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jxy/2du1.ipynb

Created March 7, 2019 19:10
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2du1.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "2DU1.ipynb",
"version": "0.3.2",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"accelerator": "TPU"
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/jxy/0a65b68ea27fbb2121c403c0cee85752/2du1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"metadata": {
"id": "Wd4yXWk9rICc",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"MIT License\n",
"\n",
"Copyright (c) 2019 Xiao-Yong Jin\n",
"\n",
"Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n",
"\n",
"The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n",
"\n",
"THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE."
]
},
{
"metadata": {
"id": "atHZ8W7jCYK-",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"import tensorflow as tf\n",
"import math\n",
"import timeit\n",
"tf.logging.set_verbosity(tf.logging.INFO)"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "9PQOoyHd-GeG",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"beta = 6.0 # 4.0\n",
"nx = 64 # 8\n",
"nt = 64 # 8\n",
"nd = 2\n",
"tau = 2 # 0.3\n",
"nstep = 50 # 3\n",
"ntraj = 256 # 2**16 # 2**10 # 2**15\n",
"nprint = 256\n",
"seed = 1331"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "6MlCMisDrsnf",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"dt = tau/nstep\n",
"tf.set_random_seed(seed)"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "mBoVn4ZcCdyf",
"colab_type": "code",
"outputId": "bcbad02b-7ee8-4be1-9a35-2ae8674b9550",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 108
}
},
"cell_type": "code",
"source": [
"field = tf.get_variable(\"field\", [nd,nx,nt], dtype=tf.float64, initializer=tf.zeros_initializer) # mu, x, t\n",
"#field = tf.get_variable(\"field\", [nd,nx,nt], dtype=tf.float64, initializer=tf.random_uniform_initializer(-math.pi, math.pi)) # mu, x, t"
],
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": [
"WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/framework/op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
"Instructions for updating:\n",
"Colocations handled automatically by placer.\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "W9JttzTPC0Re",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"plaqphase = lambda f: f[0,:] - f[1,:] - tf.roll(f[0,:], shift=-1, axis=1) + tf.roll(f[1,:], shift=-1, axis=0)\n",
"action = lambda f: (-beta)*tf.reduce_sum(tf.cos(plaqphase(f)))\n",
"#def action_and_force(f):\n",
"# with tf.GradientTape() as t:\n",
"# t.watch(f)\n",
"# s = action(f)\n",
"# return (s, t.gradient(s, f))\n",
"#force = lambda f: action_and_force(f)[1]\n",
"#def force(f):\n",
"# with tf.GradientTape() as t:\n",
"# t.watch(f)\n",
"# s = action(f)\n",
"# return t.gradient(s, f)\n",
"def force(f):\n",
" s = action(f)\n",
" return tf.gradients(s, f)[0]\n",
"def regularize(f):\n",
" p2 = 2*math.pi\n",
" f_ = f - math.pi\n",
" return p2*(f_/p2 - tf.floordiv(f_, p2) - 0.5)\n",
"topocharge = lambda f: tf.floor(0.1 + tf.reduce_sum(regularize(plaqphase(f))) / (2*math.pi))"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "jfeQHeAdX3o0",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"def leapfrog(x, p):\n",
" x_ = x + 0.5*dt*p\n",
" p_ = p + (-dt)*force(x_)\n",
" def body(i, xx, pp):\n",
" xx_ = xx + dt*pp\n",
" pp_ = pp + (-dt)*force(xx_)\n",
" return (i+1, xx_, pp_)\n",
" _, x__, pp = tf.while_loop(\n",
" lambda i, xx, pp: i < nstep-1,\n",
" body,\n",
" (0, x_, p_))\n",
" xx = x__ + 0.5*dt*pp\n",
" return (xx, pp)\n",
"def hmc(x):\n",
" p = tf.random.normal(tf.shape(x), dtype=tf.float64)\n",
