numeric::statistics Namespace Reference

Functions
numeric::Real	kl_divergence (utility::vector1< numeric::Real > const &prior, utility::vector1< numeric::Real > const &posterior)
	Returns the Kullback-Leibler divergence (aka relative entropy) between two discrete probability distributions. More...
numeric::Real	corrcoef (utility::vector1< numeric::Real > const &vec1, utility::vector1< numeric::Real > const &vec2)
numeric::Real	corrcoef_with_provided_mean_and_std_dev (utility::vector1< numeric::Real > const &vec1, numeric::Real m1, numeric::Real sd1, utility::vector1< numeric::Real > const &vec2, numeric::Real m2, numeric::Real sd2)
numeric::Real	cov (utility::vector1< numeric::Real > const &vec1, utility::vector1< numeric::Real > const &vec2)
numeric::Real	cov_with_provided_mean (utility::vector1< numeric::Real > const &vec1, numeric::Real m1, utility::vector1< numeric::Real > const &vec2, numeric::Real m2)
cmplx	errfcx (cmplx z, double relerr)
double	errf (double x)
cmplx	errf (cmplx z, double relerr)
cmplx	errfi (cmplx z, double relerr)
double	errfi (double x)
double	errfc (double x)
cmplx	errfc (cmplx z, double relerr)
double	Dawson (double x)
cmplx	Dawson (cmplx z, double relerr)
static double	sinc (double x, double sinx)
static double	sinh_taylor (double x)
static double	sqr (double x)
cmplx	w (cmplx z, double relerr)
static double	erfcx_y100 (double y100)
double	errfcx (double x)
static double	w_im_y100 (double y100, double x)
double	w_im (double x)
template<class Iterator , typename T >
T	mean (Iterator first, Iterator last, T)
	mean value of an input vector More...
template<class Iterator , typename T >
T	std_dev_with_provided_mean (Iterator first, Iterator last, T mean)
template<class Iterator , typename T >
T	std_dev (Iterator first, Iterator last, T)

Variables
static const double	expa2n2 []

Function Documentation

numeric::Real numeric::statistics::corrcoef	(	utility::vector1< numeric::Real > const &	vec1,
		utility::vector1< numeric::Real > const &	vec2
	)

References corrcoef_with_provided_mean_and_std_dev(), mean(), and std_dev_with_provided_mean().

numeric::Real numeric::statistics::corrcoef_with_provided_mean_and_std_dev	(	utility::vector1< numeric::Real > const &	vec1,
		numeric::Real	m1,
		numeric::Real	sd1,
		utility::vector1< numeric::Real > const &	vec2,
		numeric::Real	m2,
		numeric::Real	sd2
	)

References cov().

Referenced by corrcoef().

numeric::Real numeric::statistics::cov	(	utility::vector1< numeric::Real > const &	vec1,
		utility::vector1< numeric::Real > const &	vec2
	)

References cov_with_provided_mean(), and mean().

Referenced by corrcoef_with_provided_mean_and_std_dev(), and cov_with_provided_mean().

numeric::Real numeric::statistics::cov_with_provided_mean	(	utility::vector1< numeric::Real > const &	vec1,
		numeric::Real	m1,
		utility::vector1< numeric::Real > const &	vec2,
		numeric::Real	m2
	)

References cov().

Referenced by cov().

double numeric::statistics::Dawson

(

double

x

)

References w_im().

std::complex< double > numeric::statistics::Dawson	(	cmplx	z,
		double	relerr
	)

References C, cexp, cimag, creal, errfcx(), utility::is_nan(), NaN, w(), w_im(), numeric::crick_equations::x(), and numeric::crick_equations::y().

static double numeric::statistics::erfcx_y100 ( double  y100 )

static

Referenced by errfcx().

double numeric::statistics::errf

(

double

x

)

References errfcx(), and numeric::crick_equations::x().

Referenced by errf(), and errfi().

std::complex< double > numeric::statistics::errf	(	cmplx	z,
		double	relerr
	)

References C, cimag, creal, errf(), Inf, utility::is_nan(), NaN, w(), w_im(), numeric::crick_equations::x(), and numeric::crick_equations::y().

double numeric::statistics::errfc

(

double

x

)

References errfcx().

std::complex< double > numeric::statistics::errfc	(	cmplx	z,
		double	relerr
	)

References C, cexp, cimag, creal, errfcx(), Inf, w(), w_im(), numeric::crick_equations::x(), and numeric::crick_equations::y().

std::complex< double > numeric::statistics::errfcx	(	cmplx	z,
		double	relerr
	)

References C, cimag, creal, and w().

