{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## The reversible Synthesis/Decomposition reaction `A + B <-> C`\n", "#### with 1st-order kinetics for each species, taken to equilibrium.\n", "#### Exploration of debugging and diagnostics options\n", "(Adaptive variable time steps are used)\n", "\n", "_See also the experiment \"1D/reactions/reaction_4\"_ " ] }, { "cell_type": "markdown", "id": "1b7d393d-a9b5-4437-80ae-c2b3effd9ca8", "metadata": {}, "source": [ "### TAGS : \"uniform compartment\", \"under-the-hood\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "5dafa9a4-85de-49a5-925d-e268ff1402a1", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Sep. 8, 2024\"\n", "LIFE123_VERSION = \"1.0.0.beta.38\" # Version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "82191b23-e6f5-4638-a26d-3716fc728055", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!\n", " # Importing this local file will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 3, "id": "4bbaa8f3", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path\n", "\n", "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from life123 import check_version, UniformCompartment, GraphicLog" ] }, { "cell_type": "code", "execution_count": 4, "id": "4f91f11c-caf8-4ce6-a2c4-dc2a7cab7396", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": 5, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'react_3_a.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_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "22559b04-73d8-4bd2-8c8d-c95dbdb0e862", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System\n", "Specify the chemicals, the reactions, and the initial concentrations" ] }, { "cell_type": "code", "execution_count": 6, "id": "e328c104-126d-400b-89fe-c4bbe1dc2212", "metadata": {}, "outputs": [], "source": [ "# Instantiate the simulator and specify the chemicals\n", "uc = UniformCompartment(preset=\"fast\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "1521d60a-b189-40d1-be43-013a6f5ac510", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A + B <-> C (kF = 5 / kR = 2 / delta_G = -2,271.4 / K = 2.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'A', 'B', 'C'}\n" ] } ], "source": [ "# Reaction A + B <-> C , with 1st-order kinetics for each species\n", "uc.add_reaction(reactants=[\"A\" , \"B\"], products=\"C\",\n", " forward_rate=5., reverse_rate=2.)\n", "\n", "uc.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 8, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `react_3_a.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "uc.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [], "source": [ "# Set the initial concentrations of all the chemicals\n", "uc.set_conc({\"A\": 10., \"B\": 50., \"C\": 20.}, snapshot=True)" ] }, { "cell_type": "code", "execution_count": 10, "id": "a605dacf-2c67-403e-9aa9-5be25fc9f481", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", " Species 2 (C). Conc: 20.0\n", "Set of chemicals involved in reactions: {'A', 'B', 'C'}\n" ] } ], "source": [ "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 11, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.010.050.020.0Initialized state
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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.0 10.0 50.0 20.0 Initialized state" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history()" ] }, { "cell_type": "code", "execution_count": null, "id": "42f757ce-98bb-4d3f-871d-78d059cba2a9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1767907f-a74c-484c-a5ef-ef134c96f928", "metadata": {}, "source": [ "### Sneak preview of eventual equilibrum:\n", "we can preview the final equilibrium concentrations without actually running the simulation" ] }, { "cell_type": "code", "execution_count": 12, "id": "8e24fba5-d8af-475d-8701-573fb6eff788", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 0.2948774087575341, 'B': 