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#' @title projAXb
#' @param X0 The ground truth clustering matrix.
#' @param k The number of community.
#' @param n The number of nodes.
#' @return X The solution matrix of the SDP.
#' @noRd
#' @keywords internal
projAXb = function(X0, k, n){
# k is the trace of X
b = c(2*rep(1, n), k)
X = X0 - Acs(Pinv(Ac(X0, n) - b, n), n)
return(X)
}
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