Phylogenetic trees

using TensorDec
normalize_markov! = function(w,A,B,C) 
    for i in 1:size(A,2) 
        l = sum(A[j,i] for j in 1:size(A,1) ) 
        A[:,i] /= l
        w[i] *= l
    end
    for i in 1:size(B,2) 
        l = sum(B[j,i] for j in 1:size(B,1) ) 
        B[:,i] /=l
        w[i] *= l
    end
    for i in 1:size(C,2) 
        l = sum(C[j,i] for j in 1:size(B,1) ) 
        C[:,i] /=l
        w[i] *= l
    end
    w, A,B,C
end

#3 (generic function with 1 method)

A = rand(4,4); B = rand(4,4); C = rand(4,4); w = rand(4);
normalize_markov!(w,A,B,C)
fill(1.,4)'*A, fill(1.,4)'*B, fill(1.,4)'*C

([1.0 1.0 1.0 1.0], [1.0 1.0 1.0 1.0], [1.0 1.0 1.0 1.0])

t = tensor(w,A,B,C)

4×4×4 Array{Float64,3}:
[:, :, 1] =
 0.259248  0.349942  0.364485  0.085319 
 0.215528  0.270488  0.262803  0.0684887
 0.214908  0.479766  0.506224  0.0540596
 0.269875  0.450153  0.478336  0.0683525

[:, :, 2] =
 0.313488  0.384201  0.402716  0.115903 
 0.256093  0.26977   0.265292  0.0868339
 0.221668  0.521591  0.562154  0.0653809
 0.300196  0.468211  0.499396  0.0853609

[:, :, 3] =
 0.357105  0.223798  0.198387  0.143608 
 0.312446  0.211622  0.16047   0.130103 
 0.13943   0.288979  0.270791  0.0376782
 0.275407  0.277452  0.270645  0.0943938

[:, :, 4] =
 0.270442  0.247415  0.242189  0.138953 
 0.224147  0.138707  0.092527  0.101356 
 0.104812  0.344     0.350852  0.0728985
 0.187994  0.211849  0.209937  0.0853464

wd, Ad, Bd, Cd = decompose(t)
normalize_markov!(wd,Ad,Bd,Cd)

([0.718702, 10.0193, 2.8635, 2.03042], [0.158147 0.216844 0.407548 0.317121; 0.368735 0.174449 0.348307 0.0277879; 0.337246 0.298045 0.0128447 0.477643; 0.135872 0.310662 0.2313 0.177448], [0.196824 0.184114 0.632411 0.0619155; 0.549973 0.376328 0.0654333 0.386497; 0.101599 0.41063 0.0109438 0.452418; 0.151604 0.0289275 0.291212 0.0991702], [0.179996 0.35144 0.146618 0.161332; 0.125831 0.351245 0.214783 0.292323; 0.368812 0.203257 0.360999 0.0280855; 0.32536 0.0940577 0.2776 0.518259])

w

4-element Array{Float64,1}:
  2.8635040860546987
 10.019347309230545 
  2.0304186435229035
  0.7187016887591559

wd

4-element Array{Float64,1}:
  0.718701688759023 
 10.019347309230689 
  2.863504086054696 
  2.0304186435228844

A

4×4 Array{Float64,2}:
 0.407548   0.216844  0.317121   0.158147
 0.348307   0.174449  0.0277879  0.368735
 0.0128447  0.298045  0.477643   0.337246
 0.2313     0.310662  0.177448   0.135872

Ad

4×4 Array{Float64,2}:
 0.158147  0.216844  0.407548   0.317121 
 0.368735  0.174449  0.348307   0.0277879
 0.337246  0.298045  0.0128447  0.477643 
 0.135872  0.310662  0.2313     0.177448

using LinearAlgebra
norm(t-tensor(wd,Ad,Bd,Cd))

1.8522595838390253e-14