" act0 = action(x) + 0.5*tf.reduce_sum(p*p)\n",
" x_, p_ = leapfrog(x, p)\n",
" xr = regularize(x_)\n",
" act = action(xr) + 0.5*tf.reduce_sum(p_*p_)\n",
" prob = tf.random.uniform([], dtype=tf.float64)\n",
" dH = act-act0\n",
" exp_mdH = tf.exp(-dH)\n",
" acc = tf.less(prob, exp_mdH)\n",
" newx = tf.cond(acc, lambda: xr, lambda: x)\n",
" return (dH, exp_mdH, acc, newx)"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "x1DPImkddDHI",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"dH, exp_mdH, acc, field_ = hmc(field)\n",
"plaq = action(field_) / (-beta*nx*nt)\n",
"topo = topocharge(field_)\n",
"update = field.assign(field_)"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "sAH71vu5fFY7",
"colab_type": "code",
"outputId": "6a25d3cc-60aa-42ef-c0dd-03b3c8e3859e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 4522
}
},
"cell_type": "code",
"source": [
"def run():\n",
" with open(f\"tf_out_l{nx}_t{nt}_b{beta}_n{ntraj}_t{tau}_s{nstep}\", \"w\") as O:\n",
" params = f\"\"\"latsize = @[{nx}, {nt}]\n",
"volume = {nx*nt}\n",
"beta = {beta}\n",
"trajs = {ntraj}\n",
"tau = {tau}\n",
"steps = {nstep}\n",
"\"\"\"\n",
" O.write(params)\n",
" print(params)\n",
" with tf.Session() as sess:\n",
" sess.run(tf.global_variables_initializer())\n",
" plaq_, topo_ = sess.run((action(field) / (-beta*nx*nt), topocharge(field_)))\n",
" status = f\"\"\"Initial configuration: plaq: {plaq_} topo: {topo_}\"\"\"\n",
" O.write(status)\n",
" print(status)\n",
" for i in range(ntraj):\n",
" _, dH_, exp_mdH_, acc_, plaq_, topo_ = sess.run((update, dH, exp_mdH, acc, plaq, topo))\n",
" ifacc = \"ACCEPT\" if acc_ else \"REJECT\"\n",
" status = f\"\"\"Begin traj: {i+1:4} {ifacc}: dH: {dH_:< 12.8} exp(-dH): {exp_mdH_:< 12.8} plaq: {plaq_:< 12.8} topo: {topo_:< 3.3}\"\"\"\n",
" O.write(status)\n",
" if (i+1) % (ntraj//nprint) == 0:\n",
" print(status)\n",
"print(\"Run time: \", timeit.timeit('run()', \"from __main__ import run\", number=1), \" seconds\")"
],
"execution_count": 8,
"outputs": [
{
"output_type": "stream",
"text": [
"latsize = @[64, 64]\n",
"volume = 4096\n",
"beta = 6.0\n",
"trajs = 256\n",
"tau = 2\n",
"steps = 50\n",
"\n",
"Initial configuration: plaq: 1.0 topo: 0.0\n",
"Begin traj: 1 ACCEPT: dH: -8.2471512 exp(-dH): 3816.7373 plaq: 0.96220454 topo: 0.0\n",
"Begin traj: 2 ACCEPT: dH: -2.6898929 exp(-dH): 14.730098 plaq: 0.95033611 topo: 0.0\n",
"Begin traj: 3 ACCEPT: dH: -2.1079702 exp(-dH): 8.2315162 plaq: 0.94198881 topo: 0.0\n",
"Begin traj: 4 ACCEPT: dH: -0.39806415 exp(-dH): 1.4889395 plaq: 0.9394022 topo: 0.0\n",
"Begin traj: 5 ACCEPT: dH: -0.36446187 exp(-dH): 1.439739 plaq: 0.93742714 topo: 0.0\n",
"Begin traj: 6 ACCEPT: dH: -1.2066165 exp(-dH): 3.3421574 plaq: 0.93340371 topo: 0.0\n",
"Begin traj: 7 ACCEPT: dH: -0.4859068 exp(-dH): 1.6256485 plaq: 0.93150009 topo: 0.0\n",
"Begin traj: 8 ACCEPT: dH: -0.31169629 exp(-dH): 1.3657398 plaq: 0.92979908 topo: 0.0\n",
"Begin traj: 9 ACCEPT: dH: -0.1513463 exp(-dH): 1.1633995 plaq: 0.92876663 topo: 0.0\n",
"Begin traj: 10 ACCEPT: dH: -0.65799614 exp(-dH): 1.9309192 plaq: 0.92669765 topo: 0.0\n",
"Begin traj: 11 ACCEPT: dH: -0.39187757 exp(-dH): 1.4797565 plaq: 0.92470908 topo: 0.0\n",
"Begin traj: 12 ACCEPT: dH: -0.16033716 exp(-dH): 1.1739066 plaq: 0.9248211 topo: 0.0\n",
"Begin traj: 13 REJECT: dH: 0.27234605 exp(-dH): 0.76159067 plaq: 0.9248211 topo: 0.0\n",
"Begin traj: 14 ACCEPT: dH: -0.55093362 exp(-dH): 1.734872 plaq: 0.92180581 topo: 0.0\n",
"Begin traj: 15 ACCEPT: dH: -0.080743691 exp(-dH): 1.084093 plaq: 0.92144245 topo: 0.0\n",
"Begin traj: 16 ACCEPT: dH: 0.36196808 exp(-dH): 0.69630459 plaq: 0.92186558 topo: 0.0\n",
"Begin traj: 17 ACCEPT: dH: -0.080874042 exp(-dH): 1.0842343 plaq: 0.9222235 topo: 0.0\n",
