Hermite.cpp File Reference

#include "Polynomials/Hermite.hpp"
#include "Matrix/MatrixSquareGeneral.hpp"
#include "Basic/Utilities.hpp"
#include "Basic/Law.hpp"
#include "Basic/VectorHelper.hpp"
#include <math.h>

Functions
double	_convert2u (double yc, double krigest, double krigstd)
void	_calculateIn (VectorDouble &In, double yk, double sk, double u, const VectorDouble &hnYc)
void	_calculateJJ (MatrixSquareGeneral &JJ, VectorDouble &In, double yk, double sk, double u, const VectorDouble &hnYc, const VectorDouble &phi)
VectorDouble	hermitePolynomials (double y, double r, int nbpoly)
VectorDouble	hermitePolynomials (double y, double r, const VectorInt &ifacs)
VectorDouble	hermiteCondExp (VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
double	hermiteCondExpElement (double krigest, double krigstd, const VectorDouble &phi)
VectorDouble	hermiteCondStd (VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
double	hermiteCondStdElement (double krigest, double krigstd, const VectorDouble &phi)
VectorDouble	hermiteIndicator (double yc, VectorDouble krigest, VectorDouble krigstd)
double	hermiteIndicatorElement (double yc, double krigest, double krigstd)
VectorDouble	hermiteIndicatorStd (double yc, VectorDouble krigest, VectorDouble krigstd)
double	hermiteIndicatorStdElement (double yc, double krigest, double krigstd)
VectorDouble	hermiteMetal (double yc, VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
double	hermiteMetalElement (double yc, double krigest, double krigstd, const VectorDouble &phi)
VectorDouble	hermiteMetalStd (double yc, VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
double	hermiteMetalStdElement (double yc, double krigest, double krigstd, const VectorDouble &phi)
VectorDouble	hermiteCoefIndicator (double yc, int nbpoly)
VectorDouble	hermiteCoefMetal (double yc, const VectorDouble &phi)
MatrixSquareGeneral	hermiteIncompleteIntegral (double yc, int nbpoly)
VectorDouble	hermiteLognormal (double mean, double sigma, int nbpoly)
double	hermiteSeries (const VectorDouble &an, const VectorDouble &hn)
VectorDouble	hermiteCoefLower (double y, int nbpoly)
VectorDouble	hermiteIndicatorLower (double y, int nbpoly)

Function Documentation

_calculateIn()

void _calculateIn	(	VectorDouble &	In,
		double	yk,
		double	sk,
		double	u,
		const VectorDouble &	hnYc
	)

Calculate In(u,v) = int_u^v H_n(yk + sk * t) g(t) dt (with v = +Inf)

Parameters

In	Returned vector (in place)
yk	Kriged value
sk	Standard deviation of estimation error
u	Lower bound of integral (-inf if set to TEST)
hnYc	Vector of Hermite polynomials at cutoff

_calculateJJ()

void _calculateJJ	(	MatrixSquareGeneral &	JJ,
		VectorDouble &	In,
		double	yk,
		double	sk,
		double	u,
		const VectorDouble &	hnYc,
		const VectorDouble &	phi
	)

Calculate matrix JJ(n,p) = int_u_v H_n(y+st) H_p(y+st) g(t) dt (with v = +Inf)

Parameters

JJ	Output matrix
In	Preliminary calculations (see _calculateII)
yk	Kriged value
sk	Standard deviation of Krging error
u	Lower bound for integration
hnYc	Vector of Hermite polynomials at cutoff
phi

_convert2u()

double _convert2u	(	double	yc,
		double	krigest,
		double	krigstd
	)

hermiteCoefIndicator()

VectorDouble hermiteCoefIndicator	(	double	yc,
		int	nbpoly
	)

Parameters

yc	Cutoff Value
nbpoly	Number of Hermite polynomials

Returns

The vector of coefficients of the Indicator

hermiteCoefLower()

VectorDouble hermiteCoefLower	(	double	y,
		int	nbpoly
	)

Returns the vector of Hermite coefficients of the gaussian floored at 'y'

Parameters

y	Floor value
nbpoly	Number of Polynomial functions

Returns

Hermite Coefficients

hermiteCoefMetal()

VectorDouble hermiteCoefMetal	(	double	yc,
		const VectorDouble &	phi
	)

Parameters

yc	Cutoff Value
phi	Coefficients of Hermite polynomial

Returns

The vector of coefficients of the Metal Quantity

hermiteCondExp()

VectorDouble hermiteCondExp	(	VectorDouble	krigest,
		VectorDouble	krigstd,
		const VectorDouble &	phi
	)

