{ "cells": [ { "cell_type": "markdown", "id": "27ba4115-ed3e-4a13-8d1b-3a5b88d9dc02", "metadata": {}, "source": [ "# Example-04: Frequency" ] }, { "cell_type": "code", "execution_count": 1, "id": "bb26c972-d2ec-437f-89aa-2faba9efb84d", "metadata": {}, "outputs": [], "source": [ "# In this example estimation of frequencies is illustrated\n", "\n", "# Frequency and its several derivatives are computed for a simple 2D symplectic mapping\n", "# Derivatives are used to perform local Taylor approximations\n", "# Result is also compared with an analytical expression obtained from square matrix method" ] }, { "cell_type": "code", "execution_count": 2, "id": "41352809-2cc9-4a8d-9f93-4607f39461b8", "metadata": {}, "outputs": [], "source": [ "# Import\n", "\n", "import numpy\n", "\n", "from tqdm import tqdm\n", "\n", "import jax\n", "from jax import jit\n", "from jax import vmap\n", "from jax import jacrev\n", "from jax import jacfwd\n", "\n", "# Test symplectic mapping and corresponding inverse\n", "\n", "from tohubohu.util import forward4D\n", "from tohubohu.util import inverse4D\n", "\n", "# Exponential window\n", "\n", "from tohubohu import exponential\n", "\n", "# Frequency factory\n", "\n", "from tohubohu import frequency\n", "\n", "# Plotting\n", "\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "import matplotlib.patches as patches\n", "import matplotlib.ticker as ticker\n", "\n", "mpl.rcParams['text.usetex'] = True" ] }, { "cell_type": "code", "execution_count": 3, "id": "fc1edd39-078b-45f3-aeb4-0361c44e7df2", "metadata": {}, "outputs": [], "source": [ "# Set data type\n", "\n", "jax.config.update(\"jax_enable_x64\", False)" ] }, { "cell_type": "code", "execution_count": 4, "id": "f19bc88c-537b-4f52-9e47-c1fc2ba91654", "metadata": {}, "outputs": [], "source": [ "# Set device\n", "\n", "device, *_ = jax.devices('cpu')\n", "jax.config.update('jax_default_device', device)" ] }, { "cell_type": "code", "execution_count": 5, "id": "30787bef-a4ff-4d8d-9942-8bbb8de50810", "metadata": {}, "outputs": [], "source": [ "# SMM frequency expression (perturbation theory)\n", "\n", "def smm(q):\n", " return 0.238052160264804580 \\\n", " - 0.015200217416172931*q**2 \\\n", " + 0.017861595083634475*q**3 \\\n", " + 0.231845856974195660*q**4 \\\n", " - 0.590356798331802200*q**5 \\\n", " + 0.730726019348640000*q**6 \\\n", " + 0.188262070017530800*q**7 \\\n", " - 3.928891073096105300*q**8 \\\n", " + 11.87833362636719600*q**9 \\\n", " - 45.76399509742608000*q**10 \\\n", " + 157.4981904151539000*q**11 \\\n", " - 478.8969677720342000*q**12 \\\n", " + 1177.620316624183000*q**13 \\\n", " - 3147.297909882562000*q**14 \\\n", " + 10163.25232807885200*q**15 \\\n", " + 4648.468950619761000*q**16" ] }, { "cell_type": "code", "execution_count": 6, "id": "318e0013-48c0-4349-a09e-3ecb2755c23b", "metadata": {}, "outputs": [], "source": [ "# Mapping\n", "\n", "@jit\n", "def mapping(x, k):\n", " q, p = x\n", " w, a, b = k\n", " return jax.numpy.stack([p, -q + w*p + a*p**2 + b*p**3])" ] }, { "cell_type": "code", "execution_count": 7, "id": "76b3416f-e9f8-4135-ae65-a80770ac9e19", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Array([0., 0.], dtype=float32)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Define parameters and test mapping\n", "\n", "x = jax.numpy.array([0.0, 0.0])\n", "k = jax.numpy.array([0.15, 1.25, -0.5])\n", "\n", "mapping(x, k)" ] }, { "cell_type": "code", "execution_count": 8, "id": "3db8b351-cb59-44bd-926e-6819814d503b", "metadata": {}, "outputs": [], "source": [ "# Set window\n", "\n", "n = 2**10\n", "ws = exponential(n)" ] }, { "cell_type": "code", "execution_count": 