#' Runs sigex for EM algorithm
#'
#' @param param parameter list in sigex form
#' @param data mts object (sample size) x (dim)
#' @param mdl mdl object in sigex form
#'
#' @return list with M (error matricies) and S (signal estimates)
#' @export
#'
sigexRun_1_B12 = function(param, data, mdl){
TT <- dim(data)[1]
N <- dim(data)[2]
# Run sigex with updated param
signal.trendann <- sigex.signal(data,param,mdl,1)
signal.seas <- sigex.signal(data,param,mdl,2)
signal.irr <- sigex.signal(data,param,mdl,3)
extract.trendann <- sigex.extract(data,signal.trendann,mdl,param)
extract.seas <- sigex.extract(data,signal.seas,mdl,param)
extract.irr <- sigex.extract(data,signal.irr,mdl,param)
# form output into paper notation
M1 = block2array(signal.trendann[[2]], N = N, TT = TT)
M2 = block2array(signal.seas[[2]], N = N, TT = TT)
M3 = block2array(signal.irr[[2]], N = N, TT = TT)
M = list(M1, M2, M3)
S1 = extract.trendann[[1]]
S1d = diff(S1, 12)
S2 = extract.seas[[1]]
S2d = diff(S2, 12)
S3 = extract.irr[[1]]
S3d = diff(S3, 12)
S = list(S1d, S2d, S3d)
return(list(M, S))
}
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