{ "cells": [ { "cell_type": "markdown", "id": "5ac56056-ca33-4f13-8e36-564b94144c1e", "metadata": { "tags": [] }, "source": [ "

Markov Chain Monte Carlo for fun and profit

\n", "

🎲 ⛓️ 👉 🧪

" ] }, { "cell_type": "code", "execution_count": 1, "id": "eb5d773e-4cc0-48ae-bb71-7ece7ab5f936", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from numba import jit\n", "\n", "# This loads some custom styles for matplotlib\n", "import json, matplotlib\n", "\n", "with open(\"assets/matplotlibrc.json\") as f:\n", " matplotlib.rcParams.update(json.load(f))\n", "\n", "np.random.seed(\n", " 42\n", ") # This makes our random numbers reproducable but only when the notebook is run once in order" ] }, { "cell_type": "markdown", "id": "3882f3c7-854e-4394-a982-0e71696cfcc9", "metadata": {}, "source": [ "# Speeding It Up\n", "\n", "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", "\n", "I'll first write a slow version of this using the code we already have, and then use that to validate our faster version:" ] }, { "cell_type": "code", "execution_count": 2, "id": "6c7a2bd3-acc1-45b5-b127-3691ecbe98f0", "metadata": {}, "outputs": [], "source": [ "from MCFF.ising_model import energy, show_state\n", "\n", "\n", "def energy_difference_reference_implementation(state, site):\n", " state = state.copy()\n", " i, j = site\n", " energy_before_flip = energy(state)\n", " state[i, j] *= -1\n", " energy_after_flip = energy(state)\n", " return energy_after_flip - energy_before_flip" ] }, { "cell_type": "markdown", "id": "7b16f42a-0178-4753-9e9d-2f78aed40509", "metadata": {}, "source": [ "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:" ] }, { "cell_type": "code", "execution_count": 3, "id": "9627abbd-16ef-4f66-bf36-01adad101fac", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ref: 144.0, Ours: 144.0\n", "Ref: 108.0, Ours: 108.0\n", "Ref: 72.0, Ours: 72.0\n" ] } ], "source": [ "@jit(nopython=True, nogil=True)\n", "def energy_difference(state, site):\n", " # loop over the four neighbours of the site, skipping if the site is near an edge\n", " N, M = state.shape\n", " i, j = site\n", " h = 0\n", " for di, dj in [[-1, 0], [1, 0], [0, -1], [0, 1]]: # loop over N,E,S,W neighbours\n", " if (0 <= (i + di) < N) and (\n", " 0 <= (j + dj) < M\n", " ): # ignore neighbours not in the NxN grid\n", " h += state[i + di, j + dj]\n", " return 4 * state[i, j] * h\n", "\n", "\n", "# do some simple test cases that I can calculate by hand\n", "state = np.ones(\n", " shape=(3, 3)\n", ") # a simple 3x3 grid is the smallest one where the center has 4 neighbours\n", "sites = [\n", " (1, 1),\n", " (0, 1),\n", " (0, 0),\n", "] # Let's try the center, one on an edge and one on a corner\n", "\n", "for site in sites:\n", " reference = 9 * energy_difference_reference_implementation(state, site)\n", " ours = 9 * energy_difference(state, site)\n", " print(f\"Ref: {reference}, Ours: {ours}\")" ] }, { "cell_type": "markdown", "id": "d2f55f08-2932-4752-9a2e-ea566187a473", "metadata": {}, "source": [ "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:" ] }, { "cell_type": "code", "execution_count": 4, "id": "a4b71b4d-e69d-497b-bb6b-4375b16159a4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tests Passed!\n" ] } ], "source": [ "N = 50\n", "values = np.array([1, -1], dtype=np.int8)\n", "\n", "for _ in range(100):\n", " random_state = np.random.choice(values, size=(N, N))\n", " random_site = np.random.randint(N, size=2)\n", " assert np.allclose(\n", " energy_difference_reference_implementation(random_state, random_site),\n", " energy_difference(random_state, random_site),\n", " )\n", "print(\"Tests Passed!\")" ] }, { "cell_type": "markdown", "id": "e6ecbc7c-530f-494b-aa31-0a118a104328", "metadata": {}, "source": [ "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!" ] }, { "cell_type": "code", "execution_count": 5, "id": "41627f33-6672-4241-aea7-b0210bc4aba1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "60.5 µs ± 2.1 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n", "1.15 µs ± 111 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n", "54x Speedup!