Simulations for calculating fixation times and fixation probabilities in RSP evolutionary game.ipynb.ipynb

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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some parameters must be specified before the calculation starts. Without losing generality, the payoff matrix of RSP game can be written as \n",
    "![matrsp.JPG](attachment:matrsp.JPG)\n",
    "\n",
    "# So we should determine parameters a_i and b_i.\n",
    "\n",
    "# Also beta parameter in fermi function shuold be assign.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# N is the size of population\n",
    "#RP is the number of realization for averaging fixation probabilities\n",
    "#RT is the number of realization for averaging fixation times\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import seaborn as sns\n",
    "import math\n",
    "\n",
    "N=50\n",
    "\n",
    "RP=1000\n",
    "RT=3000\n",
    "\n",
    "\n",
    "\n",
    "b1=2\n",
    "b2=2\n",
    "b3=2\n",
    "a1=1\n",
    "a2=1\n",
    "a3=1\n",
    "\n",
    "beta=.001\n",
    "\n",
    "\n",
    "def pof(N,w1,w2):\n",
    "    return((-a2*w2+b3*(N-w1-w2))/N,(b1*w1-a3*(N-w1-w2))/N,(-a1*w1+b2*w2)/N)\n",
    "\n",
    "\n",
    "def fermi(x,y):\n",
    "    return(1/(1+math.exp(beta*(x-y))))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fix(N,w1,w2):\n",
    "    t=0\n",
    "    while   w1+w2>0 and N-w2>0 and N-w1>0 :\n",
    "\n",
    "        p=random.random()\n",
    "\n",
    "        h1=((N-w1-w2)*(w1)*fermi(pof(N,w1,w2)[0],pof(N,w1,w2)[2]))/(N**2-N)\n",
    "        h2=((N-w1-w2)*(w1)*fermi(pof(N,w1,w2)[2],pof(N,w1,w2)[0]))/(N**2-N)\n",
    "        h3=((N-w1-w2)*(w2)*fermi(pof(N,w1,w2)[1],pof(N,w1,w2)[2]))/(N**2-N)\n",
    "        h4=((N-w1-w2)*(w2)*fermi(pof(N,w1,w2)[2],pof(N,w1,w2)[1]))/(N**2-N)\n",
    "        h5=((w1)*(w2)*fermi(pof(N,w1,w2)[1],pof(N,w1,w2)[0]))/(N**2-N)\n",
    "        h6=((w1)*(w2)*fermi(pof(N,w1,w2)[0],pof(N,w1,w2)[1]))/(N**2-N)\n",
    "        h7=((w1)*(w1-1)+(w2)*(w2-1)+(N-w1-w2)*(N-w1-w2-1))/(2*(N**2-N))\n",
    "\n",
    "        if 0<p<2*h1:\n",
    "            w1=w1-1\n",
    "        elif 2*h1<p<2*(h1+h2):\n",
    "            w1=w1+1\n",
    "        elif 2*(h1+h2)<p<2*(h1+h2+h3):\n",
    "            w2=w2-1\n",
    "        elif 2*(h1+h2+h3)<p<2*(h1+h2+h3+h4):\n",
    "            w2=w2+1\n",
    "        elif 2*(h1+h2+h3+h4)<p<2*(h1+h2+h3+h4+h5):\n",
    "            w1=w1+1\n",
    "            w2=w2-1\n",
    "        elif 2*(h1+h2+h3+h4+h5)<p<2*(h1+h2+h3+h4+h5+h6):\n",
    "            w1=w1-1\n",
    "            w2=w2+1\n",
    "\n",
    "        t=t+1\n",
    "    return(w1,w2,N-w1-w2,t)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fixation probability of strategy P\n",
    "\n",
    "def meyp(N,w1,w2,te):\n",
    "    p=0\n",
    "    u=0\n",
    "    g=0\n",
    "    \n",
    "    for x in range (0,te):\n",
    "        az=(fix(N,w1,w2))\n",
    "        if  (az[0])==N: #R\n",
    "            p=p+1\n",
    "        elif (az[1])==N:#S\n",
