{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## 2 COUPLED reactions of different speeds, forming a \"cascade\": \n", "### `A <-> B` (fast) and `B <-> C` (slow)\n", "Taken to equilibrium. Both reactions are mostly forward. All 1st order. \n", "**The concentration of the intermediate product B manifests 1 oscillation (transient \"overshoot\")**\n", "\n", "Adaptive variable time resolution is used, with extensive diagnostics, \n", "and finally compared to a new run using fixed time intervals, with the same initial data.\n", "\n", "In part2, some diagnotic insight is explored. \n", "In part3, two identical runs (\"adaptive variable steps\" and \"fixed small steps\") are compared. \n", "\n", "LAST REVISED: Dec. 6, 2023" ] }, { "cell_type": "markdown", "id": "c8763f25-9fab-4b36-89cc-388321a16be0", "metadata": {}, "source": [ "## Bathtub analogy:\n", "A is initially full, while B and C are empty. \n", "Tubs are progressively lower (reactions are mostly forward.) \n", "A BIG pipe connects A and B: fast kinetics. A small pipe connects B and C: slow kinetics. \n", "\n", "INTUITION: B, unable to quickly drain into C while at the same time being blasted by a hefty inflow from A, \n", "will experience a transient surge, in excess of its final equilibrium level.\n", "\n", "* **[Compare with the final reaction plot (the orange line is B)](#cascade_1_plot)**" ] }, { "cell_type": "markdown", "id": "b11f68d6-d3bc-4908-93c0-eaee580acbc1", "metadata": {}, "source": [ "![2 Coupled Reactions](../../docs/2_coupled_reactions.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "4d9b4808-b2ec-4b90-a604-f7fa69af39b8", "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": "3924c013", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "from src.modules.visualization.plotly_helper import PlotlyHelper\n", "\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'cascade_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System\n", "Specify the chemicals and the reactions" ] }, { "cell_type": "code", "execution_count": 4, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "dynamics = ReactionDynamics(names=[\"A\", \"B\", \"C\"])\n", "\n", "# Reaction A <-> B (fast)\n", "dynamics.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=64., reverse_rate=8.) \n", "\n", "# Reaction B <-> C (slow)\n", "dynamics.add_reaction(reactants=[\"B\"], products=[\"C\"],\n", " forward_rate=12., reverse_rate=2.) \n", "\n", "print(\"Number of reactions: \", dynamics.number_of_reactions())" ] }, { "cell_type": "code", "execution_count": 5, "id": "00ea560d-9a49-4041-b119-6de11bfcc7af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 64 / kR = 8 / delta_G = -5,154.8 / K = 8) | 1st order in all reactants & products\n", "1: B <-> C (kF = 12 / kR = 2 / delta_G = -4,441.7 / K = 6) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'A', 'C', 'B'}\n" ] } ], "source": [ "dynamics.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 6, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `cascade_1.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "graph_data = dynamics.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2", "metadata": {}, "source": [ "## Run the simulation" ] }, { "cell_type": "code", "execution_count": 7, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (C). Conc: 0.0\n", "Set of chemicals involved in reactions: {'A', 'C', 'B'}\n" ] } ], "source": [ "dynamics.set_conc([50., 0, 0.], snapshot=True) # Set the initial concentrations of all the chemicals, in their index order\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 8, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABCcaption
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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.0 50.0 0.0 0.0 Initial state" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "## Run the reaction" ] }, { "cell_type": "code", "execution_count": 9, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n", " INFO: the tentative time step (0.02) leads to a NEGATIVE concentration of `A` from reaction A <-> B (rxn # 0): \n", " Baseline value: 50 ; delta conc: -64\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.01) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.01) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.006) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.006) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.0036) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.0036) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.00216) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.00216) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.001296) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.001296) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.6 (set to 0.0007776) [Step started at t=0, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "48 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# These settings can be tweaked to make the time resolution finer or coarser. \n", "# Here we use a \"fast\" heuristic: less conservative about taking larger steps\n", "dynamics.use_adaptive_preset(preset=\"fast\")\n", "\n", "dynamics.single_compartment_react(initial_step=0.02, reaction_duration=0.4,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "markdown", "id": "199b6238-f6ed-44a8-8130-a003444d7658", "metadata": {}, "source": [ "### Plots of changes of concentration with time\n", "Notice the variable time steps (vertical dashed lines)" ] }, { "cell_type": "code", "execution_count": 10, "id": "a2c0e793-5457-46a5-9150-388c9f562cf0", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(title=\"Coupled reactions A <-> B and B <-> C\",\n", " colors=['blue', 'orange', 'green'], show_intervals=True)" ] }, { "cell_type": "code", "execution_count": 11, "id": "844183a6-e61f-4b7a-8aa6-013f4530a74b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 19\n" ] }, { "data": { "text/plain": [ "(0.011857732428358053, 24.047031609298816)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.05)" ] }, { "cell_type": "code", "execution_count": 12, "id": "025c387b-5bd2-4666-a140-9c66630da072", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 29\n" ] }, { "data": { "text/plain": [ "(0.031934885008449314, 8.852813807230596)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"C\", t_start=0, t_end=0.05)" ] }, { "cell_type": "code", "execution_count": 13, "id": "86f3a798-4a5b-4016-b4d1-121f9fb48506", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 36\n" ] }, { "data": { "text/plain": [ "(0.07740303497735611, 23.285274847029168)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"B\", \"C\", t_start=0.05, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 14, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.00000050.0000000.0000000.000000Initial state
10.00077847.5116802.4883200.0000001st reaction step
20.00140045.6324754.3489500.018575
30.00202243.8373476.1116360.051017
40.00251942.4654387.4470970.087465
50.00301741.1425428.7256060.131851
60.00351539.8668719.9493000.183829
70.00401238.63670311.1202340.243063
80.00451037.45037812.2403910.309231
90.00500836.30629813.3116800.382022
100.00550535.20292214.3359390.461139
110.00600334.13876715.3149390.546294
120.00650133.11240416.2503860.637210
130.00699832.12245517.1439220.733623
140.00749631.16759517.9971300.835276
150.00824329.78601819.2187360.995246
160.00898928.47774220.3563371.165921
170.00973627.23876421.4147051.346531
180.01048226.06530022.3983471.536353
190.01160224.39801023.7681131.833877
200.01272222.86247424.9883862.149140
210.01384121.44791126.0719942.480095
220.01496120.14442827.0307042.824868
230.01664118.34220428.2976033.360193
240.01832016.75073429.3300123.919255
250.02000015.34421230.1585424.497247
260.02251913.47792031.1357085.386372
270.02503911.93225031.7671906.300559
280.02755810.64853732.1222317.229232
290.0313379.04418632.3244918.631323
300.0351167.83398632.13402610.031989
310.0388966.91073231.67583811.413430
320.0445645.84002630.72121113.438763
330.0502335.11447829.50932715.376196
340.0587364.33855727.53570318.125740
350.0655383.94821925.92491920.126862
360.0757423.48612923.62339322.890478
370.0839053.20756821.96162724.830805
380.0961492.84524019.70514827.449612
390.1059452.60569918.16619029.228112
400.1206382.29074516.13700631.572249
