onePcommonshock-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "end = 30\n",
    "DELTA = 0.005\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])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#def H(x): return (x>=0)*1\n",
    "\n",
    "def F1(a1, x): return 1-exp(-lambda1*x/a1)\n",
    "\n",
    "def F2(a2, x): return 1-exp(-lambda2*x/a2)\n",
    "\n",
    "#def F3(b3, x): return 1-exp(-lambda3*x/b3)\n",
    "\n",
    "def F12(a1, a2, u):\n",
    "    return (-a1*lambda2*exp(-u*lambda1/a1)+a2*lambda1*exp(-lambda2*u/a2)+a1*lambda2-a2*lambda1)/(a1*lambda2-a2*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",
    "def ER12(a1, a2):\n",
    "    return (a1/lambda1+a2/lambda2)\n",
    "\n",
    "\n",
    "\n",
    "def GR(a1,a2,x):\n",
    "    return (x>0)*(beta1*F1(a1,x) + beta2*F2(a2,x) + beta3*F12(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",
    "E1 = EGR(1,1)\n",
    "def pR(a1,a2):\n",
    "    return (1+eta)*beta*E1 - ((1+eta1)*beta*(E1-EGR(a1,a2)))\n",
    "\n",
    "def DGR1(a, j):\n",
    "    return GR(a,a,j*DELTA)-GR(a,a,(j-1)*DELTA)\n",
    "\n",
    "def pR1(a):\n",
    "    return pR(a,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#H    = numba.autojit(H,    nopython=True)\n",
    "F1  = numba.autojit(F1,  nopython=True)\n",
    "F2  = numba.autojit(F2,  nopython=True)\n",
    "F12 = numba.autojit(F12, 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)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0%, d(0.0) = 1.0\n",
      "5%, d(1.5) = 1.4782235103650043\n",
      "10%, d(3.0) = 1.8833182185721442\n",
      "15%, d(4.5) = 2.245683698738291\n",
      "20%, d(6.0) = 2.573502273438524\n",
      "25%, d(7.5) = 2.8727679334768133\n",
      "30%, d(9.0) = 3.148528903708788\n",
      "35%, d(10.5) = 3.4050822023766183\n",
      "40%, d(12.0) = 3.64609168880719\n",
      "45%, d(13.5) = 3.874685560563639\n",
      "50%, d(15.0) = 4.093538859028409\n",
      "55%, d(16.5) = 4.304943397325772\n",
      "60%, d(18.0) = 4.510867046490477\n",
      "65%, d(19.5) = 4.713003991635622\n",
      "70%, d(21.0) = 4.912817356039087\n",
      "75%, d(22.5) = 5.111575335732979\n",
      "80%, d(24.0) = 5.3103818661269315\n",
      "85%, d(25.5) = 5.510202601301696\n",
      "90%, d(27.0) = 5.711887011828197\n",
      "95%, d(28.5) = 5.916187100702831\n",
      "100%\n"
     ]
    }
   ],
   "source": [
    "for i in range(n):\n",
    "    def H(a):\n",
    "        pRR = pR1(a[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(a[0], j2)))/pRR\n",
    "        else : return  np.inf\n",
    "    MIN = differential_evolution(H, [(0.0001, 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": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = d/d[n]\n",
    "deltahat = dhat/d[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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": 8,
   "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": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "IndMin = np.argmin(deltahat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02162161842872482"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltahat[IndMin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.41"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IndMin*DELTA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "V_pcommon = V-x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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_pcommon)\n",
    "plt.xlabel('$x$', fontsize=20)\n",
    "plt.ylabel(r'$V(x)$', 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": 15,
   "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": 16,
   "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_pcommon[IND],B1[IND],B2[IND]],\n",
    "                  index=['x','V','Line1','Line2']).T\n",
    "DF.to_csv('onePcommon_30_0.005.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0%, d(0.0) = -8.881784197001252e-16\n",
      "5%, d(0.5) = 1.7763568394002505e-15\n",
      "10%, d(1.0) = 3.552713678800501e-15\n",
      "15%, d(1.5) = 7.105427357601002e-15\n",
      "20%, d(2.0) = 7.105427357601002e-15\n",
      "25%, d(2.5) = -0.013434238445213964\n",
      "30%, d(3.0) = -0.10076479505692149\n",
      "35%, d(3.5) = -0.22657627881026343\n",
      "40%, d(4.0) = -0.36742485464110786\n",
      "45%, d(4.5) = -0.5140017894141735\n",
      "50%, d(5.0) = -0.6627299196394745\n",
      "55%, d(5.5) = -0.8122592146954162\n",
      "60%, d(6.0) = -0.9620854249827957\n",
      "65%, d(6.5) = -1.1120213514087212\n",
      "70%, d(7.0) = -1.2619977488395904\n",
      "75%, d(7.5) = -1.4119890589738304\n",
      "80%, d(8.0) = -1.5619858605966073\n",
      "85%, d(8.5) = -1.7119846836325507\n",
      "90%, d(9.0) = -1.8619842505743094\n",
      "95%, d(9.5) = -2.0119840912438036\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(a):\n",
    "        j = np.arange(i+1)\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  np.inf\n",
    "    MIN = differential_evolution(nL, [(0.0001, 1.0), (0.0001, 1.0)])#,popsize=30, strategy='rand1exp')\n",
    "    supL[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(supL[i]))\n",
    "print('100%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "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
}