Detailed Description

Robust statistics.

Functions
template<typename T >
T	MAD (T *xd, int nd, T &M, bool save_flag=true)

template<typename T >
T	Median (T *xd, const int nd, bool save_flag=true)

template<typename T >
T	MedianAbsoluteDeviation (T *xd, int nd, T &M, bool save_flag=true)

template<typename T >
T	MEstimate (const T xd, int nd, const T &M, const T &MAD, T w=NULL)

void	Quantiles (double *xd, long nd)

template<typename T >
void	Quartiles (const T *xd, const int nd, T &Q1, T &Q3)

int	RobustPolyFit (double xd, const double td, int nd, int n, double c, double w=NULL)

void	StemLeafPlot (std::ostream &os, double *xd, long nd, const std::string &msg=std::string(""))

Function Documentation

◆ MAD()

template<typename T >

T gnsstk::Robust::MAD	(	T *	xd,
		int	nd,
		T &	M,
		bool	save_flag = `true`
	)

Compute the median absolute deviation of a double array of length nd; see MedianAbsoluteDeviation().

Exceptions

Exception

Definition at line 520 of file RobustStats.hpp.

◆ Median()

template<typename T >

T gnsstk::Robust::Median	(	T *	xd,
		const int	nd,
		bool	save_flag = `true`
	)

Compute median of an array of length nd; array xd is returned sorted, unless save_flag is true.

Parameters

xd	array of data.
nd	length of array xd.
save_flag	if true (default) array xd will NOT be changed, otherwise it will be sorted.

Returns: median of the data in array xd.

Exceptions

Exception

Definition at line 361 of file RobustStats.hpp.

◆ MedianAbsoluteDeviation()

template<typename T >

T gnsstk::Robust::MedianAbsoluteDeviation	(	T *	xd,
		int	nd,
		T &	M,
		bool	save_flag = `true`
	)

Compute the median absolute deviation of a double array of length nd, as well as the median (M = Median(xd,nd));

Note: this routine will trash the array xd unless save_flag is true (default).

Parameters

xd	array of data (input).
nd	length of array xd (input).
M	median of data in array xd (output).
save_flag	if true (default), array xd will NOT be trashed.

Returns: median absolute deviation of data in array xd.

Exceptions

Exception

Definition at line 467 of file RobustStats.hpp.

◆ MEstimate()

template<typename T >

T gnsstk::Robust::MEstimate	(	const T *	xd,
		int	nd,
		const T &	M,
		const T &	MAD,
		T *	w = `NULL`
	)

Compute the m-estimate. Iteratively determine the m-estimate, which is a measure of mean or median, but is less sensitive to outliers. M is the median (M=Median(xd,nd)), and MAD is the median absolute deviation (MAD=MedianAbsoluteDeviation(xd,nd,M)). Optionally, a pointer to an array, which will contain the weights on output, may be provided.

Parameters

xd	input array of data.
nd	input length of array xd.
M	input median of data in array xd.
MAD	input median absolute deviation of data in array xd.
w	output array of length nd to contain weights on output.

Returns: m-estimate of data in array xd.

Exceptions

Exception

Definition at line 541 of file RobustStats.hpp.

◆ Quantiles()

void gnsstk::Robust::Quantiles	(	double *	xd,
		long	nd
	)

Generate quantiles. Given an array xd of length nd, fill it with quantiles such that (xd,yd) gives a quantile plot. The distribution of yd is a normal distribution to the extent that this plot is a straight line, with y-intercept and slope identified with mean and standard deviation, respectively, of the distribution.

Parameters

xd	array of length nd containing quantiles on output.
nd	length of array xd.

Exceptions

Exception

Definition at line 350 of file RobustStats.cpp.

◆ Quartiles()

template<typename T >

void gnsstk::Robust::Quartiles	(	const T *	xd,
		const int	nd,
		T &	Q1,
		T &	Q3
	)

Compute the quartiles Q1 and Q3 of an array of length nd. Array is assumed sorted in ascending order. Quartile are values such that one fourth of the samples are larger (smaller) than Q3(Q1).

Parameters

xd	array of data.
nd	length of array xd.
Q1	(output) first quartile of data in array xd.
Q3	(output) third quartile of data in array xd.

Exceptions

Exception

Definition at line 425 of file RobustStats.hpp.

◆ RobustPolyFit()

int gnsstk::Robust::RobustPolyFit	(	double *	xd,
		const double *	td,
		int	nd,
		int	n,
		double *	c,
		double *	w = `NULL`
	)

Fit a polynomial of degree n to data xd, with independent variable td, using robust techniques. The post-fit residuals are returned in the data vector, and the computed weights in the result may be output as well. Specifically, the equation describing the fit is c0 + c[1]*t(j) + c[2]*t(j)*t(j) + ... c[n-1]*pow(t(j),n-1) = xd[j], where the zero-th coefficient and the independent variable are debiased by the first value; i.e. c0 = c[0]+xd[0] and t(j) = td[i]-td[0]. Specifically, to evaluate the polynomial at t, eval = f(t), do the following. xd0 = xd[0]; Robust::RobustPolyFit(xd,td,nd,n,c); eval = xd0+c[0]; tt = 1.0; for(j=1; j<nd; j++) { tt *= (t-td[0]); eval += c[j]*tt; }

Parameters

[in]	xd	array of data, of length nd; contains residuals on output.
[in]	td	array of independent variable, length nd (parallel to xd).
[in]	nd	length of arrays xd and td.
[in]	n	degree of polynomial and dimension of coefficient array.
[out]	c	array of coefficients (dimension n).
[out]	w	array of length nd to contain weights.

Returns: 0 for success, -1 for singular problem, -2 failure to converge.

Exceptions

Exception

Definition at line 368 of file RobustStats.cpp.

◆ StemLeafPlot()

void gnsstk::Robust::StemLeafPlot	(	std::ostream &	os,
		double *	xd,
		long	nd,
		const std::string &	msg = `std::string("")`
	)

Print 'stem and leaf' plot of the data in the double array xd of length nd, with an optional message, on the given output ostream. It is assumed that the input array xd is sorted in ascending order.

Parameters

os	ostream on which to write output.
xd	array of data.
nd	length of array xd.
msg	string containing optional message for output.

Exceptions

Exception

Definition at line 70 of file RobustStats.cpp.

Detailed Description

Functions

Function Documentation

◆ MAD()

◆ Median()

◆ MedianAbsoluteDeviation()

◆ MEstimate()

◆ Quantiles()

◆ Quartiles()

◆ RobustPolyFit()

◆ StemLeafPlot()