{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "### Comparison of: \n", "(1) adaptive variable time steps \n", "(2) fixed time steps \n", "(3) exact solution \n", "### for the reaction `A <-> B`,\n", "with 1st-order kinetics in both directions, taken to equilibrium.\n", "\n", "This is a continuation of the experiments `react_2_a` (fixed time steps) and `react_2_b` (adaptive variable time steps)\n", "\n", "**Background**: please see experiments `react_2_a` and `react_2_b` \n", "\n", "LAST REVISED: June 14, 2024 (using v. 1.0 beta33)" ] }, { "cell_type": "code", "execution_count": 1, "id": "3792d78d-7429-4221-a263-57b07d77b5bc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "a29db1c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData\n", "from src.modules.reactions.uniform_compartment import UniformCompartment\n", "\n", "import numpy as np\n", "import plotly.graph_objects as go\n", "from src.modules.visualization.plotly_helper import PlotlyHelper" ] }, { "cell_type": "code", "execution_count": null, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1bc60f3e-6552-43d4-aef2-a33d95811016", "metadata": {}, "source": [ "### Common set up for the chemicals and the reaction (used by all the simulations)" ] }, { "cell_type": "code", "execution_count": 3, "id": "78077d8c", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "chem = ChemData(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "chem.add_reaction(reactants=[\"A\"], products=[\"B\"], \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "chem.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "04be6f77-eb76-4c4c-a2f9-7c80ca9bd8f0", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "b496f370-290f-4f3a-8ce4-3b0f3132e43c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "23e12ad6-03b1-4856-bc39-92130e6f1b2f", "metadata": {}, "source": [ "# PART 1 - VARIABLE TIME STEPS\n", "We'll do this part first, because the number of steps taken is unpredictable; \n", "we'll note that number, and in Part 2 we'll do exactly that same number of fixed steps" ] }, { "cell_type": "code", "execution_count": 4, "id": "d3751799-542c-4d18-a4dd-36e42b63b138", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics_variable = UniformCompartment(chem_data=chem, preset=\"mid\")\n", "\n", "# Initial concentrations of all the chemicals, in their index order\n", "dynamics_variable.set_conc([10., 50.])\n", "\n", "dynamics_variable.describe_state()" ] }, { "cell_type": "markdown", "id": "9fd83080-a135-4f3d-bbf3-a1a9e815a915", "metadata": { "tags": [] }, "source": [ "### Run the reaction (VARIABLE adaptive time steps)" ] }, { "cell_type": "code", "execution_count": 5, "id": "cab9218d-0227-4d47-b128-0394c56f92c0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "19 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 17, 'norm_B': 15, 'norm_C': 15, 'norm_D': 15}\n" ] } ], "source": [ "dynamics_variable.single_compartment_react(initial_step=0.1, target_end_time=1.2,\n", " variable_steps=True, \n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"}\n", " )" ] }, { "cell_type": "markdown", "id": "01dd1821-e725-48d7-b5fc-b76b3b95edd8", "metadata": {}, "source": [ "#### The flag _variable_steps_ automatically adjusts up or down the time steps\n", "In part 2, we'll remember that it took 19 steps" ] }, { "cell_type": "code", "execution_count": 6, "id": "08985297-d0a5-4351-aef2-354ce804cde6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0008060458120676147, 1.227607771778977 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics_variable.plot_history(colors=['darkturquoise', 'orange'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "017a76cd-9f36-4e8c-a98e-e32e659f45cf", "metadata": { "tags": [] }, "source": [ "#### Notice how the reaction proceeds in smaller steps in the early times, when [A] and [B] are changing much more rapidly\n", "That resulted from passing the flag _variable_steps=True_ to single_compartment_react()" ] }, { "cell_type": "code", "execution_count": null, "id": "d213e19d-4910-4f11-88c3-64b7d997e493", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "123ed7bd-cb03-4f5d-88b3-bfa5bc316274", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "10c710ac", "metadata": {}, "source": [ "# PART 2 - FIXED TIME STEPS" ] }, { "cell_type": "markdown", "id": "e0529a0c", "metadata": {}, "source": [ "#### This is a re-do of the above simulation simulation, but with a fixed time step\n", "The fixed time step is chosen to attain the same total number of data points as obtained with the variable time steps of part 1" ] }, { "cell_type": "code", "execution_count": 8, "id": "f9736433", "metadata": {}, "outputs": [], "source": [ "dynamics_fixed = UniformCompartment(chem_data=chem) # Re-use same chemicals and reactions of part 1" ] }, { "cell_type": "code", "execution_count": 9, "id": "9fc3948d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "# Initial concentrations of all the chemicals, in their index order\n", "dynamics_fixed.set_conc([10., 50.])