Exploration of numerical errors in the implementation of substeps, for the simulation of the coupled reactions `2 S <-> U` and `S <-> X`¶

Both mostly forward. 1st-order kinetics throughout.

Same as variable_steps_1, but with substeps.

LAST REVISED: Dec. 3, 2023 THIS IS AN ARCHIVED EXPERIMENT

IMPORTANT: DO NOT ATTEMPT TO RUN THIS NOTEBOOK!¶

This is a "frozen run" that depends on an old version of Life123, for demonstration purposes¶

(current versions don't contain this implementation of substeps.) If you bypass the execution exit in the first cell, and run the other cells, you WILL NOT REPLICATE the results below!

In [1]:

# To stop the current and subsequent cells: USED TO PREVENT ACCIDENTAL RUNS OF THIS NOTEBOOK!

class StopExecution(Exception):
    def _render_traceback_(self):
        return []

raise StopExecution     # See: https://stackoverflow.com/a/56953105/5478830

In [ ]:

from experiments.get_notebook_info import get_notebook_basename

from src.modules.chemicals.chem_data import ChemData as chem
from src.modules.reactions.reaction_dynamics import ReactionDynamics

import numpy as np
from src.modules.visualization.graphic_log import GraphicLog

In [3]:

# Initialize the HTML logging
log_file = get_notebook_basename() + ".log.htm"    # Use the notebook base filename for the log file

# Set up the use of some specified graphic (Vue) components
GraphicLog.config(filename=log_file,
                  components=["vue_cytoscape_1"],
                  extra_js="https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js")

-> Output will be LOGGED into the file 'substeps_1.log.htm'

Initialize the system¶

In [4]:

# Initialize the system
chem_data = chem(names=["U", "X", "S"])

# Reaction 2 S <-> U , with 1st-order kinetics for all species (mostly forward)
chem_data.add_reaction(reactants=[(2, "S")], products="U",
                       forward_rate=8., reverse_rate=2.)

# Reaction S <-> X , with 1st-order kinetics for all species (mostly forward)
chem_data.add_reaction(reactants="S", products="X",
                       forward_rate=6., reverse_rate=3.)

chem_data.describe_reactions()

# Send the plot of the reaction network to the HTML log file
graph_data = chem_data.prepare_graph_network()
GraphicLog.export_plot(graph_data, "vue_cytoscape_1")

Number of reactions: 2 (at temp. 25 C)
0: 2 S <-> U  (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products
1: S <-> X  (kF = 6 / kR = 3 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products
[GRAPHIC ELEMENT SENT TO LOG FILE `substeps_1.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = ReactionDynamics(chem_data=chem_data)
dynamics.set_conc(conc={"U": 50., "X": 100., "S": 0.})
dynamics.describe_state()

SYSTEM STATE at Time t = 0:
3 species:
  Species 0 (U). Conc: 50.0
  Species 1 (X). Conc: 100.0
  Species 2 (S). Conc: 0.0

In [6]:

dynamics.set_diagnostics()       # To save diagnostic information about the call to single_compartment_react()
dynamics.verbose_list = ["substeps", "variable_steps"]

dynamics.single_compartment_react(time_step=0.01, stop_time=0.3, 
                                  variable_steps=True, thresholds={"low": 0.25, "high": 0.64},
                                  dynamic_substeps=2, abs_fast_threshold=100.)

df = dynamics.get_history()
df

single_compartment_react(): setting rel_fast_threshold to 100.0

reaction_step_orchestrator(): entering WHILE loop at System Time=0 with delta_time_full=0.01. Processing interval [0 - 0.01]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.005
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of 0.79 (rel. to baseline of 2.5) for the conc. of `S`: abs(31.6%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.4025 (rel. to baseline of 98.5) for the conc. of `X`: abs(-1.42%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0 from the upcoming single step (for all rxns):
    Baseline:  [ 50. 100.   0.]
    Deltas:    [-0.895  -2.9025  4.6925]
    Adjusted L2 norm:    3.4716763888888886
The current time step (0.01) leads to an 'L2 rate' (3.472) that is higher than the specified HIGH threshold (1.44):
ACTION: IMMEDIATE ABORT. Will abort this step, and re-do it with a SMALLER time interval. [The current step started at System Time: 0, and will rewind there]
reaction_step_orchestrator(): RE-DOING THE LAST REACTION STEP with the smaller time interval of 0.005

