      if(i<=j) {s=data[i]; data[i]=data[j]; data[j]=s; i++; j--;}
    } while(i<=j);
    if(j<k) l=i;
    if(k<i) m=j;
  }
  return(data[k]);
}

Referenced by dmedian().

dmean()

double dmean	(	double *	data,
		int	n,
		double *	sd )

Returns the mean in array data[0..n-1], and optionally calculates also the (sample) standard deviation of the mean.

See also

dmedian, mean, dmean_nan, fmean

Returns

Returns the mean in array data[0..n-1].

Parameters

data	Pointer to data; data is not changed in any way.
n	Length of data array.
sd	Pointer to variable where SD will be written; enter NULL if not needed.

Definition at line 73 of file median.c.

  {
  int i;
  double sumsqr=0.0, sqrsum=0.0, avg;
 
  if(n<1 || data==NULL) {if(sd!=NULL) *sd=0.0; return(0.0);}
 
  for(i=0; i<n; i++) {sumsqr+=data[i]*data[i]; sqrsum+=data[i];}
  avg=sqrsum/(double)n; if(sd==NULL) return(avg);
  if(n==1) {
    *sd=0.0;
  } else {
    sqrsum*=sqrsum;
    *sd=sqrt( (sumsqr - sqrsum/(double)n) / (double)(n-1) );
  }
  return(avg);
}

dmean_nan()

double dmean_nan	(	double *	data,
		int	n,
		double *	sd,
		int *	vn )

Returns the mean in array data[0..n-1], and optionally calculates also the standard deviation of the mean. Data may contain missing samples marked as NaNs.

See also

dmedian, mean, dmean

Returns

Returns the mean in array data[0..n-1].

Parameters

data	Pointer to data; data is not changed in any way.
n	Length of data array.
sd	Pointer to variable where SD will be written; enter NULL if not needed.
vn	Pointer to variable where number of valid (not NaN) samples will be written; enter NULL if not needed.

Definition at line 104 of file median.c.

  {
  int i, m;
  double sumsqr=0.0, sqrsum=0.0, avg;
 
  if(n<1 || data==NULL) {
    if(sd!=NULL) *sd=0.0; 
    if(vn!=NULL) *vn=0; 
    return(0.0);
  }
  for(i=m=0; i<n; i++) if(!isnan(data[i])) m++;
  if(vn!=NULL) *vn=m;
  if(m<1) {
    if(sd!=NULL) *sd=nan(""); 
    return(nan(""));
  }
  
 
  for(i=0; i<n; i++) if(!isnan(data[i])) {
    sumsqr+=data[i]*data[i]; sqrsum+=data[i];
  }
  avg=sqrsum/(double)m; if(sd==NULL) return(avg); // SD not requested
  if(m==1) {
    *sd=0.0;
  } else {
    sqrsum*=sqrsum;
    *sd=sqrt( (sumsqr - sqrsum/(double)m) / (double)(m-1) );
  }
  return(avg);
}

dmedian()

double dmedian	(	double *	data,
		int	n )

Returns the median in array data[0..n-1]. Array is partially sorted. Algorithm is based on the book Wirth N. Algorithms + data structures = programs. Englewood Cliffs, Prentice-Hall, 1976.

See also

dmean, mean, fmedian

Returns

Returns the median in array data[0..n-1].

Parameters

data	Pointer to data; array is partially sorted.
n	Length of data array.

Definition at line 48 of file median.c.

  {
  int k;
  double d1, d2;
 
  if(n<1) return(0.0);
  if(n%2) {
    k=(n-1)/2; return(d_kth_smallest(data, n, k));
  } else {
    k=n/2; d1=d_kth_smallest(data, n, k-1); d2=d_kth_smallest(data, n, k);
    return(0.5*(d1+d2));
  }
}

Referenced by dftRobustMinMaxTAC(), least_trimmed_square(), and mEstim().