got successful recursive generation for the euler equation stuff
youainti
5 years ago
parent
58f10e54ea
commit
3ca5312fab
@ -1,80 +0,0 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "complicated-passage",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"testing a recursive function builder"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "alone-individual",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def base(x,depth):\n",
|
||||
" return \"y\"+base(x)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"id": "sustainable-closing",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"'yyyx'"
|
||||
]
|
||||
},
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"base(\"x\",3)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "systematic-actor",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def all_your(fn,depth1):\n",
|
||||
" if depth1 <= 0:\n",
|
||||
" return fn\n",
|
||||
" else:\n",
|
||||
" ifn = all_your(fn,depth-1)\n",
|
||||
" return fn(ifn)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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": "3.8.8"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
@ -0,0 +1,242 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"id": "taken-punch",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import copy\n",
|
||||
"import itertools"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "driving-booth",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"testing a recursive function builder"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "permanent-training",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def compose(f,g):\n",
|
||||
" return lambda *args, **kwds: f(g(*args,**kwds))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "editorial-alliance",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"['a', 'b'] c\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"print([\"a\",\"b\"],\"c\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"id": "isolated-headset",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def appnd(lst,val):\n",
|
||||
" lst.append(val)\n",
|
||||
" return lst"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"id": "thirty-latter",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def traverse_split_right(tuplists):\n",
|
||||
" lst1,lst2 = tuplists\n",
|
||||
" lst1.append(lst2.pop(0))\n",
|
||||
" return (lst1,lst2)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"id": "oriented-context",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(['a', 'b'], ['c'])"
|
||||
]
|
||||
},
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"traverse_split_right(([\"a\"],[\"b\",\"c\"]))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "unsigned-settlement",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(['a', 'b', 'c'], ['d', 'e', 'f'])\n",
|
||||
"(['a', 'b', 'c', 'd', 'e'], ['f'])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"args = (\n",
|
||||
" [\"a\",\"b\",\"c\"],\n",
|
||||
" [\"d\",\"e\",\"f\"]\n",
|
||||
" )\n",
|
||||
"print(args)\n",
|
||||
"\n",
|
||||
"flist = [traverse_split_right,traverse_split_right,print]\n",
|
||||
"rflist = list(reversed(flist))\n",
|
||||
"\n",
|
||||
"co = compose(rflist[0],compose(rflist[1],rflist[2]))\n",
|
||||
"\n",
|
||||
"co(args)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 34,
|
||||
"id": "satellite-sacrifice",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"flist = [traverse_split_right,traverse_split_right,traverse_split_right]\n",
|
||||
"\n",
|
||||
"out_func = None\n",
|
||||
"out_func_list =[]\n",
|
||||
"\n",
|
||||
"for f in itertools.repeat(traverse_split_right,3):\n",
|
||||
" if out_func == None:\n",
|
||||
" out_func = f\n",
|
||||
" else:\n",
|
||||
" out_func = compose(f,out_func)\n",
|
||||
" \n",
|
||||
" out_func_list.append(out_func)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 39,
|
||||
"id": "certified-track",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(['a'], ['b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'])\n",
|
||||
"(['a', 'b'], ['c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'])\n",
|
||||
"(['a', 'b', 'c'], ['d', 'e', 'f', 'g', 'h', 'i', 'j'])\n",
|
||||
"(['a', 'b', 'c', 'd'], ['e', 'f', 'g', 'h', 'i', 'j'])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#test the list\n",
