scitbx::math Namespace Reference

Math utilities. More...

Classes
class	basic_statistics
	Collection of basic statistics such as min, max, mean, variance. More...
struct	median_statistics
	Median and dispersion around it. More...
class	median_functor
	functor returning a given quantile of a list of data More...
class	continued_fraction
	Continued fraction as rational number. More...
struct	erf_engine
	Port of http://www.netlib.org/specfun/erf (as of 2003 Dec 03). More...
struct	floating_point_epsilon
	Dynamic determination of the smallest floating point number such that 1 + floating_point_epsilon() differs from 1. More...
class	golay_24_12_generator
	Generator for the 4096 binary words of the Golay (24,12) code. More...
class	icosahedron
	Cartesian coordinates of points on a sphere. More...
struct	imaginary_unit_t
	The complex number i. More...
class	imaginary
	An imaginary number. More...
class	least_squares_plane
class	linear_correlation
class	linear_regression_core
class	linear_regression
class	mean_and_variance
class	sphere_3d
class	minimum_covering_sphere_3d
	Minimum covering sphere of a set of 3-dimensional points. More...
class	numeric_limits
	Extension of std::numeric_limits for LAPACK-style floating point info. More...
class	principal_axes_of_inertia
class	principal_axes_of_inertia_2d
class	unimodular_generator
struct	float_int_conversions
struct	remainder_and_quotient
	Quotient and remainder of x/y for floating point x and y. More...
Namespaces
namespace	accumulator
	Accumulators to compute partial series. Statistics are the main application.
namespace	bessel
	Family of Bessel functions.
namespace	erf_constants
	Port of http://www.netlib.org/specfun/erf (as of 2003 Dec 03).
namespace	gamma
	The Gamma function and some of his/her friends.
namespace	gaussian
	Tools for the handling of Gaussians: a Exp[-b x^2].
namespace	r3_rotation
	Algorithms for R3 (i.e. 3-dimensional space) rotation matrices.
Functions
template<typename FloatType>
FloatType	erf (FloatType const &x)
	Approximate values for erf(x).
template<typename FloatType>
af::shared< FloatType >	erf (af::const_ref< FloatType > const &x)
template<typename FloatType>
FloatType	erfc (FloatType const &x)
	Approximate values for erfc(x).
template<typename FloatType>
FloatType	erfcx (FloatType const &x)
	Approximate values for exp(x*x) * erfc(x).
template<typename FloatType>
FloatType	trim_cast (FloatType const &value)
	Returns value trimmed to the true precision of FloatType.
template<typename T>
std::complex< T >	operator* (imaginary_unit_t, std::complex< T > const &z)
template<typename T>
std::complex< T >	operator* (std::complex< T > const &z, imaginary_unit_t)
template<typename T>
imaginary< T >	operator* (imaginary_unit_t, T b)
template<typename T>
imaginary< T >	operator* (T b, imaginary_unit_t)
template<typename T>
imaginary< T >	operator/ (T a, imaginary< T > z)
	real / imaginary
template<typename T>
std::complex< T >	operator+ (T a, imaginary< T > b)
template<typename T>
std::complex< T >	operator+ (imaginary< T > b, T a)
template<typename T>
std::complex< T >	operator+ (std::complex< T > const &z, imaginary< T > y)
template<typename T>
std::complex< T >	operator+ (imaginary< T > y, std::complex< T > const &z)
template<typename T>
std::complex< T >	operator- (std::complex< T > const &z, imaginary< T > y)
template<typename T>
std::complex< T >	operator- (imaginary< T > y, std::complex< T > const &z)
template<typename T>
std::complex< T >	operator* (std::complex< T > const &z, imaginary< T > y)
template<typename T>
std::complex< T >	operator* (imaginary< T > y, std::complex< T > const &z)
template<typename T>
std::complex< T >	operator/ (std::complex< T > const &z, imaginary< T > y)
template<typename T>
std::complex< T >	operator/ (imaginary< T > y, std::complex< T > const &z)
template<typename FloatType>
void	inertia_tensor (af::const_ref< vec3< FloatType > > const &points, vec3< FloatType > const &pivot, sym_mat3< FloatType > &result)
template<typename FloatType>
void	inertia_tensor (af::const_ref< vec3< FloatType > > const &points, af::const_ref< FloatType > const &weights, vec3< FloatType > const &pivot, sym_mat3< FloatType > &result)
template<typename FloatType>
sym_mat3< FloatType >	inertia_tensor (af::const_ref< vec3< FloatType > > const &points, vec3< FloatType > const &pivot)
template<typename FloatType>
sym_mat3< FloatType >	inertia_tensor (af::const_ref< vec3< FloatType > > const &points, af::const_ref< FloatType > const &weights, vec3< FloatType > const &pivot)
template<typename FloatType>
FloatType	lambertw (FloatType const &x, unsigned max_iterations=100)
	Lambert's W function: w(x)*e^(w(x))=x.
template<typename FloatType>
FloatType	linear_interpolation (FloatType const &x, FloatType const &x1, FloatType const &x2, FloatType const &y1, FloatType const &y2)
template<typename IntType>
IntType	mod_positive (IntType ix, IntType const &iy)
template<typename IntType>
IntType	mod_short (IntType ix, IntType const &iy)
template<typename FloatType>
FloatType	fmod_short (FloatType const &x, FloatType const &y)
template<typename FloatType>
FloatType	signed_phase_error (FloatType const &phi1, FloatType const &phi2, bool deg=false)
template<typename FloatType>
af::shared< FloatType >	signed_phase_error (af::const_ref< FloatType > const &phi1, af::const_ref< FloatType > const &phi2, bool deg=false)
template<typename FloatType>
FloatType	phase_error (FloatType const &phi1, FloatType const &phi2, bool deg=false)
template<typename FloatType>
af::shared< FloatType >	phase_error (af::const_ref< FloatType > const &phi1, af::const_ref< FloatType > const &phi2, bool deg=false)
template<typename FloatType>
FloatType	nearest_phase (FloatType const &reference, FloatType const &other, bool deg=false)
template<typename FloatType>
af::shared< FloatType >	nearest_phase (af::const_ref< FloatType > const &reference, af::const_ref< FloatType > const &other, bool deg=false)
template<typename NumType1, typename NumType2>
NumType1 &	update_min (NumType1 &m, NumType2 const &x)
template<typename NumType1, typename NumType2>
NumType1 &	update_max (NumType1 &m, NumType2 const &x)
template<typename NumType>
NumType	norm (NumType x, NumType y)
	Overflow-proof sqrt(x*x + y*y).
template<typename FloatType>
FloatType	round (FloatType x, int n_digits=0)
int	iround (double x)
int	iceil (double x)
int	ifloor (double x)
int	nearest_integer (double x)
template<typename UnsignedIntType, typename SizeType>
bool	unsigned_product_leads_to_overflow (UnsignedIntType *a, SizeType n)
std::pair< int, double >	divmod (double x, double y)

