ppp_thinning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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",
    "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": [
    "if not os.path.exists('./plots/p'): os.makedirs('./plots/p')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "end = 20\n",
    "DELTA = 0.02\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": 4,
   "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": 5,
   "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": 6,
   "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": 7,
   "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": 8,
   "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": 9,
   "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)\n",
    "\n",
    "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": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0%, d(0.0) = 1.0\n",
      "5%, d(1.0) = 1.3898629462814867\n",
      "10%, d(2.0) = 1.7365785141277092\n",
      "15%, d(3.0) = 2.0510691341842526\n",
      "20%, d(4.0) = 2.341005615979088\n",
      "25%, d(5.0) = 2.6115844379252193\n",
      "30%, d(6.0) = 2.866612595370824\n",
      "35%, d(7.0) = 3.109273926941671\n",
      "40%, d(8.0) = 3.3423103034600112\n",
      "45%, d(9.0) = 3.568101175941171\n",
      "50%, d(10.0) = 3.7887196949396684\n",
      "55%, d(11.0) = 4.005978854879323\n",
      "60%, d(12.0) = 4.221470715733588\n",
      "65%, d(13.0) = 4.436599962984798\n",
      "70%, d(14.0) = 4.6526126682687154\n",
      "75%, d(15.0) = 4.8706209538027965\n",
      "80%, d(16.0) = 5.091624156545627\n",
      "85%, d(17.0) = 5.316527001054076\n",
      "90%, d(18.0) = 5.546155216355802\n",
      "95%, d(19.0) = 5.781268969281028\n",
      "100%\n"
     ]
    }
   ],
   "source": [
    "for i in range(n):\n",
    "    def H(b):\n",
    "        pRR = pR(b[0],b[1],b[2])\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])*DGR(b[0], b[1], b[2], j2)))/pRR\n",
    "        else : return  np.inf\n",
    "    MIN = differential_evolution(H, [(0.01, 1.0), (0.01, 1.0),(0.01, 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": 13,
   "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": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = d\n",
    "deltahat = dhat"
   ]
  },
  {
   "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,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'$\\hat{\\delta}(x)$', 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": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "IndMin = np.argmin(deltahat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21504377134514227"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deltahat[IndMin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.26"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IndMin*DELTA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vppp=V-x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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, Vppp)\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": 22,
   "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],Vppp[IND],B1[IND],B2[IND],B3[IND]],\n",
    "                  index=['x','V_ppp','ppp_Line1','ppp_Line2','ppp_Line3']).T\n",
    "DF.to_csv('ppp_20_0.02.csv')"
   ]
  },
  {
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}