{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0001f5af",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import newton"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2c99e193",
   "metadata": {},
   "outputs": [],
   "source": [
    "def logic(x,r):\n",
    "        return r*x*(1-x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ee8189f",
   "metadata": {},
   "source": [
    "# Caso r<3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "683ca3f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "a=[]\n",
    "b=[]\n",
    "N=20\n",
    "x0=0.6\n",
    "r=2.7\n",
    "aux=x0\n",
    "for i in range(N):\n",
    "    a.append(aux)\n",
    "    aux=logic(aux,r)\n",
    "    b.append(aux)\n",
    "    a.append(aux)\n",
    "    b.append(aux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7fcd1cba",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1cea921ce50>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(a,b)\n",
    "#plt.plot(a2,b2)\n",
    "plt.plot(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),np.linspace(min(min(a),min(b)),max(max(a),max(b)),100))\n",
    "plt.plot(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),logic(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),r))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "625f27cb",
   "metadata": {},
   "source": [
    "# Caso r<3 comparativo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5e847d13",
   "metadata": {},
   "outputs": [],
   "source": [
    "a=[]\n",
    "b=[]\n",
    "N=70\n",
    "x0=0.6\n",
    "r=2.6\n",
    "aux=x0\n",
    "for i in range(N):\n",
    "    a.append(aux)\n",
    "    aux=logic(aux,r)\n",
    "    b.append(aux)\n",
    "    a.append(aux)\n",
    "    b.append(aux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "caf6a0ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "aux2=x0+0.001\n",
    "a2=[]\n",
    "b2=[]\n",
    "for i in range(N):\n",
    "    a2.append(aux2)\n",
    "    aux2=logic(aux2,r)\n",
    "    b2.append(aux2)\n",
    "    a2.append(aux2)\n",
    "    b2.append(aux2)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ec52a01e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1cea930dfa0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(a,b)\n",
    "plt.plot(a2,b2)\n",
    "plt.plot(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),np.linspace(min(min(a),min(b)),max(max(a),max(b)),100))\n",
    "plt.plot(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),logic(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),r))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79c1e74a",
   "metadata": {},
   "source": [
    "# Caso r>3 comparativo (caótico)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "52a7ef74",
   "metadata": {},
   "outputs": [],
   "source": [
    "a=[]\n",
    "b=[]\n",
    "N=70\n",
    "x0=0.6\n",
    "r=3.6\n",
    "aux=x0\n",
    "for i in range(N):\n",
    "    a.append(aux)\n",
    "    aux=logic(aux,r)\n",
    "    b.append(aux)\n",
    "    a.append(aux)\n",
    "    b.append(aux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f511e4db",
   "metadata": {},
   "outputs": [],
   "source": [
    "aux2=x0+0.001\n",
    "a2=[]\n",
    "b2=[]\n",
    "for i in range(N):\n",
    "    a2.append(aux2)\n",
    "    aux2=logic(aux2,r)\n",
    "    b2.append(aux2)\n",
    "    a2.append(aux2)\n",
    "    b2.append(aux2)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "790c8867",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1cea9379880>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(a,b)\n",
    "plt.plot(a2,b2)\n",
    "plt.plot(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),np.linspace(min(min(a),min(b)),max(max(a),max(b)),100))\n",
    "plt.plot(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),logic(np.linspace(min(min(a),min(b)),max(max(a),max(b)),100),r))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac79f19c",
   "metadata": {},
   "source": [
    "# Clase Matriz de Leslie"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f375870",
   "metadata": {},
   "source": [