    "            u=u+1\n",
    "        elif (az[2])==N:#P\n",
    "            g=g+1\n",
    "    return(p/te,u/te,g/te ) \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "SE=[]\n",
    "SE1=[]\n",
    "SE2=[]\n",
    "\n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,x+1):\n",
    "        K=meyp(N,y,N-x,RP)\n",
    "        SE.append(K[2])\n",
    "        SE1.append(K[1])\n",
    "        SE2.append(K[0])\n",
    "        \n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "SEE=np.zeros(len(SE))\n",
    "SEE[0]=SE[0]\n",
    "SEE[1]=SE[int(N*(N+1)/2)]\n",
    "SEE[2]=SE[int((N+2)*(N+1)/2)-1]\n",
    "for x in range (1,int(N*(N+1)/2)-1):\n",
    "    SEE[x+2]=SE[x]\n",
    "for x in range (int(N*(N+1)/2)+1,int((N+2)*(N+1)/2)-1):\n",
    "    SEE[x+1]=SE[x]   \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#pro\n",
    "\n",
    "PROz=SEE\n",
    "def rey(x):\n",
    "    if x==1:\n",
    "        return([PROz[0]])\n",
    "    if x==N+1:\n",
    "        GH=[PROz[1]]\n",
    "        for s in range (int(x*(x-1)//2+2),len(PROz)):\n",
    "            GH.append(PROz[s])\n",
    "        GH.append(PROz[2])\n",
    "        return(GH)\n",
    "        \n",
    "    ui=[]\n",
    "    for j in range (int(x*(x+1)//2-x+2),int(x*(x+1)//2+2)):\n",
    "        ui.append(PROz[j])\n",
    "    return(ui)\n",
    "\n",
    "\n",
    "ER=np.zeros((N+2,2*N+1))\n",
    "for i in range (0,N+2):\n",
    "    for j in range (0,2*N+1):\n",
    "        ER[i][j]='nan'\n",
    "for j in range (1,N+2):\n",
    "    for k in range (0, len(rey(j))):\n",
    "        ER[j-1][N-len(rey(j))+2*k+1]=rey(j)[k]\n",
    "        \n",
    "        \n",
    "\n",
    "\n",
    "        \n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N-1):\n",
    "        if str(ER[x,y])=='nan' and str(ER[x,y-1])!='nan' and str(ER[x,y+1])!='nan':\n",
    "            ER[x,y]=ER[x,y+1]\n",
    "ER[N][2*N-1]=ER[N][2*N]            \n",
    " \n",
    "ax = sns.heatmap(ER,yticklabels=False,cmap='Spectral')    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fixation probability of strategy S\n",
    "\n",
    "\n",
    "SEE=np.zeros(len(SE1))\n",
    "SEE[0]=SE1[0]\n",
    "SEE[1]=SE1[int(N*(N+1)/2)]\n",
    "SEE[2]=SE1[int((N+2)*(N+1)/2)-1]\n",
    "for x in range (1,int(N*(N+1)/2)-1):\n",
    "    SEE[x+2]=SE1[x]\n",
    "for x in range (int(N*(N+1)/2)+1,int((N+2)*(N+1)/2)-1):\n",
    "    SEE[x+1]=SE1[x]   \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#pro\n",
    "\n",
    "PROz=SEE\n",
    "def rey(x):\n",
    "    if x==1:\n",
    "        return([PROz[0]])\n",
    "    if x==N+1:\n",
    "        GH=[PROz[1]]\n",
    "        for s in range (int(x*(x-1)//2+2),len(PROz)):\n",
    "            GH.append(PROz[s])\n",
    "        GH.append(PROz[2])\n",
    "        return(GH)\n",
    "        \n",
    "    ui=[]\n",
    "    for j in range (int(x*(x+1)//2-x+2),int(x*(x+1)//2+2)):\n",
    "        ui.append(PROz[j])\n",
    "    return(ui)\n",
    "\n",
    "\n",
    "ER=np.zeros((N+2,2*N+1))\n",
    "for i in range (0,N+2):\n",
