one_pre_threeline.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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",
    "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": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.98661435587542"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1/0.19)*np.log(1000000/24)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.28"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.33*4**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "if not os.path.exists('./plots/p'): os.makedirs('./plots/p')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "end = 20\n",
    "DELTA = 0.001\n",
    "n = int(end/DELTA)\n",
    "\n",
    "beta1 = 8.0\n",
    "beta2 = 4.0\n",
    "beta3 = 5.0\n",
    "\n",
    "lambda1 = 0.5\n",
    "lambda2 = 3.0\n",
    "lambda3 = 2.0\n",
    "beta = beta1 + beta2 + beta3\n",
    "\n",
    "p11 = 1.0\n",
    "p12 = 0.06\n",
    "p13 = 0.05\n",
    "\n",
    "p21 = 0.03\n",
    "p22 = 1.0\n",
    "p23 = 0.01\n",
    "\n",
    "p31 = 0.007\n",
    "p32 = 0.005\n",
    "p33 = 1.0\n",
    "\n",
    "\n",
    "eta1 = 0.35\n",
    "eta = 0.3\n",
    "c=0.3\n",
    "d = np.array((n+1)*[0.0])\n",
    "dhat = np.array(n*[0.0])\n",
    "dhat0 = np.array(n*[0.0])\n",
    "\n",
    "d[0] = 1.0\n",
    "B1 = np.array(n*[0.0])\n",
    "B2 = np.array(n*[0.0])\n",
    "B3 = np.array(n*[0.0]) \n",
    "B10 = np.array(n*[0.0])\n",
    "B20 = np.array(n*[0.0])\n",
    "B30 = np.array(n*[0.0]) \n",
    "d = np.array((n+1)*[0.0])\n",
    "dhat = np.array(n*[0.0])\n",
    "dhat0 = np.array(n*[0.0])\n",
    "d1 = np.array((n+1)*[0.0])\n",
    "dhat1 = np.array(n*[0.0])\n",
    "d[0] = 1.0\n",
    "d1[0] = 1.0\n",
    "B1 = np.array(n*[0.0])\n",
    "B2 = np.array(n*[0.0])\n",
    "B3 = np.array(n*[0.0]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "NAME = '-p-'+str(lambda1)+'-'+str(lambda2)+'-'+str(lambda3)+'-'+str(beta1)+ '-' + str(beta2) +'-'+ str(beta3)+'-'+str(p11)+'-' +str(p12)+'-'+str(p13)+'-'+str(p21)+'-'+str(p22)+'-'+str(p23)+ '-'+str(p31)+ '-'+str(p32)+ '-'+str(p33)+ '-'+str(eta1)+ '-'+str(eta) + '.pdf'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "def F1(b1, x): return 1-exp(-lambda1*x/b1)\n",
    "\n",
    "def F2(b2, x): return 1-exp(-lambda2*x/b2)\n",
    "\n",
    "def F3(b3, x): return 1-exp(-lambda3*x/b3)\n",
    "\n",
    "def F12(b1, b2, u):\n",
    "    return (-b1*lambda2*exp(-u*lambda1/b1)+b2*lambda1*exp(-lambda2*u/b2)+b1*lambda2-b2*lambda1)/(b1*lambda2-b2*lambda1)\n",
    "\n",
    "def F13(b1, b3, u):\n",
    "    return (-b1*lambda3*exp(-u*lambda1/b1)+b3*lambda1*exp(-lambda3*u/b3)+b1*lambda3-b3*lambda1)/(b1*lambda3-b3*lambda1)\n",
    "\n",
    "def F23(b2, b3, u):\n",
    "    return (-b2*lambda3*exp(-lambda2*u/b2)+b3*lambda2*exp(-lambda3*u/b3)+b2*lambda3-b3*lambda2)/(b2*lambda3-b3*lambda2)\n",
    "\n",
    "def F123(b1, b2, b3, u):\n",
    "    return (b2**2*lambda1*lambda3*(b1*lambda3-b3*lambda1)*exp(-lambda2*u/b2)-b3**2*lambda1*lambda2*(b1*lambda2-b2*lambda1)*exp(-lambda3*u/b3)-(exp(-u*lambda1/b1)*b1**2*lambda2*lambda3-(b1*lambda3-b3*lambda1)*(b1*lambda2-b2*lambda1))*(b2*lambda3-b3*lambda2))/((b2*lambda3-b3*lambda2)*(b1*lambda3-b3*lambda1)*(b1*lambda2-b2*lambda1))\n",
    "\n",
    "def GR(b1, b2, b3, x):\n",