410.1353322.03344214.47684233.489716
420.1573711.71770812.43997635.842316
430.1794111.48819510.95929937.552505
440.2124711.2379299.34477139.417300
450.2455311.0901758.39154340.518282
460.2951210.9593157.54737141.493315
470.3695060.8836537.05906142.057286
480.4810830.8745847.00183542.123581last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initial state\n", "1 0.000778 47.511680 2.488320 0.000000 1st reaction step\n", "2 0.001400 45.632475 4.348950 0.018575 \n", "3 0.002022 43.837347 6.111636 0.051017 \n", "4 0.002519 42.465438 7.447097 0.087465 \n", "5 0.003017 41.142542 8.725606 0.131851 \n", "6 0.003515 39.866871 9.949300 0.183829 \n", "7 0.004012 38.636703 11.120234 0.243063 \n", "8 0.004510 37.450378 12.240391 0.309231 \n", "9 0.005008 36.306298 13.311680 0.382022 \n", "10 0.005505 35.202922 14.335939 0.461139 \n", "11 0.006003 34.138767 15.314939 0.546294 \n", "12 0.006501 33.112404 16.250386 0.637210 \n", "13 0.006998 32.122455 17.143922 0.733623 \n", "14 0.007496 31.167595 17.997130 0.835276 \n", "15 0.008243 29.786018 19.218736 0.995246 \n", "16 0.008989 28.477742 20.356337 1.165921 \n", "17 0.009736 27.238764 21.414705 1.346531 \n", "18 0.010482 26.065300 22.398347 1.536353 \n", "19 0.011602 24.398010 23.768113 1.833877 \n", "20 0.012722 22.862474 24.988386 2.149140 \n", "21 0.013841 21.447911 26.071994 2.480095 \n", "22 0.014961 20.144428 27.030704 2.824868 \n", "23 0.016641 18.342204 28.297603 3.360193 \n", "24 0.018320 16.750734 29.330012 3.919255 \n", "25 0.020000 15.344212 30.158542 4.497247 \n", "26 0.022519 13.477920 31.135708 5.386372 \n", "27 0.025039 11.932250 31.767190 6.300559 \n", "28 0.027558 10.648537 32.122231 7.229232 \n", "29 0.031337 9.044186 32.324491 8.631323 \n", "30 0.035116 7.833986 32.134026 10.031989 \n", "31 0.038896 6.910732 31.675838 11.413430 \n", "32 0.044564 5.840026 30.721211 13.438763 \n", "33 0.050233 5.114478 29.509327 15.376196 \n", "34 0.058736 4.338557 27.535703 18.125740 \n", "35 0.065538 3.948219 25.924919 20.126862 \n", "36 0.075742 3.486129 23.623393 22.890478 \n", "37 0.083905 3.207568 21.961627 24.830805 \n", "38 0.096149 2.845240 19.705148 27.449612 \n", "39 0.105945 2.605699 18.166190 29.228112 \n", "40 0.120638 2.290745 16.137006 31.572249 \n", "41 0.135332 2.033442 14.476842 33.489716 \n", "42 0.157371 1.717708 12.439976 35.842316 \n", "43 0.179411 1.488195 10.959299 37.552505 \n", "44 0.212471 1.237929 9.344771 39.417300 \n", "45 0.245531 1.090175 8.391543 40.518282 \n", "46 0.295121 0.959315 7.547371 41.493315 \n", "47 0.369506 0.883653 7.059061 42.057286 \n", "48 0.481083 0.874584 7.001835 42.123581 last reaction step" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 15, "id": "144d0388-a632-4165-a9c5-50bc7943fc88", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0007776, in 1 step of 0.000778\n", "From time 0.0007776 to 0.002022, in 2 steps of 0.000622\n", "From time 0.002022 to 0.007496, in 11 steps of 0.000498\n", "From time 0.007496 to 0.01048, in 4 steps of 0.000746\n", "From time 0.01048 to 0.01496, in 4 steps of 0.00112\n", "From time 0.01496 to 0.02, in 3 steps of 0.00168\n", "From time 0.02 to 0.02756, in 3 steps of 0.00252\n", "From time 0.02756 to 0.0389, in 3 steps of 0.00378\n", "From time 0.0389 to 0.05023, in 2 steps of 0.00567\n", "From time 0.05023 to 0.05874, in 1 step of 0.0085\n", "From time 0.05874 to 0.06554, in 1 step of 0.0068\n", "From time 0.06554 to 0.07574, in 1 step of 0.0102\n", "From time 0.07574 to 0.08391, in 1 step of 0.00816\n", "From time 0.08391 to 0.09615, in 1 step of 0.0122\n", "From time 0.09615 to 0.1059, in 1 step of 0.0098\n", "From time 0.1059 to 0.1353, in 2 steps of 0.0147\n", "From time 0.1353 to 0.1794, in 2 steps of 0.022\n", "From time 0.1794 to 0.2455, in 2 steps of 0.0331\n", "From time 0.2455 to 0.2951, in 1 step of 0.0496\n", "From time 0.2951 to 0.3695, in 1 step of 0.0744\n", "From time 0.3695 to 0.4811, in 1 step of 0.112\n", "(48 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "markdown", "id": "c02a8f55-a671-4771-86c9-fc4d1b126bf8", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 16, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 