reaction_step_orchestrator(): entering WHILE loop at System Time=0 with delta_time_full=0.005. Processing interval [0 - 0.005]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.0025
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.22375  0.4475 ] (rel. to baseline of [49.75  1.25]) :
        elements of abs([-0.44974874 35.79999997]%) are all < (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.72562 (rel. to baseline of 99.25) for the conc. of `X`: abs(-0.731%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0 from the upcoming single step (for all rxns):
    Baseline:  [ 50. 100.   0.]
    Deltas:    [-0.47375  -1.475625  2.423125]
    Adjusted L2 norm:    0.919271440972222
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.9193) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to 0.0025) at the next round! [The current step started at System Time: 0, and will continue to 0.005]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.005 with delta_time_full=0.0025. Processing interval [0.005 - 0.0075]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.19916875  0.3983375 ] (rel. to baseline of [49.52625   2.423125]) :
        elements of abs([-0.40214785 16.43899922]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.005
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.00625
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 left tagged as 'S', based on a change of [-0.34584716  0.34584716] (rel. to baseline of [98.17308203  2.97358672]) :
        elements of abs([-0.35228308 11.63063969]%) are all < (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.005 from the upcoming single step (for all rxns):
    Baseline:  [49.52625  98.524375  2.423125]
    Deltas:    [-0.19916875 -0.69714013  1.09547763]
    Adjusted L2 norm:    0.19174930835982507
NOTICE: The chosen time step (0.0025) results in an 'L2 rate' (0.1917) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.005) at the next round! [The current step started at System Time: 0.005, and will continue to 0.0075]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.0075 with delta_time_full=0.005. Processing interval [0.0075 - 0.0125]
    All the reactions are SLOW
    Processing ALL the 2 reaction(s)
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.35252671  0.70505341] (rel. to baseline of [49.32708125  3.51860263]) :
        elements of abs([-0.71467174 20.03788122]%) are all < (100% /1)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.3619 (rel. to baseline of 97.8272) for the conc. of `X`: abs(-1.39%) > (100% /1)
EXAMINING CONCENTRATION CHANGES at System Time 0.0075 from the upcoming single step (for all rxns):
    Baseline:  [49.32708125 97.82723487  3.51860263]
    Deltas:    [-0.35252671 -1.36185044  2.06690386]
    Adjusted L2 norm:    0.6945559195102885
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.6946) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to 0.0025) at the next round! [The current step started at System Time: 0.0075, and will continue to 0.0125]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.0125 with delta_time_full=0.0025. Processing interval [0.0125 - 0.015]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.13316264  0.26632529] (rel. to baseline of [48.97455454  5.58550649]) :
        elements of abs([-0.27190169  4.76814926]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.0125
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.01375
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 left tagged as 'S', based on a change of [-0.31525682  0.31525682] (rel. to baseline of [96.14553054  6.03852302]) :
        elements of abs([-0.32789545  5.22076037]%) are all < (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.0125 from the upcoming single step (for all rxns):
    Baseline:  [48.97455454 96.46538443  5.58550649]
    Deltas:    [-0.13316264 -0.63511071  0.901436  ]
    Adjusted L2 norm:    0.13707608420309667
NOTICE: The chosen time step (0.0025) results in an 'L2 rate' (0.1371) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.005) at the next round! [The current step started at System Time: 0.0125, and will continue to 0.015]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.015 with delta_time_full=0.005. Processing interval [0.015 - 0.02]
    All the reactions are SLOW
    Processing ALL the 2 reaction(s)
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.22893622  0.45787244] (rel. to baseline of [48.8413919   6.48694248]) :
        elements of abs([-0.46873402  7.05837058]%) are all < (100% /1)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.2428 (rel. to baseline of 95.8303) for the conc. of `X`: abs(-1.3%) > (100% /1)
EXAMINING CONCENTRATION CHANGES at System Time 0.015 from the upcoming single step (for all rxns):
    Baseline:  [48.8413919  95.83027372  6.48694248]
    Deltas:    [-0.22893622 -1.24284583  1.70071827]
    Adjusted L2 norm:    0.4988355766812945
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.4988) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.015, and will continue to 0.02]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.02 with delta_time_full=0.005. Processing interval [0.02 - 0.025]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.15861813  0.31723625] (rel. to baseline of [48.61245568  8.18766075]) :
        elements of abs([-0.32629112  3.87456519]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.02
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.0225
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.57101 (rel. to baseline of 94.0008) for the conc. of `X`: abs(-0.607%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.02 from the upcoming single step (for all rxns):
    Baseline:  [48.61245568 94.58742789  8.18766075]
    Deltas:    [-0.15861813 -1.15760403  1.47484028]
    Adjusted L2 norm:    0.3933734074308033
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.3934) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.02, and will continue to 0.025]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.025 with delta_time_full=0.005. Processing interval [0.025 - 0.03]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.09803833  0.19607667] (rel. to baseline of [48.45383755  9.66250104]) :
        elements of abs([-0.20233348  2.02925379]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.025
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.0275
