#include <FadeInterval.hh>

Inheritance diagram for core::scoring::hbonds::FadeInterval:

Public Member Functions
	~FadeInterval () override
	Automatically generated virtual destructor for class deriving directly from VirtualBase. More...

	FadeInterval ()
	Constructor. More...

	FadeInterval (Real const min0, Real const fmin, Real const fmax, Real const max0, bool const smooth=false)

	FadeInterval (std::string const &name, Real const min0, Real const fmin, Real const fmax, Real const max0, bool const smooth=false)

void	value_deriv (Real const x, core::Real &val, core::Real &deriv) const

core::Real	value (Real const x) const

std::string	get_name () const

Real	get_min0 () const

Real	get_fmin () const

Real	get_fmax () const

Real	get_max0 () const

bool	get_smooth () const

void	show (std::ostream &out) const

Private Attributes
std::string const	name_

Real const	min0_

Real const	fmin_

Real const	fmax_

Real const	max0_

core::Real const	dfade_min_

core::Real const	dfade_max_

bool const	smooth_

Friends
bool	operator== (FadeInterval const &a, FadeInterval const &b)

bool	operator!= (FadeInterval const &a, FadeInterval const &b)

std::ostream &	operator<< (std::ostream &out, FadeInterval const &fade_interval)

Detailed Description

Classic FadeInterval.

stores an "fading interval" [a b c d] with a <= b <= c <= d and computes the fraction of containment for x, which is defined to be 0 if x is outside of (a,d), 1 if x is inside of [b,c], and a linear ramp otherwise. ___/--—___ i.e. (x-a)/(b-a) for x in (a,b), and (d-x)/(d-c) for x in (c,d) This is used to ensure that hbond scoring as a sum Er + ExH + ExD goes to zero at the edges.

Notes about discontinuities: if x equals a, b, c, or d then deriv = 0 if x == a == b then value = 0 if x == c == d and a < c then value = 1 if x == c == d and a == c then value = 0 In particular if a == b == c == d then for all x, value == deriv == 0

Smooth FadeInteval

Rather than using a piecewise linear fading function, use a piecewise sigmoid function to have a continuous derivative.

Look for a canonical sigmoid function f(x) such that, f(0) = 1 f(1) = 0 // goes through the the knots f'(0) = 0 f'(1) = 0 // is horizontal at the knots a continuous differative f(x-.5)-.5 is odd // symmetric

I claim, f(x) = 2x^3 - 3x^2 + 1, satisfies these constraints: f(0) = 2(0)^3 - 3(x)^2 + 1 = 1 f(1) = 2(1)^3 - 3(1)^2 + 1 = 2 - 3 + 1 = 0

f'(x) = 6x^2 - 6x = 6x(x-1) f'(0) = 6(0)(0-1) = 0 f'(1) = 6(1)(1-1) = 0

a function g(x) is odd if g(-x) = -g(x) f((-x)-.5)-.5 = 2(-x-.5)^3 - 3(-x-.5)^2 + 1 - .5 = -2x^3 - 6x^2 - 4.5x - .5 -(f(x-.5)-.5) = -2(x-.5)^3 + 3(x-.5)^2 - 1 + .5 = -2x^3 - 6x^2 - 4.5x - .5

Given the knots –a-b—c-d– transform f(x) to fill a-b and c-d to connect the linear regions.

a-b region: let z(x) = (x-a)/(b-a) and z'(x) = 1/(b-a) use g(x) = 1-f(-z(x)) = -2z^3 + 3z^2 and g'(x) = -6z(z-1)*z'(x) c-d region: let z(x) = (x-c)/(d-c) and z'(x) = 1/(d-c) use g(x) = f(z) = 2z^3 - 3z^2 + 1 and g'(x) = 6z(z-1)*z'(x)

Constructor & Destructor Documentation

core::scoring::hbonds::FadeInterval::~FadeInterval ( )

overridedefault

Automatically generated virtual destructor for class deriving directly from VirtualBase.

Auto-generated virtual destructor

core::scoring::hbonds::FadeInterval::FadeInterval ( )

Constructor.

core::scoring::hbonds::FadeInterval::FadeInterval	(	Real const	min0,
		Real const	fmin,
		Real const	fmax,
		Real const	max0,
		bool const	smooth = `false`
	)

core::scoring::hbonds::FadeInterval::FadeInterval	(	std::string const &	name,
		Real const	min0,
		Real const	fmin,
		Real const	fmax,
		Real const	max0,
		bool const	smooth = `false`
	)