"Begin traj: 18 ACCEPT: dH: -0.48557955 exp(-dH): 1.6251166 plaq: 0.92067793 topo: 0.0\n",
"Begin traj: 19 ACCEPT: dH: -0.041061843 exp(-dH): 1.0419165 plaq: 0.91905976 topo: 0.0\n",
"Begin traj: 20 ACCEPT: dH: -0.052622879 exp(-dH): 1.0540321 plaq: 0.91861249 topo: 0.0\n",
"Begin traj: 21 ACCEPT: dH: -0.17273822 exp(-dH): 1.1885549 plaq: 0.91885163 topo: 0.0\n",
"Begin traj: 22 ACCEPT: dH: -0.41829127 exp(-dH): 1.5193632 plaq: 0.91831452 topo: 0.0\n",
"Begin traj: 23 ACCEPT: dH: -0.27607823 exp(-dH): 1.317951 plaq: 0.91616228 topo: 0.0\n",
"Begin traj: 24 ACCEPT: dH: -0.18042312 exp(-dH): 1.197724 plaq: 0.91555968 topo: -1.0\n",
"Begin traj: 25 ACCEPT: dH: 0.18647572 exp(-dH): 0.82987871 plaq: 0.9162462 topo: -1.0\n",
"Begin traj: 26 ACCEPT: dH: -0.62747226 exp(-dH): 1.8728705 plaq: 0.91258408 topo: -1.0\n",
"Begin traj: 27 REJECT: dH: 0.34771628 exp(-dH): 0.70629924 plaq: 0.91258408 topo: -1.0\n",
"Begin traj: 28 ACCEPT: dH: 0.45217643 exp(-dH): 0.63624191 plaq: 0.91556491 topo: -1.0\n",
"Begin traj: 29 REJECT: dH: 0.75623511 exp(-dH): 0.46943046 plaq: 0.91556491 topo: -1.0\n",
"Begin traj: 30 REJECT: dH: 0.73042672 exp(-dH): 0.48170339 plaq: 0.91556491 topo: -1.0\n",
"Begin traj: 31 ACCEPT: dH: -0.23004875 exp(-dH): 1.2586614 plaq: 0.91661096 topo: -1.0\n",
"Begin traj: 32 ACCEPT: dH: 0.11618333 exp(-dH): 0.89031199 plaq: 0.91413485 topo: -1.0\n",
"Begin traj: 33 ACCEPT: dH: 0.041393318 exp(-dH): 0.95945169 plaq: 0.91575157 topo: -1.0\n",
"Begin traj: 34 ACCEPT: dH: 0.29430093 exp(-dH): 0.74505225 plaq: 0.91460708 topo: -1.0\n",
"Begin traj: 35 ACCEPT: dH: 0.24338222 exp(-dH): 0.78397181 plaq: 0.9168058 topo: -1.0\n",
"Begin traj: 36 ACCEPT: dH: -0.61603602 exp(-dH): 1.8515739 plaq: 0.91359242 topo: -1.0\n",
"Begin traj: 37 ACCEPT: dH: 0.11805502 exp(-dH): 0.88864716 plaq: 0.91360389 topo: -1.0\n",
"Begin traj: 38 ACCEPT: dH: -0.40445465 exp(-dH): 1.4984851 plaq: 0.91232048 topo: -1.0\n",
"Begin traj: 39 ACCEPT: dH: 0.025988987 exp(-dH): 0.97434582 plaq: 0.91296782 topo: -1.0\n",
"Begin traj: 40 ACCEPT: dH: -0.4107493 exp(-dH): 1.5079473 plaq: 0.91259896 topo: 0.0\n",
"Begin traj: 41 ACCEPT: dH: 0.19135728 exp(-dH): 0.82583748 plaq: 0.91351643 topo: 0.0\n",
"Begin traj: 42 REJECT: dH: 0.58349683 exp(-dH): 0.55794392 plaq: 0.91351643 topo: 0.0\n",
"Begin traj: 43 ACCEPT: dH: -0.069817168 exp(-dH): 1.0723121 plaq: 0.91257167 topo: 0.0\n",
"Begin traj: 44 ACCEPT: dH: 1.025199 exp(-dH): 0.35872506 plaq: 0.91772986 topo: 0.0\n",
"Begin traj: 45 ACCEPT: dH: 0.10841529 exp(-dH): 0.8972549 plaq: 0.91822952 topo: 0.0\n",
"Begin traj: 46 ACCEPT: dH: 0.023053695 exp(-dH): 0.97721001 plaq: 0.91703429 topo: 0.0\n",
"Begin traj: 47 ACCEPT: dH: -0.65085151 exp(-dH): 1.9171726 plaq: 0.91465958 topo: 0.0\n",
"Begin traj: 48 ACCEPT: dH: -0.21889682 exp(-dH): 1.2447028 plaq: 0.91416764 topo: 0.0\n",
"Begin traj: 49 ACCEPT: dH: -0.45829583 exp(-dH): 1.5813768 plaq: 0.91190437 topo: 0.0\n",
"Begin traj: 50 REJECT: dH: 0.37918946 exp(-dH): 0.68441593 plaq: 0.91190437 topo: 0.0\n",
"Begin traj: 51 ACCEPT: dH: 0.41108487 exp(-dH): 0.66293066 plaq: 0.91434297 topo: 0.0\n",
"Begin traj: 52 ACCEPT: dH: -0.010377784 exp(-dH): 1.0104318 plaq: 0.91384302 topo: 0.0\n",
"Begin traj: 53 ACCEPT: dH: -0.41207424 exp(-dH): 1.5099465 plaq: 0.91305653 topo: 0.0\n",
"Begin traj: 54 ACCEPT: dH: -0.51629421 exp(-dH): 1.6758059 plaq: 0.9111363 topo: 0.0\n",
"Begin traj: 55 REJECT: dH: 0.60741022 exp(-dH): 0.54475985 plaq: 0.9111363 topo: 0.0\n",
"Begin traj: 56 REJECT: dH: 0.44642191 exp(-dH): 0.63991373 plaq: 0.9111363 topo: 0.0\n",
"Begin traj: 57 ACCEPT: dH: 0.3711846 exp(-dH): 0.68991657 plaq: 0.9123624 topo: 0.0\n",