|
||||
"args = (\n",
|
||||
" [\"a\"],\n",
|
||||
" [\"b\",\"c\",\"d\",\"e\",\"f\",\"g\",\"h\",\"i\",\"j\"]\n",
|
||||
" )\n",
|
||||
"print(args)\n",
|
||||
"\n",
|
||||
"for fn in out_func_list:\n",
|
||||
" #reset the data each time\n",
|
||||
" a = copy.deepcopy(args)\n",
|
||||
" print(fn(a))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 38,
|
||||
"id": "interesting-moral",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(['a'], ['b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'])\n",
|
||||
"(['a', 'b'], ['c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'])\n",
|
||||
"(['a', 'b'], ['c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'])\n",
|
||||
"(['a', 'b'], ['c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'])\n",
|
||||
"(['a', 'b'], ['c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#test a non-composed list of functions\n",
|
||||
"args = (\n",
|
||||
" [\"a\"],\n",
|
||||
" [\"b\",\"c\",\"d\",\"e\",\"f\",\"g\",\"h\",\"i\",\"j\"]\n",
|
||||
" )\n",
|
||||
"print(args)\n",
|
||||
"for fn in itertools.repeat(traverse_split_right,4):\n",
|
||||
" #Reset the data each time\n",
|
||||
" a = copy.deepcopy(args)\n",
|
||||
" \n",
|
||||
" print(fn(a))\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "incorrect-migration",
|
||||
"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": "3.8.8"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
@ -0,0 +1,239 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "linear-harvey",
|
||||
"metadata": {
|
||||
"tags": []
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import torch\n",
|
||||
"from torch.autograd.functional import jacobian\n",
|
||||
"import itertools"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "honey-excuse",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Setup Functions\n",
|
||||
"## General CompositionFunctions"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "helpful-radical",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"### Set up functions to compose functions \n",
|
||||
"# These functions will \n",
|
||||
"# - compose two functions together\n",
|
||||
"# - compose a function to itself n times.\n",
|
||||
"\n",
|
||||
"def compose(f,g):\n",
|
||||
" return lambda *args: f(g(*args))\n",
|
||||
"\n",
|
||||
"def compose_recursive_functions(fn,n):\n",
|
||||
" #Set base conditions\n",
|
||||
" out_func = None\n",
|
||||
" out_func_list =[]\n",
|
||||
"\n",
|
||||
" #build the compositions of functions\n",
|
||||
" for f in itertools.repeat(fn, n):\n",
|
||||
" if out_func == None:\n",
|
||||
" out_func = f\n",
|
||||
" else:\n",
|
||||
" out_func = compose(f,out_func)\n",
|
||||
"\n",
|
||||
" out_func_list.append(out_func)\n",
|
||||
" \n",
|
||||
" return out_func_list"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "fifty-southwest",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Setup functions related to the problem"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"id": "fancy-manual",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"### Background functions\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def survival(stock, debris):\n",
|
||||
" #Gompertz distribution for simplicity\n",
|
||||
" #commonly used with saturation\n",
|
||||
" #TODO: ACTUALLY DERIVE A SURVIVAL FUNCTION. THIS IS JUST A PLACEHOLDER. PROBABLY SHOULD BE AN EXPONENTIAL DISTRIBUTION\n",
|
||||
" eta = 1.0/(SCALING@stock)\n",
|
||||
" b = 1/debris\n",
|
||||
" \n",
|
||||
" return 1 - ( b*eta*torch.exp(eta+b*stock-eta*torch.exp(b*stock)))\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def laws_of_motion(stock, debris, launches):\n",
|
||||
" \n",
|
||||
" new_stock = stock*survival(stock,debris) + launches #TODO: Launches will become a function (neural network)\n",
|
||||
" \n",
|
||||
" #TODO: Currently Ignoring autocatalysis\n",
|
||||
" new_debris = (1-DELTA)*debris + LAUNCH_DEBRIS_RATE * launches.sum() + COLLISION_DEBRIS_RATE*(1-survival(stock,debris)) @ stock\n",
|
||||
" \n",
|
||||
" return (new_stock, new_debris)\n",
|
||||
"\n",
|
||||
"#This is not a good specification of the profit function, but it will work for now.\n",
|
||||
"def profit(x):\n",
|
||||
