@ -3,7 +3,7 @@
{
"cell_type": "code",
"execution_count": 1,
"id": "closed-glenn ",
"id": "planned-choir ",
"metadata": {
"tags": []
},
@ -16,7 +16,7 @@
},
{
"cell_type": "markdown",
"id": "naval-ivory ",
"id": "japanese-split ",
"metadata": {},
"source": [
"# Setup Functions\n",
@ -26,7 +26,7 @@
{
"cell_type": "code",
"execution_count": 2,
"id": "italian-enforcemen t",
"id": "final-contes t",
"metadata": {},
"outputs": [],
"source": [
@ -62,7 +62,7 @@
},
{
"cell_type": "markdown",
"id": "fancy-tucson ",
"id": "specific-centre ",
"metadata": {},
"source": [
"## Setup functions related to the problem"
@ -71,7 +71,7 @@
{
"cell_type": "code",
"execution_count": 15,
"id": "outside-arrangement ",
"id": "grand-jesus ",
"metadata": {},
"outputs": [],
"source": [
@ -79,13 +79,8 @@
"\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",
"\n",
" #eta = 1.0/(SCALING@stock)\n",
" #b = 1/debris\n",
" #return 1 - ( b*eta*torch.exp(eta+b*stock-eta*torch.exp(b*stock)))\n",
" return 1 - torch.exp(-SCALING * stock-debris)\n",
"\n",
"def test_launch(stock, debris):\n",
@ -101,6 +96,7 @@
" return (new_stock, new_debris)\n",
"\n",
"#This is not a good specification of the profit function, but it will work for now.\n",
"#similar to Rao and Rondina's\n",
"def profit(x):\n",
" return UTIL_WEIGHTS @ x"
]
@ -108,7 +104,7 @@
{
"cell_type": "code",
"execution_count": 16,
"id": "romance-generation ",
"id": "military-tunnel ",
"metadata": {},
"outputs": [],
"source": [
@ -149,7 +145,7 @@
},
{
"cell_type": "markdown",
"id": "fluid-parks ",
"id": "hindu-recruitment ",
"metadata": {},
"source": [
"# Actual calculations"
@ -158,7 +154,7 @@
{
"cell_type": "code",
"execution_count": 17,
"id": "changing-january ",
"id": "metric-bruce ",
"metadata": {},
"outputs": [],
"source": [
@ -189,133 +185,52 @@
},
{
"cell_type": "code",
"execution_count": 19 ,
"id": "dominant-boost ",
"execution_count": 2 1,
"id": "musical-neighbor ",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([0.0000, 1.2632, 1.0526, 1.0526, 1.0892], grad_fn=<MvBackward>)\n",
"tensor([-0.9519, 1.3928, 1.0020, 1.0020, 1.0575], grad_fn=<MvBackward>)\n",
"tensor([-1.8565, 1.5150, 0.9530, 0.9530, 0.9882], grad_fn=<MvBackward>)\n",
"tensor([-2.8103, 1.6872, 0.9376, 0.9376, 0.9474], grad_fn=<MvBackward>)\n",
"tensor([-3.8626, 1.9131, 0.9505, 0.9505, 0.9408], grad_fn=<MvBackward>)\n",
"tensor([-5.0235, 2.1830, 0.9819, 0.9819, 0.9598], grad_fn=<MvBackward>)\n",
"tensor([-6.2860, 2.4869, 1.0247, 1.0247, 0.9951], grad_fn=<MvBackward>)\n",
"tensor([-7.6403, 2.8175, 1.0746, 1.0746, 1.0403], grad_fn=<MvBackward>)\n",
"tensor([-9.0802, 3.1712, 1.1293, 1.1293, 1.0918], grad_fn=<MvBackward>)\n",
"tensor([-10.6035, 3.5462, 1.1879, 1.1879, 1.1477],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-12.2108, 3.9422, 1.2501, 1.2501, 1.2075],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-13.9045, 4.3597, 1.3157, 1.3157, 1.2708],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-15.6882, 4.7995, 1.3849, 1.3849, 1.3375],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-17.5662, 5.2625, 1.4577, 1.4577, 1.4079],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-19.5432, 5.7500, 1.5345, 1.5345, 1.4820],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-21.6244, 6.2631, 1.6152, 1.6152, 1.5600],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-23.8151, 6.8033, 1.7002, 1.7002, 1.6421],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-26.1212, 7.3719, 1.7897, 1.7897, 1.7285],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-28.5486, 7.9704, 1.8839, 1.8839, 1.8195],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-31.1038, 8.6004, 1.9831, 1.9831, 1.9152],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-33.7934, 9.2636, 2.0874, 2.0874, 2.0160],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-36.6247, 9.9617, 2.1973, 2.1973, 2.1221],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-39.6049, 10.6965, 2.3129, 2.3129, 2.2338],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-42.7420, 11.4700, 2.4347, 2.4347, 2.3514],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-46.0442, 12.2842, 2.5628, 2.5628, 2.4751],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-49.5202, 13.1413, 2.6977, 2.6977, 2.6054],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-53.1792, 14.0435, 2.8397, 2.8397, 2.7425],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-57.0307, 14.9931, 2.9891, 2.9891, 2.8869],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-61.0850, 15.9928, 3.1465, 3.1465, 3.0388],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-65.3526, 17.0450, 3.3121, 3.3121, 3.1988],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-69.8449, 18.1526, 3.4864, 3.4864, 