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Changed to have launches as a global function

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temporaryWork
youainti 5 years ago
parent 9335ce1295
commit 21b91cd4e8
1 changed files with 90 additions and 78 deletions
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Code/connect_transition_to_optimality.ipynb
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@ -3,7 +3,7 @@
{
"cell_type": "code",
"execution_count": 1,
"id": "variable-telephone",
"id": "behavioral-session",
"metadata": {
"tags": []
},
@ -16,7 +16,7 @@
},
{
"cell_type": "markdown",
"id": "minimal-quarterly",
"id": "vocational-rover",
"metadata": {},
"source": [
"# Setup Functions\n",
@ -26,7 +26,7 @@
{
"cell_type": "code",
"execution_count": 2,
"id": "instructional-guide",
"id": "physical-guidance",
"metadata": {},
"outputs": [],
"source": [
@ -73,78 +73,20 @@
},
{
"cell_type": "markdown",
"id": "spread-humor",
"id": "difficult-drinking",
"metadata": {},
"source": [
"## Setup functions related to the problem"
"# functions related to transitions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "supposed-chorus",
"id": "beautiful-northwest",
"metadata": {},
"outputs": [],
"source": [
"### Classes\n",
"class States():\n",
" \"\"\"\n",
" This class represents the state variables associated with the problems.\n",
" \n",
" In this problem, the two types of states are constellation stocks and debris.\n",
" \n",
" I'm not sure how useful it will be. We'll see.\n",
" \"\"\"\n",
" def __init__(self, satellite_stock, debris):\n",
" self.stock = satellite_stock\n",
" self.debris = debris\n",
" \n",
" \n",
"\n",
"### functions\n",
"\n",
"def survival(stock, debris):\n",
" \"\"\"\n",
" This is a basic, deterministic survival function. \n",
" It is based on the CDF of an exponential distribution.\n",
" \"\"\"\n",
" #TODO: ACTUALLY DERIVE A SURVIVAL FUNCTION. THIS IS JUST A PLACEHOLDER. PROBABLY SHOULD BE AN EXPONENTIAL DISTRIBUTION\n",
" return 1 - torch.exp(-SCALING * stock - debris)\n",
"\n",
"def test_launch(stock, debris):\n",
" \"\"\"\n",
" Temporary launch function \n",
" \"\"\"\n",
" return torch.ones(5, requires_grad=True)\n",
"\n",
"def laws_of_motion(stock, debris, launches):\n",
" \"\"\"\n",
" This function updates state variables (stock and debris), according \n",
" to the laws of motion.\n",
" \n",
" It returns the state variables as \n",
" \"\"\"\n",
" \n",
" new_stock = stock*survival(stock,debris) + launches#(stock,debris) #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(stock, debris):\n",
" return UTIL_WEIGHTS @ stock"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "analyzed-drink",
"metadata": {},
"outputs": [],
"source": [
"def single_transition(item_to_iterate, laws_motion, profit, launch, stocks, debris ):\n",
"def single_transition(item_to_iterate, laws_motion, profit, stocks, debris ):\n",
" \"\"\"\n",
" This function represents the inverted envelope conditions.\n",
" It allows us to describe the derivatives of the value function evaluated at time $t+1$ in terms based in time period $t$.\n",
@ -159,7 +101,7 @@
" #it consists of the derivative of the laws of motion with respect to stocks and debris\n",
" \n",
" #Get the jacobian\n",
" a = jacobian(laws_motion, (stocks,debris,launch))\n",
" a = jacobian(laws_motion, (stocks,debris))\n",
" \n",
" #Reassemble the Jacobian nested tuples into the appropriate tensor\n",
" A = BETA * torch.cat((torch.cat((a[0][0],a[0][1]),dim=1),torch.cat((a[1][0],a[1][1]),dim=1)), dim=0)\n",
@ -183,10 +125,10 @@
" \"\"\"\n",
" \"\"\"\n",
" #unpack states and functions\n",
" stocks, debris,profit, launch, laws_motion, item_to_transition = data_in\n",
" stocks, debris,profit, laws_motion, item_to_transition = data_in\n",
" \n",
" #Calculate new states\n",
