Hermite.hpp File Reference

#include "gstlearn_export.hpp"
#include "Basic/VectorNumT.hpp"
#include "Matrix/MatrixSquareGeneral.hpp"

Functions
GSTLEARN_EXPORT VectorDouble	hermitePolynomials (double y, double r, int nbpoly)
GSTLEARN_EXPORT VectorDouble	hermitePolynomials (double y, double r, const VectorInt &ifacs)
GSTLEARN_EXPORT VectorDouble	hermiteCoefIndicator (double yc, int nbpoly)
GSTLEARN_EXPORT VectorDouble	hermiteCoefMetal (double yc, const VectorDouble &phi)
GSTLEARN_EXPORT VectorDouble	hermiteCoefLower (double y, int nbpoly)
GSTLEARN_EXPORT VectorDouble	hermiteIndicatorLower (double y, int nbpoly)
GSTLEARN_EXPORT MatrixSquareGeneral	hermiteIncompleteIntegral (double yc, int nbpoly)
GSTLEARN_EXPORT VectorDouble	hermiteLognormal (double mean, double sigma, int nbpoly)
GSTLEARN_EXPORT double	hermiteSeries (const VectorDouble &an, const VectorDouble &hn)
GSTLEARN_EXPORT VectorDouble	hermiteIndicator (double yc, VectorDouble krigest, VectorDouble krigstd)
GSTLEARN_EXPORT double	hermiteIndicatorElement (double yc, double krigest, double krigstd)
GSTLEARN_EXPORT VectorDouble	hermiteIndicatorStd (double yc, VectorDouble krigest, VectorDouble krigstd)
GSTLEARN_EXPORT double	hermiteIndicatorStdElement (double yc, double krigest, double krigstd)
GSTLEARN_EXPORT VectorDouble	hermiteMetal (double yc, VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
GSTLEARN_EXPORT double	hermiteMetalElement (double yc, double krigest, double krigstd, const VectorDouble &phi)
GSTLEARN_EXPORT VectorDouble	hermiteMetalStd (double yc, VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
GSTLEARN_EXPORT double	hermiteMetalStdElement (double yc, double krigest, double krigstd, const VectorDouble &phi)
GSTLEARN_EXPORT VectorDouble	hermiteCondExp (VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
GSTLEARN_EXPORT double	hermiteCondExpElement (double krigest, double krigstd, const VectorDouble &phi)
GSTLEARN_EXPORT VectorDouble	hermiteCondStd (VectorDouble krigest, VectorDouble krigstd, const VectorDouble &phi)
GSTLEARN_EXPORT double	hermiteCondStdElement (double krigest, double krigstd, const VectorDouble &phi)

Function Documentation

GSTLEARN_EXPORT VectorDouble hermiteCoefIndicator	(	double	yc,
		int	nbpoly
	)

Parameters

yc	Cutoff Value
nbpoly	Number of Hermite polynomials

Returns

The vector of coefficients of the Indicator

GSTLEARN_EXPORT 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

GSTLEARN_EXPORT 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

GSTLEARN_EXPORT 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

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

GSTLEARN_EXPORT 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

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

GSTLEARN_EXPORT MatrixSquareGeneral hermiteIncompleteIntegral	(	double	yc,
		int	nbpoly
	)

Parameters

yc	Cutoff Value
nbpoly	Number of Hermite polynomials

Returns

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

GSTLEARN_EXPORT 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

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

GSTLEARN_EXPORT VectorDouble hermiteIndicatorLower	(	double	y,
		int	nbpoly
	)

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

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

GSTLEARN_EXPORT 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

GSTLEARN_EXPORT 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

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

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

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

GSTLEARN_EXPORT 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)

GSTLEARN_EXPORT 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'

GSTLEARN_EXPORT 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