R/S_soft.R

In cencrne: Consistent Estimation of the Number of Communities via Regularized Network Embedding

S_soft = function(z,lambda){

  ## -----------------------------------------------------------------------------------------------------------------
  ## The name of the function: S_soft
  ## -----------------------------------------------------------------------------------------------------------------
  ## Description:
  ##            Define the soft threshold operator.
  ## -----------------------------------------------------------------------------------------------------------------
  ## Required preceding functions or packages: No
  ## -----------------------------------------------------------------------------------------------------------------
  ## Input:
  ## @ z: a float value or a vector, the independent variable.
  ## @ lambda: a float value, the tuning parameter.
  ## -----------------------------------------------------------------------------------------------------------------
  ## Output:
  ## @ The result of the soft threshold operator.
  ## -----------------------------------------------------------------------------------------------------------------
  norm.z = sqrt(sum(z^2))
  if(norm.z!=0){
    n.x = 1 - lambda/norm.z
    rho = n.x*(n.x > 0)*z
  } else{
    rho = z
  }
  return(rho)
}