0.8746 ; [B] = 7.002\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 8.0059\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 8.0\n", "Discrepancy between the two values: 0.07378 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: B <-> C\n", "Final concentrations: [B] = 7.002 ; [C] = 42.12\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 6.01608\n", " Formula used: [C] / [B]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 0.268 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "c279c0b2-754e-4574-95a6-ffbe8e162463", "metadata": {}, "source": [ "### Let's look at the final concentrations of `A` and `C` (i.e., the reactant and product of the composite reaction)" ] }, { "cell_type": "code", "execution_count": 17, "id": "c093910f-62f2-43cf-88ef-d5df935a44b8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.8745841244150234" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_final = dynamics.get_chem_conc(\"A\")\n", "A_final" ] }, { "cell_type": "code", "execution_count": 18, "id": "22636dc7-fd18-468f-8ddb-8152891eb9b5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "42.123581082850514" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C_final = dynamics.get_chem_conc(\"C\")\n", "C_final" ] }, { "cell_type": "markdown", "id": "420e0075-6b81-4836-8641-b0ccdeacf550", "metadata": {}, "source": [ "#### Their ratio:" ] }, { "cell_type": "code", "execution_count": 19, "id": "8280c0be-2f8d-4f4c-adc0-9ca7f5d5060e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "48.16412727709344" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C_final / A_final" ] }, { "cell_type": "markdown", "id": "07fe7c6c-f8dd-4460-aa08-d7c61d60bd62", "metadata": {}, "source": [ "### As expected the equilibrium constant for the overall reaction `A <-> C` (approx. 48) is indeed the product of the equilibrium constants of the two elementary reactions (K = 8 and K = 6, respectively) that we saw earlier." ] }, { "cell_type": "code", "execution_count": null, "id": "587c2018-e781-43c1-aee8-e78b7b6dc9bf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "520b3b44-7da9-49d3-9cfd-685607169f01", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "5c3f8b4f-3a75-4a21-8579-13550bcebb3c", "metadata": {}, "source": [ "# PART 2 - DIAGNOSTIC INSIGHT\n", "\n", "Perform some verification" ] }, { "cell_type": "markdown", "id": "07dd5aa4-9e71-40c1-9f15-a16a9333ed10", "metadata": {}, "source": [ "### Take a peek at the diagnostic data saved during the earlier reaction simulation" ] }, { "cell_type": "code", "execution_count": 20, "id": "5ad64dc5-ba89-4f09-b7db-da40de1df4ed", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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START_TIMEDelta ADelta BDelta Ctime_stepcaption
00.000000NaNNaNNaN0.020000aborted: neg. conc. in `A`
10.000000-32.00000032.0000000.00.010000aborted: excessive norm value(s)
20.000000-19.20000019.2000000.00.006000aborted: excessive norm value(s)
30.000000-11.52000011.5200000.00.003600aborted: excessive norm value(s)
40.000000-6.9120006.9120000.00.002160aborted: excessive norm value(s)
50.000000-4.1472004.1472000.00.001296aborted: excessive norm value(s)
60.000000-2.4883202.4883200.00.000778
70.000778-1.8792051.8792050.00.000622
80.001400-1.7951281.7951280.00.000622
90.002022-1.3719091.3719090.00.000498
100.002519-1.3228961.3228960.00.000498
110.003017-1.2756711.2756710.00.000498
120.003515-1.2301681.2301680.00.000498
130.004012-1.1863251.1863250.00.000498
140.004510-1.1440801.1440800.00.000498
150.005008-1.1033761.1033760.00.000498
160.005505-1.0641551.0641550.00.000498
170.006003-1.0263631.0263630.00.000498
180.006501-0.9899490.9899490.00.000498
190.006998-0.9548610.9548610.00.000498
200.007496-1.3815771.3815770.00.000746
210.008243-1.3082751.3082750.00.000746
220.008989-1.2389781.2389780.00.000746
230.009736-1.1734641.1734640.00.000746
240.010482-1.6672901.6672900.00.001120
250.011602-1.5355361.5355360.00.001120
260.012722-1.4145631.4145630.00.001120
270.013841-1.3034831.3034830.00.001120
280.014961-1.8022241.8022240.00.001680
290.016641-1.5914701.5914700.00.001680
300.018320-1.4065221.4065220.00.001680
