diff --git a/random/randsim.ipynb b/random/randsim.ipynb new file mode 100644 index 0000000..09a77a2 --- /dev/null +++ b/random/randsim.ipynb @@ -0,0 +1,10276 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "cb90833d", + "metadata": {}, + "outputs": [], + "source": [ + "badfraction=1/3\n", + "def dumbforwardinggoodbadweakprob(badvalfraction):\n", + " badprob=badvalfraction\n", + " goodprob=(1-badprob)^2\n", + " weakprob=1-badprob-goodprob\n", + " return(goodprob,badprob,weakprob)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "ff900e74", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.381966011250105, (0.381966011250105, 0.381966011250105, 0.236067977499790))" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "RR(3-sqrt(5))/2,dumbforwardinggoodbadweakprob(RR(3-sqrt(5))/2)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "42a80695", + "metadata": {}, + "outputs": [], + "source": [ + "goodprob,badprob,wealprob=dumbforwardinggoodbadweakprob(badfraction)" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "814dcfef", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(range(19,0,-1))" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "8970268c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[, , ]" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import random\n", + "from enum import Enum\n", + "class slottype(Enum):\n", + " GOOD=0\n", + " BAD=1\n", + " WEAK=2\n", + "def randslot():\n", + " ran=random.random()\n", + " if ran < goodprob:\n", + " return slottype.GOOD\n", + " if ran > 1- badprob:\n", + " return slottype.BAD\n", + " return slottype.WEAK\n", + "def generateepoch(epochlen):\n", + " return [randslot() for slotnum in range(epochlen)]\n", + "epochlen = 600\n", + "slots=generateepoch(epochlen)\n", + "generateepoch(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "9c47373f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(10,\n", + " [0.239699999999990,\n", + " 0.245999999999989,\n", + " 0.109900000000002,\n", + " 0.0500000000000004,\n", + " 0.0216999999999999,\n", + " 0.00870000000000000,\n", + " 0.00490000000000000,\n", + " 0.00200000000000000,\n", + " 0.000400000000000000,\n", + " 0.000400000000000000,\n", + " 0.000300000000000000,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0,\n", + " 0])" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def maxadv(slots):\n", + " advs=[]\n", + " curradv=0\n", + " for slot in slots:\n", + " match slot:\n", + " case slottype.GOOD:\n", + " curradv -= 1\n", + " case slottype.BAD:\n", + " curradv += 1\n", + " advs +=[curradv]\n", + " return max(advs)\n", + "maxadvsim=0\n", + "dist=[0 for i in range(20)]\n", + "iters=10000\n", + "for i in range(iters):\n", + " adv=maxadv(generateepoch(epochlen))\n", + " if adv > maxadvsim:\n", + " maxadvsim = adv\n", + " if adv < 20 and adv >= 0:\n", + " dist[adv] += RR(1/iters)\n", + "maxadvsim,dist " + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "id": "a736462a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1, [1, 1, 1, 1, 4, 5, 7, 9, 12, 15, 17, 21, 27, 31, 33])" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def randoptions(slots):\n", + " negadvoptions=1\n", + " options=[1 for i in range(15)]\n", + " for slot in slots:\n", + " match slot:\n", + " case slottype.GOOD:\n", + " for i in range(14,0,-1):\n", + " options[i]=options[i-1]\n", + " options[0]=negadvoptions\n", + " negadvoptions=1\n", + " case slottype.BAD:\n", + " for i in range(14,0,-1):\n", + " options[i]+=options[i-1]\n", + " options[0]+=negadvoptions\n", + " negadvoptions*=2\n", + " return negadvoptions,options\n", + "randoptions(generateepoch(epochlen))\n", + " \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "id": "12b0b761", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(8945,\n", + " 44.6270000000000,\n", + " [8,\n", + " 1,\n", + " 4,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 5,\n", + " 1,\n", + " 2,\n", + " 1,\n", + " 16,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 5,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 8,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 8,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 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+ " 1,\n", + " 2,\n", + " 4,\n", + " 2,\n", + " 1,\n", + " 5,\n", + " 1,\n", + " 4,\n", + " 3,\n", + " 1,\n", + " 1,\n", + " 21,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 1,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 5,\n", + " 2,\n", + " 4,\n", + " 1,\n", + " 2,\n", + " 3,\n", + " 11,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 1,\n", + " 4,\n", + " 1,\n", + " 8,\n", + " 8,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 1,\n", + " 9,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 1,\n", + " 3,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 1,\n", + " 4,\n", + " 3,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 4,\n", + " 1,\n", + " 1,\n", + " 4,\n", + " 3,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 1,\n", + " 2,\n", + " 12,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 5,\n", + " 3,\n", + " 5,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 1,\n", + " 1,\n", + " 1,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 2,\n", + " 1,\n", + " 3,\n", + " 5,\n", + " 1,\n", + " 9,\n", + " 29,\n", + " 2,\n", + " 1])" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def epochssim(numepochs,epochlength):\n", + " epoch=generateepoch(epochlen)\n", + " epochoptions=[]\n", + " for i in range(numepochs):\n", + " lastepoch=epoch\n", + " epoch=generateepoch(epochlen)\n", + " negadvoptions,options=randoptions(lastepoch)\n", + " adv=maxadv(epoch)\n", + " if adv < 0:\n", + " epochoptions +=[negadvoptions]\n", + " elif adv > 14:\n", + " print(\"high adv\",adv)\n", + " else:\n", + " epochoptions +=[options[adv]]\n", + " return epochoptions\n", + "a=epochssim(10000,600)\n", + "max(a),RR(sum(a)/1000),a " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6a33fd29", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "SageMath 10.1", + "language": "sage", + "name": "sagemath-10.1" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.1" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}