\n", "\n", "dynamics_fixed.describe_state()" ] }, { "cell_type": "markdown", "id": "6bb5d54d-e085-4467-856e-b7db5fe20d00", "metadata": {}, "source": [ "### Run the reaction (FIXED time steps)" ] }, { "cell_type": "code", "execution_count": 10, "id": "635630b3-93a2-40c5-bb4b-b7e0b153a450", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "19 total step(s) taken\n" ] } ], "source": [ "# Matching the total number of steps to the earlier, variable-step simulation\n", "dynamics_fixed.single_compartment_react(n_steps=19, target_end_time=1.2,\n", " variable_steps=False,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 11, "id": "7d2144b8-7331-441a-9122-918725791627", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.00000010.00000050.000000Initialized state
10.06315814.42105345.5789471st reaction step
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30.18947419.51567340.484327
40.25263220.93177639.068224
50.31578921.90068938.099311
60.37894722.56362937.436371
70.44210523.01722036.982780
80.50526323.32757236.672428
90.56842123.53991736.460083
100.63157923.68520736.314793
110.69473723.78461536.215385
120.75789523.85263136.147369
130.82105323.89916936.100831
140.88421123.93101036.068990
150.94736823.95279636.047204
161.01052623.96770336.032297
171.07368423.97790236.022098
181.13684223.98488036.015120
191.20000023.98965536.010345last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 10.000000 50.000000 Initialized state\n", "1 0.063158 14.421053 45.578947 1st reaction step\n", "2 0.126316 17.445983 42.554017 \n", "3 0.189474 19.515673 40.484327 \n", "4 0.252632 20.931776 39.068224 \n", "5 0.315789 21.900689 38.099311 \n", "6 0.378947 22.563629 37.436371 \n", "7 0.442105 23.017220 36.982780 \n", "8 0.505263 23.327572 36.672428 \n", "9 0.568421 23.539917 36.460083 \n", "10 0.631579 23.685207 36.314793 \n", "11 0.694737 23.784615 36.215385 \n", "12 0.757895 23.852631 36.147369 \n", "13 0.821053 23.899169 36.100831 \n", "14 0.884211 23.931010 36.068990 \n", "15 0.947368 23.952796 36.047204 \n", "16 1.010526 23.967703 36.032297 \n", "17 1.073684 23.977902 36.022098 \n", "18 1.136842 23.984880 36.015120 \n", "19 1.200000 23.989655 36.010345 last reaction step" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics_fixed.get_history() # The system's history, saved during the run of single_compartment_react()" ] }, { "cell_type": "code", "execution_count": 12, "id": "35c15b2d-3796-4e29-b038-a003fc98154b", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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"zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Reaction `A <-> B` . Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.000788436268068331, 1.200788436268068 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics_fixed.plot_history(colors=['darkturquoise', 'orange'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "3396051b-ecff-4a08-8c71-7c96f7429da3", "metadata": {}, "source": [ "Notice how grid points are being \"wasted\" on the tail part of the simulation, where little is happening - grid points that would be best used in the early part, as was done by the variable-step simulation of Part 1" ] }, { "cell_type": "code", "execution_count": null, "id": "8f453c61-296d-4627-8d4f-85c531eb4abc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "73229033-14a0-41cd-84fb-5d688efc2e9d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f2d90ba4-b243-4dc0-8c83-d6e73c9cd6eb", "metadata": {}, "source": [ "# PART 3 - Exact Solution" ] }, { "cell_type": "code", "execution_count": 13, "id": "33b22e64-70f3-4bf8-bb0b-0551ab11acd0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.03, 0.06, 0.09, 0.12, 0.15, 0.18, 0.21, 0.24, 0.27, 0.3 ,\n", " 0.33, 0.36, 0.39, 0.42, 0.45, 0.48, 0.51, 0.54, 0.57, 0.6 , 0.63,\n", " 0.66, 0.69, 0.72, 0.75, 0.78, 0.81, 0.84, 0.87, 0.9 , 0.93, 0.96,\n", " 0.99, 1.02, 1.05, 1.08, 1.11, 1.14, 1.17, 1.2 ])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_arr = np.linspace(0., 1.2, 41) # A relatively dense uniform grid across our time range\n", "t_arr" ] }, { "cell_type": "code", "execution_count": 14, "id": "85609da5-3ce1-4252-9f30-301e6e90941c", "metadata": {}, "outputs": [], "source": [ "# The exact solution is available for a simple scenario like the one we're simulating here\n", "A_exact, B_exact = dynamics_variable.solve_exactly(rxn_index=0, A0=10., B0=50., t_arr=t_arr)" ] }, { "cell_type": "code", "execution_count": 15, "id": "00526b58-deb1-4209-b05b-f4ca927d990b", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A (EXACT) :