40.294877408757536, 'C': 29.705122591242464}" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.find_equilibrium_conc(rxn_index=0) # This is an EXACT solution" ] }, { "cell_type": "markdown", "id": "e1f57520-6b81-49fc-8b82-b9424a5fe70f", "metadata": {}, "source": [ "The reaction will proceed forward, with `A` and `B` being consumed, and `C` being produced" ] }, { "cell_type": "code", "execution_count": null, "id": "d460fc5b-8e07-4efc-bb27-1d5093612de7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "# Run the reaction" ] }, { "cell_type": "code", "execution_count": 13, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "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", "23 total step(s) taken\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": [ "uc.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "uc.single_compartment_react(initial_step=0.004, duration=0.06,\n", " variable_steps=True,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 14, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.00000010.00000050.00000020.000000Initialized state
10.0008647.87456047.87456022.1254401st reaction step
20.0015556.60226546.60226523.397735
30.0022465.57126645.57126624.428734
40.0029384.72759444.72759425.272406
50.0036294.03174644.03174625.968254
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70.0057022.51265242.51265227.487348
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100.0088131.34080441.34080428.659196
110.0098501.11288341.11288328.887117
120.0108860.93559540.93559529.064405
130.0119230.79732140.79732129.202679
140.0134780.63521140.63521129.364789
150.0150340.52583340.52583329.474167
160.0165890.45180540.45180529.548195
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210.0378760.29543740.29543729.704563
220.0496850.29408240.29408229.705918
230.0674000.29696940.29696929.703031last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.000000 10.000000 50.000000 20.000000 Initialized state\n", "1 0.000864 7.874560 47.874560 22.125440 1st reaction step\n", "2 0.001555 6.602265 46.602265 23.397735 \n", "3 0.002246 5.571266 45.571266 24.428734 \n", "4 0.002938 4.727594 44.727594 25.272406 \n", "5 0.003629 4.031746 44.031746 25.968254 \n", "6 0.004666 3.165305 43.165305 26.834695 \n", "7 0.005702 2.512652 42.512652 27.487348 \n", "8 0.006739 2.015898 42.015898 27.984102 \n", "9 0.007776 1.634842 41.634842 28.365158 \n", "10 0.008813 1.340804 41.340804 28.659196 \n", "11 0.009850 1.112883 41.112883 28.887117 \n", "12 0.010886 0.935595 40.935595 29.064405 \n", "13 0.011923 0.797321 40.797321 29.202679 \n", "14 0.013478 0.635211 40.635211 29.364789 \n", "15 0.015034 0.525833 40.525833 29.474167 \n", "16 0.016589 0.451805 40.451805 29.548195 \n", "17 0.018922 0.376490 40.376490 29.623510 \n", "18 0.021254 0.337393 40.337393 29.662607 \n", "19 0.024754 0.306871 40.306871 29.693129 \n", "20 0.030002 0.293965 40.293965 29.706035 \n", "21 0.037876 0.295437 40.295437 29.704563 \n", "22 0.049685 0.294082 40.294082 29.705918 \n", "23 0.067400 0.296969 40.296969 29.703031 last reaction step" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history()" ] }, { "cell_type": "markdown", "id": "b1366038-2dea-4d69-a655-ae464ca22922", "metadata": {}, "source": [ "## Note: \"A\" (now largely depleted) is the limiting reagent" ] }, { "cell_type": "code", "execution_count": 15, "id": "1598a75b-0322-45ac-bf2c-21fd09049966", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.000864, in 1 step of 0.000864\n", "From time 0.000864 to 0.003629, in 4 steps of 0.000691\n", "From time 0.003629 to 0.01192, in 8 steps of 0.00104\n", "From time 0.01192 to 0.01659, in 3 steps of 0.00156\n", "From time 0.01659 to 0.02125, in 2 steps of 0.00233\n", "From time 0.02125 to 0.02475, in 1 step of 0.0035\n", "From time 0.02475 to 0.03, in 1 step of 0.00525\n", "From time 0.03 to 0.03788, in 1 step of 0.00787\n", "From time 0.03788 to 0.04969, in 1 step of 0.0118\n", "From time 0.04969 to 0.0674, in 1 step of 0.0177\n", "(23 steps total)\n" ] } ], "source": [ "uc.diagnostics.explain_time_advance()" ] }, { "cell_type": "markdown", "id": "9fb5f6b8-dde3-415d-9e90-b8d102bfd748", "metadata": {}, "source": [ "### Notice how the reaction proceeds in smaller steps in the early times, when the concentrations are changing much more rapidly.