test2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1000\n",
    "X = np.random.rand(N)*2-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = 1.0\n",
    "burnin_steps = 1000\n",
    "record_steps = 10000\n",
    "dt = 0.0001\n",
    "sigma = sqrt(2.0 * dt / beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(burnin_steps):\n",
    "    X += np.random.randn(N) * sigma\n",
    "    inbound = np.abs(X) < 1.0\n",
    "    X = np.where(inbound, X, X/X**2)\n",
    "Y = X\n",
    "for i in range(record_steps):\n",
    "    X += np.random.randn(N) * sigma\n",
    "    inbound = np.abs(X) < 1.0\n",
    "    X = np.where(inbound, X, X/X**2)\n",
    "    Y = np.concatenate((Y, X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(h, bins) = np.histogram(Y, range=(-1, 1), bins=40)\n",
    "plt.stairs(h, bins)\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": "3.11.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}