"Begin traj: 58 REJECT: dH: 0.07295567 exp(-dH): 0.92964204 plaq: 0.9123624 topo: 0.0\n",
"Begin traj: 59 REJECT: dH: 0.46507601 exp(-dH): 0.62808736 plaq: 0.9123624 topo: 0.0\n",
"Begin traj: 60 REJECT: dH: 0.64089561 exp(-dH): 0.52682039 plaq: 0.9123624 topo: 0.0\n",
"Begin traj: 61 ACCEPT: dH: 0.12047102 exp(-dH): 0.88650277 plaq: 0.91363905 topo: -1.0\n",
"Begin traj: 62 ACCEPT: dH: -0.15543248 exp(-dH): 1.1681631 plaq: 0.91376113 topo: -1.0\n",
"Begin traj: 63 REJECT: dH: 0.6037464 exp(-dH): 0.54675942 plaq: 0.91376113 topo: -1.0\n",
"Begin traj: 64 ACCEPT: dH: 0.060260909 exp(-dH): 0.94151885 plaq: 0.91314071 topo: -1.0\n",
"Begin traj: 65 ACCEPT: dH: 0.43857758 exp(-dH): 0.64495316 plaq: 0.91400291 topo: -1.0\n",
"Begin traj: 66 ACCEPT: dH: -0.13632569 exp(-dH): 1.1460551 plaq: 0.91292386 topo: -1.0\n",
"Begin traj: 67 ACCEPT: dH: -0.21871827 exp(-dH): 1.2444806 plaq: 0.91058568 topo: -1.0\n",
"Begin traj: 68 ACCEPT: dH: -0.028157625 exp(-dH): 1.0285578 plaq: 0.91224075 topo: -1.0\n",
"Begin traj: 69 REJECT: dH: 0.42128305 exp(-dH): 0.65620433 plaq: 0.91224075 topo: -1.0\n",
"Begin traj: 70 ACCEPT: dH: 0.33208063 exp(-dH): 0.71742948 plaq: 0.91308121 topo: -1.0\n",
"Begin traj: 71 ACCEPT: dH: 0.2832612 exp(-dH): 0.753323 plaq: 0.91530285 topo: -1.0\n",
"Begin traj: 72 ACCEPT: dH: -0.66281643 exp(-dH): 1.9402492 plaq: 0.91192296 topo: -1.0\n",
"Begin traj: 73 REJECT: dH: 0.7508933 exp(-dH): 0.47194478 plaq: 0.91192296 topo: -1.0\n",
"Begin traj: 74 REJECT: dH: 0.43261546 exp(-dH): 0.64880994 plaq: 0.91192296 topo: -1.0\n",
"Begin traj: 75 ACCEPT: dH: -0.24288281 exp(-dH): 1.2749192 plaq: 0.91160619 topo: -1.0\n",
"Begin traj: 76 ACCEPT: dH: -0.20257558 exp(-dH): 1.2245526 plaq: 0.9105202 topo: 0.0\n",
"Begin traj: 77 REJECT: dH: 0.47685295 exp(-dH): 0.6207338 plaq: 0.9105202 topo: 0.0\n",
"Begin traj: 78 REJECT: dH: 0.96789403 exp(-dH): 0.37988222 plaq: 0.9105202 topo: 0.0\n",
"Begin traj: 79 ACCEPT: dH: 0.38567341 exp(-dH): 0.67999257 plaq: 0.91187693 topo: 0.0\n",
"Begin traj: 80 REJECT: dH: 0.57456361 exp(-dH): 0.56295048 plaq: 0.91187693 topo: 0.0\n",
"Begin traj: 81 ACCEPT: dH: -0.1693416 exp(-dH): 1.1845247 plaq: 0.90994973 topo: 0.0\n",
"Begin traj: 82 REJECT: dH: 0.35450823 exp(-dH): 0.70151834 plaq: 0.90994973 topo: 0.0\n",
"Begin traj: 83 ACCEPT: dH: 0.47673362 exp(-dH): 0.62080788 plaq: 0.91343011 topo: 0.0\n",
"Begin traj: 84 ACCEPT: dH: -0.095004994 exp(-dH): 1.0996643 plaq: 0.91210887 topo: 0.0\n",
"Begin traj: 85 ACCEPT: dH: -0.40517466 exp(-dH): 1.4995644 plaq: 0.91208849 topo: 0.0\n",
"Begin traj: 86 ACCEPT: dH: 0.2760031 exp(-dH): 0.75881058 plaq: 0.91287424 topo: 0.0\n",
"Begin traj: 87 ACCEPT: dH: 0.30642111 exp(-dH): 0.73607659 plaq: 0.91363367 topo: 0.0\n",
"Begin traj: 88 ACCEPT: dH: 0.031291345 exp(-dH): 0.96919316 plaq: 0.91238992 topo: 0.0\n",
"Begin traj: 89 REJECT: dH: 0.42222563 exp(-dH): 0.6555861 plaq: 0.91238992 topo: 0.0\n",
"Begin traj: 90 ACCEPT: dH: 0.42442683 exp(-dH): 0.65414461 plaq: 0.91503461 topo: 0.0\n",
"Begin traj: 91 ACCEPT: dH: -0.11152116 exp(-dH): 1.1179774 plaq: 0.91378598 topo: 0.0\n",
"Begin traj: 92 ACCEPT: dH: -0.070492355 exp(-dH): 1.0730364 plaq: 0.91393087 topo: 0.0\n",
"Begin traj: 93 ACCEPT: dH: 0.0013547217 exp(-dH): 0.9986462 plaq: 0.91430661 topo: 0.0\n",
"Begin traj: 94 ACCEPT: dH: 0.030857955 exp(-dH): 0.96961329 plaq: 0.91374201 topo: 0.0\n",
"Begin traj: 95 ACCEPT: dH: -0.96119311 exp(-dH): 2.6148144 plaq: 0.9097056 topo: 0.0\n",
"Begin traj: 96 REJECT: dH: 0.93137132 exp(-dH): 0.39401302 plaq: 0.9097056 topo: 0.0\n",
"Begin traj: 97 ACCEPT: dH: 0.026358543 exp(-dH): 0.97398581 plaq: 0.91026645 topo: 0.0\n",
"Begin traj: 98 ACCEPT: dH: 0.73120104 exp(-dH): 0.48133055 plaq: 0.9116951 topo: 1.0\n",
