mirror of
https://github.com/ImperialCollegeLondon/ReCoDE_MCMCFF.git
synced 2025-06-26 08:51:16 +02:00
474 lines
130 KiB
Plaintext
474 lines
130 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "5ac56056-ca33-4f13-8e36-564b94144c1e",
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"metadata": {
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"tags": []
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},
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"source": [
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"<h1 align=\"center\">Markov Chain Monte Carlo for fun and profit</h1>\n",
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"<h1 align=\"center\"> 🎲 ⛓️ 👉 🧪 </h1>"
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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": 1,
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"id": "eb5d773e-4cc0-48ae-bb71-7ece7ab5f936",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from numba import jit\n",
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"\n",
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"# This loads some custom styles for matplotlib\n",
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"import json, matplotlib\n",
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"\n",
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"with open(\"assets/matplotlibrc.json\") as f:\n",
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" matplotlib.rcParams.update(json.load(f))\n",
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"\n",
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"np.random.seed(\n",
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" 42\n",
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") # This makes our random numbers reproducable but only when the notebook is run once in order\n",
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"\n",
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"\n",
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"def show_state(state, ax=None):\n",
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" if ax is None:\n",
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" f, ax = plt.subplots()\n",
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" ax.matshow(state, cmap=\"Greys\", vmin=-1, vmax=1)\n",
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" ax.set(xticks=[], yticks=[])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3882f3c7-854e-4394-a982-0e71696cfcc9",
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"metadata": {},
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"source": [
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"## Making it faster and the dangers of premature optimisation\n",
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"\n",
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"In order to show you a really big system will still need to make the code a bit faster. Right now we calculate the energy of each state, flip a pixel and then calculate the energy again. It turns out that you can actually directly calculate the energy change instead of doing this subtraction. Let's do this is a sort of test driven decelopment fashion: we want to write a function that when given a state and a pixel to flip, returns how much the energy goes up by (negative if down) upon performing the flip.\n",
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"\n",
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"I'll first write a slow version of this using the code we already have, and then use that to validate our faster version:"
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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": "6c7a2bd3-acc1-45b5-b127-3691ecbe98f0",
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"metadata": {},
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"outputs": [],
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"source": [
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"from MCFF.ising_model import energy\n",
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"\n",
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"\n",
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"def energy_difference_reference_implementation(state, site):\n",
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" state = state.copy()\n",
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" i, j = site\n",
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" energy_before_flip = energy(state)\n",
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" state[i, j] *= -1\n",
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" energy_after_flip = energy(state)\n",
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" return energy_after_flip - energy_before_flip"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7b16f42a-0178-4753-9e9d-2f78aed40509",
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"metadata": {},
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"source": [
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"Now if you stare at the definition of energy long enough, you can convince yourself that the energy change when you flip one pixel only depends on the four surounding pixels in a simple way:"
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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": "9627abbd-16ef-4f66-bf36-01adad101fac",
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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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"Ref: 16.0, Ours: 16.0\n",
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"Ref: 12.0, Ours: 12.0\n",
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"Ref: 8.0, Ours: 8.0\n"
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]
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}
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],
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"source": [
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"@jit(nopython=True, nogil=True)\n",
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"def energy_difference(state, site):\n",
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" # loop over the four neighbours of the site, skipping if the site is near an edge\n",
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" N, M = state.shape\n",
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" i, j = site\n",
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" h = 0\n",
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" for di, dj in [[-1, 0], [1, 0], [0, -1], [0, 1]]: # loop over N,E,S,W neighbours\n",
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" if (0 <= (i + di) < N) and (\n",
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" 0 <= (j + dj) < M\n",
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" ): # ignore neighbours not in the NxN grid\n",
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" h += state[i + di, j + dj]\n",
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" return 4 * state[i, j] * h / (N * M)\n",
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"\n",
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"\n",
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"# do some simple test cases that I can calculate by hand\n",
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"state = np.ones(\n",
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" shape=(3, 3)\n",
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") # a simple 3x3 grid is the smallest one where the center has 4 neighbours\n",
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"sites = [\n",
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" (1, 1),\n",
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" (0, 1),\n",
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" (0, 0),\n",
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"] # Let's try the center, one on an edge and one on a corner\n",
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"\n",
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"for site in sites:\n",
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" reference = 9 * energy_difference_reference_implementation(state, site)\n",
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" ours = 9 * energy_difference(state, site)\n",
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" print(f\"Ref: {reference}, Ours: {ours}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d2f55f08-2932-4752-9a2e-ea566187a473",
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"metadata": {},
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"source": [
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"Ok these simple tests looks good! I was struggling both with the correct factors of two and the sign, so seeing the outputs compared helped a lot. Now let's test against some random data:"
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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": "a4b71b4d-e69d-497b-bb6b-4375b16159a4",
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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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"Tests Passed!\n"
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]
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}
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],
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"source": [
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"N = 50\n",
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"values = np.array([1, -1], dtype=np.int8)\n",
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"\n",
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"for _ in range(100):\n",
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" random_state = np.random.choice(values, size=(N, N))\n",
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" random_site = np.random.randint(N, size=2)\n",
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" assert np.allclose(\n",
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" energy_difference_reference_implementation(random_state, random_site),\n",
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" energy_difference(random_state, random_site),\n",
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" )\n",
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"print(\"Tests Passed!\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e6ecbc7c-530f-494b-aa31-0a118a104328",
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"metadata": {},
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"source": [
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"Ok great! And this function is much much faster because it only has to look at four pixels rather than all $N^2$ of them!"