310.020000-1.8662921.8662920.00.002519
320.022519-1.5456701.5456700.00.002519
330.025039-1.2837131.2837130.00.002519
340.027558-1.6043511.6043510.00.003779
350.031337-1.2102001.2102000.00.003779
360.035116-0.9232540.9232540.00.003779
370.038896-1.0707061.0707060.00.005669
380.044564-0.7255490.7255490.00.005669
390.050233-0.7759200.7759200.00.008503
400.058736-0.3903380.3903380.00.006802
410.065538-0.4620900.4620900.00.010204
420.075742-0.2785610.2785610.00.008163
430.083905-0.3623280.3623280.00.012244
440.096149-0.2395410.2395410.00.009796
450.105945-0.3149530.3149530.00.014693
460.120638-0.2573040.2573040.00.014693
470.135332-0.3157330.3157330.00.022040
480.157371-0.2295130.2295130.00.022040
490.179411-0.2502660.2502660.00.033060
500.212471-0.1477540.1477540.00.033060
510.245531-0.1308600.1308600.00.049590
520.295121-0.0756620.0756620.00.074385
530.369506-0.0090680.0090680.00.111577
\n", "
" ], "text/plain": [ " START_TIME Delta A Delta B Delta C time_step \\\n", "0 0.000000 NaN NaN NaN 0.020000 \n", "1 0.000000 -32.000000 32.000000 0.0 0.010000 \n", "2 0.000000 -19.200000 19.200000 0.0 0.006000 \n", "3 0.000000 -11.520000 11.520000 0.0 0.003600 \n", "4 0.000000 -6.912000 6.912000 0.0 0.002160 \n", "5 0.000000 -4.147200 4.147200 0.0 0.001296 \n", "6 0.000000 -2.488320 2.488320 0.0 0.000778 \n", "7 0.000778 -1.879205 1.879205 0.0 0.000622 \n", "8 0.001400 -1.795128 1.795128 0.0 0.000622 \n", "9 0.002022 -1.371909 1.371909 0.0 0.000498 \n", "10 0.002519 -1.322896 1.322896 0.0 0.000498 \n", "11 0.003017 -1.275671 1.275671 0.0 0.000498 \n", "12 0.003515 -1.230168 1.230168 0.0 0.000498 \n", "13 0.004012 -1.186325 1.186325 0.0 0.000498 \n", "14 0.004510 -1.144080 1.144080 0.0 0.000498 \n", "15 0.005008 -1.103376 1.103376 0.0 0.000498 \n", "16 0.005505 -1.064155 1.064155 0.0 0.000498 \n", "17 0.006003 -1.026363 1.026363 0.0 0.000498 \n", "18 0.006501 -0.989949 0.989949 0.0 0.000498 \n", "19 0.006998 -0.954861 0.954861 0.0 0.000498 \n", "20 0.007496 -1.381577 1.381577 0.0 0.000746 \n", "21 0.008243 -1.308275 1.308275 0.0 0.000746 \n", "22 0.008989 -1.238978 1.238978 0.0 0.000746 \n", "23 0.009736 -1.173464 1.173464 0.0 0.000746 \n", "24 0.010482 -1.667290 1.667290 0.0 0.001120 \n", "25 0.011602 -1.535536 1.535536 0.0 0.001120 \n", "26 0.012722 -1.414563 1.414563 0.0 0.001120 \n", "27 0.013841 -1.303483 1.303483 0.0 0.001120 \n", "28 0.014961 -1.802224 1.802224 0.0 0.001680 \n", "29 0.016641 -1.591470 1.591470 0.0 0.001680 \n", "30 0.018320 -1.406522 1.406522 0.0 0.001680 \n", "31 0.020000 -1.866292 1.866292 0.0 0.002519 \n", "32 0.022519 -1.545670 1.545670 0.0 0.002519 \n", "33 0.025039 -1.283713 1.283713 0.0 0.002519 \n", "34 0.027558 -1.604351 1.604351 0.0 0.003779 \n", "35 0.031337 -1.210200 1.210200 0.0 0.003779 \n", "36 0.035116 -0.923254 0.923254 0.0 0.003779 \n", "37 0.038896 -1.070706 1.070706 0.0 0.005669 \n", "38 0.044564 -0.725549 0.725549 0.0 0.005669 \n", "39 0.050233 -0.775920 0.775920 0.0 0.008503 \n", "40 0.058736 -0.390338 0.390338 0.0 0.006802 \n", "41 0.065538 -0.462090 0.462090 0.0 0.010204 \n", "42 0.075742 -0.278561 0.278561 0.0 0.008163 \n", "43 0.083905 -0.362328 0.362328 0.0 0.012244 \n", "44 0.096149 -0.239541 0.239541 0.0 0.009796 \n", "45 0.105945 -0.314953 0.314953 0.0 0.014693 \n", "46 0.120638 -0.257304 0.257304 0.0 0.014693 \n", "47 0.135332 -0.315733 0.315733 0.0 0.022040 \n", "48 0.157371 -0.229513 0.229513 0.0 0.022040 \n", "49 0.179411 -0.250266 0.250266 0.0 0.033060 \n", "50 0.212471 -0.147754 0.147754 0.0 0.033060 \n", "51 0.245531 -0.130860 0.130860 0.0 0.049590 \n", "52 0.295121 -0.075662 0.075662 0.0 0.074385 \n", "53 0.369506 -0.009068 0.009068 0.0 0.111577 \n", "\n", " caption \n", "0 aborted: neg. conc. in `A` \n", "1 aborted: excessive norm value(s) \n", "2 aborted: excessive norm value(s) \n", "3 aborted: excessive norm value(s) \n", "4 aborted: excessive norm value(s) \n", "5 aborted: excessive norm value(s) \n", "6 \n", "7 \n", "8 \n", "9 \n", "10 \n", "11 \n", "12 \n", "13 \n", "14 \n", "15 \n", "16 \n", "17 \n", "18 \n", "19 \n", "20 \n", "21 \n", "22 \n", "23 \n", "24 \n", "25 \n", "26 \n", "27 \n", "28 \n", "29 \n", "30 \n", "31 \n", "32 \n", "33 \n", "34 \n", "35 \n", "36 \n", "37 \n", "38 \n", "39 \n", "40 \n", "41 \n", "42 \n", "43 \n", "44 \n", "45 \n", "46 \n", "47 \n", "48 \n", "49 \n", "50 \n", "51 \n", "52 \n", "53 " ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Concentration increments due to reaction 0 (A <-> B)\n", "# Note that [C] is not affected\n", "dynamics.get_diagnostic_rxn_data(rxn_index=0)" ] }, { "cell_type": "code", "execution_count": 21, "id": "71f62382-f07a-416d-876f-97832c1f79e5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: B <-> C\n" ] }, { "data": { "text/html": [ "