    "### Conejos de Fibonacci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "85b67e4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 1], [1, 0]]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matriz_c=[[1,1],[1,0]]\n",
    "Matriz_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0a349539",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.61803399 -0.61803399]\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.eig(Matriz_c)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "617059fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.618033988749895"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1+np.sqrt(5))/2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cc5ced0",
   "metadata": {},
   "source": [
    "El máximo es el primer valor propio y su vector asociado sera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "33054d2c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.85065081 0.52573111]\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.eig(Matriz_c)[1].T[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2553e3f0",
   "metadata": {},
   "source": [
    "$x_n= A_1 \\lambda_1^n + A_2 \\lambda_2^n$\n",
    "\n",
    "$1=x_0=A_1 + A_2 $\n",
    "\n",
    "$1=x_1=A_1 \\lambda_1 + A_2 \\lambda_2 $\n",
    "\n",
    "Reemplazando $1=A_1 \\lambda _1 + (1-A_1) \\lambda_2=\\lambda_2+A_1\\sqrt{5}=\\dfrac{1-\\sqrt{5}}{2}+A_1\\sqrt{5} $, \n",
    "\n",
    "por lo que $A_1=\\dfrac{1+\\sqrt{5}}{2\\sqrt{5}}$ y $A_2=\\dfrac{\\sqrt{5}-1}{2\\sqrt{5}}$ \n",
    "\n",
    "Finalmente para $n$ grande $x_n\\approx \\dfrac{1+\\sqrt{5}}{2\\sqrt{5}}\\left(\\dfrac{1+\\sqrt{5}}{2}\\right)^n$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e985de48",
   "metadata": {},
   "source": [
    "### Comparacion con http://bandicoot.maths.adelaide.edu.au/Leslie_matrix/leslie.cgi?initial_pop[0]=0&initial_pop[1]=100&initial_pop[2]=100&initial_pop[3]=100&initial_pop[4]=0&initial_pop[5]=0&initial_pop[6]=0&initial_pop[7]=0&birth_rates[0]=0&birth_rates[1]=0&birth_rates[2]=0.8&birth_rates[3]=0.5&birth_rates[4]=0&birth_rates[5]=0&birth_rates[6]=0&birth_rates[7]=0&survival_rates[0]=0.95&survival_rates[1]=0.9&survival_rates[2]=0.739&survival_rates[3]=0&survival_rates[4]=0&survival_rates[5]=0&survival_rates[6]=0&survival_rates[7]=0&Submit+Leslie+Matrix=Submit+Leslie+Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c5a75256",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Numpy\n",
      "0.019802032589678185\n",
      "\n",
      "\n",
      "Original Pagina\n",
      "0.01980262729617973\n",
      "\n",
      "\n",
      "Newton\n",
      "0.0198020325896784\n",
      "\n",
      "\n",
      "Aproximado\n",
      "0.019145084934558642\n",
      "\n",
      "\n",
      "Explota\n"
     ]
    }
   ],
   "source": [
    "m=[0,0,0.8,0.6]\n",
    "s=[1,0.95,0.9,0.75]\n",
    "l=[]\n",
    "f=[]\n",
    "aux=1\n",
    "for i in range(len(s)):\n",
    "    aux=aux*s[i]\n",
    "    l.append(aux)\n",
    "    f.append(l[i]*m[i])\n",
    "def F(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))\n",
    "    return aux2\n",
    "def Fp(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))*(-(i+1))\n",
    "    return aux2\n",
    "def F2(r):\n",
    "    return F(r)-1\n",
    "\n",
    "r=np.log(1.02)\n",
    "\n",
    "N=len(s)\n",
    "M=np.zeros((N,N))\n",
    "M[0]=m\n",
    "for i in range(N-1):\n",
    "    M[i+1][i]=s[i+1]\n",
    "print(\"Original Numpy\")\n",
    "print(np.log(max(abs(np.linalg.eig(M)[0]))))\n",
    "print(\"\\n\")\n",
    "print(\"Original Pagina\")\n",
    "print(r)\n",
    "print(\"\\n\")\n",
    "print( \"Newton\")\n",
    "print(newton(F2, 0))\n",
    "print(\"\\n\")\n",
    "print( \"Aproximado\")\n",
    "print((1-F(0))/Fp(0))\n",
    "print(\"\\n\")\n",
    "print( \"Explota\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "77d150b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Numpy\n",
      "-0.05208964748385038\n",
      "\n",
      "\n",
      "Original Pagina\n",
      "-0.052346480372209236\n",
      "\n",
      "\n",
      "Newton\n",
      "-0.05208964748385024\n",
      "\n",
      "\n",
      "Aproximado\n",
      "-0.05854175316452894\n",
      "\n",
      "\n",
      "Se extingue\n"
