cleaned up files, got a working transition function
youainti
5 years ago
parent
823880e07a
commit
c9e6637157
@ -0,0 +1,285 @@
|
|||||||
|
{
|
||||||
|
"cells": [
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 1,
|
||||||
|
"id": "recorded-albany",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"import torch\n",
|
||||||
|
"from torch.autograd.functional import jacobian"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 2,
|
||||||
|
"id": "senior-characterization",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"tensor([1.0000, 1.0000, 1.0000, 1.0000, 0.5000], requires_grad=True)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 2,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"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_()"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 3,
|
||||||
|
"id": "sublime-trance",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"launch = torch.ones(5, requires_grad=True)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 4,
|
||||||
|
"id": "double-climb",
|
||||||
|
"metadata": {
|
||||||
|
"tags": []
|
||||||
|
},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"debris = torch.tensor([2.2],requires_grad=True)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 5,
|
||||||
|
"id": "blind-reunion",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"scaling = torch.ones(5)\n",
|
||||||
|
"delta = 0.9 \n",
|
||||||
|
"launch_debris_rate = 0.05\n",
|
||||||
|
"collision_debris_rate = 0.07"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 6,
|
||||||
|
"id": "worldwide-winning",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"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\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 g(stock, debris, launches):\n",
|
||||||
|
" new_stock = stock*survival(stock,debris) + launches\n",
|
||||||
|
" \n",
|
||||||
|
" #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"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 7,
|
||||||
|
"id": "naughty-transport",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"tensor([0.8600, 0.8600, 0.8600, 0.8600, 0.8802], grad_fn=<RsubBackward1>)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 7,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"survival(stocks,debris)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 8,
|
||||||
|
"id": "large-trigger",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"(tensor([[-0.0142, 0.0271, 0.0271, 0.0271, 0.0271],\n",
|
||||||
|
" [ 0.0271, -0.0142, 0.0271, 0.0271, 0.0271],\n",
|
||||||
|
" [ 0.0271, 0.0271, -0.0142, 0.0271, 0.0271],\n",
|
||||||
|
" [ 0.0271, 0.0271, 0.0271, -0.0142, 0.0271],\n",
|
||||||
|
" [ 0.0251, 0.0251, 0.0251, 0.0251, -0.0142]]),\n",
|
||||||
|
" tensor([[0.0825],\n",
|
||||||
|
" [0.0825],\n",
|
||||||
|
" [0.0825],\n",
|
||||||
|
" [0.0825],\n",
|
||||||
|
" [0.0634]]))"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 8,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"#Get the derivatives seperately\n",
|
||||||
|
"jacobian(survival, (stocks,debris))"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 9,
|
||||||
|
"id": "prime-projector",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"tensor([[-0.0142, 0.0271, 0.0271, 0.0271, 0.0271, 0.0825],\n",
|
||||||
|
" [ 0.0271, -0.0142, 0.0271, 0.0271, 0.0271, 0.0825],\n",
|
||||||
|
" [ 0.0271, 0.0271, -0.0142, 0.0271, 0.0271, 0.0825],\n",
|
||||||
|
" [ 0.0271, 0.0271, 0.0271, -0.0142, 0.0271, 0.0825],\n",
|
||||||
|
" [ 0.0251, 0.0251, 0.0251, 0.0251, -0.0142, 0.0634]])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 9,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"#Get the derivatives as a single result\n",
|
||||||
|
"torch.cat(jacobian(survival, (stocks,debris)), axis=1)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 10,
|
||||||
|
"id": "urban-decision",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"(tensor([1.8600, 1.8600, 1.8600, 1.8600, 1.4401], grad_fn=<AddBackward0>),\n",
|
||||||
|
" tensor([0.5134], grad_fn=<AddBackward0>))"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 10,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"#Testing state updates\n",
|
||||||
|
"g(stocks, debris, launch)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 11,
|
||||||
|
"id": "congressional-kelly",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"((tensor([[0.8457, 0.0271, 0.0271, 0.0271, 0.0271],\n",
|
||||||
|
" [0.0271, 0.8457, 0.0271, 0.0271, 0.0271],\n",
|
||||||
|
" [0.0271, 0.0271, 0.8457, 0.0271, 0.0271],\n",
|
||||||
|
" [0.0271, 0.0271, 0.0271, 0.8457, 0.0271],\n",
|
||||||
|
" [0.0126, 0.0126, 0.0126, 0.0126, 0.8731]]),\n",
|
||||||
|
" tensor([[0.0825],\n",
|
||||||
|
" [0.0825],\n",
|
||||||
|
" [0.0825],\n",
|
||||||
|
" [0.0825],\n",
|
||||||
|
" [0.0317]]),\n",
|
||||||
|
" tensor([[1., 0., 0., 0., 0.],\n",
|
||||||
|
" [0., 1., 0., 0., 0.],\n",
|
||||||
|
" [0., 0., 1., 0., 0.],\n",
|
||||||
|
" [0., 0., 0., 1., 0.],\n",
|
||||||
|
" [0., 0., 0., 0., 1.]])),\n",
|
||||||
|
" (tensor([[0.0042, 0.0042, 0.0042, 0.0042, 0.0013]]),\n",
|
||||||
|
" tensor([[0.0747]]),\n",
|
||||||
|
" tensor([[0.0500, 0.0500, 0.0500, 0.0500, 0.0500]])))"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 11,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"#Note the two tuples of jacobians: the first is for stock evolution, the second is for debris evolution\n",
|
||||||
|
"jacobian(g, (stocks,debris,launch))"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"id": "identified-insertion",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"## Next step: Construct the intertemporal-transition function(s)\n",
|
||||||
|
" - Note: There are a couple of different ways to do this\n",
|
||||||
|
" - Just a single period transition function, manually iterated\n",
|
||||||
|
" - A recursive function that creates a $p$ period iterated function\n",
|
||||||
|
" - A recursive function that returns a list of functions iterated from 1 to $p$ periods\n",
|
||||||
|
"\n",
|
||||||
|
"I am planning on doing the latter, as each version is needed."
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "utility-browse",
|
||||||
|
"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
|
||||||
|
}
|
||||||
Loading…
Reference in New Issue