9, "id": "165506e1-b69d-4859-be22-7fdc3b8953c6", "metadata": {}, "outputs": [], "source": [ "# Set initial conditions\n", "\n", "qs = jax.numpy.linspace(-0.350, 0.525, 2**10)\n", "ps = jax.numpy.copy(qs)\n", "xs = jax.numpy.stack([qs, ps]).T" ] }, { "cell_type": "code", "execution_count": 10, "id": "7a78d3e1-2160-479c-a09a-1a49621be6a1", "metadata": {}, "outputs": [], "source": [ "# Set frequency factory\n", "\n", "fn = frequency(ws, mapping)" ] }, { "cell_type": "code", "execution_count": 11, "id": "5cc40453-082d-4437-80cb-ae754cbca9f6", "metadata": {}, "outputs": [], "source": [ "# Compute frequencies for given initials\n", "\n", "out = vmap(fn, (0, None))(xs, k).squeeze()\n", "mat = smm(qs)" ] }, { "cell_type": "code", "execution_count": 12, "id": "712e3b94-430c-4192-8da4-cf1740617992", "metadata": {}, "outputs": [], "source": [ "# Compute frequencies at a coarse grid along with several derivatives\n", "# Note, frequency can't be computed at the origin\n", "\n", "Qs = jax.numpy.array([-0.3, -0.2, -0.1, 0.1, 0.2, 0.3, 0.4])\n", "Ps = jax.numpy.copy(Qs)\n", "Xs = jax.numpy.stack([Qs, Ps]).T\n", "\n", "Fs = []\n", "for X in Xs:\n", " f0 = fn(X, k).squeeze()\n", " f1 = jacrev(fn)(X, k).squeeze()\n", " f2 = jacrev(jacrev(fn))(X, k).squeeze()\n", " f3 = jacrev(jacrev(jacrev(fn)))(X, k).squeeze()\n", " f4 = jacrev(jacrev(jacrev(jacrev(fn))))(X, k).squeeze()\n", " f5 = jacrev(jacrev(jacrev(jacrev(jacrev(fn)))))(X, k).squeeze()\n", " fs = [f0, f1, f2, f3, f4, f5]\n", " Fs.append(fs)" ] }, { "cell_type": "code", "execution_count": 13, "id": "33c76499-98f7-4a98-aca0-7950ad3fd37f", "metadata": {}, "outputs": [], "source": [ "# Series evaluation function\n", "\n", "def evaluate(fs, x):\n", " f0, f1, f2, f3, f4, f5 = fs\n", " return f0 + \\\n", " 1/1 * f1 @ x + \\\n", " 1/2 * f2 @ x @ x + \\\n", " 1/(2*3) * f3 @ x @ x @ x + \\\n", " 1/(2*3*4) * f4 @ x @ x @ x @ x + \\\n", " 1/(2*3*4*5) * f5 @ x @ x @ x @ x @ x" ] }, { "cell_type": "code", "execution_count": 14, "id": "c7007b98-58ce-4c60-8fdf-8702930fe5b2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot\n", "\n", "flag = True\n", "line = jax.numpy.linspace(-0.1, 0.1, 101)\n", "line = jax.numpy.stack([line, line]).T\n", "plt.figure(figsize=(12, 6))\n", "ax = plt.subplot(111)\n", "ax.errorbar(qs, out, color='black', marker=None, fmt='-', lw=3.0, label='tracking', alpha=0.50, zorder=0)\n", "ax.errorbar(qs, mat, color='black', fmt=':', marker=None, lw=2.0, label='smm (perturbation theory)', alpha=0.75, zorder=1)\n", "for X, fs in zip(Xs, Fs):\n", " q, p = X\n", " plt.errorbar(q, evaluate(fs, 0*X), marker='x', fmt=' ', color='blue', ms=6) \n", " x, *_ = (X + line).T\n", " y = vmap(evaluate, (None, 0))(fs, line)\n", " if flag:\n", " flag = False\n", " plt.errorbar(x, y, color='blue', fmt='--', marker=None, label='autodiff', alpha=0.75)\n", " else:\n", " plt.errorbar(x, y, color='blue', fmt='--', marker=None, alpha=0.75)\n", "ax.set_xlim(-0.350 - 0.05, 0.525 + 0.05)\n", "ax.set_ylim(0.2370, 0.2400)\n", "ax.tick_params(width=2, labelsize=18)\n", "ax.tick_params(axis='x', length=10, direction='in')\n", "ax.tick_params(axis='y', length=10, direction='in')\n", "ax.set_ylabel(r'$\\nu (q)$', fontsize=24)\n", "ax.set_xlabel(r'$q$', fontsize=24)\n", "plt.legend(loc=4, ncol=3, frameon=False, prop={'size': 24})\n", "plt.setp(ax.spines.values(), linewidth=2.0)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "df0105d0-85e8-4013-8929-6003d63dee27", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [ "myt0_gMIOq7b", "5d97819c" ], "name": "03_frequency.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.7" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false } }, "nbformat": 4, "nbformat_minor": 5 }