{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Phylogenetic trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#3 (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using TensorDec\n",
    "normalize_markov! = function(w,A,B,C) \n",
    "    for i in 1:size(A,2) \n",
    "        l = sum(A[j,i] for j in 1:size(A,1) ) \n",
    "        A[:,i] /= l\n",
    "        w[i] *= l\n",
    "    end\n",
    "    for i in 1:size(B,2) \n",
    "        l = sum(B[j,i] for j in 1:size(B,1) ) \n",
    "        B[:,i] /=l\n",
    "        w[i] *= l\n",
    "    end\n",
    "    for i in 1:size(C,2) \n",
    "        l = sum(C[j,i] for j in 1:size(B,1) ) \n",
    "        C[:,i] /=l\n",
    "        w[i] *= l\n",
    "    end\n",
    "    w, A,B,C\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([1.0 1.0 1.0 1.0], [1.0 1.0 1.0 1.0], [1.0 1.0 1.0 1.0])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = rand(4,4); B = rand(4,4); C = rand(4,4); w = rand(4);\n",
    "normalize_markov!(w,A,B,C)\n",
    "fill(1.,4)'*A, fill(1.,4)'*B, fill(1.,4)'*C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4×4 Array{Float64,3}:\n",
       "[:, :, 1] =\n",
       " 0.259248  0.349942  0.364485  0.085319 \n",
       " 0.215528  0.270488  0.262803  0.0684887\n",
       " 0.214908  0.479766  0.506224  0.0540596\n",
       " 0.269875  0.450153  0.478336  0.0683525\n",
       "\n",
       "[:, :, 2] =\n",
       " 0.313488  0.384201  0.402716  0.115903 \n",
       " 0.256093  0.26977   0.265292  0.0868339\n",
       " 0.221668  0.521591  0.562154  0.0653809\n",
       " 0.300196  0.468211  0.499396  0.0853609\n",
       "\n",
       "[:, :, 3] =\n",
       " 0.357105  0.223798  0.198387  0.143608 \n",
       " 0.312446  0.211622  0.16047   0.130103 \n",
       " 0.13943   0.288979  0.270791  0.0376782\n",
       " 0.275407  0.277452  0.270645  0.0943938\n",
       "\n",
       "[:, :, 4] =\n",
       " 0.270442  0.247415  0.242189  0.138953 \n",
       " 0.224147  0.138707  0.092527  0.101356 \n",
       " 0.104812  0.344     0.350852  0.0728985\n",
       " 0.187994  0.211849  0.209937  0.0853464"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = tensor(w,A,B,C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([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])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wd, Ad, Bd, Cd = decompose(t)\n",
    "normalize_markov!(wd,Ad,Bd,Cd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       "  2.8635040860546987\n",
       " 10.019347309230545 \n",
       "  2.0304186435229035\n",
       "  0.7187016887591559"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       "  0.718701688759023 \n",
       " 10.019347309230689 \n",
       "  2.863504086054696 \n",
       "  2.0304186435228844"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       " 0.407548   0.216844  0.317121   0.158147\n",
       " 0.348307   0.174449  0.0277879  0.368735\n",
       " 0.0128447  0.298045  0.477643   0.337246\n",
       " 0.2313     0.310662  0.177448   0.135872"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       " 0.158147  0.216844  0.407548   0.317121 \n",
       " 0.368735  0.174449  0.348307   0.0277879\n",
       " 0.337246  0.298045  0.0128447  0.477643 \n",
       " 0.135872  0.310662  0.2313     0.177448 "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8522595838390253e-14"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "norm(t-tensor(wd,Ad,Bd,Cd))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.0.0",
   "language": "julia",
   "name": "julia-1.0"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.0.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}