    "    return (x>0)*(beta1*(1-p12)*(1-p13)*F1(b1, x) + beta2*(1-p21)*(1-p23)*F2(b2, x) + beta3*(1-p31)*(1-p32)*F3(b3, x) + (beta1*p12*(1-p13) + beta2*p21*(1-p23))*F12(b1, b2, x) + (beta1*p13*(1-p12) + beta2*p31*(1-p32))*F13(b1, b3, x) + (beta2*p23*(1-p21)+beta3*p23*(1-p31))*F23(b2, b3, x) + (beta1*p11*p12*p13 + beta2*p21*p22*p23 + beta3*p31*p32*p33)*F123(b1, b2, b3, x))/beta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "F1=numba.jit(F1,nopython = True)\n",
    "F2=numba.jit(F2,nopython = True)\n",
    "F3=numba.jit(F3,nopython = True)\n",
    "\n",
    "F12=numba.jit(F12,nopython = True)\n",
    "F13=numba.jit(F13,nopython = True)\n",
    "F23=numba.jit(F23,nopython = True)\n",
    "\n",
    "F123=numba.jit(F123,nopython = True)\n",
    "GR=numba.jit(GR,nopython = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.jit(nopython = True) \n",
    "def DGR(b1, b2, b3, j):\n",
    "    return GR(b1,b2,b3,j*DELTA)-GR(b1,b2,b3,(j-1)*DELTA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.jit(nopython = True) \n",
    "def DGR1(b, j):\n",
    "    return DGR(b,b,b,j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "def IR(i,b1,b2,b3):\n",
    "    j = np.arange(i+1)\n",
    "    return np.sum(d[i-j]*DGR(b1, b2, b3, j))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.jit(nopython = True) \n",
    "def E(b1,b2,b3): \n",
    "    return ((b3*((p23*(1+(p22-1)*p21)-(p32-1)*p31)*beta2+((1-p31)*p23+(-1+(p33+1)*p32)*p31-p32+1)*beta3+(1+(p11-1)*p12)*p13*beta1)*lambda2+b2*((1+p21*(p22-1)*p23)*beta2+((1-p31)*p23+p31*p32*p33)*beta3+(1+p13*(p11-1))*p12*beta1)*lambda3)*lambda1+lambda2*((p21*(p22-1)*p23+(1-p32)*p31+p21)*beta2+beta3*p31*p32*p33+(1+p13*(p11-1)*p12)*beta1)*lambda3*b1)/(lambda2*lambda3*lambda1*beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "E1 = E(1,1,1)\n",
    "@numba.jit(nopython = True) \n",
    "def pR(b1,b2,b3):\n",
    "    return (1+eta)*beta*E1 - ((1+eta1)*beta*(E1-E(b1,b2,b3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "E1 = E(1,1,1)\n",
    "@numba.jit(nopython = True) \n",
    "def pR1(b):\n",
    "    return pR(b,b,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0%, d(0.0) = 1.0\n",
      "5%, d(1.0) = 1.5011346082663721\n",
      "10%, d(2.0) = 1.887476849720031\n",
      "15%, d(3.0) = 2.2325296433351545\n",
      "20%, d(4.0) = 2.5502669122005397\n",
      "25%, d(5.0) = 2.846611343327067\n",
      "30%, d(6.0) = 3.1257901226829605\n",
      "35%, d(7.0) = 3.3913205046374753\n",
      "40%, d(8.0) = 3.6462273294809453\n",
      "45%, d(9.0) = 3.8931337727808226\n",
      "50%, d(10.0) = 4.1343240020534555\n",
      "55%, d(11.0) = 4.371794422912574\n",
      "60%, d(12.0) = 4.60729717553887\n",
      "65%, d(13.0) = 4.842377330841784\n",
      "70%, d(14.0) = 5.078404749193985\n",
      "75%, d(15.0) = 5.316601386325586\n",
      "80%, d(16.0) = 5.558064705770387\n",
      "85%, d(17.0) = 5.803787789178343\n",
      "90%, d(18.0) = 6.05467659931097\n",
      "95%, d(19.0) = 6.311564819609826\n",
      "100%\n"
     ]
    }
   ],
   "source": [
    "for i in range(n):\n",
    "    def H(b):\n",
    "        pRR = pR1(b[0])\n",
    "        j1 = np.arange(i)\n",
    "        j2 = np.arange(1,i+1)\n",
    "        if pRR>0: return ((c+beta)*d[i]-0.5*beta*sum((d[i-j1]+d[i-j2])*DGR1(b[0], j2)))/pRR\n",
    "        else : return  np.inf\n",
    "    MIN = differential_evolution(H, [(0.000001, 1.0)])#,popsize=30, strategy='rand1exp')\n",
    "    dhat[i] = MIN.fun\n",
    "    d[i+1]=d[i]+DELTA*dhat[i]\n",
    "\n",
    "    B1[i] = MIN.x[0]\n",
    "    #B2[i] = MIN.x[1]\n",