"Begin traj: 99 ACCEPT: dH: 0.085183067 exp(-dH): 0.91834415 plaq: 0.9125954 topo: 1.0\n",
"Begin traj: 100 ACCEPT: dH: -0.61330326 exp(-dH): 1.8465209 plaq: 0.90978721 topo: 1.0\n",
"Begin traj: 101 ACCEPT: dH: 0.58918184 exp(-dH): 0.554781 plaq: 0.91205604 topo: 1.0\n",
"Begin traj: 102 ACCEPT: dH: -0.0072126575 exp(-dH): 1.0072387 plaq: 0.91341119 topo: 1.0\n",
"Begin traj: 103 ACCEPT: dH: 0.14311081 exp(-dH): 0.86665803 plaq: 0.91324167 topo: 1.0\n",
"Begin traj: 104 ACCEPT: dH: -0.19587272 exp(-dH): 1.2163721 plaq: 0.91433534 topo: 1.0\n",
"Begin traj: 105 ACCEPT: dH: 0.034934319 exp(-dH): 0.96566884 plaq: 0.91400061 topo: 1.0\n",
"Begin traj: 106 ACCEPT: dH: 0.38447734 exp(-dH): 0.68080637 plaq: 0.91477181 topo: 1.0\n",
"Begin traj: 107 ACCEPT: dH: -0.65351125 exp(-dH): 1.9222786 plaq: 0.9116215 topo: 1.0\n",
"Begin traj: 108 ACCEPT: dH: -0.32089614 exp(-dH): 1.3783624 plaq: 0.90949451 topo: 1.0\n",
"Begin traj: 109 REJECT: dH: 0.3685615 exp(-dH): 0.69172866 plaq: 0.90949451 topo: 1.0\n",
"Begin traj: 110 ACCEPT: dH: 0.18878664 exp(-dH): 0.82796314 plaq: 0.91266605 topo: 1.0\n",
"Begin traj: 111 ACCEPT: dH: 0.058382684 exp(-dH): 0.9432889 plaq: 0.91215398 topo: 1.0\n",
"Begin traj: 112 ACCEPT: dH: -0.03593914 exp(-dH): 1.0365928 plaq: 0.91136302 topo: 1.0\n",
"Begin traj: 113 ACCEPT: dH: 0.21941022 exp(-dH): 0.80299225 plaq: 0.91319072 topo: 1.0\n",
"Begin traj: 114 ACCEPT: dH: 0.16235354 exp(-dH): 0.85014059 plaq: 0.91364339 topo: 1.0\n",
"Begin traj: 115 ACCEPT: dH: 0.32641506 exp(-dH): 0.72150566 plaq: 0.91580792 topo: 1.0\n",
"Begin traj: 116 ACCEPT: dH: -0.25263397 exp(-dH): 1.287412 plaq: 0.91413709 topo: 1.0\n",
"Begin traj: 117 ACCEPT: dH: 0.35711359 exp(-dH): 0.69969301 plaq: 0.91317054 topo: 1.0\n",
"Begin traj: 118 ACCEPT: dH: -0.27404892 exp(-dH): 1.3152791 plaq: 0.91450242 topo: 1.0\n",
"Begin traj: 119 ACCEPT: dH: -0.40912885 exp(-dH): 1.5055057 plaq: 0.91213142 topo: 1.0\n",
"Begin traj: 120 REJECT: dH: 0.29529335 exp(-dH): 0.74431321 plaq: 0.91213142 topo: 1.0\n",
"Begin traj: 121 REJECT: dH: 0.45137691 exp(-dH): 0.6367508 plaq: 0.91213142 topo: 1.0\n",
"Begin traj: 122 ACCEPT: dH: 0.0094707392 exp(-dH): 0.99057397 plaq: 0.91235185 topo: 2.0\n",
"Begin traj: 123 REJECT: dH: 0.72605695 exp(-dH): 0.48381293 plaq: 0.91235185 topo: 2.0\n",
"Begin traj: 124 ACCEPT: dH: 0.043094495 exp(-dH): 0.95782088 plaq: 0.91220175 topo: 2.0\n",
"Begin traj: 125 ACCEPT: dH: -0.17967513 exp(-dH): 1.1968285 plaq: 0.9117238 topo: 2.0\n",
"Begin traj: 126 ACCEPT: dH: -0.12125752 exp(-dH): 1.1289156 plaq: 0.91109941 topo: 2.0\n",
"Begin traj: 127 REJECT: dH: 0.60619663 exp(-dH): 0.54542137 plaq: 0.91109941 topo: 2.0\n",
"Begin traj: 128 REJECT: dH: 0.31592718 exp(-dH): 0.72911254 plaq: 0.91109941 topo: 2.0\n",
"Begin traj: 129 ACCEPT: dH: 0.29190298 exp(-dH): 0.74684099 plaq: 0.91174559 topo: 2.0\n",
"Begin traj: 130 ACCEPT: dH: 0.34700233 exp(-dH): 0.70680368 plaq: 0.91382378 topo: 2.0\n",
"Begin traj: 131 ACCEPT: dH: 0.14437578 exp(-dH): 0.86556242 plaq: 0.91485047 topo: 2.0\n",
"Begin traj: 132 ACCEPT: dH: -0.26081098 exp(-dH): 1.2979823 plaq: 0.91244414 topo: 2.0\n",
"Begin traj: 133 ACCEPT: dH: -0.3405533 exp(-dH): 1.4057252 plaq: 0.91106923 topo: 3.0\n",
"Begin traj: 134 REJECT: dH: 0.22459183 exp(-dH): 0.79884222 plaq: 0.91106923 topo: 3.0\n",
"Begin traj: 135 ACCEPT: dH: 0.26310905 exp(-dH): 0.76865807 plaq: 0.91342927 topo: 3.0\n",
"Begin traj: 136 ACCEPT: dH: 0.050936786 exp(-dH): 0.95033874 plaq: 0.91356671 topo: 3.0\n",
"Begin traj: 137 ACCEPT: dH: 0.17475103 exp(-dH): 0.83966605 plaq: 0.91444979 topo: 3.0\n",
"Begin traj: 138 ACCEPT: dH: 0.28192928 exp(-dH): 0.75432703 plaq: 0.91409922 topo: 3.0\n",