" return UTIL_WEIGHTS @ x"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"id": "dietary-vault",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def single_transition(item_to_iterate, laws_motion, profit,launch, stocks, debris ):\n",
|
||||
" #TODO: change launch from a direct tensor, to a function.\n",
|
||||
" \n",
|
||||
" #Calculate the inverse\n",
|
||||
" bA = BETA * jacobian(laws_motion, (stocks,debris,launch))[0][0]\n",
|
||||
" #TODO: figure out some diagnostics for this section\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" return bA.inverse() @ (item_to_iterate - jacobian(profit,stocks))\n",
|
||||
"\n",
|
||||
"# This function wraps the single transition and handles updating dates etc.\n",
|
||||
"def transition_wrapper(data_in):\n",
|
||||
" #unpack states and functions\n",
|
||||
" stocks, debris,profit, launch, laws_motion,item_to_transition = data_in\n",
|
||||
" \n",
|
||||
" #Calculate new states\n",
|
||||
" new_stocks, new_debris = laws_motion(stocks,debris,launch)\n",
|
||||
" \n",
|
||||
" #WARNING: RECURSION: You may break your head...\n",
|
||||
" #This gets the transition of the value function derivatives over time.\n",
|
||||
" transitioned = single_transition(\n",
|
||||
" item_to_transition, #item to iterate, i.e. the derivatives of the value function\n",
|
||||
" laws_motion, profit, launch, #functions #TODO: reimplement with launch as a function\n",
|
||||
" stocks, debris #states\n",
|
||||
" )\n",
|
||||
" \n",
|
||||
" #collects the data back together for return, including the updated state variables\n",
|
||||
" data_out = new_stocks, new_debris, profit, launch, laws_motion, transitioned\n",
|
||||
" \n",
|
||||
" return data_out"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "illegal-thriller",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Actual calculations"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"id": "coated-dressing",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"#set states\n",
|
||||
"stocks = torch.ones(5)\n",
|
||||
"#Last one is different\n",
|
||||
"stocks[-1] = 0.5\n",
|
||||
"#now add the tracking requirement in place\n",
|
||||
"stocks.requires_grad_()\n",
|
||||
"\n",
|
||||
"#Setup Debris\n",
|
||||
"debris = torch.tensor([2.2],requires_grad=True)\n",
|
||||
"\n",
|
||||
"#CHANGE LATER: Launch is currently a value, should be a function (i.e. neural network)\n",
|
||||
"launch = torch.ones(5, requires_grad=True)\n",
|
||||
"\n",
|
||||
"#compose the functions together.\n",
|
||||
"base_data = (stocks,debris, profit, launch, laws_of_motion, torch.ones(5, requires_grad=True))\n",
|
||||
"\n",
|
||||
"#Parameters\n",
|
||||
"SCALING = torch.ones(5)\n",
|
||||
"DELTA = 0.9 \n",
|
||||
"LAUNCH_DEBRIS_RATE = 0.005\n",
|
||||
"COLLISION_DEBRIS_RATE = 0.0007\n",
|
||||
"UTIL_WEIGHTS = torch.tensor([1,-0.2,0,0,0])\n",
|
||||
"BETA = 0.95"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"id": "analyzed-transfer",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"tensor([-0.1543, 1.3888, 1.1316, 1.1316, 1.1553], grad_fn=<MvBackward>)\n",
|
||||
"tensor([-1.2150, 1.6724, 1.1912, 1.1912, 1.2161], grad_fn=<MvBackward>)\n",
|
||||
"tensor([-2.3316, 1.9710, 1.2539, 1.2539, 1.2801], grad_fn=<MvBackward>)\n",
|
||||
"tensor([nan, nan, nan, nan, nan], grad_fn=<MvBackward>)\n",
|
||||
"tensor([nan, nan, nan, nan, nan], grad_fn=<MvBackward>)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#calculate results for first 5 iterations\n",
|
||||
"for f in compose_recursive_functions(transition_wrapper,5):\n",
|
||||
" result = f(base_data)\n",
|
||||
" print(result[5])"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "confidential-stadium",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Note how this fails on the last few iterations.\n",
|
||||
"I need to get better model functions (profit, laws_of_motion, etc) together to test this out.\n",
|
||||
"\n",
|
||||
"Maybe with a standard RBC model?\n",
|
||||
"\n",
|
||||
"Also, maybe I can create a `Model` class that upon construction will capture the necesary constants, functions, etc."
|
||||
]
|
||||
}
|
||||
],
|
||||
"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": "3.8.8"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
Loading…
Reference in New Issue