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.54181 (rel. to baseline of 92.874) for the conc. of `X`: abs(-0.583%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.025 from the upcoming single step (for all rxns):
    Baseline:  [48.45383755 93.42982386  9.66250104]
    Deltas:    [-0.09803833 -1.09759656  1.29367323]
    Adjusted L2 norm:    0.3208800177210416
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.3209) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.025, and will continue to 0.03]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.03 with delta_time_full=0.005. Processing interval [0.03 - 0.035]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [-0.04531102  0.09062204] (rel. to baseline of [48.35579922 10.95617427]) :
        elements of abs([-0.09370339  0.82713218]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.03
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.0325
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.51559 (rel. to baseline of 91.8041) for the conc. of `X`: abs(-0.562%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.03 from the upcoming single step (for all rxns):
    Baseline:  [48.35579922 92.33222729 10.95617427]
    Deltas:    [-0.04531102 -1.04373516  1.1343572 ]
    Adjusted L2 norm:    0.26424471594327414
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.2642) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.03, and will continue to 0.035]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.035 with delta_time_full=0.005. Processing interval [0.035 - 0.04]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.00051638 -0.00103275] (rel. to baseline of [48.3104882  12.09053147]) :
        elements of abs([ 0.00106887 -0.00854184]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.035
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.0375
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 left tagged as 'S', based on a change of [-0.49198909  0.49198909] (rel. to baseline of [90.78518641 12.59332081]) :
        elements of abs([-0.54192661  3.90674623]%) are all < (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.035 from the upcoming single step (for all rxns):
    Baseline:  [48.3104882  91.28849213 12.09053147]
    Deltas:    [ 5.16376907e-04 -9.95294805e-01  9.94262051e-01]
    Adjusted L2 norm:    0.21990767124245347
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.2199) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.01) at the next round! [The current step started at System Time: 0.035, and will continue to 0.04]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.04 with delta_time_full=0.01. Processing interval [0.04 - 0.05]
    All the reactions are SLOW
    Processing ALL the 2 reaction(s)
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.08056339 -0.16112678] (rel. to baseline of [48.31100457 13.08479352]) :
        elements of abs([ 0.16675992 -1.23140484]%) are all < (100% /1)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.9237 (rel. to baseline of 90.2932) for the conc. of `X`: abs(-2.13%) > (100% /1)
EXAMINING CONCENTRATION CHANGES at System Time 0.04 from the upcoming single step (for all rxns):
    Baseline:  [48.31100457 90.29319733 13.08479352]
    Deltas:    [ 0.08056339 -1.92370831  1.76258153]
    Adjusted L2 norm:    0.757093084208906
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.7571) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to 0.005) at the next round! [The current step started at System Time: 0.04, and will continue to 0.05]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.05 with delta_time_full=0.005. Processing interval [0.05 - 0.055]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.10997932 -0.21995864] (rel. to baseline of [48.39156796 14.84737505]) :
        elements of abs([ 0.2272696  -1.48146487]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.05
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.0525
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 left tagged as 'S', based on a change of [-0.43180887  0.43180887] (rel. to baseline of [87.92942848 15.17745627]) :
        elements of abs([-0.49108572  2.84506746]%) are all < (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.05 from the upcoming single step (for all rxns):
    Baseline:  [48.39156796 88.36948902 14.84737505]
    Deltas:    [ 0.10997932 -0.87186941  0.65191077]
    Adjusted L2 norm:    0.13302659662028024
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.133) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.01) at the next round! [The current step started at System Time: 0.05, and will continue to 0.055]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.055 with delta_time_full=0.01. Processing interval [0.055 - 0.065]
    All the reactions are SLOW
    Processing ALL the 2 reaction(s)
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.26991192 -0.53982384] (rel. to baseline of [48.50154729 15.49928582]) :
        elements of abs([ 0.55650167 -3.48289493]%) are all < (100% /1)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.695 (rel. to baseline of 87.4976) for the conc. of `X`: abs(-1.94%) > (100% /1)
EXAMINING CONCENTRATION CHANGES at System Time 0.055 from the upcoming single step (for all rxns):
    Baseline:  [48.50154729 87.49761961 15.49928582]
    Deltas:    [ 0.26991192 -1.69497144  1.1551476 ]
    Adjusted L2 norm:    0.47557184462533697
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.4756) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.055, and will continue to 0.065]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.065 with delta_time_full=0.01. Processing interval [0.065 - 0.075]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.35692549 -0.71385098] (rel. to baseline of [48.77145921 16.65443342]) :
        elements of abs([ 0.73183271 -4.28625196]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.065
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.07
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.76268 (rel. to baseline of 85.0152) for the conc. of `X`: abs(-0.897%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.065 from the upcoming single step (for all rxns):
    Baseline:  [48.77145921 85.80264817 16.65443342]
    Deltas:    [ 0.35692549 -1.5500879   0.83623692]
    Adjusted L2 norm:    0.3588289447220748
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.3588) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.065, and will continue to 0.075]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.075 with delta_time_full=0.01. Processing interval [0.075 - 0.085]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.41668593 -0.83337187] (rel. to baseline of [49.1283847  17.49067034]) :