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z0to3/pqZHjolGWWVj8kV53XTdRXFuSKrUcTY8CSQ1bjzRVbjzxdZjTtjZDXufF3IqtQoMg249tGT2ZHV2pmV9eiXKatyHlkHyU5BZoElFljq+KdB7WrAg28/aZa8+pAZseLaM3XQTI2sTUZZZbR1aun7Oz4eBfwQQFb9cK7qKMhqVeT9HZdpwP5YV3EkZLUK6v6Oiaz6Y13VkVw8uqbVAksipI1WA643DbjZNN1OZFUYN5oGXE+UkdV3r8quH1l18Re00aNrht98dGGk1cxOm8nlH5qX1kvN9PDpLg5NjRIJIKslwlVQGllVEELJLSCrJQOuuDyyWnEAJR8eWS0ZsILyLmRVTqPeo2tSAUwXX2p1z6rUSVfkzU7VFaE9/7xzkuekdiKrcq+p9LD/wMGF2w/TBZZkYaVakZVzkhfTgI1BVh38ZW31nNUlr/8/ydTg4TceSY42ccInFqYHz/Qf56ADSpRBAFktg6qemsiqnizK6gRZLYusjrrIqo4cyuoCWS2LrJ66rmQ1K5rZs8uOkuaR1UZ1souuyqNrahdYynPParowUu3th+m+IsU7Hnt6oX25TzZdiZhpwEwD7vhvbStZlQP0zIwmU4Plntahfd9Ljjl+0ufN0VPm7mk1Pf0d90EBtwSQVbc8tVVDVrUl4r4fZNU9U00VkVVNabjvBVl1z1RbRZeyqu3c6McdAUZWHbDMI6sLh5mdMiOv/pVZ8cubTO/E3jlpXflJc/jsryWfeekhgKzqyaKMTpDVMqjqqoms6srDdTfIqmuiuuohq7ryKKMbZLUMqvHVRFYdZFpIVueP1zMzZpb+aptZtud20zv5TvJdWTH40NnXzz2jlZFWB8l0VgJZ7Yyf9r2RVe0Jdd4fsto5Q80VkFXN6XTeG7LaOUPtFZBV7Qnp6A9ZdZBDO7KaHlZEdelL/8Ys/fU2O9K6L/n21MjZ5shZ/7M5evp/Y2Z7hx10SIl2CCCr7VALZx9kNZys2u0UWW2XXBj7Iath5NRul8hqu+TC2Q9ZDSerKjtFVh3Q70RW08P3jf6DWbL3EbsI0w4z+PbcDdaTKz5ixk7+ohldfbGZWrbOQaeUKEIAWS1CK7xtkdXwMivaMbJalFhY2yOrYeVVtFtktSix8LZHVsPLrIqOkVUH1F3IatqGjK6KsA7vtR9vfSf5tjyndWz1RYm4Thx/voOOKZGHALKah1K42yCr4WaXt3NkNS+pMLdDVsPMLW/XyGpeUuFuh6yGm53PzpFVB7RdymraTs/MxJyw2sfdyIfc4zoztNqMnvTFRFzHT/ysg84p0YwAshr39YGsxp2vnB2yGnfGyGrc+SKrceeb/oyO/yw5w04JIKudErT7lyGr2baG3nzMLJHRViutvRNvmtm+pfPTg+dGW01Pn4OzoEQtAWQ17msCWY07X2Q1/nyR1bgzRlbjzhdZjT9fV2eIrDogWbaspi0Ovv39uZFWO+LaP7on+fbYyf84Edaxky82MwPHOTgbSqQEkNW4rwVkNe58kdX480VW484YWY07X2Q1/nxdnSGy6oCkL1lNWx04tGvhvtaBQ3+ffHv8hE/O3ddqP6aHz3BwVpRAVuO+BpDVuPNFVuPPF1mNO2NkNe58kdVj893+6FNm8213m2uuuMhsuuoS1RfA1nu+Zbbdv8NsueFqs/HCC0rtFVl1gNe3rKYty32sI6/832bpi//a9B99Ifn2zOBqc/SMK8yRM64y00vOdHB23VsCWY07e2Q17nyR1fjzRVbjzhhZjTvfbpHVcz99pVl71unm4fu2tAx0w8ZN5qvXXJbI387de8zl195cdx+RWXmJLO564r5F20iNCz623tz6tS8vfL9VD/J+7Uvq1vt+up1Iqry+vu1B8+T2rS3PrZMNkNVO6M3vW5WsLrQ+O2WG3/y2WfH8vzD9h3628O3xkz5njp52pZ0i/AWe19pGzshqG9AC2gVZDSisNltlgaU2wQWyG7IaSFBttomstgkuoN1iXw1YRh+/++Tfmf0HDpq/uPUrZv26NQ3TSbdNpTaV1QfuvKnhfjfecpfZ+9bb5t47rk/qfum625PP6Z/l62Y9NBrJlbrySoW3WS8XX7nZfHbDR0sdCUZWHfylrlxW58+hZ/qIGXrrr+0jbx5LPveNvZK8M7l8vV09+PP243NmfOUnHZxxd5RAVuPOGVmNO185O2Q17oyR1bjzRVbjzjf9GR3zWaYi96Ndz5nVJ56waLSz9rxrpS+PrEqNdDRWvpYpxLUjrc16kH0v/eJnWopms15qJbuMPJFVB1S1yGr2VOS+1qF5aR3a/0Ty1mzvEiOjrWMirqs+Z6cJv8fB2cdbAlmNN1s5M2Q17nyR1fjzRVbjzhhZjTtf17L687Fx8/rkpHdovzU8bE4Z6D/muFnBe+GlV1tOl5Upt9lR1Lyymo6Orjx++THi2ayHvPXlxJptm75XK8kug0BWHdDUKKvpacnzWmWUVcR1eJ8dbT36YvLW1LJ1VlrtSKuV1vETf98BhfhKIKvxZZo9I2Q17nyR1fjzRVbjzhhZjTtf17L6lVdeM//qjTe9Q/vG6aeaf37ySccct3bEsVZGa3eQ97PC1+qe1ewCTDL9d9/+g8fcF9ush1Ry80hmK7Gt7d11CMiqA6KaZTV7ev1Hf2mG3hBplWnC3517yz6jNRlplQ876jq1pPF8egeogiqBrAYVV+FmkdXCyILbgWnAwUVWqGFktRCu4DZGVoOLrHDDLu9ZvW3vG+Y7Bw8X7qHTHa5ffZK5cMXyY8rUTusVoWw2FbiRrDa7Z1UOKtIpixzJq3ZKb7MeWglo9oRabYusdnoVedg/FFldQDE7O3dvayKtf236jzyXvDU1snbuvtaTPm/G7Iir6en1QE/vIZBVvdm46AxZdUFRdw1kVXc+nXaHrHZKUPf+yKrufFx051JWXfTjqkajUVGZqtto5dx2pwE3umc1Tw/1Vg6ux4BpwK6ujArrBCerGVY904fNktf/oxl5+R4zeOCZhXcmV5xnjp56uRk75Q/sc1tPr5BudYdGVqtj7+PIyKoPytUeA1mtln/ZR0dWyyZcbX1ktVr+Po4eq6w2WnRIhLTRc0nbWWCpdvXf7OrAeXpotBqw7Pvq3rdyrQbMAks+/qY4OEbIspo9fXnszdKX7zZLXvsr0zv5zsJbEyd83IxacR1d/Qf2Oa6rHBALowSyGkZO7XaJrLZLLpz9kNVwsmqnU2S1HWrh7IOshpNVu53GKquNVtmt92iZlF2jR9fUYyvPWRWZ3PHY0w2fs/rUMzvrrvRb20O9EdjaEWAeXdPuFa5ov1hkNUXaO7HXDO3/GzO07wkzuO8/mf7RPclbM4Mr7aNvPmUmTviUXZjpU2Zq6fsVpeC+FWTVPVNNFZFVTWmU0wuyWg5XLVWRVS1JlNMHsloOV01VY5XVdhmnU3o3XnhBuyW87pfeL9toarOrZlhgyQHJ2GQ1i6Rv9Ndm6O2/MYP7/1Mir31jLydvTw+dYiasuI6LuJ74KfsYnN90QFJXCWRVVx6uu0FWXRPVVw9Z1ZeJy46QVZc09dVCVvVl4rojZHUx0UbTcl1zd1FPRoK33b+j4bRmF8dIayCrDmjGLKtZPP1HX5iT1vlR196JN+bEdclvzI24rvxkIq/TS85wQLX6Eshq9RmU2QGyWiZdHbWRVR05lNUFsloWWR11kVUdOZTZBbJaJt14aiOrDrLsFlldJK6Hd1tpteIqo652xLV38kDytqwonEirnSYsAjszeLIDwtWUQFar4e7rqMiqL9LVHQdZrY69jyMjqz4oV3cMZLU69r6OjKz6Ih32cZBVB/l1o6xmsfWO77WLMn3TLHljuxl8++mFt2QxpuT5rSs/beX194JbVRhZdfCXQ3EJZFVxOI5aQ1YdgVRaBllVGoyjtpBVRyAVl0FWFYejqDVk1UEY3S6rWYR9Y6/YR+FYcX31ATNw6CeL6MqCTOMnfc6MrfycmVi1wcz2DjugX14JZLU8thoqI6saUii3B2S1XL5VV0dWq06g3OMjq+Xy1VAdWdWQgv4ekFUHGSGr9SHKPa5Db/313Mf+J4080zV9iajKI3GSUdeTPm8ml3/QQRJuSyCrbnlqq4asakvEfT/Iqnummioiq5rScN8LsuqeqbaKyKq2RHT2g6w6yAVZbQ2xd/ItM3jgh2bgnR/OfT74Q3uf68GFHSeXn2smj/sdM2E/5PPk8g+0LlryFshqyYArLo+sVhyAh8Mjqx4gV3gIZLVC+B4Ojax6gFzxIZDVigMI5PDIqoOgkNXiEPuP/MIMWnEdsOKayOuhHy8Ume1dYiaOt8K64rfnPlt5nR4+rfhBOtwDWe0QoPLdkVXlATloD1l1AFFxCWRVcTgOWkNWHUBUXgJZVR6QkvaQVQdBIKudQeyZmbQjrv9lTl5l5NV+9I3+aqHo9PDpZtJK60RGXn3c74qsdpar9r2RVe0Jdd4fsto5Q80VkFXN6XTeG7LaOUPtFZDVxQnxnNX6Vyyy6uBvMrLqAGKmhKwuPHjQymtm2nD2ftfJ5evnpgwnAvs7Zmr5OW4bmK+GrJaCVU1RZFVNFKU1gqyWhlZFYWRVRQylNYGsloZWTeFYZXXn7j3m8mtvPobzlhuuNhsvvKAh/w0bN5mvXnNZsk2jGrLzNVdclNTYdv8Os+uJ+xbVkxoXfGy9ufVrX174/rmfvtKsPet08/B9W+oeW96vfUndet9Pt5NzkdfXtz1onty+tdRrCll1gBdZdQCxSYl++0zXhVHXZMrwu6sMz/YtnbvPVcQ1ud/1t8300ClOGkJWnWBUWwRZVRuNs8aQVWcoVRZCVlXG4qwpZNUZSrWFYpfVB+68yaxftybhf+Mtd5mnntnZUOy23vMt890n/25BKFNZzdaoDVJq7n3rbXPvHdcnb33putuTz+mf5eu07v4DB81f3PqVhX7kvUYjuVJXXqnwNuvl4is3m89u+KjZdNUlpV1nyKoDtMiqA4g5S/TMjGcWaZobfe0be3lh7+nh98zd5zo/6iryOts7mLP64s2Q1bawBbMTshpMVG03iqy2jS6IHZHVIGJqu0lktW10wezYTbKaimHtSGgaVq305ZFV2TcdjZWvN9929zEjrWndH+16zqw+8YRFI66y76Vf/ExL0WzWS61kl3HxIasOqCKrDiC2WaJv/LW5RZrSxZrs9OGe6aML1SaXf2hhkSaR2Kmlv5X7SMhqblRBboisBhlboaaR1UK4gtsYWQ0uskINI6uFcAW5sVNZPfhzY0Zf989hhf29csniGX315K7eqGe2WZlymx1FzSurqQSvPH75MeKZrfHCS68umrKbt7702Gzb9L1GEu4iEGTVAUVk1QFERyXkftehfd+zz3V9wgy/+Zjpndi7qPLkivPMxMqPz00Ztl9PjZzd8MjIqqNQlJZBVpUG47AtZNUhTIWlkFWFoThsCVl1CFNpKaey+uxXjPn5v/J/pud9w5jf+ueLjtvoflO517TRdFmR1azwtbpnNVtHRHjf/oPH3JNaO+qZFeJWI73ZE2oltrW9uw4BWXVAFFl1ALGkEnJ/65CVVpHXwbefNj0zY4uONDO4yo68zsvrcVZkj/+Yme1blmyDrJYUipKyyKqSIEpsA1ktEa6C0siqghBKbAFZLRGuktJOZXXXbca8/h3/Z7bO3i962oV1ZTU7UtpKDhvJarN7VuWgUlcWOZJX7ZTe2qnFIrXpVOBWAoqs+r+USj0isloqXmfFRVQHDzxjBg4+a8X1+8nXtSOvcrDJ5R+097yeZ2ZPON/0r/642df7Xmc9UEgPAWRVTxZldYKslkVWR11kVUcOZXWBrJZFVk9dp7Kq57QaTputneqbbbndacCN7lltNDIr04XT1XvrrRxcDyPTgBVdXO22gqy2S67i/WZnzMDhn5r+Qz+1Kwzbj/mv+8YX3/MwPXKWmVz2geRjarn9bD+mlr6v4uY5fKcEkNVOCerfH1nVn9KMCqAAACAASURBVFEnHSKrndDTvy+yqj+jTjvsJlmVKbn1HjWTMmxngaXa+2CzqwM3WvhIpDh9hE6j1YBl31f3vpVrNWAWWOr0b4Gn/ZFVT6B9HGZ2yo68/iSZMrzkyI/t4k3PmJ7Dzx9zZLnXdWrZOckobPJ56fvtZyuwPf0+uuQYDgggqw4gKi+BrCoPqMP2kNUOASrfHVlVHpCD9mKX1VpEzRYhavTomnqY5d5Xkckdjz3d8Dmr8piceiv91gpuvRHY7OirHJ9H1zi42F2VkP+RkOBr54fL/3Y8/+IryWHqPVQXWXWVgK466T2rB1/faUded5l+O/I6cNB+fWSX6Tv64jHNzgyeZEdc19pFm94793nJWjO91H69bK2Z7RnSdXJ0Y5DV+C8CZDXujJHVuPNFVuPOV84uVlltN7l0Su/GCy9ot4TX/dL7ZdNpxWUdnAWW5skK8H/3wLcTKc3Kau0KWyKuq1auWPTAXWS1rMuz2rqNFljqmT5i+o8+b+X1OftZPp43fUfmvu6dfOeYpuXZr1MiranALrNfj4jUNl6JuNoz746jI6vx54ysxp0xshp3vshq3Pkiq8fm22harsYrIZ3WnE4pLrNHZHWebnpj8+XX3rxIVmv/l6Pe/yIgq2VeotXVLroacO/km1Zgf2n6RVyPWJmdF1n5s7HTixe/euYEVqTVSmwyApsIrP16+PTqTrqLjoysxh82shp3xshq3Pkiq3Hni6zGn6+rM0RWLUkZLf1nl3/BnH3maSYrq/XmaNf7HrLq6nLUVaeorDbqvm/0H6zEpvL6rsj2jf7qmF1m+0YWBFamE08n04rnphbPDK7UBSjwbpDVwAPM0T6ymgNSwJsgqwGHl6N1ZDUHpMA3YRpw4AF6ar/rZTW7clatiOaVVU9ZcZiYCEyPG3Pol3MfB+c/p1+Pv3XsmQ6tMsZOHzYr7CJO8pH92gouLwhAAAIQgAAEIAABCMRGoKtltXZKb7uyyshqbH8t5s7H1chqITp2urBMJZZFnAYO7bRf/8J+/onpG32pbpnZvmXJY3Qml5+bjL5OyyrFS8+2U4nPNDMDxxU6dLdtzMhq/Ikzshp3xoysxp0vI6tx5ytnx8hq/Bm7OMOul9XNt91dl6MsC73pqktMvXtWZZ/s8tPIqotLUV+NSmS1AYae6cNWWn+WiGv/4Z8lHwOHd5neiX0Nwc0MrkoWcUoEdska+/Waua/th7zX7S9kNf4rAFmNO2NkNe58kdW480VW48/X1RlWIqsigPsPHKp7Ds2eQeTqpBvVqTftl9WAy6aut74mWW1EqXd8b/Jc2P7RF+zHHrsqsf18dI/9eKHOok7vVklGZK28JqOwIrDDIrK/MSe3S87UG4rDzpBVhzCVlkJWlQbjqC1k1RFIpWWQVaXBOGyLkVWHMCMu5V1W6z36RQvfRg+95TmrWhLy20cIstqMSN/YK3ZV4l8k8tonH2Mv2T/PyayM1DZ7yYrE6ceMfD102tyfh+a/H4HQIqt+/z5VcTRktQrq/o6JrPpjXcWRkNUqqPs9JrLql3eoR/Muq/KIGB/P5PEZCNOAfdL2d6zQZbUZKRmRldFXuRc2ecROIrH2z1Zweyf25oIcutAiq7liDnojZDXo+Fo2j6y2RBT0Bshq0PHlah5ZzYWp6zdCVh1cAsiqA4gKS8Qsq01FdvKA6R1/zfTNf/SOv558nX7uG3vd9I69Znpmx5qmJlONp4dOMTNDpyafp4dPtV/bz/bPyWf75+nBU8xs/4pK0kdWK8Hu9aDIqlfc3g+GrHpH7vWAyKpX3JUcDFmtBHtwB/UuqzKl9rMbPposXhTLC1mNJcnF59GtsporTbtqcTLN2I7M9trP8nXf+Ktzn+c/nI3Q2unHpqc/V1tFNkJWi9AKc1tkNczc8naNrOYlFeZ2yGqYuRXpGlktQqt7t/Uuq7WPi4kBPbIaQ4rHngOy2mGuDoVWHsMzM3Bict/szODqZDXjmYFVdjGo37Bfn2hm+o+be29otZntHc7VOLKaC1PQGyGrQcfXsnlktSWioDdAVoOOL1fzyGouTF2/kXdZlXtWm72qXA243asBWW2XnO79kFUP+bQQ2t7JfQ2fMduoO5l+nDy2xy4ClUptKrizfUuTqcemb8jMLjnDnHDciNk7fmIpI7ce6HGIFgSQ1bgvEWQ17nyR1bjzlbNDVuPP2MUZepdVF01rq4GsakvETT/IqhuOLqrI82R7pw4sLADVO/mOvYd2r+mbeMX0yNf2fZmS3GO3kffaeckje2btdGMZoRWZTe6ntXIrI7gycjubjO4eb++xtaO4dpR3tt++V2Akt52e2KczAshqZ/y0742sak+os/6Q1c74hbA3shpCStX3iKw6yABZdQBRYQlkVWEoeVqaH61NBNd+9E3YBaFEbMd+ZXpmxhPhNXYbkVuZCmyOvJinatNtEsG1oiujufJKnlXb22eF93Q7LXloTmrnR3xFeEV+ZdRXvserPALIanlsNVRGVjWkUF4PyGp5bLVURla1JKG7j0pkVe5b3Xzb3YvIhPw4G2RV90XebnfIarvkwthv4Z7V/UftqO1BO0JrR2Wn7Sit/dxj/5x8llFb+d7UO3NfH/O9dCR3tq2Tnu0bmRu1FXm1I7fJ6G2/ldm+FfZr+zn53rzc9qWju+kIr92md0lbx+2WnZDVuJNGVuPOF1mNO185O2Q1/oxdnKF3Wd16z7fMtvt3mAfuvMmsX7cmOYedu/eYy6+92VxzxUVBrhKMrLq4FPXVQFb1ZeKyI5cLLMnzanvmR3Rl1FZGb2UUV0Z0e6aPWMm1o7yJBL9j+ibfsp/t9+S9meaP/2l1vonMWrmVl4zuyjTmZOqyXXRKXsmIbo+9P3d+dDf5nn1PtlmY8my/JzWkVmwvZDW2RBefD7Iad77Iatz5Iqvx5+vqDL3L6oaNm8ylX/zMMVIqEvvQI4+bJ7dvdXVu3uogq95Qez0QsuoVt/eDuZTVTppPpTURXBFdK75mZto+Ckj+nArv4WRKc++U/WzFt5N7c/P0KgtSzfbNraqcldrkzxkZzgpxWldWaE5fUkNqLbw3f6/vwp9LeixRWh9ZzZN2uNsgq+Fml6dzZDUPpbC3YWQ17Px8de9dVmU14HpTftOpwawG7Ct6jtOKALLailDY72uR1U4oisD2TB9OSsg9uPKS0VsZxZXX3P250wvSm3zP3sNrpsffHQm238vW6aSfTvaVRw7JSHD6Su7rtVOgF/48P3Kc/Hn+fuD0vWSxK7sQVvpKV3xetWLI7Ds4vnAvsbyf3jvcSa/sq4MAsqojh7K6QFbLIqunLrKqJwvNnXiXVUZWNV8O9JYlgKzGfT3EIKtlJZQuQiX1F6Y3zx8sK8OJNybTmcfn37UjwiLI6bZWpEWE01dfzdTnZBS54lftQlfpdOqkrflVobMtpitE17ZdK8zp+63kOF2UqxGGVvtXjK/SwyOrleIv/eDIaumIKz8Aslp5BEE04F1WuWc1iOuCJi0BZDXuywBZ1ZWv3L8r4pu+kmnP86PG8r3e+WnS8nV6P/DCtnYRLFkAa0GK51d8HhroNRMTE00FWheF9rrJTtuuV6F2KnfdbWpGsuttk94D3bDLHrsCtkztbvJKH//UbJtF/2FQZ8N0FB5Zbe96CWUvZDWUpNrvE1ltn1037eldVgUuqwF30yUW7rkiq+Fml6dzZDUPpbC3yXPPau1CV+l06kSKZXGsibcWQUhWhbZTrWtfsmp0VpjT99OFteqRrB21rrtNB88ODju9zrrPLj7WqFIrKa43st5OV8kCZ5l7t9up0ek+2UXWOq3V7v7ynyYzLf4zI1t72ZIBMzk1Y8Ynp9s95DH75fmPG2cHa1IoebwZL1YD5hrIRaASWc3VWUAbscBSQGEVaBVZLQArwE2R1QBDK9hyHlktWFLl5tlp2+1L8bv3Ojc6yfQe6EbvpwuCNYMk8i//CdDslS421vA403YUfuLdUXiVodAUBJQT0CDMfX/wonJKtKeBALLqIAVk1QFEhSWQVYWhOGwJWXUIU2mpbpFVpfhLb6vZNOA8i4ZlR9HrNmsXIksWJOvwVTttvcNybe2e5z8S2ipcYCeZSSDT+fO++vt6zOzsrJmeybtH6+3yzGZoXaXDLdLHnHVYJord/0l7zyiP4tw5idwEvMmqrAIsz1GVZ6w2e7EacO7s2LBkAshqyYArLo+sVhyAh8Mjqx4gV3gI7lmtEL6HQ3PParmQNSxwt/qM3yr3JKkeBQFvshoFrQYnwchqnOkiq3Hmmp