    "    for j in range (0,2*N+1):\n",
    "        ER[i][j]='nan'\n",
    "for j in range (1,N+2):\n",
    "    for k in range (0, len(rey(j))):\n",
    "        ER[j-1][N-len(rey(j))+2*k+1]=rey(j)[k]\n",
    "        \n",
    "        \n",
    "\n",
    "\n",
    "        \n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N-1):\n",
    "        if str(ER[x,y])=='nan' and str(ER[x,y-1])!='nan' and str(ER[x,y+1])!='nan':\n",
    "            ER[x,y]=ER[x,y+1]\n",
    "ER[N][2*N-1]=ER[N][2*N]            \n",
    "            \n",
    "\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fixation probability of strategy R\n",
    "\n",
    "\n",
    "SEE=np.zeros(len(SE2))\n",
    "SEE[0]=SE2[0]\n",
    "SEE[1]=SE2[int(N*(N+1)/2)]\n",
    "SEE[2]=SE2[int((N+2)*(N+1)/2)-1]\n",
    "for x in range (1,int(N*(N+1)/2)-1):\n",
    "    SEE[x+2]=SE2[x]\n",
    "for x in range (int(N*(N+1)/2)+1,int((N+2)*(N+1)/2)-1):\n",
    "    SEE[x+1]=SE2[x]   \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#pro\n",
    "\n",
    "PROz=SEE\n",
    "def rey(x):\n",
    "    if x==1:\n",
    "        return([PROz[0]])\n",
    "    if x==N+1:\n",
    "        GH=[PROz[1]]\n",
    "        for s in range (int(x*(x-1)//2+2),len(PROz)):\n",
    "            GH.append(PROz[s])\n",
    "        GH.append(PROz[2])\n",
    "        return(GH)\n",
    "        \n",
    "    ui=[]\n",
    "    for j in range (int(x*(x+1)//2-x+2),int(x*(x+1)//2+2)):\n",
    "        ui.append(PROz[j])\n",
    "    return(ui)\n",
    "\n",
    "\n",
    "ER=np.zeros((N+2,2*N+1))\n",
    "for i in range (0,N+2):\n",
    "    for j in range (0,2*N+1):\n",
    "        ER[i][j]='nan'\n",
    "for j in range (1,N+2):\n",
    "    for k in range (0, len(rey(j))):\n",
    "        ER[j-1][N-len(rey(j))+2*k+1]=rey(j)[k]\n",
    "        \n",
    "        \n",
    "\n",
    "\n",
    "        \n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N-1):\n",
    "        if str(ER[x,y])=='nan' and str(ER[x,y-1])!='nan' and str(ER[x,y+1])!='nan':\n",
    "            ER[x,y]=ER[x,y+1]\n",
    "ER[N][2*N-1]=ER[N][2*N] \n",
    "ER[N-1][2*N-2]=ER[N-1][2*N-3]\n",
    "ER[N-1][2*N-1]=ER[N-1][2*N-2]            \n",
    "\n",
    "ax = sns.heatmap(ER,yticklabels=False,cmap='Spectral')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fixation Times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fixation time of strategy P\n",
    "\n",
    "def meytg(N,w1,w2,te):\n",
    "    if N-w1-w2==0:\n",
    "        return('nan','nan','nan')\n",
    "    if w1+w2==0:\n",
    "        return(1,0,0)\n",
    "    \n",
    "    if w2==0:\n",
    "        return('nan','nan','nan')\n",
    "    if w2==N:\n",
    "        return(0,1,0)\n",
    "    \n",
    "    \n",
    "    if w1==0:\n",
    "        return('nan','nan','nan')\n",
    "    if w1==N:\n",
    "        return(0,0,1)\n",
    "     \n",
    "    ttp=0\n",
    "    p=0\n",
    "    tts=0\n",
    "    s=0\n",
    "    ttr=0\n",
    "    r=0\n",
    "    while p+s+r<te:\n",
    "        az=fix(N,w1,w2)\n",
    "        if (az[2])==N:\n",