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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": "41627f33-6672-4241-aea7-b0210bc4aba1",
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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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"64.3 µs ± 3.62 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n",
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"1.2 µs ± 156 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n",
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"56x Speedup!\n"
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]
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}
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],
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"source": [
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"N = 100\n",
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"random_state = np.random.choice(values, size=(N, N))\n",
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"random_site = np.random.randint(N, size=2)\n",
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"\n",
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"reference = %timeit -n 1000 -o energy_difference_reference_implementation(random_state, random_site)\n",
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"ours = %timeit -n 1000 -o energy_difference(random_state, random_site)\n",
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"print(f\"{reference.best / ours.best:.0f}x Speedup!\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0311b4d9-43b7-42ab-ad19-973094020c03",
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"metadata": {},
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"source": [
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"We get a good speedup that increases with N and should be about $N^2$ for very large values of N. Ok so how do we use this? Well we need to rewrite mcmc yet again:"
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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": 6,
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"id": "942ce715-0f55-43b5-a1e0-91057fd4ecc1",
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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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"2.58 s ± 33.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
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"69.5 ms ± 2.64 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
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"37x speedup!\n"
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]
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}
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],
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"source": [
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"@jit(nopython=True, nogil=True)\n",
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"def old_mcmc_generator(initial_state, steps, T, stepsize=1000, energy=energy):\n",
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" N, M = initial_state.shape\n",
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" assert N == M\n",
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"\n",
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" current_state = initial_state.copy()\n",
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" E = N**2 * energy(current_state)\n",
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" for _ in range(steps):\n",
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" for _ in range(stepsize):\n",
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" i, j = np.random.randint(N), np.random.randint(N)\n",
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"\n",
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" # modify the state a little, here we just flip a random pixel\n",
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" current_state[i, j] *= -1\n",
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" new_E = N**2 * energy(current_state)\n",
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"\n",
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" if (new_E < E) or np.exp(-(new_E - E) / T) > np.random.random():\n",
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" E = new_E\n",
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" else:\n",
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" current_state[i, j] *= -1 # reject the change we made\n",
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" yield current_state.copy()\n",
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" return\n",
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"\n",
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"\n",
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"@jit(nopython=True, nogil=True)\n",
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"def mcmc_generator(\n",
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" initial_state, steps, T, stepsize=1000, energy_difference=energy_difference\n",
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"):\n",
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" N, M = initial_state.shape\n",
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" assert N == M\n",
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"\n",
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" current_state = initial_state.copy()\n",
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" for _ in range(steps):\n",
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" for _ in range(stepsize):\n",
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" i, j = np.random.randint(N), np.random.randint(N)\n",
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"\n",
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" # calculate the energy change if we were to flip this pixel but don't actually do it\n",
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" change_in_E = N**2 * energy_difference(current_state, (i, j))\n",
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"\n",
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" if change_in_E < 0 or np.exp(-change_in_E / T) > np.random.random():\n",
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" current_state[i, j] *= -1 # accept the change!\n",
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"\n",
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" yield current_state.copy()\n",
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" return\n",
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"\n",
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"\n",
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"N_steps = 1000\n",
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"stepsize = 100\n",
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"N = 100\n",
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"initial_state = np.ones(shape=(N, N))\n",
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"old = %timeit -o [_ for s in old_mcmc_generator(initial_state, T = 5, steps = N_steps, stepsize = stepsize)]\n",
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"new = %timeit -o [_ for s in mcmc_generator(initial_state, T = 5, steps = N_steps, stepsize = stepsize)]\n",
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"print(f\"{old.best / new.best:.0f}x speedup!\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bd67385b-c8b3-4c1b-bb96-6856eaa6aa7e",
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"metadata": {},
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"source": [
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"We can now comfortably look at much larger systems!"