4Vshp3vnJ2yGrcGSOrceeLrMadb/ozOv6z5Aw7JeBdVhs9Z1VWCX7okcfNk9u3dnpO3vdHVr0j93JAZNUL5soOgqxWht7bgZFVb6grORCyWgl2bwdFVr2hruxArAZcGfqgDqxGVtMVgpkGHNT1E3WzyGrU8RpkNe58GVmNP19kNe6MkdW482VkNf58XZ2hGlm98Za7zFPP7GRk1VWy1OmYALLaMULVBZBV1fE4aY6RVScY1RZBVtVG46QxZNUJRtVFGFlVHY+a5rzIar3nqtYjsOWGq83GCy9QAydvI0wDzksqrO2Q1bDyKtotslqUWHjbI6vhZVakY2S1CK3wtkVWw8usaMfIalFi3bm9F1nNom10z2rI+JHVkNNr3DuyGmeu6Vkhq3HnK2eHrMadMbIad77Iatz5pj+j4z9LzrBTAt5ltdOGNe6PrGpMpfOekNXOGWqugKxqTsdNb8iqG45aqyCrWpNx0xey6oaj5iqMrGpOR09vyKqDLJBVBxAVlkBWFYbisCVk1SFMpaWQVaXBOGoLWXUEUmkZZFVpMA7bQlYdwoy4lHdZ3bl7j7n82psbImU14IivtsBODVkNLLCC7SKrBYEFuDmyGmBoBVpGVgvACnBTZDXA0Aq2jKwWBNalm3uX1Q0bN5kLPrbenH/eOebr2x5cWP334is3m89u+KjZdNUlwUXByGpwkeVqGFnNhSnYjZDVYKPL3TiymhtVkBsiq0HGlrtpZDU3qmA3RFaDjc5r495lNV1g6ewzTzP/443fWJBVWTE4K69eKXR4MGS1Q4BKd0dWlQbjqC1k1RFIxWWQVcXhOGgNWXUAUXEJZFVxOI5aQ1YdgYy8TGWyKo+oEXFNp/2mj7dhGnDkV1xAp4esBhRWG60iq21AC2wXZDWwwAq2i6wWBBbY5shqYIG10S6y2ga0LtzFu6zKdN9z3nemufVrXzbZr2+85S7z1DM7F0ZaQ8qCkdWQ0srfK7Kan1WIWyKrIaZWrGdktRiv0LZGVkNLrFi/yGoxXiFujayGmJr/nr3Lau0pyuhq+nrgzpvM+nVr/FPo8IjIaocAle6OrCoNxlFbyKojkIrLIKuKw3HQGrLqAKLiEsiq4nActYasOgIZeZnKZTUGvshqDCkeew7Iapy5pmeFrMadr5wdshp3xshq3Pkiq3Hnm/6Mjv8sOcNOCXiX1XSBJblnNZYXshpLkovPA1mNM1dkNe5cs2eHrMadNbIad77Iatz5Iqvx5+vqDJFVBySRVQcQFZZAVhWG4rAlRlYdwlRaCllVGoyjtpBVRyCVlkFWlQbjsC2mATuEGXEp77Ia8vNUG10HyGqcf0OQ1ThzZWQ17lwZWe2efJHVuLNGVuPOl5HV+PN1dYbeZXXn7j2Lnq/q6kSqrIOsVkm/vGMjq+Wx1VCZkVUNKZTbAyOr5fKtujqyWnUC5R4fWS2Xr4bqjKxqSEF/D95lNbv6bz08PGdV/0XTLR0iq3EnjazGnW/6v/b8Z2K8OSOr8WYrZ4asxp0vI6vx5+vqDL3LqqvGNdXhlyFNabjrBVl1x1JjJWRVYypue2Jk1S1PbdWQVW2JuO0HWXXLU2M1RlY1pqKvJ++y2mg14K33fMs89Mjj5sntW/VRatERshpcZLkaRlZzYQp2I2Q12OhyN46s5kYV5IbIapCx5W4aWc2NKtgNkdVgo/PauBpZ3f7oU2bzbXcbpgF7zZ+DNSGArMZ9eSCrcecrZ4esxp0xshp3vshq3PmmP6PjP0vOsFMCamT1xlvuMk89s9P7yKocd8djTy/iWCvMsoLx8y++kmyz9qzTzcP3bVm0PSOrnV6GOvdHVnXm4qorZNUVSb11kFW92bjoDFl1QVFvDWRVbzauOmNk1RXJuOt4kdV01LQVyi03XG02XnhBq82cvi8i+i+vv8qsX7cmqVs7HflL191u9u0/uCCosv2qlSvMvXdcv9AHsuo0EjXFkFU1UZTSCLJaClZVRZFVVXE4bwZZdY5UVUFkVVUcpTSDrJaCNbqiXmQ1S63RPatayMqjdS6/9mbzwJ03JQK7YeMm89VrLluQaBHvr297cNEIMLKqJT23fSCrbnlqq4asakvEfT/Iqnummioiq5rScN8LsuqeqbaKyKq2RHT2411WdWJ4tysZSX1uz8uJjNaKq2xV73vIqvZU2+sPWW2PWyh7IauhJNV+n8hq++xC2BNZDSGl9ntEVttnF8qeyGooSVXbJ7I6z19GUPcfOJT8Kb1nNa+sHjo6WW2KHL0UAv19vWagv8eMjk+XUp+i1RLo6ekxI8N95sjoVLWNcPTSCCwfGTD8fC4Nb+WFR4b7zdjEtJmZma28FxpwT0D+w3jaZjs5NeO+OBVVEJCf0bwg0IpAJbKaFcPaBqteDVjuWd12/45EWJHVVpdP3O8jq3Hni6zGna+cHbIad8bIatz5Iqtx55v+jI7/LDnDTgl4l9V6CxR1ehKu95f7apvds1r7iB2mAbtOQEc9pgHryKGsLpgGXBZZPXWZBqwnizI6YRpwGVT11GQasJ4syuqEacBlkY2rrndZ1bbAkozyyv2p6av2ETqsBhzXBV/kbJDVIrTC2xZZDS+zoh0jq0WJhbU9shpWXkW7RVaLEgtve2Q1vMyq6LjrZTX7DNU0AJ6zWsWlqO+YyKq+TFx2hKy6pKmzFrKqMxdXXSGrrkjqrIOs6szFZVfIqkua8dbyLqsih5/d8FGz6apLoqHKNOBoolx0IshqnLmmZ4Wsxp2vnB2yGnfGyGrc+SKrceeb/oyO/yw5w04JeJfVes8p7fQkqt4fWa06gXKOj6yWw1VLVWRVSxLl9YGslsdWQ2VkVUMK5fWArJbHVktlRla1JKG7D++yKvesNntVvRpwO3Ehq+1Q078Psqo/o046RFY7oRfGvshqGDm12yWy2i65MPZDVsPIqZMukdVO6HXPvt5lNUa0yGqMqRqDrMaZa3pWyGrc+crZIatxZ4ysxp0vshp3vunP6PjPkjPslACy2ilBuz+y6gCiwhLIqsJQHLaErDqEqbQUsqo0GEdtIauOQCotg6wqDcZhW4ysOoQZcalKZDW7Au+WG642Gy+8wMj04PPPW2fuveP64HAjq8FFlqthZDUXpmA3QlaDjS5348hqblRBboisBhlb7qaR1dyogt0QWQ02Oq+Ne5dVEdVVK1ckUirPOP3qNZclsrr1nm+Zhx55fNEzT72S6OBgyGoH8BTviqwqDsdBa8iqA4jKSyCrygPqsD1ktUOAyndHVpUH5KA9ZNUBxC4o4V1WZQT1gTtvMuvXrVkkq7JK8Obb7jYssNQFV10gp4isBhJUm20iq22CC2g3ZDWgsNpoFVltA1pAuyCrAYXVZqvIapvgumw377Iqo6l/cetXjpFVRla77MoL4HSR1QBC6qBFZLUDeIHsiqwGElSbbSKrbYILZDdkNZCgOmgTWe0AXhft6l1Wb7zlLvPUMzuT6b7pNOCzzzzNXH7tzeaiz3/c3Pq1LweHn2nAwUWWq2FkNRemYDdCVoONLnfjyGpuVEFuiKwGGVvuppHV3KiC3RBZDTY6r417l1U5u3TKb/ZMr7niIrPpqku8nryrgyGrrkjqqoOs6srDdTfIqmui+uohq/oycdkRsuqSpr5ayKq+TFx3hKy6JhpnvUpkNTaUyGpsic6dD7IaZ67pWSGrcecrZ4esxp0xshp3vshq3PmmP6PjP0vOsFMC3mX1S9fdbn7w7O5jFlLi0TWdRsn+rgkgq66J6qqHrOrKo4xukNUyqOqpiazqyaKMTpDVMqjqqsnIqq48tHbjXVblPtVLv/iZY6b8ssCS1kuke/tCVuPOHlmNO19GVuPPF1mNO2NkNe58GVmNP19XZ+hdVmUEdcsNVyfPVs2+eHSNq0ip44oAsuqKpM46yKrOXFx2xciqS5r6aiGr+jJx2RGy6pKmzlqMrOrMRVtX3mWVkVVtlwD9NCKArMZ9bSCrcefLyGr8+SKrcWeMrMadLyOr8efr6gy9y6pM9912/w7zwJ03Jc9aldfO3XuSR9eEuiIwCyy5uhx11UFWdeXhuhtk1TVRffUYWdWXicuOkFWXNPXVQlb1ZeK6I0ZWXRONs553WRWM9R5dU29qcCjIkdVQkirWJ7JajFdoWyOroSVWvF9ktTizkPZAVkNKq3ivyGpxZqHtgayGllg1/VYiq9WcanlHRVbLY1tlZWS1SvrlHxtZLZ9x1UdAVqtOoNzjI6vl8q26OrJadQLlHx9ZLZ9xDEdAVh2kiKw6gKiwBLKqMBSHLSGrDmEqLYWsKg3GUVvIqiOQSssgq0qDcdgWsuoQZsSlKpFVWWRp/4FDdbHueuK+4HAjq8FFlqthZDUXpmA3QlaDjS5348hqblRBboisBhlb7qaR1dyogt0QWQ02Oq+Ne5fVi6/cbFatXGHuveN6ryda5sGQ1TLpVlcbWa2OvY8jI6s+KFd7DGS1Wv5lHx1ZLZtwtfWR1Wr5+zg6suqDcvjH8C6rjZ6zGjJKZDXk9Br3jqzGmWt6Vshq3PnK2SGrcWeMrMadL7Iad77pz+j4z5Iz7JQAstopQbs/suoAosISyKrCUBy2hKw6hKm0FLKqNBhHbSGrjkAqLYOsKg3GYVuMrDqEGXEp77Iq04A/u+GjZtNVl0SDFVmNJspFJ4KsxpkrI6tx55o9O2Q17qyR1bjzRVZ153twZsa8MzPdUZPnr17R0f7s3B0EvMuqPGP169seNE9u3xoNYWQ1miiR1TijrHtWjKzGHzayGnfGRWR1fHbGvDHd/Bfr/fYX76P2F/Air7FZY96cniyyS1vbvmF7m5i1B6vwJfzGPR5/sL/XzMzMmin7kb72T0+ZI5k/e2xn4VBvz1bfw36bxRF7TYf+mv3IB0M/Bfr3QMC7rMo9q81erAbsIXUOkYsAI6u5MAW7EbIabHS5G+9WWc0z4vHa1JSZNo3lJ4+EvWPF7lCLX5hfm5kyU7M9DTMbtzVaSWQjOejt6TEz8wL366nyhTH3hceGEOgCAit6e81xvX0dnemv1q/raH927g4C3mU1RqyMrMaYqjHIapy5pmeFrMadr5xdEVkVeZual7dxK0Bv2hGc9CVSdrDOdLdGsnbQ7i/v1b6kxjvTzUdD3rRyJ8dv9Jqy772W6S3+FN2c4ZAV25P7+psWW2l/8R7p6S10wGG7+Ul9A4X2aWfjk21vQ42dv52Shfc5wfaw1HL09RoZ7jdT9u/LxOS7f2dW2gx99lDvXE/otT30+uNQrweRRJHF0F/csxp6gn76R1YdcEZWHUBUWAJZVRiKw5aQVYcwHZaqHRV8U6Yezo/eiUyKVKavI1bc3s5I5H4riPK99PWGHTscn/9Fd9zMWAF9dxpoLNPo6qFfaoVrZV/zEY+T7PtDpvEvu/32d/FT+5tL2HH2l+UVLeTllN4B09/TWL777P6ntZDIFbbXFXUkctWKQXPw6JSZnJoxp9oa/R5FyuElT6kGBLhnNf5LA1mNP2MXZ1iJrMp9q5tvu3tR/1tuuNpsvPACF+fkvQay6h25lwMiq14wV3YQZLU1+uzUSrlP7G076pe+EjHMiKKM9qUqOG7dRO6xS1+1I4pz284JjJaRwpNF3uaFqM/0JPKTvmQURUZ0al8ywrOyzuiGjM7V+/5SOxpS7/vZuifZ48goYKNXv/TW33yEsHWycWxR5J7VOM64u84CWY0/b2Q1/oxdnKF3Wd16z7fMtvt3mAfuvMmsX7cmOYedu/eYy6+92VxzxUVBrhKMrLq4FPXVQFb1ZeKyo1hkVRbZkFFCeaWjkNkRSJHKo/Mjk7+e304kc//8dNSsOL5hJbLZFFSX/BvVqh0VrJ2a+Z6Bd0f7hmwRkcz0VTtN8QMrl5p3Dk4kbycCmpG8WKbR+chE6zGQVa3JuOkLWXXDUXMVZFVzOnp68y6rGzZuMpd+8TPHSKlI7EOPPB7kKsHIqp4L2mUnyKpLmvpqaZLV9H7Jl+cXiZERTVmU5vWZSSuPc6OUqWDKKOXBeUEtezXI92Smgcpo30n2Xq30dVyfnQKaWVwjmYY5P1oq+pgdmZTtZMpo+qodPcwex+WVUuSeVZfHpZYfAsiqH85VHQVZrYq8v+Miq/5Yh3wk77IqqwHXm/KbTg1mNeCQL6e4ekdW48qz9mxcy6oIpkxtFfFMV1JN76lMF9xJp8Omq5u6GMnMLhyTjkJm7zfM3leY3j+YnY6aFUe5z1FGNmN5IauxJFn/PJDVuPNFVuPOV84OWY0/Yxdn6F1WGVl1ERs1fBBAVn1Qru4YWVmVtSbThX3kszyOI1kB1k6LlT8ftBJ60E6hTVeFFfmUP8sIpzwUXbZp9yX3Ny6390Sm01JX9Myt8pg+FmDF/AjmCjuNNRmhTP5s97H7iYim91m2e/yY90NWY07XrsJ73JA5cGQyWWCJV3wEkNX4Mq09I2Q1/oxdnKF3WeWeVRexUcMHAWTVB+VyjpHexymjnPutTD4/NWEmrGCmD7V/LRkFNeZVeUyIvXfTxaNA0tVIz7CPsUhHNtN7KtMFd9IRzXR109hGMstJs/2qyGr77ELYE1kNIaX2e0RW22cXyp7IaihJVdund1mV02U14GpD5+j5CCCr+Tj52krEU0Y2ZUVamXKbfD3/zMn9dgRUpFQWGGp3aq089kKEM10JS+2KEAAAIABJREFUNn1+YrriazqSmT7nL50+m11F1hcLjpOPALKaj1OoWyGroSaXr29kNR+nkLdCVkNOz1/vlciqv9PzcyQWWPLD2fdRkFU/xGUK7atWRGV0U4RUFhWSVWtl9FO+J/d5yohokZcIpIxantDTb2T1WHlciEhnulrsSXb0c8ROvT3nhBFzwK4WW9YCP0V6Zlv3BJBV90w1VURWNaXhvhdk1T1TbRWRVW2J6OzHu6x+6brbzQ+e3W1qF1KShZfOP2+dufeO63WSatIVshpcZLkaRlZzYWq6USsRFTnNu6JtPQE9wUroyfY+TnkkiYx4rrT3e+Z9BqXrBZY6p0UF1wSQVddEddVDVnXl4bobZNU1UX31kFV9mWjsyLusssCSxsuAnuoRQFabXxeuRFRWnxXBlCm4p9pHpbzHjojKqrXp92QRobwCWuRKRlaL0ApzW2Q1zNzydo2s5iUV5nbIapi5FekaWS1Cq3u39S6rPLqmey+20M68W2V12j7Xc+/0ZPJsz9ftyKd83mun4e61U3L32j/L5zfsfaNyf2ir10l21HO1FVEZ/ZTPq+3029Xp15n3+uwUXd8vZNU3cf/HQ1b9M/d5RGTVJ23/x0JW/TP3fURk1TfxMI/nXVYZWQ3zQunGrmOW1XH7yJV/mJwyL9pVcl+094a+bAVUvpbvvWm/zjM1t9WI6GlWTuURK1pfyKrWZNz1hay6Y6mxErKqMRV3PSGr7lhqrYSsak1GV1/eZVXbo2vSe2izsdTeT3vxlZvN8y++kmyy9qzTzcP3bVmUIves6rqoXXUTuqzKNN1/sAL6sh0Nlc8v2dHS5yft4kX2o9WjWkIX0TzXALKah1LY2yCrYefXqntktRWhsN9HVsPOL0/3yGoeSmzjXVYFuaZH18hI75Pbty5cCTfecpd56pmdC98Tmd23/+CCoIq4rlq5YtFCUMhqnH+RQpBVGQF9fnLC/GJi3Lxop+W+bEdJRUxltHR/i2m6Z/UP2lVw+81Z9j7Rdz8GjfYRUVdXG7LqiqTeOsiq3mxcdIasuqCotwayqjcbV50hq65Ixl2nElnVjHTn7j3m8mtvNg/ceZNZv26NEZn96jWXmY0XXpC0LaL99W0PLhJcZFVzou33pklWp+zzRGVU9AUrortETifHzc8nREonGp7gkL0PVB7JIiL6mwOD5ky7gFFWUOW5ot38QlbjTx9ZjTtjZDXufJHVuPOVs0NW48/YxRkiqzUUZZryQ488nshorbjKpvW+h6y6uBT11ahKVuWZoj+ZGEtGTH9mP35uR02ft1I6boW13mutFdH324/ftCOlZ9oFjN4z0GfW9g+VsoKuvpTa7whZbZ9dKHsiq6Ek1V6fyGp73ELZC1kNJan2+0RW22fXTXsiq5m0UxHdcsPVyUhqXlntpguGc3VH4KWJSfPL8XHzi7Gx5PMvx+zHuF3kyI6Y1r4G7Cjo+4aGzHuHBs37hofe/Xpo2Jwy0O+uKSpBAAIQgAAEIAABCEBACQFkdT6IVEyvueIis+mqS5Lv5pVVRlaVXM2O23A1sir3ju6x95DusaOje+xUXvks03n32JV3J+w9p7UvGR1dM2in7trpu2vsaOkaGTW13/uNgQHHZ9jd5RhZjT9/RlbjzpiR1bjzZWQ17nzl7BhZjT9jF2eIrFqK6YJP6X2qWbD17lndfNvdJrtiMLLq4lLUV6OorI5Z8UykVITUTt99IRVUK6YHpo+V0tX2HtI1IqRWQmUKr0ip/FkktdvvJ/VxNSCrPihXewxktVr+ZR8dWS2bcLX1kdVq+fs4OrLqg3L4x+h6Wa23YFI2VlYDDv8ib/cMmsmqLGwkUvrC/EjpnKROmFftM0prX8fZZ42KgJ6dyKgdJbVyOjdiOmDkETG8qiGArFbD3edRkVWftP0fC1n1z9znEZFVn7SrORayWg330I7a1bKaTvOtF1p636q8x3NWQ7us3fSbyurPDhw1u62I7rYLHSUfVlTlc+1ryPQk03cTEZ2XUZm+u2Zw0Kzq7XPTFFWcEUBWnaFUWwhZVRuNk8aQVScY1RZBVtVG46wxZNUZyqgLdbWsukqWacCuSOqoI6vw/r1djfcnVkqfGR81P7OLH8mjY7KvlX195v12xd0P2EWPzrajpucODJn3WyllpFRHhnm6QFbzUAp7G2Q17PxadY+stiIU9vvIatj55ekeWc1DiW2QVQfXALLqAGJFJV6SUVI7lXe3ldNk9NR+yHTeWjFdZ2V0nZ3Gm3wMDiefB7v8OaUVRebssMiqM5RqCyGraqNx0hiy6gSj2iLIqtponDWGrDpDGXUhZNVBvMiqA4geSsjo6C+snD47PmaetdN4fzIxap9heuxjYk61Cx+dZx8J8/GREfNfLVtqfnO61wxxb6mHhPweAln1y7uKoyGrVVD3d0xk1R/rKo6ErFZB3e8xkVW/vEM9GrLqIDlk1QHEkkr82i589OToqHlq/Kh5fOyIOTizeFVembZ7rp3Ke54dLf0d+/Eh+3Fq/9xzS4uuBlzSKVC2JALIaklgFZVFVhWFUUIryGoJUBWVRFYVhVFSK8hqSWAjK4usOggUWXUA0VGJI/bxMd8fGzVPjB01T9oPuf80+zrLLnz0seEl5oN2Gq98fr/9c6PHxCCrjkJRWgZZVRqMw7aQVYcwFZZCVhWG4rAlZNUhTKWlkFWlwShrC1l1EAiy6gBimyUOWzn9kZ3WKx/P2vtO5fNbM9ML1eT5pTKl98ODc6OnH7Zf530hq3lJhbkdshpmbkW6RlaL0ApvW2Q1vMyKdIysFqEV5rbIapi5+e4aWXVAHFl1ALFAiZ9Ojs/JqUiqFdTnMqOnx/f1zknp4BLzEftZRPV4+5zTdl7IajvUwtkHWQ0nq3Y7RVbbJRfGfshqGDm12yWy2i65cPZDVsPJqspOkVUH9JFVBxCblHhlaiqR0mftY2Tk84/s4kiTmUfJyKipiOlHrJiKnMpoqosXsuqCot4ayKrebFx1hqy6IqmzDrKqMxdXXSGrrkjqrYOs6s1GU2fIqoM0kFUHEDMljs5P7ZWR0x/bUVT5/Mb01MIWZ/YNJGKayOm8pPa4bSGphqyWAFVRSWRVURgltYKslgRWSVlkVUkQJbWBrJYEVlFZZFVRGIpbQVYdhIOsdg7xZ/NS+mM7avqjmkfKLO/tsVI6sjBy+pGBYbPSTvct+4Wslk242vrIarX8fRwdWfVBubpjIKvVsfdxZGTVB+Vqj4GsVss/lKMjqw6SQlaLQ3xNpvYm957aqb3z95+Om9mFQh+cn9qbLo60dmCo+EE63ANZ7RCg8t2RVeUBOWgPWXUAUXEJZFVxOA5aQ1YdQFReAllVHpCS9pBVB0Egq60hjsnU3mTUdH7lXiuor2em9r6nf25qb7I4khVT+brRI2VaH83NFsiqG45aqyCrWpNx1xey6o6lxkrIqsZU3PWErLpjqbUSsqo1GV19IasO8kBW60N8Y3raPuv0iHnKiukTo4ftfafvPlJG9viQFdMNwyPm0/Z5pzKCOtRT/tTeInEjq0VohbctshpeZkU7RlaLEgtre2Q1rLyKdousFiUW3vbIaniZVdExsuqAOrL6LsT9VkgfPXrE7Bg9ZL5vp/hOZVbtPbWv32xYsjSR0w1DI/a+0z4H9MsrgayWx1ZDZWRVQwrl9oCslsu36urIatUJlHt8ZLVcvhqqI6saUtDfA7LqIKNul9Ujdorvo0cPmx3244mxowuCOtTTYz5uxfRTVkw/YyV17YCbR8o4iCxXCWQ1F6ZgN0JWg40ud+PIam5UQW6IrAYZW+6mkdXcqILdEFkNNjqvjSOrDnB3o6zKs0+fHj9q/taOnv7t6FHz6vz9pyfb0dNPDC0xH7eC+omRJUYeMxPqC1kNNbl8fSOr+TiFvBWyGnJ6rXtHVlszCnkLZDXk9PL1jqzm49TtWyGrDq6AbpFVuec0EVQ7evq3o6PmpenJhN4J9jEyiZxaSf3EkhGztj+sEdRGlwCy6uAvh+ISyKricBy1hqw6Aqm0DLKqNBhHbSGrjkAqLoOsKg5HUWvIqoMwYpbVAzMzc3JqP562o6jPTU4kxJbZxZBkiu8n7AJJn7Cium4wDkHNXg7IqoO/HIpLIKuKw3HUGrLqCKTSMsiq0mActYWsOgKpuAyyqjgcRa0hqw7CiE1W5R5UEVOZ3iuS+rN5QR00PVZO50ZPZST1Q/ZZqDG/kNWY0zUGWY07Xzk7ZDXujJHVuPNFVuPON/0ZHf9ZcoadEkBWOyVo949FVl+z96H+1ZF3zF8ePmheyzwD9Vz73NN/PLLUXLx0uTkrkim+eWJHVvNQCncbZDXc7PJ2jqzmJRXmdshqmLnl7RpZzUsq3O0YWQ03O5+dI6sOaIcsq/Jome+MHkkk9XE7kpq+3tM/YC5ZusJcMrIsuFV8HUSalEBWXZHUWQdZ1ZmLy66QVZc09dVCVvVl4rIjZNUlTZ21kFWduWjrCll1kEiIsvqf7TTfJ6ycPm5F9aeT4wmFk+1zTz8zvNT8njwL1U71lftSu/mFrMadPrIad75ydshq3Bkjq3Hni6zGnW/6Mzr+s+QMOyWArHZK0O4fiqzK1F4ZPX1i7Ij5npXUUTuqKq/fTZ6DuiR5Fuo5dsovrzkCyGrcVwKyGne+yGr8+SKrcWeMrMadL7Iaf76uzhBZdUBSu6w+ZRdJSiX15/OLJZ1un4cqcjr3MWKG7OJJvBYTQFbjviKQ1bjzRVbjzxdZjTtjZDXufJHV+PN1dYbIqgOSGmX1V1OTdgR1bprv9+xnuTdVXp+0j5r5jP2Qab7vYxS1afrIqoO/HIpLIKuKw3HUGtOAHYFUWgZZVRqMo7aQVUcgFZfhnlXF4ShqDVl1EIYmWU1HUB+3gvrC/CjqmX0D5vfsar4yivppO+W3j0HUXKkjq7kwBbsRshpsdLkbR1ZzowpyQ2Q1yNhyN42s5kYV7IbIarDReW0cWXWAW4OsPmnvQ/3X7xww3x9/d0XfDw0Omz9aZlf0tY+cWdrliyW1EzOy2g61cPZBVsPJqt1OkdV2yYWxH7IaRk7tdomstksunP2Q1XCyqrJTZNUB/apkVab2/r+jh82fv/O22TW/ou+K3l7zX9tHzoikyvNRebVPAFltn10IeyKrIaTUWY/Iamf8tO+NrGpPqLP+kNXO+IWwN7IaQkrV94isOsjAt6y+ZO9H/c7RI+bbVlSfsY+gkdeHh4bNhfaxM1/o4ueiOohyUQlk1TVRXfWQVV15lNENsloGVT01kVU9WZTRCbJaBlVdNZFVXXlo7QZZdZCML1mV0dNH7YJJ3z56yOyemEg6v8AuliSCeqG9H/UUu8IvL3cEkFV3LDVWQlY1puK2J2TVLU9t1ZBVbYm47QdZdctTYzVkVWMq+npCVh1kUras/mc7eiqS+qiV1F9PTSUdi5wmkmo/lnE/qoMUjy2BrJaCVU1RZFVNFKU1gqyWhlZFYWRVRQylNYGsloZWTWFkVU0UqhtBVh3EU5asflcEdX4k9cDMTCKlIqepqDponRJNCCCrcV8eyGrc+crZIatxZ4ysxp0vshp3vunP6PjPkjPslACy2ilBu79LWR0zs+bbRw5bSbUfRw8bGUdd3deXjKJ+YcmyZNovLz8EkFU/nKs6CrJaFXl/x0VW/bGu4kjIahXU/R0TWfXHuqojMbJaFfmwjousOsjLhay+OTOdyKlI6hOjc4+fWTswuDCK+mH7GBpefgkgq355+z4asuqbuP/jIav+mfs8IrLqk7b/YyGr/pn7PiKy6pt4mMdDVh3k1omsjs/OmH9/6B3zfx46YF6bnrsf9WQ7kvo/LD/B/JNlxxl5FA2vagggq9Vw93VUZNUX6eqOg6xWx97HkZFVH5SrOwayWh17X0dGVn2RDvs4yKqD/NqRVXlG6kOHD5k/PfiWeWN6OulCRlL/ePnx5uKly80QiyY5SKazEshqZ/y0742sak+o8/6Q1c4Zaq6ArGpOp/PekNXOGWqvgKxqT0hHf8iqgxyKyqpM9/0/DuwzL07NPX7m3IEhc91xK5PFk3jpIYCs6smijE6Q1TKo6qqJrOrKw3U3yKprorrqIau68iijG2S1DKrx1URWHWSaV1Z3HDlkttvHz3zHrvArr9+1iyVdbAV148hys5zpvg6ScFsCWXXLU1s1ZFVbIu77QVbdM9VUEVnVlIb7XpBV90y1VURWtSWisx9k1UEurWRVHkHzsB1NFVGdsdN/19uR1I12qq98nNLX76ADSpRBAFktg6qemsiqnizK6gRZLYusjrrIqo4cyuoCWS2LrJ66yKqeLDR3gqw6SKeRrH5/fNRsP3LQfhw2h+1CSmv6B+ck1Y6mnm3vT+WlmwCyqjufTrtDVjslqH9/ZFV/Rp10iKx2Qk//vsiq/ow67RBZ7ZRgd+yPrM7nvHP3HnP5tTebB+68yaxft2ZR+hdfudk8/+IryffWnnW6efi+LYver5XVH4+PmYftI2i222m/b9gVfuU5qRtHViSi+sHBoe64siI4S2Q1ghCbnAKyGne+cnbIatwZI6tx54usxp1v+jM6/rPkDDslgKxaghs2bjL7DxxKWNbK6peuu93s239wQVBFXFetXGHuveP6BfaprD43OZFM9RVJfXFq0iy3K/pevNTek7p0hfndoSWdZsX+ngkgq56Bez4csuoZeAWHQ1YrgO7xkMiqR9gVHApZrQC650MysuoZeKCHQ1bng2s0sioi+9VrLjMbL7wg2XL7o0+Zr2970Dy5fetC5P/ljbmFk7bbR9Hsmhw38mRUWTRp47Ll5veHlwZ6adA2shr3NYCsxp2vnB2yGnfGyGrc+SKrceeb/oyO/yw5w04JIKtNZLWewNZ+78/f3Gf+L/vxQzv1V17/aMnSRFQvslN+eYVNAFkNO79W3SOrrQiF/z6yGn6Gzc4AWY07X2Q17nyR1fjzdXWGyGqHstrzo58kFdYMDpo/OfFks3E5kurq4qy6Tn9frxno7zGj49NVt8LxSyDQ09NjRob7zJHRqRKqU1IDgeUjA+bQ0UkNrdBDCQRGhvvN2MS0mZmZLaE6JasmIP9hPG2znZyaqboVjl8SAfkZzQsCrQggqx3K6h+9+CvzicEl5p8ed5zpt7/88oqHALIaT5b1zgRZjTtfOTtkNe6MkdW480VW4843/Rkd/1lyhp0SQFabyKq8Ve+e1c233W12PXHfAvtWz1ntNCT2r4YA04Cr4e7rqEwD9kW6uuMwDbg69j6OzDRgH5SrOwbTgKtj7+vILLDki3TYx0FWW8hqkdWAw74U6L6WALIa9zWBrMadr5wdshp3xshq3Pkiq3Hnm/6Mjv8sOcNOCSCrlmD20TUCdOXxyxet9lv0OaudhsL+OgggqzpyKKsLZLUssnrqIqt6siijE2S1DKp6aiKrerIoqxNGVssiG1ddZNVBnkwDdgBRYQlkVWEoDltCVh3CVFoKWVUajKO2kFVHIJWWQVaVBuOwLWTVIcyISyGrDsJFVh1AVFgCWVUYisOWkFWHMJWWQlaVBuOoLWTVEUilZZBVpcE4bAtZdQgz4lLIqoNwkVUHEBWWQFYVhuKwJWTVIUylpZBVpcE4agtZdQRSaRlkVWkwDttCVh3CjLgUsuogXGTVAUSFJZBVhaE4bAlZdQhTaSlkVWkwjtpCVh2BVFoGWVUajMO2kFWHMCMuhaw6CBdZdQBRYQlkVWEoDltCVh3CVFoKWVUajKO2kFVHIJWWQVaVBuOwLWTVIcyISyGrDsJFVh1AVFgCWVUYisOWkFWHMJWWQlaVBuOoLWTVEUilZZBVpcE4bAtZdQgz4lLIqoNwkVUHEBWWQFYVhuKwJWTVIUylpZBVpcE4agtZdQRSaRlkVWkwDttCVh3CjLgUshpxuJwaBCAAAQhAAAIQgAAEIACBUAkgq6EmR98QgAAEIAABCEAAAhCAAAQiJoCsRhwupwYBCEAAAhCAAAQgAAEIQCBUAshqqMnRNwQgAAEIQAACEIAABCAAgYgJIKtthnvxlZvN8y++kuy99qzTzcP3bWmzErtVSaBIjl+67nbzg2d3L2p31xP3Vdk+x25BoEi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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.combine_plots(fig_list=[fig_fixed, fig_variable, fig_exact],\n", " xrange=[0, 