"Begin traj: 139 ACCEPT: dH: 0.0007522429 exp(-dH): 0.99924804 plaq: 0.91478642 topo: 3.0\n",
"Begin traj: 140 ACCEPT: dH: -0.3935255 exp(-dH): 1.4821971 plaq: 0.91242216 topo: 3.0\n",
"Begin traj: 141 ACCEPT: dH: -0.12805712 exp(-dH): 1.1366179 plaq: 0.91284225 topo: 3.0\n",
"Begin traj: 142 ACCEPT: dH: 0.68012159 exp(-dH): 0.50655539 plaq: 0.915993 topo: 3.0\n",
"Begin traj: 143 ACCEPT: dH: -0.14276103 exp(-dH): 1.1534541 plaq: 0.91609428 topo: 4.0\n",
"Begin traj: 144 ACCEPT: dH: -0.66415425 exp(-dH): 1.9428467 plaq: 0.9127774 topo: 4.0\n",
"Begin traj: 145 REJECT: dH: 0.36830391 exp(-dH): 0.69190687 plaq: 0.9127774 topo: 4.0\n",
"Begin traj: 146 ACCEPT: dH: 0.64960023 exp(-dH): 0.52225452 plaq: 0.91420508 topo: 4.0\n",
"Begin traj: 147 ACCEPT: dH: -0.18136442 exp(-dH): 1.198852 plaq: 0.91474985 topo: 4.0\n",
"Begin traj: 148 ACCEPT: dH: -0.52459851 exp(-dH): 1.6897803 plaq: 0.91254432 topo: 4.0\n",
"Begin traj: 149 REJECT: dH: 0.45635135 exp(-dH): 0.63359119 plaq: 0.91254432 topo: 4.0\n",
"Begin traj: 150 ACCEPT: dH: 0.38779905 exp(-dH): 0.67854868 plaq: 0.91431872 topo: 4.0\n",
"Begin traj: 151 ACCEPT: dH: -0.027182222 exp(-dH): 1.027555 plaq: 0.91326051 topo: 4.0\n",
"Begin traj: 152 ACCEPT: dH: -0.15349655 exp(-dH): 1.1659038 plaq: 0.91408638 topo: 4.0\n",
"Begin traj: 153 ACCEPT: dH: 0.16682534 exp(-dH): 0.84634742 plaq: 0.91538712 topo: 4.0\n",
"Begin traj: 154 ACCEPT: dH: -0.59455554 exp(-dH): 1.8122253 plaq: 0.91045632 topo: 3.0\n",
"Begin traj: 155 REJECT: dH: 0.78514596 exp(-dH): 0.45605313 plaq: 0.91045632 topo: 3.0\n",
"Begin traj: 156 ACCEPT: dH: -0.65666754 exp(-dH): 1.9283554 plaq: 0.90910934 topo: 2.0\n",
"Begin traj: 157 REJECT: dH: 0.29725054 exp(-dH): 0.74285788 plaq: 0.90910934 topo: 2.0\n",
"Begin traj: 158 ACCEPT: dH: 0.45894918 exp(-dH): 0.63194736 plaq: 0.90975123 topo: 2.0\n",
"Begin traj: 159 ACCEPT: dH: 0.40048021 exp(-dH): 0.66999823 plaq: 0.91190278 topo: 2.0\n",
"Begin traj: 160 ACCEPT: dH: -0.036240561 exp(-dH): 1.0369053 plaq: 0.91248989 topo: 2.0\n",
"Begin traj: 161 ACCEPT: dH: 0.53880707 exp(-dH): 0.58344384 plaq: 0.91436331 topo: 3.0\n",
"Begin traj: 162 ACCEPT: dH: -0.1900444 exp(-dH): 1.2093033 plaq: 0.91342047 topo: 4.0\n",
"Begin traj: 163 ACCEPT: dH: -0.02337318 exp(-dH): 1.0236485 plaq: 0.9143867 topo: 4.0\n",
"Begin traj: 164 ACCEPT: dH: -0.92463165 exp(-dH): 2.5209395 plaq: 0.90912358 topo: 4.0\n",
"Begin traj: 165 REJECT: dH: 0.52909715 exp(-dH): 0.58913663 plaq: 0.90912358 topo: 4.0\n",
"Begin traj: 166 ACCEPT: dH: -0.083085498 exp(-dH): 1.0866347 plaq: 0.90927944 topo: 3.0\n",
"Begin traj: 167 ACCEPT: dH: 0.1531254 exp(-dH): 0.85802212 plaq: 0.91050682 topo: 3.0\n",
"Begin traj: 168 ACCEPT: dH: 0.24111553 exp(-dH): 0.78575084 plaq: 0.91065728 topo: 3.0\n",
"Begin traj: 169 ACCEPT: dH: 0.31826306 exp(-dH): 0.72741141 plaq: 0.91192617 topo: 3.0\n",
"Begin traj: 170 ACCEPT: dH: -0.73425127 exp(-dH): 2.0839211 plaq: 0.90924417 topo: 3.0\n",
"Begin traj: 171 REJECT: dH: 0.60217629 exp(-dH): 0.54761856 plaq: 0.90924417 topo: 3.0\n",
"Begin traj: 172 ACCEPT: dH: 0.11135152 exp(-dH): 0.89462422 plaq: 0.90904322 topo: 3.0\n",
"Begin traj: 173 ACCEPT: dH: -0.43788861 exp(-dH): 1.5494323 plaq: 0.90816347 topo: 3.0\n",
"Begin traj: 174 ACCEPT: dH: 0.34371613 exp(-dH): 0.7091302 plaq: 0.90883473 topo: 3.0\n",
"Begin traj: 175 ACCEPT: dH: 0.49568561 exp(-dH): 0.60915312 plaq: 0.91085042 topo: 3.0\n",
"Begin traj: 176 ACCEPT: dH: 0.049652152 exp(-dH): 0.95156037 plaq: 0.91209235 topo: 3.0\n",
"Begin traj: 177 ACCEPT: dH: 0.10108287 exp(-dH): 0.90385812 plaq: 0.91248746 topo: 3.0\n",
"Begin traj: 178 ACCEPT: dH: 0.52526239 exp(-dH): 0.59140017 plaq: 0.91361069 topo: 3.0\n",
