Nothing

```
# DESP/R/DESP_SPT.R by A. S. Dalalyan and S. Balmand Copyright (C) 2015-
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License (version 3) as published by
# the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# A copy of the GNU General Public License is available at
# http://www.r-project.org/Licenses/
#
DESP_SPT <-
function(X,B,method='1',Theta=NULL) {
# estimation of the diagonal of the precision matrix using shortest path trees, when the true value of B is known or has already been estimated
# the observations of the data matrix X are assumed to have zero mean
# main function
# read the sample size and the number of variables
D = dim(X);
n = D[1]; # n is the sample size
p = D[2]; # p is the dimension
# compute the sample cov matrix
if(is.null(Theta))
{
S = crossprod(X)/n;
}
else
{
S = crossprod(X - Theta %*% MASS::ginv(B))/n;
}
if (method=='1'){ # considers only the presence or absence of edges to build the shortest path trees
G = DESP_Weighted_Graph(matrix(1,p,p)*sign(B),n);
trees = DESP_SPT_MaxDegreeRoot(G);
Phi = DESP_SPT_Phi(S,B,trees);
}
else if (method=='2'){ # chooses the root as the node of maximal degree
G = DESP_Weighted_Graph(B,n);
trees = DESP_SPT_MaxDegreeRoot(G);
Phi = DESP_SPT_Phi(S,B,trees);
}
else if (method=='2.1'){ # chooses the root as the node of maximal degree and limits the height of shortest path trees to 1
G = DESP_Weighted_Graph(B,n);
trees = DESP_SPT_MaxDegreeRoot2(G);
Phi = DESP_SPT_Phi2(S,B,trees);
}
else if (method=='3'){ # get the maximum weighted tree among all shortest path trees for each connected component
G = DESP_Weighted_Graph(B,n);
trees = DESP_SPT_MaxWeight(G);
Phi = DESP_SPT_Phi(S,B,trees);
}
return(1/Phi);
}
DESP_SPT_Phi <-
function(S,B,trees) {
# estimation of the inverse of the diagonal of the precision matrix using shortest path trees
# read the sample size and the number of variables
D = dim(S);
p = D[2]; # p is the dimension
Phi = c(1:p)*0;
Dlt = c(1:p)*0;
penult = trees$penult;
for (i in c(1:p)){
j = penult[i];
m = 1;
h = i;
while (j != h){ # j different of the root of the considered tree
m = m * B[h,j] / B[j,h];
h = j;
j = penult[j];
}
Dlt[i] = m;
}
cc = trees$cc;
for(r in c(1:length(cc))){
dc = Dlt; dc[-cc[[r]]] = 0;
dr = sum(diag(crossprod(diag(dc),crossprod(S,B))))/(length(cc[[r]]));
idc = 1/dc; idc[-cc[[r]]] = 0;
Phi = Phi + dr * idc;
}
return(Phi);
}
DESP_SPT_Phi2 <-
function(S,B,trees) {
# estimation of the inverse of the diagonal of the precision matrix using shortest path trees - of maximum height equal to 1
# read the sample size and the number of variables
D = dim(S);
p = D[2]; # p is the dimension
Phi = c(1:p)*0;
for (spt in trees){
Dlt = c(1:p)*0;
penult = spt$penult;
for (i in c(1:p)){
j = penult[i];
m = 1;
h = i;
while (j != h){ # j different of the root of the considered tree
m = m * B[h,j] / B[j,h];
h = j;
j = penult[j];
}
Dlt[i] = m;
}
nodes = spt$nodes;
cc = spt$cc;
dc = Dlt; dc[-cc] = 0;
dr = sum(diag(crossprod(diag(dc),crossprod(S,B))))/(length(cc));
idc = 1/dc; idc[-nodes] = 0;
Phi = Phi + dr * idc;
}
return(Phi);
}
```

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