Untitled3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "end = 20\n",
    "DELTA = 0.01\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",
    "\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": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Fp(b1, x): return 1-exp(-lambda1*x/b1)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0002497813463256948"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DGR1(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.jit(nopython = True) \n",
    "def DGR1(b1, j):\n",
    "    return -exp(-lambda1*j*DELTA/b1)+exp(-lambda1*(j-1)*DELTA/b1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.jit(nopython = True) \n",
    "def E(b1): \n",
    "    return b1/lambda1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "E1 = E(1)\n",
    "@numba.jit(nopython = True) \n",
    "def pR1(b1):\n",
    "    return (1+eta)*beta1*E1 - ((1+eta1)*beta1*(E1-E(b1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0%, d(0.0) = 1.0\n",
      "5%, d(1.0) = 1.3836822865605507\n",
      "10%, d(2.0) = 1.7400551493181173\n",
      "15%, d(3.0) = 2.0741783538479446\n",
      "20%, d(4.0) = 2.390474160971868\n",
      "25%, d(5.0) = 2.6928186680859003\n",
      "30%, d(6.0) = 2.984620738168696\n",
      "35%, d(7.0) = 3.2688901801324857\n",
      "40%, d(8.0) = 3.548296607270865\n",
      "45%, d(9.0) = 3.8252203458992105\n",
      "50%, d(10.0) = 4.101796496654805\n",
      "55%, d(11.0) = 4.37995304862694\n",
      "60%, d(12.0) = 4.661443965028875\n",
      "65%, d(13.0) = 4.94787788001531\n",
      "70%, d(14.0) = 5.240743063236855\n",
      "75%, d(15.0) = 5.541429090121759\n",
      "80%, d(16.0) = 5.851245938932979\n",
      "85%, d(17.0) = 6.171440489685755\n",
      "90%, d(18.0) = 6.503211204450849\n",
      "95%, d(19.0) = 6.8477208954194095\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+beta1)*d[i]-0.5*beta1*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": 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, 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": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = d\n",
    "deltahat = dhat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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": 50,
   "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": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27638540773597886"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IndMin = np.argmin(deltahat)\n",
    "\n",
    "deltahat[IndMin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.16"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IndMin*DELTA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "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": 54,
   "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": [
    "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": 55,
   "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": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0%, d(0.0) = 0.14497598717096077\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/khaled/.local/lib/python3.8/site-packages/scipy/optimize/_numdiff.py:497: RuntimeWarning: invalid value encountered in subtract\n",
      "  df = fun(x) - f0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5%, d(1.0) = 3.434795921615887\n",
      "10%, d(2.0) = 4.5943990451244545\n",
      "15%, d(3.0) = 5.669588976333905\n",
      "20%, d(4.0) = 6.694273440213095\n",
      "25%, d(5.0) = 7.659763155606939\n",
      "30%, d(6.0) = 8.585862519887215\n",
      "35%, d(7.0) = 9.477365960542727\n",
      "40%, d(8.0) = 10.356058878342068\n",
      "45%, d(9.0) = 11.179682066822792\n",
      "50%, d(10.0) = 12.061998178811805\n",
      "55%, d(11.0) = 12.784544083615202\n",
      "60%, d(12.0) = 13.786033139601585\n",
      "65%, d(13.0) = 14.641274555672368\n",
      "70%, d(14.0) = 15.494231123924152\n",
      "75%, d(15.0) = 16.349453213973874\n",
      "80%, d(16.0) = 17.202351139929448\n",
      "85%, d(17.0) = 18.06642614002334\n",
      "90%, d(18.0) = 18.922193329972288\n",
      "95%, d(19.0) = 19.77963212361948\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+beta1)*V[i] + beta1*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": 58,
   "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": 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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}