"Begin traj: 179 ACCEPT: dH: -0.14827389 exp(-dH): 1.1598305 plaq: 0.91396817 topo: 3.0\n",
"Begin traj: 180 ACCEPT: dH: -0.31489936 exp(-dH): 1.3701214 plaq: 0.9118015 topo: 2.0\n",
"Begin traj: 181 ACCEPT: dH: 0.12956555 exp(-dH): 0.878477 plaq: 0.91334866 topo: 2.0\n",
"Begin traj: 182 ACCEPT: dH: 0.18587871 exp(-dH): 0.83037431 plaq: 0.91313587 topo: 2.0\n",
"Begin traj: 183 ACCEPT: dH: 0.26532678 exp(-dH): 0.76695528 plaq: 0.91492177 topo: 2.0\n",
"Begin traj: 184 ACCEPT: dH: -0.18901862 exp(-dH): 1.2080635 plaq: 0.91329729 topo: 2.0\n",
"Begin traj: 185 ACCEPT: dH: 0.0055455743 exp(-dH): 0.99446977 plaq: 0.91334229 topo: 2.0\n",
"Begin traj: 186 ACCEPT: dH: 0.68317272 exp(-dH): 0.50501218 plaq: 0.91759852 topo: 2.0\n",
"Begin traj: 187 ACCEPT: dH: -0.58739374 exp(-dH): 1.7992929 plaq: 0.91497993 topo: 2.0\n",
"Begin traj: 188 ACCEPT: dH: 0.58801384 exp(-dH): 0.55542936 plaq: 0.91813984 topo: 2.0\n",
"Begin traj: 189 ACCEPT: dH: -0.56564587 exp(-dH): 1.7605845 plaq: 0.91613681 topo: 2.0\n",
"Begin traj: 190 REJECT: dH: 0.13596073 exp(-dH): 0.87287691 plaq: 0.91613681 topo: 2.0\n",
"Begin traj: 191 ACCEPT: dH: -0.24587483 exp(-dH): 1.2787395 plaq: 0.91537027 topo: 2.0\n",
"Begin traj: 192 ACCEPT: dH: 0.47267954 exp(-dH): 0.62332979 plaq: 0.91627632 topo: 2.0\n",
"Begin traj: 193 ACCEPT: dH: -0.21489888 exp(-dH): 1.2397365 plaq: 0.91536025 topo: 2.0\n",
"Begin traj: 194 ACCEPT: dH: -0.16132565 exp(-dH): 1.1750676 plaq: 0.91485276 topo: 2.0\n",
"Begin traj: 195 ACCEPT: dH: 0.043856352 exp(-dH): 0.95709143 plaq: 0.91473873 topo: 2.0\n",
"Begin traj: 196 ACCEPT: dH: -0.04703049 exp(-dH): 1.048154 plaq: 0.91420457 topo: 2.0\n",
"Begin traj: 197 ACCEPT: dH: -0.1758517 exp(-dH): 1.1922612 plaq: 0.91514215 topo: 2.0\n",
"Begin traj: 198 ACCEPT: dH: 0.79232313 exp(-dH): 0.45279168 plaq: 0.91748785 topo: 2.0\n",
"Begin traj: 199 ACCEPT: dH: -0.25595412 exp(-dH): 1.2916935 plaq: 0.91636919 topo: 2.0\n",
"Begin traj: 200 ACCEPT: dH: -0.42770557 exp(-dH): 1.5337344 plaq: 0.91376635 topo: 2.0\n",
"Begin traj: 201 ACCEPT: dH: -0.35760696 exp(-dH): 1.4299035 plaq: 0.91357012 topo: 2.0\n",
"Begin traj: 202 ACCEPT: dH: -0.12676095 exp(-dH): 1.1351456 plaq: 0.91275909 topo: 2.0\n",
"Begin traj: 203 ACCEPT: dH: 0.27291072 exp(-dH): 0.76116074 plaq: 0.91417291 topo: 2.0\n",
"Begin traj: 204 ACCEPT: dH: 0.085481194 exp(-dH): 0.91807041 plaq: 0.91296156 topo: 2.0\n",
"Begin traj: 205 REJECT: dH: 0.19026778 exp(-dH): 0.82673772 plaq: 0.91296156 topo: 2.0\n",
"Begin traj: 206 ACCEPT: dH: 0.36516422 exp(-dH): 0.69408266 plaq: 0.91541724 topo: 2.0\n",
"Begin traj: 207 ACCEPT: dH: -0.50503742 exp(-dH): 1.6570475 plaq: 0.91393549 topo: 2.0\n",
"Begin traj: 208 ACCEPT: dH: 0.24170732 exp(-dH): 0.78528598 plaq: 0.91339151 topo: 2.0\n",
"Begin traj: 209 ACCEPT: dH: -0.57523187 exp(-dH): 1.7775426 plaq: 0.91072934 topo: 2.0\n",
"Begin traj: 210 ACCEPT: dH: 0.53772979 exp(-dH): 0.58407272 plaq: 0.91462295 topo: 2.0\n",
"Begin traj: 211 ACCEPT: dH: 0.011519124 exp(-dH): 0.98854697 plaq: 0.91384506 topo: 2.0\n",
"Begin traj: 212 ACCEPT: dH: 0.27246522 exp(-dH): 0.76149991 plaq: 0.91562552 topo: 2.0\n",
"Begin traj: 213 ACCEPT: dH: 0.32718365 exp(-dH): 0.72095133 plaq: 0.91678428 topo: 2.0\n",
"Begin traj: 214 ACCEPT: dH: -0.22892429 exp(-dH): 1.2572469 plaq: 0.91588535 topo: 2.0\n",
"Begin traj: 215 ACCEPT: dH: 0.24825184 exp(-dH): 0.78016344 plaq: 0.91707419 topo: 2.0\n",
"Begin traj: 216 ACCEPT: dH: -0.5647426 exp(-dH): 1.758995 plaq: 0.91353236 topo: 2.0\n",
"Begin traj: 217 ACCEPT: dH: -0.39146201 exp(-dH): 1.4791417 plaq: 0.91182678 topo: 2.0\n",
"Begin traj: 218 ACCEPT: dH: -0.88145914 exp(-dH): 2.4144201 plaq: 0.90965332 topo: 2.0\n",
"Begin traj: 219 REJECT: dH: 0.070968441 exp(-dH): 0.93149129 plaq: 0.90965332 topo: 2.0\n",