    "   # B3[i] = MIN.x[2]\n",
    "    if i%(n//20)==0: \n",
    "        print(str(round(100*i/n))+'%', end=', ')\n",
    "        print('d('+str(round(i*DELTA,2))+') = '+str(d[i]))\n",
    "print('100%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "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.ylim(.99,1.10)\n",
    "plt.xlim(0,3.08)\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": 182,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = d\n",
    "deltahat = dhat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "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.xlim(8,10)\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "#plt.savefig(\"./plots/ExcessOfLoss/DELTA\" + NAME, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "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,i*DELTA,i)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x,deltahat[0:i])\n",
    "plt.xlabel('$x$', fontsize=20)\n",
    "plt.ylabel(r'$\\hat{V}(x)$', fontsize=20)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "#plt.savefig(\"./plots/ExcessOfLoss/DELTAhat\" +NAME, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "IndMin = np.argmin(deltahat)\n",
    "\n",
    "deltahat[IndMin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.286"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IndMin*DELTA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "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": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vpp=V-x\n",
    "\n",
    "x = np.linspace(0,end,n+1)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x, Vpp)\n",
    "plt.xlabel('$x$', fontsize=20)\n",
    "plt.ylabel(r'$V(x)-x$', fontsize=20)\n",
    "#plt.xlim(0,17.5)\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": 191,
   "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": 194,
   "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],Vpp[IND],B1[IND],B2[IND],B3[IND]],\n",
    "                  index=['x','V_ppp','ppp_Line1','ppp_Line2','ppp_Line3']).T\n",
    "DF.to_csv('onep_20_0.02.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0%, d(0.0) = 0.0\n",
      "5%, d(1.0) = -0.0111203585217865\n",
      "10%, d(2.0) = -0.011773120072305687\n",
      "15%, d(3.0) = -0.011636656604537166\n",
      "20%, d(4.0) = -0.011263971274047435\n",
      "25%, d(5.0) = -0.010807827271236192\n",
      "30%, d(6.0) = -0.010335241870762957\n",
      "35%, d(7.0) = -0.00989253849431293\n",
      "40%, d(8.0) = -0.00950972243765591\n",
      "45%, d(9.0) = -0.009195762885894965\n",
      "50%, d(10.0) = -0.00895301455778963\n",
      "55%, d(11.0) = -0.008769128086839828\n",
      "60%, d(12.0) = -0.008653273970935516\n",
      "65%, d(13.0) = -0.04322084942270976\n",
      "70%, d(14.0) = -0.17481031489245424\n",
      "75%, d(15.0) = -0.3660561656583923\n",
      "80%, d(16.0) = -0.5931556128744546\n",
      "85%, d(17.0) = -0.8418971887060138\n",
      "90%, d(18.0) = -1.1037892827591236\n",
      "95%, d(19.0) = -1.3736484387596875\n",
      "100%\n"
     ]
    }
   ],
   "source": [
    "supL = np.array(n*[0.0])\n",
    "B1 = np.array(n*[0.0])\n",
    "B2 = np.array(n*[0.0])\n",
    "B3 = np.array(n*[0.0])\n",
    "\n",
    "for i in range(n):\n",
    "    def nL(b):       \n",
    "        j = np.arange(i+1)\n",
    "        pRR = pR1(b[0])\n",
    "        if pRR>0: return -(pRR*Vp[i]-(c+beta)*V[i] + beta*np.sum(V[i-j]*DGR1(b[0],j)))\n",
