drayl_int3D {DRAYL}

Three Dimensional Rayleigh Density by Integration

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")