Calculate the Conditional Expectation: E[Z | Z1=z1, Z2=z2, ..., Zn=zn] = int Phi(y_kk + s_k u) g(u) du

Parameters

krigest	Vector of Kriging estimates
krigstd	Vector of Kriging standard deviations
phi	Array of Hermite coefficients

Returns

Conditional Expectation

hermiteCondExpElement()

double hermiteCondExpElement	(	double	krigest,
		double	krigstd,
		const VectorDouble &	phi
	)

hermiteCondStd()

VectorDouble hermiteCondStd	(	VectorDouble	krigest,
		VectorDouble	krigstd,
		const VectorDouble &	phi
	)

Vector of conditional variances (same dimension as krigest and krigstd)

Parameters

krigest	Vector of Kriging estimate
krigstd	Vector of Kriging standard deviations
phi	Array of Hermite coefficients

Returns

hermiteCondStdElement()

double hermiteCondStdElement	(	double	krigest,
		double	krigstd,
		const VectorDouble &	phi
	)

hermiteIncompleteIntegral()

MatrixSquareGeneral hermiteIncompleteIntegral	(	double	yc,
		int	nbpoly
	)

Parameters

yc	Cutoff Value
nbpoly	Number of Hermite polynomials

Returns

The matrix of Incomplete Integral (Dimension: nbpoly * nbpoly)

hermiteIndicator()

VectorDouble hermiteIndicator	(	double	yc,
		VectorDouble	krigest,
		VectorDouble	krigstd
	)

Parameters

yc	Cutoff Value
krigest	Estimation
krigstd	Standard deviation of estimation error

Returns

The indicator above Cutoff

hermiteIndicatorElement()

double hermiteIndicatorElement	(	double	yc,
		double	krigest,
		double	krigstd
	)

hermiteIndicatorLower()

VectorDouble hermiteIndicatorLower	(	double	y,
		int	nbpoly
	)

hermiteIndicatorStd()

VectorDouble hermiteIndicatorStd	(	double	yc,
		VectorDouble	krigest,
		VectorDouble	krigstd
	)

hermiteIndicatorStdElement()

double hermiteIndicatorStdElement	(	double	yc,
		double	krigest,
		double	krigstd
	)

hermiteLognormal()

VectorDouble hermiteLognormal	(	double	mean,
		double	sigma,
		int	nbpoly
	)

Hermite coefficient for a lognormal transform mean * exp(sigma * Y + 1/2 * sigma^2)

Parameters

mean	Mean value
sigma	Standard deviation
nbpoly	Number of Hermite polynomials

Returns

The array of coefficients

hermiteMetal()

VectorDouble hermiteMetal	(	double	yc,
		VectorDouble	krigest,
		VectorDouble	krigstd,
		const VectorDouble &	phi
	)

Parameters

yc	Cutoff Value
krigest	Estimation
krigstd	Standard deviation of estimation error
phi	Hermite coefficients

Returns

The Metal

hermiteMetalElement()

double hermiteMetalElement	(	double	yc,
		double	krigest,
		double	krigstd,
		const VectorDouble &	phi
	)

hermiteMetalStd()

VectorDouble hermiteMetalStd	(	double	yc,
		VectorDouble	krigest,
		VectorDouble	krigstd,
		const VectorDouble &	phi
	)

hermiteMetalStdElement()

double hermiteMetalStdElement	(	double	yc,
		double	krigest,
		double	krigstd,
		const VectorDouble &	phi
	)

hermitePolynomials() [1/2]

VectorDouble hermitePolynomials	(	double	y,
		double	r,
		const VectorInt &	ifacs
	)

Returns the vector of Hermite Polynomials selected by ranks

Parameters

y	Target variable
r	Change of support coefficient
ifacs	Vector of ranks (staring from 0)

Returns

The vector of Hi(y) where 'i' is in 'ifacs'

hermitePolynomials() [2/2]

VectorDouble hermitePolynomials	(	double	y,
		double	r,
		int	nbpoly
	)

Calculation of the Hermite Polynomials for a given value

Parameters

y	Gaussian value for which the Hermite polynomials are calculated
r	Change of support coefficient
nbpoly	Number of Hermite polynomials

Returns

The vector of polynomials (Dimension: nbpoly)

hermiteSeries()

double hermiteSeries	(	const VectorDouble &	an,
		const VectorDouble &	hn
	)

Evaluate the Hermite expansion

Parameters

an	Series of coefficients of the Hermite polynomials
hn	Hermite polynomial values

Returns

The result of the expansion