SAMM (version 1.1.1)

sigcovfuncs_cppforR: Covariance and Sigma Functions

Description

The "kernel" functions end with "cov_cppforR" and sigma functions end with "Sig_cppforR". Check table below and the examples for details and usage. Documentation for some of these functions is missing. Let \(K\) be a given covariance matrix, \(D\) be a given Euclidean distance matrix, let \(q\) be the dimension of desired sigma or covariance matrices.

Arguments

params

a numeric vector for the parameters (a mapping of the original parameters)

data

a numeric matrix (see examples and details)

Value

A kernel or sigma matrix.

Details

function name

function ref

params

data

formula

IdentSig_cppforR

Ident

1

matrix(q,1,1)

\(A=\sigma I_q\)

ar1hetcov_cppforR

ar1het

q

matrix(q,1,1)

\(A_{ij}=\sigma_i\sigma_j\rho^{|i-j|}\),

\(\sigma_1=1\)

arma11cov_cppforR

arma11

2

matrix(q,1,1)

\(A_{ij}=(\lambda\rho^{|i-j|-1}*\)

\(1(i\neq j)+1(i=j))\)

FA1hetSig_cppforR

FA1het

2q-2

matrix(q,1,1)

\(f_if_j+\sigma_{ii}1(i=j) \)

\(f_1=1,\) \(\sigma_1=1\)

FA1homSig_cppforR

FA1hom

q

matrix(q,1,1)

\(f_if_j+\sigma 1(i=j)\)

\(f_1=1\)

compsymmcov_cppforR

compsymm

1

matrix(q,1,1)

\(A_{ij}=\rho\), \(i\neq j;\)

\(A_{ij}=1\), \(i=j\)

compsymmhetSig_cppforR

compsymmhet

q+1

matrix(q,1,1)

\(A_{ij}=\sigma_i\sigma_j\rho,\) \(i\neq j\)

\(A_{ij}=\sigma_i\sigma_j,\) \(i= j\)

compsymmhetcov_cppforR

compsymmhet

q

matrix(q,1,1)

\(A_{ij}=\sigma_i\sigma_j\rho,\) \(i\neq j\)

\(A_{ij}=\sigma_i\sigma_j,\) \(i= j\)

\(\sigma_1=1\)

compsymmhomSig_cppforR

compsymmhom

2

matrix(q,1,1)

\(A_{ij}=\sigma\rho\), \(i\neq j;\)

\(A_{ij}=\sigma\), \(i=j\)

diagSig_cppforR

diag

q

matrix(q,1,1)

\(diag(\sigma_1,..,\sigma_q)\)

diagcov_cppforR

Diag

q-1

matrix(q,1,1)

\(diag(1,\sigma_2,..,\sigma_q)\)

expcov_cppforR

exp

1

M

\(exp(-\sigma*d_{ij})\)

M defines D

lincombcov_cppforR

lincomb

k

\((K_1;\ldots; K_k)\)

\(\sum^k_{j=1}w_jK_j\)

rbfcov_cppforR

rbf

1

M

\(exp(-\sigma*d^2_{ij})\)

M defines D

ar1cov_cppforR

ar1

1

matrix(nrow, 1,1)

\(A_{ij}=\rho^{|i-j|}\)

relmatcov_cppforR

RelMat

1

M

Genetic Similarity+

M is coded as -1, 0, 1

\(\sigma I\)

unstrcov_cppforR

unstr

\(\frac{q(q+1)}{2}-1\)

matrix(q,1,1)

\(A_{ij}=\sigma_i\sigma_j\rho_{ij}\)

\(\sigma_1=1,\)

\(\rho_{ii}=1\)

ConstMatcov_cppforR

Const

0

K

\(A=K\)

expdistcov_cppforR

expdist

1

D

\(exp(-\sigma d_{ij})\)

rbfdistcov_cppforR

rbfdist

1

D

\(exp(-\sigma d^2_{ij})\)

splincov_cppforR

splin

1

D

\(1-\rho d_{ij},\) \(\rho d_{ij}\leq 1\)

\(0,\) \(\rho d_{ij}> 1\)

function name

function ref

params

data

formula

IdentSig_cppforR

Ident

1

matrix(q,1,1)

\(A=\sigma I_q\)

ar1hetcov_cppforR

ar1het

q

matrix(q,1,1)

\(A_{ij}=\sigma_i\sigma_j\rho^{|i-j|}\),

\(\sigma_1=1\)

arma11cov_cppforR

Examples

# NOT RUN {
library(SAMM)
n=100
nsample=80
rhotrans=5
ar1cov_cppforR(c(rhotrans),matrix(5))
rho=(2/pi)*atan(rhotrans)
rho
tan((pi/2)*(rho))

M1<-matrix(rbinom(n*300, 2, .2)-1, nrow=n)
K1<-relmatcov_cppforR(c(.01), M1)

M2<-matrix(rbinom(n*300, 2, .2)-1, nrow=n)
K2<-relmatcov_cppforR(c(0.03), M2)
W=(diag(5)[sample(1:5,n, replace=TRUE),])
covY<-3*K1+5*K2+10*(W%*%ar1cov_cppforR(c(rhotrans),matrix(5))%*%t(W))
K1[1:5,1:5]
dim(W)
dim(ar1cov_cppforR(c(6),matrix(5)))
Y<-10+crossprod(chol(covY),rnorm(n))


#training set
Trainset<-sample(1:n,nsample)
ytrain=Y[Trainset]
Xtrain=matrix(rep(1, n)[Trainset], ncol=1)
Ztrain=diag(n)[Trainset,]
Wtrain=W[Trainset,]

samout<-SAMM(Y=matrix(ytrain,ncol=1),X=Xtrain,
Zlist=list(Ztrain, Ztrain), Klist=list(K1,K2),
lambda=0, W=Wtrain,R=list("ar1",c(0),matrix(5,1,1)),
Siglist=list("","",""), corfunc=c(F,F,T), corfuncfixed=c(F,F,F),
sigfunc=c(F,F,F),mmalg="dermm_reml2", tolparconv=1e-10,
tolparinv=1e-10,maxiter=1000,geterrors=F)
samout$corfuncparamslist[[3]]
rhohat=(2/pi)*atan(samout$corfuncparamslist[[3]])
rhohat
ar1cov_cppforR(c(samout$corfuncparamslist[[3]]),matrix(5,1,1))
# }

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