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START_TIMEDelta ADelta BDelta Ctime_stepcaption
00.0000000.00.0000000.0000000.010000aborted: excessive norm value(s)
10.0000000.00.0000000.0000000.006000aborted: excessive norm value(s)
20.0000000.00.0000000.0000000.003600aborted: excessive norm value(s)
30.0000000.00.0000000.0000000.002160aborted: excessive norm value(s)
40.0000000.00.0000000.0000000.001296aborted: excessive norm value(s)
50.0000000.00.0000000.0000000.000778
60.0007780.0-0.0185750.0185750.000622
70.0014000.0-0.0324420.0324420.000622
80.0020220.0-0.0364480.0364480.000498
90.0025190.0-0.0443870.0443870.000498
100.0030170.0-0.0519780.0519780.000498
110.0035150.0-0.0592340.0592340.000498
120.0040120.0-0.0661680.0661680.000498
130.0045100.0-0.0727910.0727910.000498
140.0050080.0-0.0791170.0791170.000498
150.0055050.0-0.0851550.0851550.000498
160.0060030.0-0.0909170.0909170.000498
170.0065010.0-0.0964130.0964130.000498
180.0069980.0-0.1016530.1016530.000498
190.0074960.0-0.1599700.1599700.000746
200.0082430.0-0.1706750.1706750.000746
210.0089890.0-0.1806100.1806100.000746
220.0097360.0-0.1898220.1898220.000746
230.0104820.0-0.2975240.2975240.001120
240.0116020.0-0.3152630.3152630.001120
250.0127220.0-0.3309540.3309540.001120
260.0138410.0-0.3447730.3447730.001120
270.0149610.0-0.5353250.5353250.001680
280.0166410.0-0.5590620.5590620.001680
290.0183200.0-0.5779920.5779920.001680
300.0200000.0-0.8891250.8891250.002519
310.0225190.0-0.9141880.9141880.002519
320.0250390.0-0.9286730.9286730.002519
330.0275580.0-1.4020911.4020910.003779
340.0313370.0-1.4006661.4006660.003779
350.0351160.0-1.3814421.3814420.003779
360.0388960.0-2.0253332.0253330.005669
370.0445640.0-1.9374331.9374330.005669
380.0502330.0-2.7495442.7495440.008503
390.0587360.0-2.0011232.0011230.006802
400.0655380.0-2.7636152.7636150.010204
410.0757420.0-1.9403271.9403270.008163
420.0839050.0-2.6188072.6188070.012244
430.0961490.0-1.7785001.7785000.009796
440.1059450.0-2.3441372.3441370.014693
450.1206380.0-1.9174671.9174670.014693
460.1353320.0-2.3526002.3526000.022040
470.1573710.0-1.7101891.7101890.022040
480.1794110.0-1.8647951.8647950.033060
490.2124710.0-1.1009821.1009820.033060
500.2455310.0-0.9750330.9750330.049590
510.2951210.0-0.5639720.5639720.074385
520.3695060.0-0.0662950.0662950.111577
\n", "
" ], "text/plain": [ " START_TIME Delta A Delta B Delta C time_step \\\n", "0 0.000000 0.0 0.000000 0.000000 0.010000 \n", "1 0.000000 0.0 0.000000 0.000000 0.006000 \n", "2 0.000000 0.0 0.000000 0.000000 0.003600 \n", "3 0.000000 0.0 0.000000 0.000000 0.002160 \n", "4 0.000000 0.0 0.000000 0.000000 0.001296 \n", "5 0.000000 0.0 0.000000 0.000000 0.000778 \n", "6 0.000778 0.0 -0.018575 0.018575 0.000622 \n", "7 0.001400 0.0 -0.032442 0.032442 0.000622 \n", "8 0.002022 0.0 -0.036448 0.036448 0.000498 \n", "9 0.002519 0.0 -0.044387 0.044387 0.000498 \n", "10 0.003017 0.0 -0.051978 0.051978 0.000498 \n", "11 0.003515 0.0 -0.059234 0.059234 0.000498 \n", "12 0.004012 0.0 -0.066168 0.066168 0.000498 \n", "13 0.004510 0.0 -0.072791 0.072791 0.000498 \n", "14 0.005008 0.0 -0.079117 0.079117 0.000498 \n", "15 0.005505 0.0 -0.085155 0.085155 0.000498 \n", "16 0.006003 0.0 -0.090917 0.090917 0.000498 \n", "17 0.006501 0.0 -0.096413 0.096413 0.000498 \n", "18 0.006998 0.0 -0.101653 0.101653 0.000498 \n", "19 0.007496 0.0 -0.159970 0.159970 0.000746 \n", "20 0.008243 0.0 -0.170675 0.170675 0.000746 \n", "21 0.008989 0.0 -0.180610 0.180610 0.000746 \n", "22 0.009736 0.0 -0.189822 0.189822 0.000746 \n", "23 0.010482 0.0 -0.297524 0.297524 0.001120 \n", "24 0.011602 0.0 -0.315263 0.315263 0.001120 \n", "25 0.012722 0.0 -0.330954 0.330954 0.001120 \n", "26 0.013841 0.0 -0.344773 0.344773 0.001120 \n", "27 0.014961 0.0 -0.535325 0.535325 0.001680 \n", "28 0.016641 0.0 -0.559062 0.559062 0.001680 \n", "29 0.018320 0.0 -0.577992 0.577992 0.001680 \n", "30 0.020000 0.0 -0.889125 0.889125 0.002519 \n", "31 0.022519 0.0 -0.914188 0.914188 0.002519 \n", "32 0.025039 0.0 -0.928673 0.928673 0.002519 \n", "33 0.027558 0.0 -1.402091 1.402091 0.003779 \n", "34 0.031337 0.0 -1.400666 1.400666 0.003779 \n", "35 0.035116 0.0 -1.381442 1.381442 0.003779 \n", "36 0.038896 0.0 -2.025333 2.025333 0.005669 \n", "37 0.044564 0.0 -1.937433 1.937433 0.005669 \n", "38 0.050233 0.0 -2.749544 2.749544 0.008503 \n", "39 0.058736 0.0 -2.001123 2.001123 0.006802 \n", "40 0.065538 0.0 -2.763615 2.763615 0.010204 \n", "41 0.075742 0.0 -1.940327 1.940327 0.008163 \n", "42 0.083905 0.0 -2.618807 2.618807 0.012244 \n", "43 0.096149 0.0 -1.778500 1.778500 0.009796 \n", "44 0.105945 0.0 -2.344137 2.344137 0.014693 \n", "45 0.120638 0.0 -1.917467 1.917467 0.014693 \n", "46 0.135332 0.0 -2.352600 2.352600 0.022040 \n", "47 0.157371 0.0 -1.710189 1.710189 0.022040 \n", "48 0.179411 0.0 -1.864795 1.864795 0.033060 \n", "49 0.212471 0.0 -1.100982 1.100982 0.033060 \n", "50 0.245531 0.0 -0.975033 0.975033 0.049590 \n", "51 0.295121 0.0 -0.563972 0.563972 0.074385 \n", "52 0.369506 0.0 -0.066295 0.066295 0.111577 \n", "\n", " caption \n", "0 aborted: excessive norm value(s) \n", "1 aborted: excessive norm value(s) \n", "2 aborted: excessive norm value(s) \n", "3 aborted: excessive norm value(s) \n", "4 aborted: excessive norm value(s) \n", "5 \n", "6 \n", "7 \n", "8 \n", "9 \n", "10 \n", "11 \n", "12 \n", "13 \n", "14 \n", "15 \n", "16 \n", "17 \n", "18 \n", "19 \n", "20 \n", "21 \n", "22 \n", "23 \n", "24 \n", "25 \n", "26 \n", "27 \n", "28 \n", "29 \n", "30 \n", "31 \n", "32 \n", "33 \n", "34 \n", "35 \n", "36 \n", "37 \n", "38 \n", "39 \n", "40 \n", "41 \n", "42 \n", "43 \n", "44 \n", "45 \n", "46 \n", "47 \n", "48 \n", "49 \n", "50 \n", "51 \n", "52 " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Concentration increments due to reaction 1 (B <-> C)\n", "# Note that [A] is not affected. \n", "# Also notice that the 0-th row from the A <-> B reaction isn't seen here, because that step was aborted\n", "# early on, before even getting to THIS reaction\n", "dynamics.get_diagnostic_rxn_data(rxn_index=1)" ] }, { "cell_type": "code", "execution_count": null, "id": "46fdcb5b-ed5f-43a9-9829-533039666d0c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "a539f288-e9bc-44c3-a03a-982174b2babf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "de51ec27-1d0f-4bfb-83f0-b1c79b436d75", "metadata": { "tags": [] }, "source": [ "# PART 3 : Re-run with very small constant steps, and compare with original run" ] }, { "cell_type": "markdown", "id": "ff9fffab-a1f5-4497-9d7b-c3db023d1bd2", "metadata": {}, "source": [ "We'll use **constant steps of size 0.0005** , which is 1/4 of the smallest steps (the \"substep\" size) previously used in the variable-step run" ] }, { "cell_type": "code", "execution_count": 22, "id": "93418d81-12fa-417d-9906-1dd24a40de48", "metadata": {}, "outputs": [], "source": [ "dynamics2 = ReactionDynamics(shared=dynamics) # Re-use the same chemicals and reactions of the previous simulation" ] }, { "cell_type": "code", "execution_count": 23, "id": "ecf2029b-57a7-4db4-9b30-c854da91fb76", "metadata": { "tags": [] }, "outputs": [], "source": [ "dynamics2.set_conc([50., 0, 0.], snapshot=True)" ] }, { "cell_type": "code", "execution_count": 24, "id": "00777982-d633-4c12-8c92-2ece6bf00e5e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "800 total step(s) taken\n" ] } ], "source": [ "dynamics2.single_compartment_react(initial_step=0.0005, reaction_duration=0.4,\n", " variable_steps=False,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " ) " ] }, { "cell_type": "code", "execution_count": 25, "id": "6bb61113-a081-4366-893d-f94894c44ec2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (801) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics2.plot_history(title=\"Coupled