Referenced by Dawson(), errf(), errfc(), and w().

double numeric::statistics::errfcx

(

double

x

)

References erfcx_y100(), and numeric::crick_equations::x().

std::complex< double > numeric::statistics::errfi	(	cmplx	z,
		double	relerr
	)

References C, cimag, creal, and errf().

double numeric::statistics::errfi

(

double

x

)

References Inf, and w_im().

numeric::Real numeric::statistics::kl_divergence	(	utility::vector1< numeric::Real > const &	prior,
		utility::vector1< numeric::Real > const &	posterior
	)

Returns the Kullback-Leibler divergence (aka relative entropy) between two discrete probability distributions.

References numeric::log().

template<class Iterator , typename T >

T numeric::statistics::mean ( Iterator  first, Iterator  last, T    )

inline

mean value of an input vector

References basic::T().

Referenced by corrcoef(), cov(), std_dev(), and std_dev_with_provided_mean().

static double numeric::statistics::sinc ( double  x, double  sinx  )

inlinestatic

References numeric::crick_equations::x().

Referenced by w().

static double numeric::statistics::sinh_taylor ( double  x )

inlinestatic

References numeric::crick_equations::x().

Referenced by w().

static double numeric::statistics::sqr ( double  x )

inlinestatic

References numeric::crick_equations::x().

Referenced by w().

template<class Iterator , typename T >

T numeric::statistics::std_dev ( Iterator  first, Iterator  last, T    )

inline

References mean(), std_dev_with_provided_mean(), and basic::T().

template<class Iterator , typename T >

T numeric::statistics::std_dev_with_provided_mean ( Iterator  first, Iterator  last, T  mean  )

inline

References mean(), and basic::T().

Referenced by corrcoef(), and std_dev().

std::complex< double > numeric::statistics::w	(	cmplx	z,
		double	relerr
	)

References C, cexp, cimag, utility::copysign(), creal, errfcx(), expa2n2, utility::is_inf(), utility::is_nan(), numeric::log(), NaN, pi, sinc(), sinh_taylor(), sqr(), w_im(), numeric::crick_equations::x(), and numeric::crick_equations::y().

Referenced by basic::sampling::orientations::QuatSet::Add(), Dawson(), errf(), errfc(), errfcx(), basic::sampling::orientations::Quaternion::euler(), numeric::deriv::helper(), basic::sampling::orientations::Quaternion::Normalize(), numeric::operator<<(), utility::io::mpi_stream::basic_mpi_streambuf< Elem, Tr, ElemA, ByteT, ByteAT >::overflow(), basic::sampling::orientations::Quaternion::Print(), basic::sampling::orientations::QuaternionGrid::QuaternionGrid(), numeric::linear_algebra::qzvec(), basic::sampling::orientations::Quaternion::rotation_matrix(), numeric::HomogeneousTransform< double >::show_stream(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::visit(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::visit_lax(), and utility::options::OptionCollection::wrapped().

double numeric::statistics::w_im

(

double

x

)

References w_im_y100(), and numeric::crick_equations::x().

Referenced by Dawson(), errf(), errfc(), errfi(), and w().

static double numeric::statistics::w_im_y100 ( double  y100, double  x  )

static

References NaN, and numeric::crick_equations::x().

Referenced by w_im().

Variable Documentation

const double numeric::statistics::expa2n2[]

static

Initial value:

= {
  7.64405281671221563e-01, 3.41424527166548425e-01, 8.91072646929412548e-02, 1.35887299055460086e-02,
  1.21085455253437481e-03, 6.30452613933449404e-05, 1.91805156577114683e-06, 3.40969447714832381e-08,
  3.54175089099469393e-10, 2.14965079583260682e-12, 7.62368911833724354e-15, 1.57982797110681093e-17,
  1.91294189103582677e-20, 1.35344656764205340e-23, 5.59535712428588720e-27, 1.35164257972401769e-30,
  1.90784582843501167e-34, 1.57351920291442930e-38, 7.58312432328032845e-43, 2.13536275438697082e-47,
  3.51352063787195769e-52, 3.37800830266396920e-57, 1.89769439468301000e-62, 6.22929926072668851e-68,
  1.19481172006938722e-73, 1.33908181133005953e-79, 8.76924303483223939e-86, 3.35555576166254986e-92,
  7.50264110688173024e-99, 9.80192200745410268e-106, 7.48265412822268959e-113, 3.33770122566809425e-120,
  8.69934598159861140e-128, 1.32486951484088852e-135, 1.17898144201315253e-143, 6.13039120236180012e-152,
  1.86258785950822098e-160, 3.30668408201432783e-169, 3.43017280887946235e-178, 2.07915397775808219e-187,
  7.36384545323984966e-197, 1.52394760394085741e-206, 1.84281935046532100e-216, 1.30209553802992923e-226,
  5.37588903521080531e-237, 1.29689584599763145e-247, 1.82813078022866562e-258, 1.50576355348684241e-269,
  7.24692320799294194e-281, 2.03797051314726829e-292, 3.34880215927873807e-304,
  0.0 
}

Referenced by w().