---

Detailed Description

Math utilities.

---

Function Documentation

FloatType scitbx::math::erf

(

FloatType const &

x

)

[inline]

Approximate values for erf(x).

See also: scitbx::math::erf_engine

Referenced by term::integral_dx_at_x().

FloatType scitbx::math::erfc

(

FloatType const &

x

)

[inline]

Approximate values for erfc(x).

See also: scitbx::math::erf_engine

FloatType scitbx::math::erfcx

(

FloatType const &

x

)

[inline]

Approximate values for exp(x*x) * erfc(x).

See also: scitbx::math::erf_engine

FloatType scitbx::math::lambertw	(	FloatType const &	x,
		unsigned	max_iterations = 100
	)			[inline]

Lambert's W function: w(x)*e^(w(x))=x.

Based on the implementation by Gunter Kuhnle, gk@uni-leipzig.de

Algorithm originally developed by Keith Briggs, Department of Plant Sciences, e-mail:kmb28@cam.ac.uk

http://more.btexact.com/people/briggsk2/W-ology.html

See also: http://documents.wolfram.com/mathematica/functions/ProductLog

References floating_point_epsilon::get().

FloatType scitbx::math::trim_cast

(

FloatType const &

value

)

[inline]

Returns value trimmed to the true precision of FloatType.

Some optimizers maintain a higher precision for some calculations. To avoid this and trim value to the true precision of FloatType, value is converted to a base-256 string and then back to FloatType.

Referenced by floating_point_epsilon::get().