reactions A <-> B and B <-> C , re-run with CONSTANT STEPS\",\n", " colors=['blue', 'orange', 'green'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "3e27e613-21d9-4e99-ba9a-87b3a5393a44", "metadata": {}, "source": [ "_(Notice that the vertical steps are now equally spaced - and that there are so many of them that we're only showing some)_" ] }, { "cell_type": "code", "execution_count": 26, "id": "e884f562-a723-4208-88e5-ba0bf36e5e3a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 24\n" ] }, { "data": { "text/plain": [ "(0.011934802021672202, 24.03028826511689)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics2.curve_intersection(t_start=0, t_end=0.05, chem1=\"A\", chem2=\"B\")" ] }, { "cell_type": "code", "execution_count": 27, "id": "5b01f35a-17ac-4965-8a21-f300783c1e2c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 65\n" ] }, { "data": { "text/plain": [ "(0.03259520587890533, 9.081194286771336)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics2.curve_intersection(t_start=0, t_end=0.05, chem1=\"A\", chem2=\"C\")" ] }, { "cell_type": "code", "execution_count": 28, "id": "5dae6925-3f3b-49ca-81f9-3cb8f19fdd55", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 159\n" ] }, { "data": { "text/plain": [ "(0.07932921476313338, 23.238745930657448)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics2.curve_intersection(t_start=0.05, t_end=0.1, chem1=\"B\", chem2=\"C\")" ] }, { "cell_type": "code", "execution_count": 29, "id": "4fd2ea95-76e3-4cdf-9ea0-ecd37a515cb5", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.000050.0000000.0000000.000000Initial state
10.000548.4000001.6000000.0000001st reaction step
20.001046.8576003.1328000.009600
30.001545.3706884.6009250.028387
40.002043.9372306.0068060.055964
..................
7960.39800.9254947.32915141.745354
7970.39850.9251957.32722141.747584
7980.39900.9248987.32530341.749800
7990.39950.9246027.32339641.752002
8000.40000.9243097.32150141.754190last reaction step
\n", "

801 rows × 5 columns

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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.0000 50.000000 0.000000 0.000000 Initial state\n", "1 0.0005 48.400000 1.600000 0.000000 1st reaction step\n", "2 0.0010 46.857600 3.132800 0.009600 \n", "3 0.0015 45.370688 4.600925 0.028387 \n", "4 0.0020 43.937230 6.006806 0.055964 \n", ".. ... ... ... ... ...\n", "796 0.3980 0.925494 7.329151 41.745354 \n", "797 0.3985 0.925195 7.327221 41.747584 \n", "798 0.3990 0.924898 7.325303 41.749800 \n", "799 0.3995 0.924602 7.323396 41.752002 \n", "800 0.4000 0.924309 7.321501 41.754190 last reaction step\n", "\n", "[801 rows x 5 columns]" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2 = dynamics2.get_history()\n", "df2" ] }, { "cell_type": "markdown", "id": "45d5883d-c2c6-40a7-80b4-8a5976b8dfcd", "metadata": {}, "source": [ "## Notice that we now did 800 steps - vs. the 48 of the earlier variable-resolution run!" ] }, { "cell_type": "markdown", "id": "0f590255-1555-43d5-9adb-ace15ac80aa4", "metadata": {}, "source": [ "## Let's compare some entries with the coarser previous variable-time run" ] }, { "cell_type": "markdown", "id": "bfef068e-d576-4c3c-bda8-b0b51c5f88da", "metadata": {}, "source": [ "#### Let's compare the plots of [B] from the earlier (variable-step) run, and the latest (high-precision, fixed-step) one:" ] }, { "cell_type": "code", "execution_count": 30, "id": "b2917e15-1c3a-4597-bc9b-22f0a83b3e08", "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": [ "PlotlyHelper.combine_plots(fig_list=[fig1, fig2], title=\"The 2 runs, contrasted together\", \n", " curve_labels=[\"B (adaptive variable steps)\", \"B (fixed small steps)\"])" ] }, { "cell_type": "markdown", "id": "791e4d10-3173-4139-8216-09209acdfe6a", "metadata": {}, "source": [ "#### They overlap fairly well! The 800 fixed-timestep points vs. the 48 adaptable variable-timestep ones" ] }, { "cell_type": "code", "execution_count": null, "id": "893df3ce-7cb3-4eec-b8a4-397334f65dd4", "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 }