\n" ] } ], "source": [ "N = 100\n", "random_state = np.random.choice(values, size=(N, N))\n", "random_site = np.random.randint(N, size=2)\n", "\n", "reference = %timeit -n 1000 -o energy_difference_reference_implementation(random_state, random_site)\n", "ours = %timeit -n 1000 -o energy_difference(random_state, random_site)\n", "print(f\"{reference.best / ours.best:.0f}x Speedup!\")" ] }, { "cell_type": "markdown", "id": "0311b4d9-43b7-42ab-ad19-973094020c03", "metadata": {}, "source": [ "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:" ] }, { "cell_type": "code", "execution_count": 6, "id": "942ce715-0f55-43b5-a1e0-91057fd4ecc1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.57 s ± 25.7 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n", "65.2 ms ± 557 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n", "39x speedup!\n" ] } ], "source": [ "@jit(nopython=True, nogil=True)\n", "def old_mcmc_generator(initial_state, steps, T, stepsize=1000, energy=energy):\n", " N, M = initial_state.shape\n", " assert N == M\n", "\n", " current_state = initial_state.copy()\n", " E = N**2 * energy(current_state)\n", " for _ in range(steps):\n", " for _ in range(stepsize):\n", " i, j = np.random.randint(N), np.random.randint(N)\n", "\n", " # modify the state a little, here we just flip a random pixel\n", " current_state[i, j] *= -1\n", " new_E = N**2 * energy(current_state)\n", "\n", " if (new_E < E) or np.exp(-(new_E - E) / T) > np.random.random():\n", " E = new_E\n", " else:\n", " current_state[i, j] *= -1 # reject the change we made\n", " yield current_state.copy()\n", " return\n", "\n", "\n", "@jit(nopython=True, nogil=True)\n", "def mcmc_generator(\n", " initial_state, steps, T, stepsize=1000, energy_difference=energy_difference\n", "):\n", " N, M = initial_state.shape\n", " assert N == M\n", "\n", " current_state = initial_state.copy()\n", " for _ in range(steps):\n", " for _ in range(stepsize):\n", " i, j = np.random.randint(N), np.random.randint(N)\n", "\n", " # calculate the energy change if we were to flip this pixel but don't actually do it\n", " change_in_E = N**2 * energy_difference(current_state, (i, j))\n", "\n", " if change_in_E < 0 or np.exp(-change_in_E / T) > np.random.random():\n", " current_state[i, j] *= -1 # accept the change!\n", "\n", " yield current_state.copy()\n", " return\n", "\n", "\n", "N_steps = 1000\n", "stepsize = 100\n", "N = 100\n", "initial_state = np.ones(shape=(N, N))\n", "old = %timeit -o [_ for s in old_mcmc_generator(initial_state, T = 5, steps = N_steps, stepsize = stepsize)]\n", "new = %timeit -o [_ for s in mcmc_generator(initial_state, T = 5, steps = N_steps, stepsize = stepsize)]\n", "print(f\"{old.best / new.best:.0f}x speedup!\")" ] }, { "cell_type": "markdown", "id": "bd67385b-c8b3-4c1b-bb96-6856eaa6aa7e", "metadata": {}, "source": [ "We can now comfortably look at much larger systems!" ] }, { "cell_type": "code", "execution_count": 7, "id": "ca619dc7-9b3f-45f7-ad0d-751b60b37cdb", "metadata": {}, "outputs": [], "source": [ "### Simulation Inputs ###\n", "N = 500 # Use an NxN system\n", "steps = 5 # How many times to sample the state\n", "stepsize = (\n", " 5 * N**2\n", ") # How many individual monte carlo flips to do in between each sample\n", "initial_state = np.random.choice(\n", " np.array([-1, 1], dtype=np.int8), size=(N, N)\n", ") # the intial state to use\n", "T = 3.5\n", "\n", "### Simulation Code ###\n", "critical_states = [\n", " s for s in mcmc_generator(initial_state, steps=steps, stepsize=stepsize, T=T)\n", "]" ] }, { "cell_type": "code", "execution_count": 8, "id": "4c7b0ef0-b630-49c7-9ea5-f60325309751", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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)" ] } ], "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 }