     ]
    }
   ],
   "source": [
    "m=[0,0,0.2,0.3,0.5,0.1,0]\n",
    "s=[1,1,0.95,0.95,0.7,0.4,0.2]\n",
    "l=[]\n",
    "f=[]\n",
    "aux=1\n",
    "for i in range(len(s)):\n",
    "    aux=aux*s[i]\n",
    "    l.append(aux)\n",
    "    f.append(l[i]*m[i])\n",
    "def F(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))\n",
    "    return aux2\n",
    "def Fp(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))*(-(i+1))\n",
    "    return aux2\n",
    "def F2(r):\n",
    "    return F(r)-1\n",
    "\n",
    "r=np.log(0.949)\n",
    "\n",
    "N=len(s)\n",
    "M=np.zeros((N,N))\n",
    "M[0]=m\n",
    "for i in range(N-1):\n",
    "    M[i+1][i]=s[i+1]\n",
    "print(\"Original Numpy\")\n",
    "print(np.log(max(abs(np.linalg.eig(M)[0]))))\n",
    "print(\"\\n\")\n",
    "print(\"Original Pagina\")\n",
    "print(r)\n",
    "print(\"\\n\")\n",
    "print( \"Newton\")\n",
    "print(newton(F2, 0))\n",
    "print(\"\\n\")\n",
    "print( \"Aproximado\")\n",
    "print((1-F(0))/Fp(0))\n",
    "print(\"\\n\")\n",
    "print( \"Se extingue\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8cd02a8f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Numpy\n",
      "-2.337279352769967e-05\n",
      "\n",
      "\n",
      "Original Pagina\n",
      "-2.4000288004632086e-05\n",
      "\n",
      "\n",
      "Newton\n",
      "-2.3372792509843604e-05\n",
      "\n",
      "\n",
      "Aproximado\n",
      "-2.3373717084514114e-05\n",
      "\n",
      "\n",
      "Converge\n"
     ]
    }
   ],
   "source": [
    "m=[0,0,0.8,0.5]\n",
    "s=[1,0.95,0.9,0.739]\n",
    "l=[]\n",
    "f=[]\n",
    "aux=1\n",
    "for i in range(len(s)):\n",
    "    aux=aux*s[i]\n",
    "    l.append(aux)\n",
    "    f.append(l[i]*m[i])\n",
    "def F(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))\n",
    "    return aux2\n",
    "def Fp(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))*(-(i+1))\n",
    "    return aux2\n",
    "\n",
    "def F2(r):\n",
    "    return F(r)-1\n",
    "\n",
    "r=np.log(0.999976)\n",
    "\n",
    "N=len(s)\n",
    "M=np.zeros((N,N))\n",
    "M[0]=m\n",
    "for i in range(N-1):\n",
    "    M[i+1][i]=s[i+1]\n",
    "print(\"Original Numpy\")\n",
    "print(np.log(max(abs(np.linalg.eig(M)[0]))))\n",
    "print(\"\\n\")\n",
    "print(\"Original Pagina\")\n",
    "print(r)\n",
    "print(\"\\n\")\n",
    "print( \"Newton\")\n",
    "print(newton(F2, 0))\n",
    "print(\"\\n\")\n",
    "print( \"Aproximado\")\n",
    "print((1-F(0))/Fp(0))\n",
    "print(\"\\n\")\n",
    "print( \"Converge\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee0d5ba0",
   "metadata": {},
   "source": [
    "### Ejercicio 1.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f0aaae87",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El R_0 es: 5.90430658\n",
      "El r_1 aproximado es: 0.20543241493649214\n",
      "Newton: 0.4836376675564584\n"
     ]
    }
   ],
   "source": [
    "l=[1.0000,0.8335, 0.7313, 0.5881 ,0.4334 ,0.2928 ,0.1813 ,0.1029 ,0.0535,0.0255]\n",
    "m=[0.0000,0.6504,2.3939,2.9727,2.4662,1.7043,1.0815,0.6683,0.4286,0.300]\n",
    "f=[]\n",
    "for i in range(len(l)):\n",
    "    f.append(l[i]*m[i])\n",
    "def F(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))\n",
    "    return aux2\n",
    "def Fp(r):\n",
    "    aux2=0\n",
    "    for i in range(len(f)):\n",
    "        aux2=aux2+f[i]*np.exp(r*(-(i+1)))*(-(i+1))\n",
    "    return aux2\n",
    "print(\"El R_0 es:\",F(0))\n",
    "print(\"El r_1 aproximado es:\",(1-F(0))/(Fp(0)))\n",
    "print( \"Newton:\",newton(F2, 0))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "82c6a595",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Numpy\n",
      "0.48363766755645826\n"
     ]
    }
   ],
   "source": [
    "s=[l[0]]\n",
    "for i in range(1,len(l)):\n",
    "    s.append(l[i]/l[i-1])\n",
    "N=len(s)\n",
    "M=np.zeros((N,N))\n",
    "M[0]=m\n",
    "for i in range(N-1):\n",
    "    M[i+1][i]=s[i+1]\n",
    "print(\"Original Numpy\")\n",
    "print(np.log(max(abs(np.linalg.eig(M)[0]))))"
   ]
  }
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