OU-Acorr-manuale-e+6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c7f80873-306a-4f53-8944-42df92f2bad3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random \n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np \n",
    "import scipy\n",
    "\n",
    "\n",
    "#inizialmente pensavo di inserire i parametri da un file o da tastiera, tuttavia ho pensato che considerando che i parametri sono soltanto quattro e che il Python è precompilato sarebbe stato più veloce cambiarli direttamente nel codice qui sotto.\n",
    "t = 1000000 #int(input()) #tempo totale della simulazione\n",
    "n = 100 #int(input()) #numero di intervalli per ogni step\n",
    "x0 = 0 #float(input()) #valore iniziale\n",
    "gamma = 0.1 #float(input()) #valore di gamma, 0.1 fa ottenere buoni risultati\n",
    "\n",
    "dt = 1/n #lasso di tempo per ogni intervallo\n",
    "N = t*n #numero totali di punti"
   ]
  },
  {
   "cell_type": "raw",
   "id": "03c4ea94-015a-426a-ae04-12f96c70785a",
   "metadata": {},
   "source": [
    "plt.style.use(['science','notebook','grid'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e848056a-3a27-4847-9ae4-e4001d2fd6d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = np.zeros(N) #creo un array vuoto pieno di zeri\n",
    "\n",
    "for i in range(0,N):\n",
    "    Z[i] = random.gauss(0,2*dt) #popolo Z di numeri generati gaussianamente, la media è 0 e la varianza 2*dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "30b0a214-a4b2-46c8-b5a1-411abf88f2b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualizziamo Z per vedere se è effettivamente la gaussiana voluta\n",
    "wts1 = np.ones_like(Z) / len(Z) #np.ones_like(Z) crea un array lungo quanto Z ma popolato solo da 1s, è una normalizzazione\n",
    "\n",
    "plt.title(\"gaussiana\")\n",
    "plt.xlabel(\"valori\")\n",
    "plt.ylabel(\"frequenza\")\n",
    "plt.hist(Z,200,weights=wts1) #weights è il fattore moltiplicativo dato ad ogni valore\n",
    "plt.show() #in una IDE non serve a niente, da terminale meglio metterlo perchè a volte non mostra i grafici nonostante li computi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2178d82f-e33e-4ab5-8252-64a75593bd00",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.zeros(N) #creo un array vuoto piena di zeri\n",
    "x[0] = x0 #ci aggiungo l'elemento x0\n",
    "\n",
    "for i in range(0,N-1):\n",
    "    xplus1 = x[i] - (gamma * x[i] * dt) + Z[i] #eulero, qui calcolo l'elemento x[i+1] basandomi su x del passo precedente, h=gamma*x, g=1\n",
    "    x[i+1] = xplus1 #qui popolo x con gli elementi x[i+1] trovati"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "407f8e86-da80-482e-995f-889dd4ca2278",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualizziamo l'andamento dei punti\n",
    "plt.title(\"andamento temporale dei punti x\")\n",
    "plt.xlabel(\"tempo\")\n",
    "plt.ylabel(\"x\")\n",
    "plt.plot(x) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fc950556-202a-4792-86c1-48b92dc32046",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualizziamo la distribuzione dei punti, normalizzata\n",
    "wts2 = np.ones_like(x) / len(x) #np.ones_like(x) crea un array lungo quanto x ma popolato solo da 1s\n",
    "\n",
    "plt.title(\"distribuzione normalizzata dei punti\")\n",
    "plt.xlabel(\"punti\")\n",
    "plt.ylabel(\"frequenza\")\n",
    "plt.hist(x,200, weights=wts2)  #weights è il fattore moltiplicativo dato ad ogni valore\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d30a90e2-f737-464b-9437-d85cb2e79e7b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la media è: 0.0026434792467116656\n",
      "la varianza è: 0.20080686252295873\n"
     ]
    }
   ],
   "source": [
    "print(\"la media è:\", np.mean(x))\n",
    "print(\"la varianza è:\", np.var(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0666c4c0-7cd5-4de5-bb16-1156c281f78b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000000\n"
     ]
    }
   ],
   "source": [
    "print(len(x))"
   ]
  },
  {
   "cell_type": "raw",
   "id": "cf2e75f0-bebc-430e-945d-c15ecfd35a5b",
   "metadata": {},
   "source": [
    "acorr = []\n",
    "lags = range(10000)\n",
    "norm = float(np.correlate(x,x))\n",
    "acorr = []\n",
    "x1 = x\n",
    "x2 = x"
   ]
  },
  {
   "cell_type": "raw",
   "id": "639857db-dcea-482b-95d5-4cbc926907a5",
   "metadata": {
    "tags": []
   },
   "source": [
    "acorr.append(norm)\n",
    "\n",
    "for lag in lags:\n",
    "    #for i in range(n):\n",
    "        #x1 = np.delete(x1, 0)\n",
    "        #x2 = np.delete(x2, -1)\n",
    "    x1 = np.delete(x1, 0)\n",
    "    x2 = np.delete(x2, -1)    \n",
    "    val = float(np.correlate(x1,x2))\n",
    "    acorr.append(val)\n"
   ]
  },
  {
   "cell_type": "raw",
   "id": "81d90b31-6bf9-4b5a-8949-b588af972c49",
   "metadata": {},
   "source": [
    "acorrnorm = np.array(acorr)\n",
    "acorrnorm = acorrnorm / norm\n",
    "acorrnorm = np.delete(acorrnorm, -1)"
   ]
  },
  {
   "cell_type": "raw",
   "id": "dea7fdef-aed7-4c40-a208-39839d63bbd4",
   "metadata": {},
   "source": [
    "plt.figure(figsize=(8,6)) #must come BEFORE the actual plot\n",