3.3671],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-74.5736, 19.3186, 3.6699, 3.6699, 3.5443],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-79.5511, 20.5459, 3.8630, 3.8630, 3.7309],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-84.7907, 21.8378, 4.0664, 4.0664, 3.9272],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-90.3060, 23.1976, 4.2804, 4.2804, 4.1339],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-96.1115, 24.6291, 4.5057, 4.5057, 4.3515],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-102.2227, 26.1359, 4.7428, 4.7428, 4.5805],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-108.6555, 27.7220, 4.9924, 4.9924, 4.8216],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-115.4268, 29.3916, 5.2552, 5.2552, 5.0754],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-122.5545, 31.1490, 5.5318, 5.5318, 5.3425],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-130.0574, 32.9990, 5.8229, 5.8229, 5.6237],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-137.9552, 34.9463, 6.1294, 6.1294, 5.9197],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-146.2686, 36.9961, 6.4520, 6.4520, 6.2313],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-155.0196, 39.1538, 6.7916, 6.7916, 6.5592],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-164.2312, 41.4251, 7.1490, 7.1490, 6.9044],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-173.9275, 43.8158, 7.5253, 7.5253, 7.2678],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-184.1343, 46.3325, 7.9213, 7.9213, 7.6503],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-194.8782, 48.9815, 8.3382, 8.3382, 8.0530],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-206.1876, 51.7701, 8.7771, 8.7771, 8.4768],\n",
" grad_fn=<MvBackward>)\n",
"tensor([-218.0922, 54.7053, 9.2391, 9.2391, 8.9230],\n",
" grad_fn=<MvBackward>)\n"
"(tensor([1.9592, 1.9592, 1.9592, 1.9592, 1.4664], grad_fn=<AddBackward0>), tensor([0.2451], grad_fn=<AddBackward0>), <function profit at 0x7f000d27fdc0>, tensor([1., 1., 1., 1., 1.], requires_grad=True), <function laws_of_motion at 0x7f003e976b80>, tensor([0.0000, 1.2632, 1.0526, 1.0526, 1.0892], grad_fn=<MvBackward>))\n",
"(tensor([2.7431, 2.7431, 2.7431, 2.7431, 2.2016], grad_fn=<AddBackward0>), tensor([0.0503], grad_fn=<AddBackward0>), <function profit at 0x7f000d27fdc0>, tensor([1., 1., 1., 1., 1.], requires_grad=True), <function laws_of_motion at 0x7f003e976b80>, tensor([-0.9519, 1.3928, 1.0020, 1.0020, 1.0575], grad_fn=<MvBackward>))\n",
"(tensor([3.5752, 3.5752, 3.5752, 3.5752, 2.9700], grad_fn=<AddBackward0>), tensor([0.0307], grad_fn=<AddBackward0>), <function profit at 0x7f000d27fdc0>, tensor([1., 1., 1., 1., 1.], requires_grad=True), <function laws_of_motion at 0x7f003e976b80>, tensor([-1.8565, 1.5150, 0.9530, 0.9530, 0.9882], grad_fn=<MvBackward>))\n",
"(tensor([4.4781, 4.4781, 4.4781, 4.4781, 3.8222], grad_fn=<AddBackward0>), tensor([0.0284], grad_fn=<AddBackward0>), <function profit at 0x7f000d27fdc0>, tensor([1., 1., 1., 1., 1.], requires_grad=True), <function laws_of_motion at 0x7f003e976b80>, tensor([-2.8103, 1.6872, 0.9376, 0.9376, 0.9474], grad_fn=<MvBackward>))\n",
"(tensor([5.4286, 5.4286, 5.4286, 5.4286, 4.7409], grad_fn=<AddBackward0>), tensor([0.0280], grad_fn=<AddBackward0>), <function profit at 0x7f000d27fdc0>, tensor([1., 1., 1., 1., 1.], requires_grad=True), <function laws_of_motion at 0x7f003e976b80>, tensor([-3.8626, 1.9131, 0.9505, 0.9505, 0.9408], grad_fn=<MvBackward>))\n"
]
}
],
"source": [
"#calculate results for first 5 iterations\n",
"for f in compose_recursive_functions(transition_wrapper,50 ):\n",
"for f in compose_recursive_functions(transition_wrapper,5):\n",
" result = f(base_data)\n",
" print(result[5])"
" print(result)\n",
" #need to write down what this is."
]
},
{
"cell_type": "markdown",
"id": "unnecessary-architec t",
"id": "portable-placement",
"metadata": {},
"source": [
"# Notes on work so far\n",
"the issue below was resolved by choosing a different loss function. The point of needing to do a search over the determinant of A still holds.\n",
">>\n",
"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",
"Alternatively, I can check for areas where the determinant of $A$ is zero, possibly by doing some sort of grid search?\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."
"Also, maybe I can create a `Model` class that upon construction will capture the necesary constants, functions, etc.\n",
"\n",
"I need to change the launch to be a neural network function that takes two inputs."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "varying-organization ",
"id": "frequent-subcommittee",
"metadata": {},
"outputs": [],
"source": []