\n", "#### The argument argument _variable_steps=True_ dynamically adjusts the initial_step (which is initially found to be too large, leading to some backtracking)" ] }, { "cell_type": "code", "execution_count": 16, "id": "226c1b6e-6838-46f3-aab1-9cb20c409724", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "x=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(colors=['red', 'darkorange', 'green'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "c02a8f55-a671-4771-86c9-fc4d1b126bf8", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 18, "id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + B <-> C\n", "Final concentrations: [A] = 0.297 ; [B] = 40.3 ; [C] = 29.7\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.48209\n", " Formula used: [C] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 2.5\n", "Discrepancy between the two values: 0.7163 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "uc.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "e2ea05d1-6e9b-4f62-88e6-192e058078f6", "metadata": {}, "source": [ "Compare with the values we saw earlier for the exact solution of the equilibrium values: \n", "{'A': 0.2948774087575341, 'B': 40.294877408757536, 'C': 29.705122591242464} \n", "\n", "It's instructive to compare the exact values with the last few points from the simulation: " ] }, { "cell_type": "code", "execution_count": 19, "id": "fcc82495-c952-4200-b316-157aac1ef22f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
210.0378760.29543740.29543729.704563
220.0496850.29408240.29408229.705918
230.0674000.29696940.29696929.703031last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "21 0.037876 0.295437 40.295437 29.704563 \n", "22 0.049685 0.294082 40.294082 29.705918 \n", "23 0.067400 0.296969 40.296969 29.703031 last reaction step" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "36087ae6-1bd5-4db1-881f-bf6e1dbd6439", "metadata": {}, "source": [ "The 2nd-to-last simulation point, rather than the last one, is actually closer to the exact equilibrium values. \n", "That's because by that time the variable steps are getting so large that they introduce some error. \n", "If we were to run the simulation longer (not shown), we'd see the variable steps continuing to grow, and then suddenly being reduced; \n", "then continued cycles of growth and reduction (\"hitting the brakes whenever getting too fast\")" ] }, { "cell_type": "code", "execution_count": null, "id": "e1b89183-ddc6-48f2-8ecf-7c2e8a922e01", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "635c27c1-37c9-4ca0-8684-03de92380fb6", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "5c747824-a170-439e-96a5-dd35bc81e08b", "metadata": {}, "source": [ "# _Everthing below is just for diagnostic insight_ \n", "## _into the adaptive variable time steps_ \n", "This information is available because we made a call to `dynamics.set_diagnostics()` prior to running the simulation" ] }, { "cell_type": "code", "execution_count": 20, "id": "06c8c7e9-edd9-45e1-b4a0-508f0b379c42", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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START_TIMEDelta ADelta BDelta Cnorm_Anorm_Bnorm_Cnorm_Dactionstep_factortime_stepcaption
00.000000-9.840000-9.8400009.8400003.227520e+01NaNNoneNoneABORT0.60.004000excessive norm value(s)
10.000000-5.904000-5.9040005.9040001.161907e+01NaNNoneNoneABORT0.60.002400excessive norm value(s)
20.000000-3.542400-3.5424003.5424004.182866e+00NaNNoneNoneABORT0.60.001440excessive norm value(s)