    "plt.plot(lags, acorrnorm) #Alpha is the opacity, density is the normalization\n",
    "#plt.errorbar(x, y, yerr, ls='', color='k')\n",
    "#plt.scatter(x, y, color='k', s=30, zorder=1000)\n",
    "#plt.locator_params(y=20) this is about the density of thicks on both axis I could add <, axis='x'> inside the parentesis, to do just for one axis\n",
    "plt.xlabel('100 lags')\n",
    "plt.ylabel('Autocorrelation')\n",
    "plt.title('Autocorrelation curve')\n",
    "plt.yscale('log')\n",
    "plt.xscale('linear')\n",
    "#plt.xlim(0,3000) #questo limita l'asse x\n",
    "#plt.ylim(0.1 ,1) #questo limite superiormente l'asse y\n",
    "#plt.savefig('curva_gain1_log.jpg') #always save before plt.show() it should be \"namefile.png\" or \"namefile.pdf\"\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "raw",
   "id": "9c59c8fd-e4ee-4c77-a278-5dee78f8cecf",
   "metadata": {},
   "source": [
    "plt.figure(figsize=(8,6)) #must come BEFORE the actual plot\n",
    "plt.plot(lags, acorrnorm) #Alpha is the opacity, density is the normalization\n",
    "#plt.errorbar(x, y, yerr, ls='', color='k')\n",
    "#plt.scatter(x, y, color='k', s=30, zorder=1000)\n",
    "#plt.locator_params(y=20) this is about the density of thicks on both axis I could add <, axis='x'> inside the parentesis, to do just for one axis\n",
    "plt.xlabel('100 lags')\n",
    "plt.ylabel('Autocorrelation')\n",
    "plt.title('Autocorrelation curve')\n",
    "plt.yscale('log')\n",
    "plt.xscale('linear')\n",
    "plt.xlim(0,3000) #questo limita l'asse x\n",
    "plt.ylim(0.1 ,1) #questo limite superiormente l'asse y\n",
    "#plt.savefig('curva_gain1_log.jpg') #always save before plt.show() it should be \"namefile.png\" or \"namefile.pdf\"\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cb8930e3-b705-46de-9fdb-87c6a258552d",
   "metadata": {},
   "outputs": [],
   "source": [
    "acorr = []\n",
    "lags = range(100)\n",
    "norm = float(np.correlate(x,x))\n",
    "acorr = []\n",
    "x1 = x\n",
    "x2 = x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4501815c-f986-459e-b357-1d15283dfc11",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[10], line 5\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m lag \u001b[38;5;129;01min\u001b[39;00m lags:\n\u001b[1;32m      4\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n):\n\u001b[0;32m----> 5\u001b[0m         x1 \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdelete\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      6\u001b[0m         x2 \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mdelete(x2, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m      7\u001b[0m     \u001b[38;5;66;03m#x1 = np.delete(x1, 0)\u001b[39;00m\n\u001b[1;32m      8\u001b[0m     \u001b[38;5;66;03m#x2 = np.delete(x2, -1)    \u001b[39;00m\n",
      "File \u001b[0;32m<__array_function__ internals>:180\u001b[0m, in \u001b[0;36mdelete\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/numpy/lib/function_base.py:5185\u001b[0m, in \u001b[0;36mdelete\u001b[0;34m(arr, obj, axis)\u001b[0m\n\u001b[1;32m   5182\u001b[0m     slobj[axis] \u001b[38;5;241m=\u001b[39m keep\n\u001b[1;32m   5183\u001b[0m     new \u001b[38;5;241m=\u001b[39m arr[\u001b[38;5;28mtuple\u001b[39m(slobj)]\n\u001b[0;32m-> 5185\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m wrap:\n\u001b[1;32m   5186\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m wrap(new)\n\u001b[1;32m   5187\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "acorr.append(norm)\n",
    "\n",
    "for lag in lags:\n",
    "    for i in range(n):\n",
    "        x1 = np.delete(x1, 0)\n",
    "        x2 = np.delete(x2, -1)\n",
    "    #x1 = np.delete(x1, 0)\n",
    "    #x2 = np.delete(x2, -1)    \n",
    "    val = float(np.correlate(x1,x2))\n",
    "    acorr.append(val)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3266d5d-34c9-46b9-bad9-7b4dfdb97663",
   "metadata": {},
   "outputs": [],
   "source": [
    "acorrnorm = np.array(acorr)\n",
    "acorrnorm = acorrnorm / norm\n",
    "acorrnorm = np.delete(acorrnorm, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0821e284-e7c3-45c8-b91e-6b26025019d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(8,6)) #must come BEFORE the actual plot\n",
    "plt.plot(lags, acorrnorm) #Alpha is the opacity, density is the normalization\n",
    "#plt.errorbar(x, y, yerr, ls='', color='k')\n",
    "#plt.scatter(x, y, color='k', s=30, zorder=1000)\n",
    "#plt.locator_params(y=20) this is about the density of thicks on both axis I could add <, axis='x'> inside the parentesis, to do just for one axis\n",
    "plt.xlabel('Lag')\n",
    "plt.ylabel('Autocorrelation')\n",
    "plt.title('Autocorrelation curve')\n",
    "plt.yscale('log')\n",
    "plt.xscale('linear')\n",
    "#plt.xlim(0,3000) #questo limita l'asse x\n",
    "#plt.ylim(0.1 ,1) #questo limite superiormente l'asse y\n",
    "#plt.savefig('curva_gain1_log.jpg') #always save before plt.show() it should be \"namefile.png\" or \"namefile.pdf\"\n",
    "plt.show()"
   ]
  }
 ],
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