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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": 7,
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"id": "ca619dc7-9b3f-45f7-ad0d-751b60b37cdb",
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"metadata": {},
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"outputs": [],
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"source": [
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"### Simulation Inputs ###\n",
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"N = 500 # Use an NxN system\n",
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"steps = 5 # How many times to sample the state\n",
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"stepsize = (\n",
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" 5 * N**2\n",
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") # How many individual monte carlo flips to do in between each sample\n",
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"initial_state = np.random.choice(\n",
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" np.array([-1, 1], dtype=np.int8), size=(N, N)\n",
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") # the intial state to use\n",
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"T = 3.5\n",
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"\n",
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"### Simulation Code ###\n",
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"critical_states = [\n",
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" s for s in mcmc_generator(initial_state, steps=steps, stepsize=stepsize, T=T)\n",
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"]"
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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": 8,
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"id": "4c7b0ef0-b630-49c7-9ea5-f60325309751",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 1800x360 with 5 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"fig, axes = plt.subplots(\n",
|
|
" ncols=len(critical_states), figsize=(5 * len(critical_states), 5)\n",
|
|
")\n",
|
|
"\n",
|
|
"for s, ax in zip(critical_states, axes):\n",
|
|
" show_state(s, ax=ax)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "aeb46049-4e33-44df-a523-aaee231e2a0d",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Average Color and 'Susceptability'\n",
|
|
"\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "e7595584-4d1c-4734-912f-a6692308dc7d",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"### The measurement we will make ###\n",
|
|
"def average_color(state):\n",
|
|
" return np.mean(state)\n",
|
|
"\n",
|
|
"\n",
|
|
"### Simulation Inputs ###\n",
|
|
"Ns = np.array(\n",
|
|
" [\n",
|
|
" 30,\n",
|
|
" ]\n",
|
|
") # Use an NxN system\n",
|
|
"Ts = np.linspace(4, 5.5, 20) # What temperatures to use\n",
|
|
"steps = 1000 # How many times to sample the state\n",
|
|
"stepsize = (\n",
|
|
" lambda N: N**2\n",
|
|
") # How many individual monte carlo flips to do in between each sample\n",
|
|
"N_repeats = 2 # How many times to repeat each run at fixed temperature\n",
|
|
"\n",
|
|
"### Simulation Code ###\n",
|
|
"average_color_data = np.array(\n",
|
|
" [\n",
|
|
" [\n",
|
|
" [\n",
|
|
" [\n",
|
|
" average_color(s)\n",
|
|
" for s in mcmc_generator(\n",
|
|
" np.ones(shape=(N, N)), steps=steps, stepsize=stepsize(N), T=T\n",
|
|
" )\n",
|
|
" ]\n",
|
|
" for _ in range(N_repeats)\n",
|
|
" ]\n",
|
|
" for T in Ts\n",
|
|
" ]\n",
|
|
" for N in Ns\n",
|
|
" ]\n",
|
|
")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"id": "5d9d37a1-2ceb-4f63-8e40-9362880bd469",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"mean_color = np.mean(average_color_data, axis=(-2, -1))\n",
|
|
"color_susceptability = np.std(average_color_data, axis=-1).mean(axis=-1)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"id": "22aaa06b-6580-4b16-a15b-2fe35b8af8d3",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<matplotlib.legend.Legend at 0x7fec41728eb0>"
|
|
]
|
|
},
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
},
|
|
{
|
|
"data": {
|
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"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"fig, axes = plt.subplots(nrows=2, sharex=\"col\")\n",
|
|
"\n",
|
|
"for i, N in enumerate(Ns):\n",
|
|
" axes[0].plot(Ts, mean_color[i], label=f\"N = {N}\")\n",
|
|
" axes[1].plot(Ts, color_susceptability[i])\n",
|
|
"\n",
|
|
"axes[0].legend()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"id": "47d24c1d-9854-46a4-9da2-e1d4a382b09e",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"### try combining mpiere, itertools.product and xarray"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python [conda env:recode]",
|
|
"language": "python",
|
|
"name": "conda-env-recode-py"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.9.12"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|