drayl_int3D: Three Dimensional Rayleigh Density by Integration

In DRAYL: Computation of Rayleigh Densities of Arbitrary Dimension

Description

A three dimensional Rayleigh density by integration.

Usage

drayl_int3D(r,omega,sigma,cor,method)

Arguments

r	Evaluation point.
omega	Omega construct necessary for the Integration method.
sigma	Variances of the signals.
cor	Correlation structure.
method	Integration methods, either "Kronrod","Clenshaw","Simpson","Romberg","TOMS614" or "mixed".

Value

Evaluates the 3D Rayleigh density at the point r, for the values omega,sigma and cor as specified by Bealieu's method.

Examples

# Matrix
K3 = matrix(0,nrow = 6,ncol = 6)
sigma3 = sqrt(c(0.5,1,1.5))
diag(K3) = c(0.5,0.5,1,1,1.5,1.5)

# rho_12 rho_13 rho_23
rho3<-c(0.9,0.8,0.7)

K3[1,3]=K3[3,1]=K3[2,4]=K3[4,2]=sigma3[1]*sigma3[2]*rho3[1]
K3[1,5]=K3[5,1]=K3[2,6]=K3[6,2]=sigma3[1]*sigma3[3]*rho3[2]
K3[3,5]=K3[5,3]=K3[4,6]=K3[6,4]=sigma3[2]*sigma3[3]*rho3[3]

cor3 = rho3

mat<-diag(3)
mat[1,2]=mat[2,1]=cor3[1]
mat[1,3]=mat[3,1]=cor3[2]
mat[2,3]=mat[3,2]=cor3[3]

omega3=mat

drayl_int3D(c(1,1,1),omega = omega3,sigma = sigma3,cor = cor3, method = "Romberg")

DRAYL documentation built on Aug. 21, 2019, 9:05 a.m.