    "            ttp=ttp+az[3]\n",
    "            p=p+1\n",
    "        if (az[1])==N:\n",
    "            tts=tts+az[3]\n",
    "            s=s+1\n",
    "        if (az[0])==N:\n",
    "            ttr=ttr+az[3]\n",
    "            r=r+1\n",
    "\n",
    "    return([ttp/p,tts/s,ttr/r])  \n",
    "\n",
    "#time\n",
    "TP=[]\n",
    "TS=[]\n",
    "TR=[]\n",
    "\n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,x+1):\n",
    "        K=meytg(N,y,N-x,RT)\n",
    "        TP.append(K[0])\n",
    "        TS.append(K[1])\n",
    "        TR.append(K[2])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "TII=np.zeros(len(TP))\n",
    "TII[0]=TP[0]\n",
    "TII[1]=TP[int(N*(N+1)/2)]\n",
    "TII[2]=TP[int((N+2)*(N+1)/2)-1]\n",
    "for x in range (1,int(N*(N+1)/2)-1):\n",
    "    TII[x+2]=TP[x]\n",
    "for x in range (int(N*(N+1)/2)+1,int((N+2)*(N+1)/2)-1):\n",
    "    TII[x+1]=TP[x]  \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#time\n",
    "\n",
    "JKL=TII\n",
    "def reyt(x):\n",
    "    if x==1:\n",
    "        return([JKL[0]])\n",
    "    if x==N+1:\n",
    "        GH=[JKL[1]]\n",
    "        for s in range (int(x*(x-1)//2+2),len(JKL)):\n",
    "            GH.append(JKL[s])\n",
    "        GH.append(JKL[2])\n",
    "        return(GH)\n",
    "        \n",
    "    ui=[]\n",
    "    for j in range (int(x*(x+1)//2-x+2),int(x*(x+1)//2+2)):\n",
    "        ui.append(JKL[j])\n",
    "    return(ui)\n",
    "\n",
    "\n",
    "ERt=np.zeros((N+2,2*N+1))\n",
    "for i in range (0,N+2):\n",
    "    for j in range (0,2*N+1):\n",
    "        ERt[i][j]='nan'\n",
    "for j in range (1,N+2):\n",
    "    for k in range (0, len(reyt(j))):\n",
    "        ERt[j-1][N-len(reyt(j))+2*k+1]=reyt(j)[k]\n",
    "        \n",
    "        \n",
    "\n",
    "\n",
    "        \n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N-1):\n",
    "        if str(ERt[x,y])=='nan' and str(ERt[x,y-1])!='nan' and str(ERt[x,y+1])!='nan':\n",
    "            ERt[x,y]=ERt[x,y+1]            \n",
    "ERt[N][2*N-1]=ERt[N][2*N] \n",
    "\n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N+1):\n",
    "        if ERt[x,y]==0:\n",
    "            ERt[x,y]='nan'\n",
    "ERt[N][0]=0\n",
    "ax = sns.heatmap(ERt,yticklabels=False,cmap='Spectral') \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fixation time of strategy S\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "TII=np.zeros(len(TS))\n",
    "TII[0]=TS[0]\n",
    "TII[1]=TS[int(N*(N+1)/2)]\n",
    "TII[2]=TS[int((N+2)*(N+1)/2)-1]\n",
    "for x in range (1,int(N*(N+1)/2)-1):\n",
    "    TII[x+2]=TS[x]\n",
    "for x in range (int(N*(N+1)/2)+1,int((N+2)*(N+1)/2)-1):\n",
    "    TII[x+1]=TS[x]  \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#time\n",
    "\n",
    "JKL=TII\n",
    "def reyt(x):\n",
    "    if x==1:\n",
    "        return([JKL[0]])\n",
    "    if x==N+1:\n",
    "        GH=[JKL[1]]\n",
    "        for s in range (int(x*(x-1)//2+2),len(JKL)):\n",
    "            GH.append(JKL[s])\n",
    "        GH.append(JKL[2])\n",
    "        return(GH)\n",
    "        \n",
    "    ui=[]\n",
    "    for j in range (int(x*(x+1)//2-x+2),int(x*(x+1)//2+2)):\n",
    "        ui.append(JKL[j])\n",
    "    return(ui)\n",
    "\n",
    "\n",
    "ERt=np.zeros((N+2,2*N+1))\n",
    "for i in range (0,N+2):\n",
    "    for j in range (0,2*N+1):\n",
    "        ERt[i][j]='nan'\n",
    "for j in range (1,N+2):\n",
    "    for k in range (0, len(reyt(j))):\n",
    "        ERt[j-1][N-len(reyt(j))+2*k+1]=reyt(j)[k]\n",
    "\n",
    "        \n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N-1):\n",
    "        if str(ERt[x,y])=='nan' and str(ERt[x,y-1])!='nan' and str(ERt[x,y+1])!='nan':\n",
    "            ERt[x,y]=ERt[x,y+1]            \n",
    "ERt[N][2*N-1]=ERt[N][2*N] \n",
    "\n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N+1):\n",
    "        if ERt[x,y]==0:\n",
    "            ERt[x,y]='nan'\n",
    "ERt[N-1][2*N-2]=ERt[N-1][2*N-3]\n",
    "ERt[N-1][2*N-1]=ERt[N-1][2*N-2]\n",
    "ERt[N][0]=np.nan\n",
    "sns.heatmap(ERt,yticklabels=False,cmap='Spectral') \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fixation time of strategy R\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "TII=np.zeros(len(TR))\n",
    "TII[0]=TR[0]\n",
    "TII[1]=TR[int(N*(N+1)/2)]\n",
    "TII[2]=TR[int((N+2)*(N+1)/2)-1]\n",
    "for x in range (1,int(N*(N+1)/2)-1):\n",
    "    TII[x+2]=TR[x]\n",
    "for x in range (int(N*(N+1)/2)+1,int((N+2)*(N+1)/2)-1):\n",
    "    TII[x+1]=TR[x]  \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#time\n",
    "\n",
    "JKL=TII\n",
    "def reyt(x):\n",
    "    if x==1:\n",
    "        return([JKL[0]])\n",
    "    if x==N+1:\n",
    "        GH=[JKL[1]]\n",
    "        for s in range (int(x*(x-1)//2+2),len(JKL)):\n",
    "            GH.append(JKL[s])\n",
    "        GH.append(JKL[2])\n",
    "        return(GH)\n",
    "        \n",
    "    ui=[]\n",
    "    for j in range (int(x*(x+1)//2-x+2),int(x*(x+1)//2+2)):\n",
    "        ui.append(JKL[j])\n",
    "    return(ui)\n",
    "\n",
    "\n",
    "ERt=np.zeros((N+2,2*N+1))\n",
    "for i in range (0,N+2):\n",
    "    for j in range (0,2*N+1):\n",
    "        ERt[i][j]='nan'\n",
    "for j in range (1,N+2):\n",
    "    for k in range (0, len(reyt(j))):\n",
    "        ERt[j-1][N-len(reyt(j))+2*k+1]=reyt(j)[k]\n",
    "\n",
    "        \n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N-1):\n",
    "        if str(ERt[x,y])=='nan' and str(ERt[x,y-1])!='nan' and str(ERt[x,y+1])!='nan':\n",
    "            ERt[x,y]=ERt[x,y+1]            \n",
    "ERt[N][2*N-1]=ERt[N][2*N] \n",
    "\n",
    "for x in range (0,N+1):\n",
    "    for y in range (0,2*N+1):\n",
    "        if ERt[x,y]==0:\n",
    "            ERt[x,y]='nan'\n",
    "ERt[N-1][2*N-2]=ERt[N-1][2*N-3]\n",
    "ERt[N-1][2*N-1]=ERt[N-1][2*N-2]\n",
    "\n",
    "ERt[N-1][2*N-1]=np.nan\n",
    "ERt[N-1][2*N-2]=np.nan\n",
    "\n",
    "\n",
    "sns.heatmap(ERt,yticklabels=False,cmap='Spectral') \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}