" new_stocks, new_debris = laws_motion(stocks,debris,launch)\n",
" new_stocks, new_debris = laws_motion(stocks,debris)\n",
" \n",
" #WARNING: RECURSION: You may break your head...\n",
" #This gets the transition of the value function derivatives over time.\n",
@ -195,19 +137,89 @@
" #functions\n",
" laws_motion, \n",
" profit, \n",
" launch, #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",
" data_out = new_stocks, new_debris, profit, laws_motion, transitioned\n",
" \n",
" return data_out"
]
},
{
"cell_type": "markdown",
"id": "martial-station",
"id": "entertaining-theorem",
"metadata": {},
"source": [
"## Setup functions related to the problem"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "modern-kentucky",
"metadata": {},
"outputs": [],
"source": [
"### Classes\n",
"class States():\n",
" \"\"\"\n",
" This class represents the state variables associated with the problems.\n",
" \n",
" In this problem, the two types of states are constellation stocks and debris.\n",
" \n",
" I'm not sure how useful it will be. We'll see. It is missing a lot\n",
" \"\"\"\n",
" def __init__(self, satellite_stock, debris):\n",
" self.stock = satellite_stock\n",
" self.debris = debris\n",
" \n",
" \n",
"\n",
"### functions\n",
"\n",
"def survival(stock, debris):\n",
" \"\"\"\n",
" This is a basic, deterministic survival function. \n",
" It is based on the CDF of an exponential distribution.\n",
" \"\"\"\n",
" #SURVIVAL FUNCTION BASED ON AN EXPONENTIAL DISTRIBUTION\n",
" return 1 - torch.exp(-SCALING * stock - debris)\n",
"\n",
"def test_launch(stock, debris):\n",
" \"\"\"\n",
" Temporary launch function \n",
" \"\"\"\n",
" return torch.ones(5, requires_grad=True)\n",
"\n",
"def laws_of_motion(stock, debris):\n",
" \"\"\"\n",
" This function updates state variables (stock and debris), according \n",
" to the laws of motion.\n",
" \n",
" It returns the state variables as \n",
" \"\"\"\n",
" l = launches(stock,debris)\n",
" #Notes: Launches is a global function.\n",
" s = survival(stock,debris)\n",
" #Notes: Survival is a global function.\n",
" \n",
" new_stock = stock*s + l\n",
" \n",
" \n",
" #TODO: Currently Ignoring autocatalysis\n",
" new_debris = (1-DELTA)*debris + LAUNCH_DEBRIS_RATE * l.sum() + COLLISION_DEBRIS_RATE*(1-s) @ 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(stock, debris):\n",
" return UTIL_WEIGHTS @ stock"
]
},
{
"cell_type": "markdown",
"id": "broadband-technique",
"metadata": {},
"source": [
"# Actual calculations"
@ -216,7 +228,7 @@
{
"cell_type": "code",
"execution_count": 5,
"id": "ambient-breakfast",
"id": "adjustable-harvey",
"metadata": {},
"outputs": [],
"source": [
@ -231,10 +243,10 @@
"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",
"launches = test_launch\n",
"\n",
"#compose the functions together.\n",
"base_data = (stocks,debris, profit, launch, laws_of_motion, torch.ones(6, requires_grad=True))\n",
"base_data = (stocks,debris, profit, laws_of_motion, torch.ones(6, requires_grad=True))\n",
"\n",
"#Parameters\n",
"SCALING = torch.ones(5)\n",
@ -248,7 +260,7 @@
{
"cell_type": "code",
"execution_count": 6,
"id": "deluxe-remains",
"id": "cordless-wages",
"metadata": {},
"outputs": [
{
@ -287,12 +299,12 @@
"#Get the values from 5 transitions\n",
"for f in compose_recursive_functions(transition_wrapper,5):\n",
" result = f(base_data)\n",
" print(result[5], \"\\n\"*3)"
" print(result[4], \"\\n\"*3)"
]
},
{
"cell_type": "markdown",
"id": "parallel-classroom",
"id": "shaped-zambia",
"metadata": {},
"source": [
"Also, maybe I can create a `Model` class that upon construction will capture the necesary constants, functions, etc.\n"
@ -301,7 +313,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "copyrighted-freeze",
"id": "canadian-excitement",
"metadata": {},
"outputs": [],
"source": []

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