Classes
class	itpp::Stat
	A class for sampling a signal and calculating statistics. More...

Functions
double	itpp::mean (const vec &v)
	The mean value.

std::complex< double >	itpp::mean (const cvec &v)
	The mean value.

double	itpp::mean (const svec &v)
	The mean value.

double	itpp::mean (const ivec &v)
	The mean value.

double	itpp::mean (const mat &m)
	The mean value.

std::complex< double >	itpp::mean (const cmat &m)
	The mean value.

double	itpp::mean (const smat &m)
	The mean value.

double	itpp::mean (const imat &m)
	The mean value.

template<class T >
double	itpp::geometric_mean (const Vec< T > &v)
	The geometric mean of a vector.

template<class T >
double	itpp::geometric_mean (const Mat< T > &m)
	The geometric mean of a matrix.

template<class T >
double	itpp::median (const Vec< T > &v)
	The median.

double	itpp::norm (const cvec &v)
	Calculate the 2-norm: norm(v)=sqrt(sum(abs(v).^2))

template<class T >
double	itpp::norm (const Vec< T > &v)
	Calculate the 2-norm: norm(v)=sqrt(sum(abs(v).^2))

double	itpp::norm (const cvec &v, int p)
	Calculate the p-norm: norm(v,p)=sum(abs(v).^2)^(1/p)

template<class T >
double	itpp::norm (const Vec< T > &v, int p)
	Calculate the p-norm: norm(v,p)=sum(abs(v).^2)^(1/p)

double	itpp::norm (const cvec &v, const std::string &s)
	Calculate the Frobenius norm for s = "fro" (equal to 2-norm)

template<class T >
double	itpp::norm (const Vec< T > &v, const std::string &s)
	Calculate the Frobenius norm for s = "fro" (equal to 2-norm)

double	itpp::norm (const mat &m, int p)

double	itpp::norm (const cmat &m, int p)

double	itpp::norm (const mat &m, const std::string &s)
	Calculate the Frobenius norm of a matrix for s = "fro".

double	itpp::norm (const cmat &m, const std::string &s)
	Calculate the Frobenius norm of a matrix for s = "fro".

double	itpp::variance (const cvec &v)
	The variance of the elements in the vector. Normalized with N-1 to be unbiased.

template<class T >
double	itpp::variance (const Vec< T > &v)
	The variance of the elements in the vector. Normalized with N-1 to be unbiased.

template<class T >
double	itpp::energy (const Vec< T > &v)
	Calculate the energy: squared 2-norm. energy(v)=sum(abs(v).^2)

bool	itpp::within_tolerance (double x, double xref, double tol=1e-14)
	Return true if the input value `x` is within the tolerance `tol` of the reference value `xref`.

bool	itpp::within_tolerance (std::complex< double > x, std::complex< double > xref, double tol=1e-14)
	Return true if the input value `x` is within the tolerance `tol` of the reference value `xref`.

bool	itpp::within_tolerance (const vec &x, const vec &xref, double tol=1e-14)
	Return true if the input vector `x` is elementwise within the tolerance `tol` of the reference vector `xref`.

bool	itpp::within_tolerance (const cvec &x, const cvec &xref, double tol=1e-14)
	Return true if the input vector `x` is elementwise within the tolerance `tol` of the reference vector `xref`.

bool	itpp::within_tolerance (const mat &X, const mat &Xref, double tol=1e-14)
	Return true if the input matrix `X` is elementwise within the tolerance `tol` of the reference matrix `Xref`.

bool	itpp::within_tolerance (const cmat &X, const cmat &Xref, double tol=1e-14)
	Return true if the input matrix `X` is elementwise within the tolerance `tol` of the reference matrix `Xref`.

double	itpp::moment (const vec &x, const int r)
	Calculate the central moment of vector x.

double	itpp::skewness (const vec &x)
	Calculate the skewness excess of the input vector x.

double	itpp::kurtosisexcess (const vec &x)
	Calculate the kurtosis excess of the input vector x.

double	itpp::kurtosis (const vec &x)
	Calculate the kurtosis of the input vector x.

Detailed Description

Function Documentation

ITPP_EXPORT double itpp::norm	(	const mat &	m,
		int	p = `2`
	)

Calculate the p-norm of a real matrix

p = 1: max(svd(m)) p = 2: max(sum(abs(X)))

Default if no p is given is the 2-norm

Definition at line 105 of file misc_stat.cpp.

References itpp::abs(), it_assert, itpp::max(), itpp::sum(), and itpp::svd().

ITPP_EXPORT double itpp::norm	(	const cmat &	m,
		int	p = `2`
	)

Calculate the p-norm of a complex matrix

p = 1: max(svd(m)) p = 2: max(sum(abs(X)))

Default if no p is given is the 2-norm

Definition at line 121 of file misc_stat.cpp.

References itpp::abs(), it_assert, itpp::max(), itpp::sum(), and itpp::svd().

ITPP_EXPORT double itpp::moment	(	const vec &	x,
		const int	r
	)

Calculate the central moment of vector x.

The $r$ th sample central moment of the samples in the vector $\mathbf{x}$ is defined as

$m_r = \mathrm{E}[x-\mu]^r = \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \mu)^r$

where $\mu$ is the sample mean.

Definition at line 174 of file misc_stat.cpp.

References itpp::mean(), and itpp::pow().

Referenced by itpp::kurtosisexcess(), and itpp::skewness().

ITPP_EXPORT double itpp::skewness ( const vec & x )

Calculate the skewness excess of the input vector x.

The skewness is a measure of the degree of asymmetry of distribution. Negative skewness means that the distribution is spread more to the left of the mean than to the right, and vice versa if the skewness is positive.

The skewness of the samples in the vector $\mathbf{x}$ is

$\gamma_1 = \frac{\mathrm{E}[x-\mu]^3}{\sigma^3}$