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251 lines
7.5 KiB
Plaintext
251 lines
7.5 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "sustained-board",
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"metadata": {
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"tags": []
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},
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"outputs": [],
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"source": [
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"import torch\n",
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"from torch.autograd.functional import jacobian\n",
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"import itertools"
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]
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},
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{
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"cell_type": "markdown",
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"id": "numeric-victoria",
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"metadata": {},
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"source": [
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"# Setup Functions\n",
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"## General CompositionFunctions"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "virtual-arlington",
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"metadata": {},
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"outputs": [],
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"source": [
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"### Set up functions to compose functions \n",
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"# These functions will \n",
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"# - compose two functions together\n",
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"# - compose a function to itself n times.\n",
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"\n",
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"def compose(f,g):\n",
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" return lambda *args: f(g(*args))\n",
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"\n",
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"def compose_recursive_functions(fn,n):\n",
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" #Set base conditions\n",
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" out_func = None\n",
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" out_func_list =[]\n",
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"\n",
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" #build the compositions of functions\n",
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" for f in itertools.repeat(fn, n):\n",
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" if out_func == None:\n",
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" out_func = f\n",
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" else:\n",
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" out_func = compose(f,out_func)\n",
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"\n",
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" out_func_list.append(out_func)\n",
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" \n",
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" return out_func_list"
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]
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},
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{
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"cell_type": "markdown",
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"id": "wrapped-message",
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"metadata": {},
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"source": [
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"## Setup functions related to the problem"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "neutral-vietnamese",
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"metadata": {},
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"outputs": [],
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"source": [
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"### Background functions\n",
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"\n",
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"\n",
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"def survival(stock, debris):\n",
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" #Gompertz distribution for simplicity\n",
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" #commonly used with saturation\n",
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" #TODO: ACTUALLY DERIVE A SURVIVAL FUNCTION. THIS IS JUST A PLACEHOLDER. PROBABLY SHOULD BE AN EXPONENTIAL DISTRIBUTION\n",
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" eta = 1.0/(SCALING@stock)\n",
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" b = 1/debris\n",
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" \n",
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" return 1 - ( b*eta*torch.exp(eta+b*stock-eta*torch.exp(b*stock)))\n",
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"\n",
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"def test_launch(stock, debris):\n",
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" return torch.ones(5, requires_grad=True)\n",
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"\n",
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"def laws_of_motion(stock, debris, launches):\n",
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" \n",
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" new_stock = stock*survival(stock,debris) + launches(stock,debris) #TODO: Launches will become a function (neural network)\n",
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" \n",
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" #TODO: Currently Ignoring autocatalysis\n",
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" new_debris = (1-DELTA)*debris + LAUNCH_DEBRIS_RATE * launches.sum() + COLLISION_DEBRIS_RATE*(1-survival(stock,debris)) @ stock\n",
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" \n",
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" return (new_stock, new_debris)\n",
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"\n",
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"#This is not a good specification of the profit function, but it will work for now.\n",
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"def profit(x):\n",
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" return UTIL_WEIGHTS @ x"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "considered-configuration",
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"metadata": {},
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"outputs": [],
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"source": [
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"def single_transition(item_to_iterate, laws_motion, profit,launch, stocks, debris ):\n",
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" #TODO: change launch from a direct tensor, to a function.\n",
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" \n",
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" #Calculate the inverse\n",
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" bA = BETA * jacobian(laws_motion, (stocks,debris,launch))[0][0]\n",
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" #TODO: figure out some diagnostics for this section\n",
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" \n",
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" \n",
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" return bA.inverse() @ (item_to_iterate - jacobian(profit,stocks))\n",
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"\n",
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"# This function wraps the single transition and handles updating dates etc.\n",
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"def transition_wrapper(data_in):\n",
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" #unpack states and functions\n",
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" stocks, debris,profit, launch, laws_motion,item_to_transition = data_in\n",
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" \n",
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" #Calculate new states\n",
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" new_stocks, new_debris = laws_motion(stocks,debris,launch)\n",
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" \n",
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" #WARNING: RECURSION: You may break your head...\n",
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" #This gets the transition of the value function derivatives over time.\n",
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" transitioned = single_transition(\n",
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" item_to_transition, #item to iterate, i.e. the derivatives of the value function\n",
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" laws_motion, profit, launch, #functions #TODO: reimplement with launch as a function\n",
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" stocks, debris #states\n",
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" )\n",
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" \n",
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" #collects the data back together for return, including the updated state variables\n",
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" data_out = new_stocks, new_debris, profit, launch, laws_motion, transitioned\n",
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" \n",
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" return data_out"
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]
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},
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{
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"cell_type": "markdown",
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"id": "premium-lesbian",
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"metadata": {},
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"source": [
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"# Actual calculations"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "suffering-google",
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"metadata": {},
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"outputs": [],
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"source": [
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"#set states\n",
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"stocks = torch.ones(5)\n",
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"#Last one is different\n",
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"stocks[-1] = 0.5\n",
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"#now add the tracking requirement in place\n",
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"stocks.requires_grad_()\n",
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"\n",
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"#Setup Debris\n",
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"debris = torch.tensor([2.2],requires_grad=True)\n",
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"\n",
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"#CHANGE LATER: Launch is currently a value, should be a function (i.e. neural network)\n",
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"launch = torch.ones(5, requires_grad=True)\n",
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"\n",
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"#compose the functions together.\n",
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"base_data = (stocks,debris, profit, launch, laws_of_motion, torch.ones(5, requires_grad=True))\n",
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"\n",
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"#Parameters\n",
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"SCALING = torch.ones(5)\n",
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"DELTA = 0.9 \n",
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"LAUNCH_DEBRIS_RATE = 0.005\n",
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"COLLISION_DEBRIS_RATE = 0.0007\n",
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"UTIL_WEIGHTS = torch.tensor([1,-0.2,0,0,0])\n",
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"BETA = 0.95"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "checked-medication",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"tensor([-0.1543, 1.3888, 1.1316, 1.1316, 1.1553], grad_fn=<MvBackward>)\n",
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"tensor([-1.2150, 1.6724, 1.1912, 1.1912, 1.2161], grad_fn=<MvBackward>)\n",
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"tensor([-2.3316, 1.9710, 1.2539, 1.2539, 1.2801], grad_fn=<MvBackward>)\n",
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"tensor([nan, nan, nan, nan, nan], grad_fn=<MvBackward>)\n",
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"tensor([nan, nan, nan, nan, nan], grad_fn=<MvBackward>)\n"
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]
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}
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],
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"source": [
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"#calculate results for first 5 iterations\n",
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"for f in compose_recursive_functions(transition_wrapper,5):\n",
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" result = f(base_data)\n",
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" print(result[5])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "wanted-principal",
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"metadata": {},
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"source": [
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"Note how this fails on the last few iterations.\n",
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"I need to get better model functions (profit, laws_of_motion, etc) together to test this out.\n",
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"Alternatively, I can check for areas where the determinant of $A$ is zero, possibly by doing some sort of grid search?\n",
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"\n",
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"Maybe with a standard RBC model?\n",
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"\n",
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"Also, maybe I can create a `Model` class that upon construction will capture the necesary constants, functions, etc."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "solid-correlation",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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