30.000000-2.125440-2.1254402.1254401.505832e+000.212544NoneNoneOK (high)0.80.000864
40.000864-1.272295-1.2722951.2722955.395782e-010.161570NoneNoneOK (stay)1.00.000691
50.001555-1.030999-1.0309991.0309993.543195e-010.156158NoneNoneOK (stay)1.00.000691
60.002246-0.843672-0.8436720.8436722.372610e-010.151433NoneNoneOK (stay)1.00.000691
70.002938-0.695848-0.6958480.6958481.614015e-010.147189NoneNoneOK (low)1.50.000691
80.003629-0.866441-0.8664410.8664412.502399e-010.214905NoneNoneOK (stay)1.00.001037
90.004666-0.652653-0.6526530.6526531.419851e-010.206189NoneNoneOK (stay)1.00.001037
100.005702-0.496755-0.4967550.4967558.225505e-020.197701NoneNoneOK (stay)1.00.001037
110.006739-0.381056-0.3810560.3810564.840115e-020.189025NoneNoneOK (stay)1.00.001037
120.007776-0.294038-0.2940380.2940382.881949e-020.179857NoneNoneOK (stay)1.00.001037
130.008813-0.227921-0.2279210.2279211.731599e-020.169988NoneNoneOK (stay)1.00.001037
140.009850-0.177288-0.1772880.1772881.047695e-020.159305NoneNoneOK (stay)1.00.001037
150.010886-0.138275-0.1382750.1382756.373314e-030.147793NoneNoneOK (low)1.50.001037
160.011923-0.162110-0.1621100.1621108.759877e-030.203318NoneNoneOK (stay)1.00.001555
170.013478-0.109377-0.1093770.1093773.987793e-030.172190NoneNoneOK (stay)1.00.001555
180.015034-0.074029-0.0740290.0740291.826757e-030.140784NoneNoneOK (low)1.50.001555
190.016589-0.075315-0.0753150.0753151.890774e-030.166698NoneNoneOK (stay)1.00.002333
200.018922-0.039097-0.0390970.0390975.095229e-040.103846NoneNoneOK (low)1.50.002333
210.021254-0.030522-0.0305220.0305223.105277e-040.090464NoneNoneOK (low)1.50.003499
220.024754-0.012906-0.0129060.0129065.551890e-050.042056NoneNoneOK (low)1.50.005249
230.0300020.0014720.001472-0.0014727.220164e-070.005007NoneNoneOK (low)1.50.007873
240.037876-0.001355-0.0013550.0013556.116239e-070.004585NoneNoneOK (low)1.50.011810
250.0496850.0028860.002886-0.0028862.776401e-060.009814NoneNoneOK (low)1.50.017715
\n", "
" ], "text/plain": [ " START_TIME Delta A Delta B Delta C norm_A norm_B norm_C \\\n", "0 0.000000 -9.840000 -9.840000 9.840000 3.227520e+01 NaN None \n", "1 0.000000 -5.904000 -5.904000 5.904000 1.161907e+01 NaN None \n", "2 0.000000 -3.542400 -3.542400 3.542400 4.182866e+00 NaN None \n", "3 0.000000 -2.125440 -2.125440 2.125440 1.505832e+00 0.212544 None \n", "4 0.000864 -1.272295 -1.272295 1.272295 5.395782e-01 0.161570 None \n", "5 0.001555 -1.030999 -1.030999 1.030999 3.543195e-01 0.156158 None \n", "6 0.002246 -0.843672 -0.843672 0.843672 2.372610e-01 0.151433 None \n", "7 0.002938 -0.695848 -0.695848 0.695848 1.614015e-01 0.147189 None \n", "8 0.003629 -0.866441 -0.866441 0.866441 2.502399e-01 0.214905 None \n", "9 0.004666 -0.652653 -0.652653 0.652653 1.419851e-01 0.206189 None \n", "10 0.005702 -0.496755 -0.496755 0.496755 8.225505e-02 0.197701 None \n", "11 0.006739 -0.381056 -0.381056 0.381056 4.840115e-02 0.189025 None \n", "12 0.007776 -0.294038 -0.294038 0.294038 2.881949e-02 0.179857 None \n", "13 0.008813 -0.227921 -0.227921 0.227921 1.731599e-02 0.169988 None \n", "14 0.009850 -0.177288 -0.177288 0.177288 1.047695e-02 0.159305 None \n", "15 0.010886 -0.138275 -0.138275 0.138275 6.373314e-03 0.147793 None \n", "16 0.011923 -0.162110 -0.162110 0.162110 8.759877e-03 0.203318 None \n", "17 0.013478 -0.109377 -0.109377 0.109377 3.987793e-03 0.172190 None \n", "18 0.015034 -0.074029 -0.074029 0.074029 1.826757e-03 0.140784 None \n", "19 0.016589 -0.075315 -0.075315 0.075315 1.890774e-03 0.166698 None \n", "20 0.018922 -0.039097 -0.039097 0.039097 5.095229e-04 0.103846 None \n", "21 0.021254 -0.030522 -0.030522 0.030522 3.105277e-04 0.090464 None \n", "22 0.024754 -0.012906 -0.012906 0.012906 5.551890e-05 0.042056 None \n", "23 0.030002 0.001472 0.001472 -0.001472 7.220164e-07 0.005007 None \n", "24 0.037876 -0.001355 -0.001355 0.001355 6.116239e-07 0.004585 None \n", "25 0.049685 0.002886 0.002886 -0.002886 2.776401e-06 0.009814 None \n", "\n", " norm_D action step_factor time_step caption \n", "0 None ABORT 0.6 0.004000 excessive norm value(s) \n", "1 None ABORT 0.6 0.002400 excessive norm value(s) \n", "2 None ABORT 0.6 0.001440 excessive norm value(s) \n", "3 None OK (high) 0.8 0.000864 \n", "4 None OK (stay) 1.0 0.000691 \n", "5 None OK (stay) 1.0 0.000691 \n", "6 None OK (stay) 1.0 0.000691 \n", "7 None OK (low) 1.5 0.000691 \n", "8 None OK (stay) 1.0 0.001037 \n", "9 None OK (stay) 1.0 0.001037 \n", "10 None OK (stay) 1.0 0.001037 \n", "11 None OK (stay) 1.0 0.001037 \n", "12 None OK (stay) 1.0 0.001037 \n", "13 None OK (stay) 1.0 0.001037 \n", "14 None OK (stay) 1.0 0.001037 \n", "15 None OK (low) 1.5 0.001037 \n", "16 None OK (stay) 1.0 0.001555 \n", "17 None OK (stay) 1.0 0.001555 \n", "18 None OK (low) 1.5 0.001555 \n", "19 None OK (stay) 1.0 0.002333 \n", "20 None OK (low) 1.5 0.002333 \n", "21 None OK (low) 1.5 0.003499 \n", "22 None OK (low) 1.5 0.005249 \n", "23 None OK (low) 1.5 0.007873 \n", "24 None OK (low) 1.5 0.011810 \n", "25 None OK (low) 1.5 0.017715 " ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.diagnostics.get_diagnostic_decisions_data() # diagnostic data about concentration changes at every step - EVEN aborted ones" ] }, { "cell_type": "code", "execution_count": 21, "id": "4e3012c6-c870-411c-bb80-7e1076233ca3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A + B <-> C\n" ] }, { "data": { "text/html": [ "
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START_TIMEtime_stepDelta ADelta BDelta Cratecaption
00.0000000.004000-9.840000-9.8400009.8400002460.000000aborted: excessive norm value(s)
10.0000000.002400-5.904000-5.9040005.9040002460.000000aborted: excessive norm value(s)
20.0000000.001440-3.542400-3.5424003.5424002460.000000aborted: excessive norm value(s)
30.0000000.000864-2.125440-2.1254402.1254402460.000000
40.0008640.000691-1.272295-1.2722951.2722951840.704596
50.0015550.000691-1.030999-1.0309991.0309991491.607041
60.0022460.000691-0.843672-0.8436720.8436721220.590807
70.0029380.000691-0.695848-0.6958480.6958481006.724671
80.0036290.001037-0.866441-0.8664410.866441835.687508
90.0046660.001037-0.652653-0.6526530.652653629.487372
100.0057020.001037-0.496755-0.4967550.496755479.122900
110.0067390.001037-0.381056-0.3810560.381056367.530575
120.0077760.001037-0.294038-0.2940380.294038283.601647
130.0088130.001037-0.227921-0.2279210.227921219.831166
140.0098500.001037-0.177288-0.1772880.177288170.994900
150.0108860.001037-0.138275-0.1382750.138275133.366974
160.0119230.001555-0.162110-0.1621100.162110104.237355
170.0134780.001555-0.109377-0.1093770.10937770.330011
180.0150340.001555-0.074029-0.0740290.07402947.600851
190.0165890.002333-0.075315-0.0753150.07531532.285157
200.0189220.002333-0.039097-0.0390970.03909716.759651
210.0212540.003499-0.030522-0.0305220.0305228.722521
220.0247540.005249-0.012906-0.0129060.0129062.458788
230.0300020.0078730.0014720.001472-0.001472-0.186932
240.0378760.011810-0.001355-0.0013550.0013550.114699
250.0496850.0177150.0028860.002886-0.002886-0.162918
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" ], "text/plain": [ " START_TIME time_step Delta A Delta B Delta C rate \\\n", "0 0.000000 0.004000 -9.840000 -9.840000 9.840000 2460.000000 \n", "1 0.000000 0.002400 -5.904000 -5.904000 5.904000 2460.000000 \n", "2 0.000000 0.001440 -3.542400 -3.542400 3.542400 2460.000000 \n", "3 0.000000 0.000864 -2.125440 -2.125440 2.125440 2460.000000 \n", "4 0.000864 0.000691 -1.272295 -1.272295 1.272295 1840.704596 \n", "5 0.001555 0.000691 -1.030999 -1.030999 1.030999 1491.607041 \n", "6 0.002246 0.000691 -0.843672 -0.843672 0.843672 1220.590807 \n", "7 0.002938 0.000691 -0.695848 -0.695848 0.695848 1006.724671 \n", "8 0.003629 0.001037 -0.866441 -0.866441 0.866441 835.687508 \n", "9 0.004666 0.001037 -0.652653 -0.652653 0.652653 629.487372 \n", "10 0.005702 0.001037 -0.496755 -0.496755 0.496755 479.122900 \n", "11 0.006739 0.001037 -0.381056 -0.381056 0.381056 367.530575 \n", "12 0.007776 0.001037 -0.294038 -0.294038 0.294038 283.601647 \n", "13 0.008813 0.001037 -0.227921 -0.227921 0.227921 219.831166 \n", "14 0.009850 0.001037 -0.177288 -0.177288 0.177288 170.994900 \n", "15 0.010886 0.001037 -0.138275 -0.138275 0.138275 133.366974 \n", "16 0.011923 0.001555 -0.162110 -0.162110 0.162110 104.237355 \n", "17 0.013478 0.001555 -0.109377 -0.109377 0.109377 70.330011 \n", "18 0.015034 0.001555 -0.074029 -0.074029 0.074029 47.600851 \n", "19 0.016589 0.002333 -0.075315 -0.075315 0.075315 32.285157 \n", "20 0.018922 0.002333 -0.039097 -0.039097 0.039097 16.759651 \n", "21 0.021254 0.003499 -0.030522 -0.030522 0.030522 8.722521 \n", "22 0.024754 0.005249 -0.012906 -0.012906 0.012906 2.458788 \n", "23 0.030002 0.007873 0.001472 0.001472 -0.001472 -0.186932 \n", "24 0.037876 0.011810 -0.001355 -0.001355 0.001355 0.114699 \n", "25 0.049685 0.017715 0.002886 0.002886 -0.002886 -0.162918 \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 \n", "4 \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 " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.diagnostics.get_diagnostic_rxn_data(rxn_index=0) # diagnostic run data of the requested SINGLE reaction" ] }, { "cell_type": "code", "execution_count": 22, "id": "a5cee533-a63c-4ff8-9427-e9b64cf4885a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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TIMEABCcaption
00.00000010.00000050.00000020.000000
10.0008647.87456047.87456022.125440
20.0015556.60226546.60226523.397735
30.0022465.57126645.57126624.428734
40.0029384.72759444.72759425.272406
50.0036294.03174644.03174625.968254
60.0046663.16530543.16530526.834695
70.0057022.51265242.51265227.487348
80.0067392.01589842.01589827.984102
90.0077761.63484241.63484228.365158
100.0088131.34080441.34080428.659196
110.0098501.11288341.11288328.887117
120.0108860.93559540.93559529.064405
130.0119230.79732140.79732129.202679
140.0134780.63521140.63521129.364789
150.0150340.52583340.52583329.474167
160.0165890.45180540.45180529.548195
170.0189220.37649040.37649029.623510
180.0212540.33739340.33739329.662607
190.0247540.30687140.30687129.693129
200.0300020.29396540.29396529.706035
210.0378760.29543740.29543729.704563
220.0496850.29408240.29408229.705918
230.0674000.29696940.29696929.703031
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" ], "text/plain": [ " TIME A B C caption\n", "0 0.000000 10.000000 50.000000 20.000000 \n", "1 0.000864 7.874560 47.874560 22.125440 \n", "2 0.001555 6.602265 46.602265 23.397735 \n", "3 0.002246 5.571266 45.571266 24.428734 \n", "4 0.002938 4.727594 44.727594 25.272406 \n", "5 0.003629 4.031746 44.031746 25.968254 \n", "6 0.004666 3.165305 43.165305 26.834695 \n", "7 0.005702 2.512652 42.512652 27.487348 \n", "8 0.006739 2.015898 42.015898 27.984102 \n", "9 0.007776 1.634842 41.634842 28.365158 \n", "10 0.008813 1.340804 41.340804 28.659196 \n", "11 0.009850 1.112883 41.112883 28.887117 \n", "12 0.010886 0.935595 40.935595 29.064405 \n", "13 0.011923 0.797321 40.797321 29.202679 \n", "14 0.013478 0.635211 40.635211 29.364789 \n", "15 0.015034 0.525833 40.525833 29.474167 \n", "16 0.016589 0.451805 40.451805 29.548195 \n", "17 0.018922 0.376490 40.376490 29.623510 \n", "18 0.021254 0.337393 40.337393 29.662607 \n", "19 0.024754 0.306871 40.306871 29.693129 \n", "20 0.030002 0.293965 40.293965 29.706035 \n", "21 0.037876 0.295437 40.295437 29.704563 \n", "22 0.049685 0.294082 40.294082 29.705918 \n", "23 0.067400 0.296969 40.296969 29.703031 " ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.diagnostics.get_diagnostic_conc_data() # diagnostic concentration data saved during the run, regardless of how much history we requested to save" ] }, { "cell_type": "code", "execution_count": null, "id": "1918451d", "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 }