"Begin traj: 220 ACCEPT: dH: 0.06478034 exp(-dH): 0.93727332 plaq: 0.90953537 topo: 2.0\n",
"Begin traj: 221 ACCEPT: dH: 0.32196671 exp(-dH): 0.72472232 plaq: 0.91044073 topo: 2.0\n",
"Begin traj: 222 ACCEPT: dH: 0.46448689 exp(-dH): 0.62845749 plaq: 0.91447348 topo: 2.0\n",
"Begin traj: 223 ACCEPT: dH: -0.13662954 exp(-dH): 1.1464034 plaq: 0.913223 topo: 2.0\n",
"Begin traj: 224 REJECT: dH: 0.35828055 exp(-dH): 0.69887698 plaq: 0.913223 topo: 2.0\n",
"Begin traj: 225 ACCEPT: dH: -0.20145671 exp(-dH): 1.2231833 plaq: 0.91308419 topo: 2.0\n",
"Begin traj: 226 ACCEPT: dH: 0.0058394397 exp(-dH): 0.99417758 plaq: 0.91134232 topo: 2.0\n",
"Begin traj: 227 ACCEPT: dH: 0.25465866 exp(-dH): 0.77518105 plaq: 0.91267259 topo: 2.0\n",
"Begin traj: 228 ACCEPT: dH: 0.062713504 exp(-dH): 0.93921252 plaq: 0.91378331 topo: 2.0\n",
"Begin traj: 229 ACCEPT: dH: -0.093546932 exp(-dH): 1.0980621 plaq: 0.9116662 topo: 2.0\n",
"Begin traj: 230 ACCEPT: dH: -0.32415071 exp(-dH): 1.3828557 plaq: 0.90874115 topo: 2.0\n",
"Begin traj: 231 ACCEPT: dH: 0.48312815 exp(-dH): 0.61685077 plaq: 0.91178257 topo: 2.0\n",
"Begin traj: 232 ACCEPT: dH: -0.1935442 exp(-dH): 1.213543 plaq: 0.91021453 topo: 2.0\n",
"Begin traj: 233 ACCEPT: dH: 0.33574254 exp(-dH): 0.71480712 plaq: 0.91226988 topo: 2.0\n",
"Begin traj: 234 REJECT: dH: 0.6176525 exp(-dH): 0.53920875 plaq: 0.91226988 topo: 2.0\n",
"Begin traj: 235 ACCEPT: dH: -0.12404895 exp(-dH): 1.1320713 plaq: 0.91245162 topo: 2.0\n",
"Begin traj: 236 ACCEPT: dH: 0.04227853 exp(-dH): 0.95860274 plaq: 0.91340639 topo: 2.0\n",
"Begin traj: 237 ACCEPT: dH: -0.082620213 exp(-dH): 1.0861292 plaq: 0.9131198 topo: 2.0\n",
"Begin traj: 238 REJECT: dH: 0.28208584 exp(-dH): 0.75420894 plaq: 0.9131198 topo: 2.0\n",
"Begin traj: 239 REJECT: dH: 0.37273536 exp(-dH): 0.68884751 plaq: 0.9131198 topo: 2.0\n",
"Begin traj: 240 ACCEPT: dH: 0.29704943 exp(-dH): 0.74300729 plaq: 0.91501654 topo: 2.0\n",
"Begin traj: 241 ACCEPT: dH: 0.026720407 exp(-dH): 0.97363342 plaq: 0.91530931 topo: 2.0\n",
"Begin traj: 242 ACCEPT: dH: -0.15721324 exp(-dH): 1.1702451 plaq: 0.91310362 topo: 2.0\n",
"Begin traj: 243 ACCEPT: dH: 0.36159968 exp(-dH): 0.69656116 plaq: 0.9139973 topo: 2.0\n",
"Begin traj: 244 ACCEPT: dH: -0.42335749 exp(-dH): 1.5270801 plaq: 0.91386521 topo: 2.0\n",
"Begin traj: 245 ACCEPT: dH: 0.31386894 exp(-dH): 0.73061478 plaq: 0.91231161 topo: 2.0\n",
"Begin traj: 246 ACCEPT: dH: 0.060475906 exp(-dH): 0.94131645 plaq: 0.9144216 topo: 2.0\n",
"Begin traj: 247 ACCEPT: dH: 0.14827455 exp(-dH): 0.86219437 plaq: 0.91611874 topo: 2.0\n",
"Begin traj: 248 ACCEPT: dH: 0.20500553 exp(-dH): 0.81464281 plaq: 0.91595021 topo: 2.0\n",
"Begin traj: 249 ACCEPT: dH: -0.56436432 exp(-dH): 1.7583297 plaq: 0.91389784 topo: 2.0\n",
"Begin traj: 250 ACCEPT: dH: 0.37430545 exp(-dH): 0.6877668 plaq: 0.91534686 topo: 1.0\n",
"Begin traj: 251 ACCEPT: dH: 0.077003074 exp(-dH): 0.92588701 plaq: 0.91462365 topo: 1.0\n",
"Begin traj: 252 ACCEPT: dH: -0.20306348 exp(-dH): 1.2251502 plaq: 0.91449178 topo: 1.0\n",
"Begin traj: 253 ACCEPT: dH: -0.48930441 exp(-dH): 1.6311812 plaq: 0.91226465 topo: 0.0\n",
"Begin traj: 254 ACCEPT: dH: -0.18957098 exp(-dH): 1.2087309 plaq: 0.9118588 topo: 0.0\n",
"Begin traj: 255 REJECT: dH: 0.4725514 exp(-dH): 0.62340967 plaq: 0.9118588 topo: 0.0\n",
"Begin traj: 256 ACCEPT: dH: 0.040481734 exp(-dH): 0.96032671 plaq: 0.91234233 topo: 0.0\n",
"Run time: 11.453835413999514 seconds\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "hHs_jrh6yFy5",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
""
],
"execution_count": 0,
"outputs": []
}
]
}
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