    "        else : return  np.inf\n",
    "    MIN = differential_evolution(nL, [(0.000001, 1.0)])#,popsize=30, strategy='rand1exp')\n",
    "    supL[i] = -MIN.fun\n",
    "    #d[i+1]=d[i]+DELTA*dhat[i]\n",
    "    B1[i] = MIN.x[0]\n",
    "    if i%(n//20)==0: \n",
    "        print(str(round(100*i/n))+'%', end=', ')\n",
    "        print('d('+str(round(i*DELTA,2))+') = '+str(supL[i]))\n",
    "print('100%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "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": 195,
   "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": 197,
   "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],supL,1-Vp, B1[IND],B2[IND],B3[IND]],\n",
    "                  index=['x','L','ppp_Line1','1-V','ppp_Line2','ppp_Line3']).T\n",
    "DF.to_csv('TestOneP.csv')"
   ]
  },
  {
   "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": [
    "delta = d/d[n]\n",
    "deltahat = dhat/d[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0,end,n+1)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x,delta)\n",
    "plt.xlabel('$x$', fontsize=25)\n",
    "plt.ylabel(r'$\\delta(x)$', fontsize=25)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.savefig(\"./plots/p/DELTA\" +NAME, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0,end,n)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x,deltahat)\n",
    "plt.xlabel('$x$', fontsize=25)\n",
    "plt.ylabel(r'$\\hat{\\delta}(x)$', fontsize=30)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.savefig(\"./plots/p/DELTAhat\" +NAME, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = n\n",
    "x = np.arange(m)*DELTA\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x,B1[0:m],label='$b_1(x)$',linestyle='--')\n",
    "plt.plot(x,B2[0:m],label='$b_2(x)$')\n",
    "plt.plot(x,B3[0:m],label='$b_3(x)$',linestyle='-.')\n",
    "plt.xlabel('$x$', fontsize=25)\n",
    "plt.axhline(y=0, color='k');plt.axvline(x=0, color='k')\n",
    "plt.grid( color='0.7', linestyle='--')\n",
    "plt.legend(fontsize=16)\n",
    "plt.savefig(\"./plots/p/RE\" +NAME, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = np.array((n+1)*[0.0])\n",
    "dhat1 = np.array(n*[0.0])\n",
    "d1[0] = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def IR1(i,b1,b2,b3):\n",
    "    j = np.arange(i+1)\n",
    "    return np.sum(d1[i-j]*DGR(b1, b2, b3, j))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(n):\n",
    "    def H(b):\n",
    "        pRR = pR(b[0],b[0],b[0])\n",
    "        if pRR>0: return beta*(d1[i]-IR1(i,b[0],b[0],b[0]))/pRR\n",
    "        else : return    np.inf\n",
    "    MIN = differential_evolution(H, [(0, 1)],tol=0.0005)\n",
    "    dhat1[i] = MIN.fun\n",
    "    d1[i+1]=d1[i]+DELTA*dhat1[i]\n",
    "    if i%(n//20)==0: \n",
    "        print(str(round(100*i/n))+'%', end=', ')\n",
    "print('100%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta1 = d1/d1[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0,end,n+1)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(x,delta,label=r'$\\delta$')\n",
    "plt.plot(x,delta1,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": [
    "import pandas as pd\n",
    "DF = pd.DataFrame([delta,delta1[0:(n+1)]],index=['delta','delta1']).T\n",
    "DF.to_csv('proportional.csv')"
   ]
  },
  {
   "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": []
  }
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