0.4], ylabel=\"concentration [A]\",\n", " title=\"Variable time steps vs. Fixed vs. Exact soln, for [A] in reaction `A<->B`\",\n", " legend_title=\"Simulation run\") # All the 3 plots put together: show only the initial part (but it's all there; you can zoom out!)" ] }, { "cell_type": "markdown", "id": "3d37253d-7510-4384-abd6-4bb5cc18ef95", "metadata": {}, "source": [ "#### Not surprisingly, the adaptive variable time steps outperform the fixed ones (for the same total number of points in the time grid), at times when there's pronounced change. \n", "If you zoom out on the plot (by hovering on it, and using the Plotly controls that appear on the right, above), you can see all 3 curves essentially converging as the reaction approaches equilibrium." ] }, { "cell_type": "code", "execution_count": null, "id": "353e5490-2cca-4f05-8f60-b6a34524a715", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "d83e4e09-853c-46af-9669-295dcff914b9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "4375bea1-4a14-486f-906d-92b5ba588e79", "metadata": { "tags": [] }, "source": [ "# PART 5 - Repeating Part 4 with a coarser grid\n", "#### The advantage of adaptive variable step will be even more prominent" ] }, { "cell_type": "code", "execution_count": 20, "id": "71c89174-9c43-428f-bac5-af9ef17e35d3", "metadata": {}, "outputs": [], "source": [ "# A coarser version of the variable-step simulation of Part 1\n", "dynamics_variable_new = UniformCompartment(chem_data=chem, preset=\"fast\") # Re-use same chemicals and reactions of part 2\n", "\n", "dynamics_variable_new.set_conc([10., 50.])" ] }, { "cell_type": "code", "execution_count": 21, "id": "e38d2dcb-1ea1-4728-a26f-126821669d6a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "14 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 3\n", "Norm usage: {'norm_A': 13, 'norm_B': 9, 'norm_C': 9, 'norm_D': 9}\n" ] } ], "source": [ "dynamics_variable_new.single_compartment_react(initial_step=0.1, target_end_time=1.2,\n", " variable_steps=True,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"}\n", " )" ] }, { "cell_type": "markdown", "id": "aa18698d-2dea-4a83-a166-de67565e918b", "metadata": {}, "source": [ "### Note that the variable-step simulation is now taking 14 steps instead of the earlier 19" ] }, { "cell_type": "code", "execution_count": 22, "id": "6ce6eae6-0c4a-4908-9670-d096445d08b4", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_variable = dynamics_variable_new.plot_history(chemicals='A', colors='darkturquoise', title=\"VARIABLE time steps\",\n", " show_intervals=True, show=True)" ] }, { "cell_type": "code", "execution_count": 23, "id": "5638d0b4-77e8-425e-ad5e-f80849abf4d3", "metadata": {}, "outputs": [], "source": [ "# Now, a coarser version of the fixed-step simulation of Part 2\n", "dynamics_fixed_new = UniformCompartment(chem_data=dynamics_fixed.chem_data) # Re-using same chemicals and reactions of part 2\n", "\n", "dynamics_fixed_new.set_conc([10., 50.])" ] }, { "cell_type": "code", "execution_count": 24, "id": "e8170d78-43f1-4b2a-ba68-43605a03c374", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "14 total step(s) taken\n" ] } ], "source": [ "# Matching the NEW total number of steps\n", "dynamics_fixed_new.single_compartment_react(n_steps=14, target_end_time=1.2,\n", " variable_steps=False,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 25, "id": "a2052848-23c2-4524-8052-862d2b7a9795", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_fixed = dynamics_fixed_new.plot_history(chemicals='A', colors='blue', title=\"FIXED time steps\",\n", " show_intervals=True, show=True)" ] }, { "cell_type": "markdown", "id": "6a13881a-0e2a-4a7c-89e3-a00724064b4d", "metadata": {}, "source": [ "#### Notice the jaggedness at the left (jaggedness NOT present with the same number of total grid points, with the variable-step simulation)" ] }, { "cell_type": "code", "execution_count": 26, "id": "78261e52-b7c2-4a31-915d-861b33778859", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "FIXED time steps
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.combine_plots(fig_list=[fig_fixed, fig_variable, fig_exact],\n", " curve_labels = [\"FIXED time steps\", \"VARIABLE time steps\", \"EXACT solution\"],\n", " xrange=[0, 0.4], ylabel=\"concentration [A]\",\n", " title=\"Fixed vs. Variable time steps vs. Exact soln, for [A] in reaction `A<->B`\",\n", " legend_title=\"Simulation run\")" ] }, { "cell_type": "markdown", "id": "a4399ddd-d4c7-4342-ab47-55f04d77b755", "metadata": {}, "source": [ "### With fewer grid points, the advantage of adaptive variable timesteps is more pronounced \n", "If you zoom out the plot, and scroll to later times, you can see that the advantage later disappears when there's \"less happening\" (change-wise), closer to equilibrium" ] }, { "cell_type": "code", "execution_count": null, "id": "d53d0255-2d5d-4d9b-8830-1f94b841f68c", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }