one_XL_common_shock-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numba\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import time\n",
    "import math\n",
    "\n",
    "from numpy import exp, sum\n",
    "from scipy.optimize import differential_evolution\n",
    "\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "end = 20\n",
    "DELTA = 0.01\n",
    "n = int(end/DELTA)\n",
    "\n",
    "lambda1 = 0.4\n",
    "lambda2 = 2.0\n",
    "#lambda3 = 4.0\n",
    "\n",
    "beta1 = 15.0\n",
    "beta2 = 4.0\n",
    "beta3 = 0.5\n",
    "beta = beta1 + beta2 + beta3\n",
    "\n",
    "eta1 = 0.35\n",
    "eta = 0.3\n",
    "c=0.3\n",
    "d = np.array((n+1)*[0.0])\n",
    "d[0] = 1.0\n",
    "\n",
    "dhat = np.array(n*[0.0])\n",
    "\n",
    "B1 = np.array(n*[0.0])\n",
    "B2 = np.array(n*[0.0])\n",
    "B3 = np.array(n*[0.0])\n",
    "B4 = np.array(n*[0.0])\n",
    "B5 = np.array(n*[0.0])\n",
    "\n",
    "B11 = np.array(n*[0.0])\n",
    "B12 = np.array(n*[0.0])\n",
    "B31 = np.array(n*[0.0])\n",
    "B32 = np.array(n*[0.0])\n",
    "B21 = np.array(n*[0.0])\n",
    "B22 = np.array(n*[0.0])\n",
    "B41 = np.array(n*[0.0])\n",
    "B42 = np.array(n*[0.0])\n",
    "B51 = np.array(n*[0.0])\n",
    "B52 = np.array(n*[0.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def H(x): return (x>=0)*1\n",
    "\n",
    "def FR1(a1,lambda1,x):\n",
    "    return exp(-lambda1*x)*(H(x-a1)-1)+1\n",
    "\n",
    "def FR12(a1,a2,x):\n",
    "    return (-lambda2*(H(x-a1-a2)-H(x-a1))*exp(lambda2*(-x+a1)-lambda1*a1)+lambda1*(H(x-a1-a2)-H(x-a2))*exp(lambda1*(-x+a2)-lambda2*a2)+H(x-a2)*exp(-lambda2*x)*lambda1-H(x-a1)*exp(-lambda1*x)*lambda2 - exp(-lambda2*x)*lambda1 + exp(-lambda1*x)* lambda2 + lambda1-lambda2)/(lambda1-lambda2)\n",
    "\n",
    "def ER12(a1,a2):\n",
    "    return 1/lambda2+1/lambda1-1/(exp(lambda2*a2)*lambda2)-1/(exp(lambda1*a1)*lambda1)\n",
    "\n",
    "def GR(a1,a2,x):\n",
    "    return H(x)*(beta1*FR1(a1,lambda1,x) + beta2*FR1(a2,lambda2,x) + beta3*FR12(a1,a2,x))/beta\n",
    "\n",
    "def EGR(a1,a2):\n",
    "    return(beta1*ER12(a1,0) + beta2*ER12(0,a2) + beta3*ER12(a1,a2))/beta\n",
    "\n",
    "def DGR(a1, a2, j):\n",
    "    return GR(a1,a2,j*DELTA)-GR(a1,a2,(j-1)*DELTA)\n",
    "\n",
    "def DGR1(a, j):\n",
    "    return GR(a,a,j*DELTA)-GR(a,a,(j-1)*DELTA)\n",
    "\n",
    "E1 = EGR(np.inf,np.inf)\n",
    "def pR(a1,a2):\n",
    "    return (1+eta)*beta*E1 - ((1+eta1)*beta*(E1-EGR(a1,a2)))\n",
    "def pR1(a):\n",
    "    return pR(a,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "H    = numba.autojit(H,    nopython=True)\n",
    "FR1  = numba.autojit(FR1,  nopython=True)\n",
    "FR12 = numba.autojit(FR12, nopython=True)\n",
    "ER12 = numba.autojit(ER12, nopython=True)\n",
    "GR   = numba.autojit(GR,   nopython=True)\n",
    "EGR  = numba.autojit(EGR,  nopython=True)\n",
    "DGR  = numba.autojit(DGR,  nopython=True)\n",
    "pR   = numba.autojit(pR,   nopython=True)\n",
    "DGR1  = numba.autojit(DGR1,  nopython=True)\n",
    "pR1   = numba.autojit(pR1,   nopython=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "INF = 50.0\n",
    "@numba.autojit(nopython = True) \n",
    "def Hinf(a,d,i):\n",
    "    j1 = np.arange(i)\n",
    "    j2 = np.arange(1,i+1)\n",
    "    if a[0] < 0.0 : a[0]=0.0\n",
    "   # if a[1] < 0.0 : a[1]=0.0\n",
    "    a[0] = math.floor(a[0]/DELTA)*DELTA\n",
    "   # a[1] = math.floor(a[1]/DELTA)*DELTA\n",
    "    pRR = pR1(a[0])\n",
    "    if pRR>0: return ((beta+c)*d[i]-0.5*beta*sum((d[i-j1]+d[i-j2])*DGR1(a[0], j2)))/pRR\n",
    "    else : return  1000.0\n",
    "\n",
    "@numba.autojit(nopython = True) \n",
    "def Hinf1(a,d,i):\n",
    "    return Hinf([INF,a[0]],d,i)\n",
    "\n",
    "@numba.autojit(nopython = True) \n",
    "def Hinf2(a,d,i):\n",
    "    return Hinf([a[0],INF],d,i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5%, d(1.0) = 1.3309149349692266, time = 5.7 seconds\n",
      "10%, d(2.0) = 1.6104903546180327, time = 6.2 seconds\n",
      "15%, d(3.0) = 1.8445633097135954, time = 6.7 seconds\n",
      "20%, d(4.0) = 2.0463512616280446, time = 7.4 seconds\n",
      "25%, d(5.0) = 2.225372192096138, time = 8.1 seconds\n",
      "30%, d(6.0) = 2.387629361683947, time = 8.9 seconds\n",
      "35%, d(7.0) = 2.5372024317923167, time = 9.9 seconds\n",
      "40%, d(8.0) = 2.676948709075248, time = 11.0 seconds\n",
      "45%, d(9.0) = 2.8089471284255216, time = 12.1 seconds\n",
      "50%, d(10.0) = 2.934762123558919, time = 13.5 seconds\n",
      "55%, d(11.0) = 3.0556034035428503, time = 14.8 seconds\n",
      "60%, d(12.0) = 3.1724296912730896, time = 16.3 seconds\n",
      "65%, d(13.0) = 3.286017904864306, time = 17.8 seconds\n",
      "70%, d(14.0) = 3.3970105456628663, time = 19.4 seconds\n",
      "75%, d(15.0) = 3.505948701079505, time = 21.1 seconds\n",
      "80%, d(16.0) = 3.6132955386695014, time = 22.9 seconds\n",
      "85%, d(17.0) = 3.7194532822575948, time = 24.8 seconds\n",
      "90%, d(18.0) = 3.824775638766138, time = 26.8 seconds\n",
      "95%, d(19.0) = 3.929577009581985, time = 28.8 seconds\n",
      "100%, d(20.0) = 4.034139373464164, time = 31.0 seconds\n"
     ]
    }
   ],
   "source": [
    "L11=L21=0.00001\n",
    "U11=U21=60.0\n",
    "L12=L22=90.000001\n",
    "U12=U22=150.0\n",
    "TIME=time.time()\n",
    "for i in range(n):\n",
    "    MIN1  = differential_evolution(Hinf ,args=(d,i),  bounds= [(L11, U11)])\n",
    "    B1[i] = MIN1.x[0]\n",
    "    #B2[i] = MIN1.x[1]\n",
    "    if ( B1[i] < 20) : \n",
    "        L11 = np.maximum(0,B1[i] - 0.5)\n",
    "        U11 = L11 + 1\n",
    "       # L21 = np.maximum(0,B2[i] - 0.1)\n",
    "       # U21 = L21 + 0.2\n",
    "    #else :\n",
    "      #  L11 = 0.0000001\n",
    "      #  U11 = 90\n",
    "       # L21 = 0.0000001\n",
    "       # U21 = 90\n",
    "    #MIN2   = differential_evolution(Hinf ,args=(d,i),  bounds= [(L12, U12), (L22,   U22)],tol=0.0005)\n",
    "    #B12[i] = MIN2.x[0]\n",
    "    #B22[i] = MIN2.x[1]\n",
    "    #if (B12[i] > 0.00001) & (B12[i]> 80) : \n",
    "     #   L12 = np.maximum(0,B12[i] - 0.1)\n",
    "      #  U12 = L12 + 0.4\n",
    "    #if (B22[i] > 0.00001) & (B22[i]> 80) : \n",
    "     #   L22 = np.maximum(0,B22[i] - 0.1)\n",
    "      #  U22 = L22+0.4\n",
    "   # MIN1   = differential_evolution(Hinf1 ,args=(d,i),  bounds= [(L2, U2)],tol=0.0005)\n",
    "   # MIN2   = differential_evolution(Hinf2 ,args=(d,i),  bounds= [(L1, U1)],tol=0.0005)\n",
    "    \n",
    "    #vals = np.array([MIN1.fun,MIN2.fun])\n",
    "   # Ind = vals.argmin()\n",
    "    \n",
    "  #  if Ind==0:\n",
    "       # B1[i] = MIN1.x[0]\n",
    "       # B2[i] = MIN1.x[1]\n",
    "    #if Ind==1:\n",
    "        #B1[i] = MIN2.x[0]\n",
    "        #B2[i] = MIN2.x[1]\n",
    "   # if Ind==2:\n",
    "     #   B1[i] = MIN.x[0]\n",
    "     #   B2[i] = INF\n",
    "    #if Ind==3:\n",
    "      #  B1[i] = INF\n",
    "      #  B2[i] = INF\n",
    "    \n",
    "    #if (B1[i] > 0.00001) & (B1[i]< 75) : \n",
    "        #L1 = np.maximum(0,B1[i] - 0.1)\n",
    "       # U1 = L1 + 0.2\n",
    "    #if (B2[i] > 0.00001) & (B2[i]< 75) : \n",
    "        #L2 = np.maximum(0,B2[i] - 0.1)\n",
    "        #U2 = L2+0.2\n",
    "        \n",
    "    dhat[i] = MIN1.fun\n",
    "    d[i+1]=d[i]+DELTA*dhat[i]\n",
    "    \n",
    "    if (i+1)%(n//20)==0: \n",
    "        print(str(round(100*(i+1)/n))+'%, ' + 'd('+str(round((i+1)*DELTA,2))+') = '+\n",
    "                           str(d[i+1]) + ', time = '+str(round(time.time()-TIME,1))+' seconds')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = d/d[n]\n",
    "deltahat = dhat/d[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,end,n+1)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x, delta)\n",
    "plt.xlabel('$x$', fontsize=20)\n",
    "plt.ylabel(r'$\\delta(x)$', fontsize=20)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "B1 = np.maximum(0,B1)\n",
    "B2 = np.maximum(0,B2)\n",
    "\n",
    "m = n\n",
    "up = round(B1[n-1],1)\n",
    "x = np.arange(m)*DELTA\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x,B1[0:m],label='$b_1(x)$',alpha=0.7)\n",
    "#plt.plot(x,B2[0:m],label='$b_2(x)$',alpha=0.7)\n",
    "plt.xlabel('$x$', fontsize=25)\n",
    "#plt.xlim((0,6))\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "#plt.yticks([0,up,2*up,4*up],[0,up,2*up,r'$\\infty$'],fontsize=16)\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.legend(fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,end,n)\n",
    "plt.figure(figsize=(12,6))\n",
    "#plt.xlim(0,2)\n",
    "#plt.plot(x,delta1,label=r'$\\delta$')\n",
    "plt.plot(x,dhat,label=r'$\\delta_1$')\n",
    "plt.legend(fontsize=16)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.show()"
   ]
  },
  {
   "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": []
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "IndMin = np.argmin(dhat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10452919244800249"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dhat[IndMin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.92"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IndMin*DELTA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0,end,n+1)\n",
    "v = delta\n",
    "vhat = deltahat\n",
    "V = v/vhat[IndMin]\n",
    "Vp = vhat/vhat[IndMin]\n",
    "\n",
    "V[IndMin+1:] = V[IndMin] + np.arange(IndMin+1, n+1)*DELTA - (IndMin)*DELTA\n",
    "Vp[IndMin+1:] = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "V_coXLXL=V-x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,end,n+1)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x, V_coXLXL)\n",
    "plt.xlabel('$x$', fontsize=20)\n",
    "plt.ylabel(r'$V(x)$', fontsize=20)\n",
    "#plt.xlim(0,5)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "IND = np.arange(0,n)\n",
    "x = np.linspace(0,end,n+1)\n",
    "DF = pd.DataFrame([x[IND],V_coXLXL[IND],B1[IND],B2[IND]],\n",
    "                  index=['x','V','Line1','Line2']).T\n",
    "DF.to_csv('oneXLcommon_20_0.01.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,end,n)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x, Vp)\n",
    "plt.xlabel('$x$', fontsize=20)\n",
    "plt.ylabel(r\"$V'(x)$\", fontsize=20)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "supL = np.array(n*[0.0])\n",
    "B1 = np.array(n*[0.0])\n",
    "B2 = np.array(n*[0.0])\n",
    "INF = 30.0\n",
    "@numba.autojit(nopython = True) \n",
    "def nL(a,d,i):\n",
    "    j = np.arange(i+1)\n",
    "    if a[0] < 0.0 : a[0]=0.0\n",
    "    if a[1] < 0.0 : a[1]=0.0\n",
    "    a[0] = math.floor(a[0]/DELTA)*DELTA\n",
    "    a[1] = math.floor(a[1]/DELTA)*DELTA\n",
    "    pRR = pR(a[0],a[1])\n",
    "    if pRR>0: return -(pRR*Vp[i]-(c+beta)*V[i] + beta*np.sum(V[i-j]*DGR(a[0],a[1],j)))\n",
    "    else : return  1000.0\n",
    "\n",
    "@numba.autojit(nopython = True) \n",
    "def nL1(a,d,i):\n",
    "    return Hinf([INF,a[0]],d,i)\n",
    "\n",
    "@numba.autojit(nopython = True) \n",
    "def nL2(a,d,i):\n",
    "    return Hinf([a[0],INF],d,i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5%, supL(1.0) = -0.00378829555253013\n",
      "10%, supL(2.0) = -0.005486571960947373\n",
      "15%, supL(3.0) = -0.001993676782138465\n",
      "20%, supL(4.0) = -0.1034280750979164\n",
      "25%, supL(5.0) = -0.28977469711505677\n",
      "30%, supL(6.0) = -0.4879112632227205\n",
      "35%, supL(7.0) = -0.6876582920143051\n",
      "40%, supL(8.0) = -0.8876240163562272\n",
      "45%, supL(9.0) = -1.087619375523488\n",
      "50%, supL(10.0) = -1.2876187473187883\n",
      "55%, supL(11.0) = -1.4876186622875025\n",
      "60%, supL(12.0) = -1.6876186507779067\n",
      "65%, supL(13.0) = -1.8876186492199452\n",
      "70%, supL(14.0) = -2.087618649008988\n",
      "75%, supL(15.0) = -2.287618648980441\n",
      "80%, supL(16.0) = -2.4876186489762517\n",
      "85%, supL(17.0) = -2.687618648976013\n",
      "90%, supL(18.0) = -2.887618648975945\n",
      "95%, supL(19.0) = -3.087618648975706\n",
      "100%, supL(20.0) = -3.287618648976178\n"
     ]
    }
   ],
   "source": [
    "L1=L2=-2.0\n",
    "U1=U2=5.0\n",
    "\n",
    "TIME=time.time()\n",
    "for i in range(n):\n",
    "    MIN   = differential_evolution(nL ,args=(d,i),  bounds= [(L1, U1), (L2,   U2)],tol=0.0005)\n",
    "    MIN1   = differential_evolution(nL1 ,args=(d,i),  bounds= [(L2, U2)],tol=0.0005)\n",
    "    MIN2   = differential_evolution(nL2 ,args=(d,i),  bounds= [(L1, U1)],tol=0.0005)\n",
    "    \n",
    "    vals = np.array([MIN.fun,MIN1.fun,MIN2.fun, Hinf([INF,INF],d,i)])\n",
    "    Ind = vals.argmin()\n",
    "    \n",
    "    if Ind==0:\n",
    "        B1[i] = MIN.x[0]\n",
    "        B2[i] = MIN.x[1]\n",
    "    if Ind==1:\n",
    "        B1[i] = INF\n",
    "        B2[i] = MIN1.x[0]\n",
    "    if Ind==2:\n",
    "        B1[i] = MIN.x[0]\n",
    "        B2[i] = INF\n",
    "    if Ind==3:\n",
    "        B1[i] = INF\n",
    "        B2[i] = INF\n",
    "    supL[i] =  -np.min(vals)\n",
    "    if (B1[i] > 0.00001) & (B1[i]< INF) : \n",
    "        L1 = np.maximum(0,B1[i] - 0.1)\n",
    "        U1 = L1 + 0.2\n",
    "    if (B2[i] > 0.00001) & (B2[i]< INF) : \n",
    "        L2 = np.maximum(0,B2[i] - 0.1)\n",
    "        U2 = L2+0.2\n",
    "        \n",
    "    #dhat[i] = np.min(vals)\n",
    "    #d[i+1]=d[i]+DELTA*dhat[i]\n",
    "    \n",
    " \n",
    "    if (i+1)%(n//20)==0: \n",
    "        print(str(round(100*(i+1)/n))+'%, ' + 'supL('+str(round((i+1)*DELTA,2))+') = '+str(supL[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,end,n)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x, supL, label = r\"sup L\")\n",
    "plt.plot(x, 1-Vp, label = r\"1-V'\")\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,end,n)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x, B1)\n",
    "plt.plot(x, B2)\n",
    "#plt.plot(x, B3)\n",
    "plt.xlim(0,8)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.show()"
   ]
  },
  {
   "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": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}