        elements of abs([ 0.8481572  -4.76466511]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.075
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.08
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.71831 (rel. to baseline of 83.5135) for the conc. of `X`: abs(-0.86%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.075 from the upcoming single step (for all rxns):
    Baseline:  [49.1283847  84.25256027 17.49067034]
    Deltas:    [ 0.41668593 -1.45737909  0.62400723]
    Adjusted L2 norm:    0.2985517781508984
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.2986) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.075, and will continue to 0.085]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.085 with delta_time_full=0.01. Processing interval [0.085 - 0.095]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.45827279 -0.91654559] (rel. to baseline of [49.54507063 18.11467757]) :
        elements of abs([ 0.92496143 -5.05968479]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.085
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.09
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.6808 (rel. to baseline of 82.0967) for the conc. of `X`: abs(-0.829%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.085 from the upcoming single step (for all rxns):
    Baseline:  [49.54507063 82.79518117 18.11467757]
    Deltas:    [ 0.45827279 -1.37929103  0.46274545]
    Adjusted L2 norm:    0.25851011704346205
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.2585) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.085, and will continue to 0.095]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.095 with delta_time_full=0.01. Processing interval [0.095 - 0.105]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.48612697 -0.97225395] (rel. to baseline of [50.00334342 18.57742301]) :
        elements of abs([ 0.97218894 -5.23352429]%) are all < (100% /1)
    * FAST REACTIONS: [1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.095
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [1]).  'Local' system time: 0.1
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.64862 (rel. to baseline of 80.752) for the conc. of `X`: abs(-0.803%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.095 from the upcoming single step (for all rxns):
    Baseline:  [50.00334342 81.41589014 18.57742301]
    Deltas:    [ 0.48612697 -1.31253893  0.34028498]
    Adjusted L2 norm:    0.23054130444294735
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.2305) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.02) at the next round! [The current step started at System Time: 0.095, and will continue to 0.105]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.105 with delta_time_full=0.02. Processing interval [0.105 - 0.125]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of 1.0073 (rel. to baseline of 50.4895) for the conc. of `U`: abs(1.99%) > (100% /1)
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.105
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.115
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.84753 (rel. to baseline of 18.1712) for the conc. of `S`: abs(-4.66%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.2748 (rel. to baseline of 78.8353) for the conc. of `X`: abs(-1.62%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.105 from the upcoming single step (for all rxns):
    Baseline:  [50.48947039 80.10335121 18.917708  ]
    Deltas:    [ 1.93464617 -2.54282322 -1.32646911]
    Adjusted L2 norm:    1.3298140056859387
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (1.33) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to 0.01) at the next round! [The current step started at System Time: 0.105, and will continue to 0.125]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.125 with delta_time_full=0.01. Processing interval [0.125 - 0.135]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.125
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.13
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.18868846 -0.37737693] (rel. to baseline of [52.60352495 17.86809286]) :
        elements of abs([ 0.35869928 -2.11201572]%) are all < (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.61783 (rel. to baseline of 76.9249) for the conc. of `X`: abs(-0.803%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.125 from the upcoming single step (for all rxns):
    Baseline:  [52.42411656 77.56052799 17.59123888]
    Deltas:    [ 0.36809685 -1.25350083  0.51730712]
    Adjusted L2 norm:    0.2193740298950499
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.2194) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.02) at the next round! [The current step started at System Time: 0.125, and will continue to 0.135]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.135 with delta_time_full=0.02. Processing interval [0.135 - 0.155]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -1.5714 (rel. to baseline of 18.1085) for the conc. of `S`: abs(-8.68%) > (100% /1)
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.135
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.145
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.69527 (rel. to baseline of 17.7399) for the conc. of `S`: abs(-3.92%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.1887 (rel. to baseline of 75.1043) for the conc. of `X`: abs(-1.58%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.135 from the upcoming single step (for all rxns):
    Baseline:  [52.79221342 76.30702716 18.108546  ]
    Deltas:    [ 1.5261513  -2.39143474 -0.66086786]
    Adjusted L2 norm:    0.9427604737997322
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.9428) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to 0.01) at the next round! [The current step started at System Time: 0.135, and will continue to 0.155]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.155 with delta_time_full=0.01. Processing interval [0.155 - 0.165]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.155
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.16
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.16421051 -0.32842101] (rel. to baseline of [54.4730882  17.72353472]) :
        elements of abs([ 0.30145254 -1.85302209]%) are all < (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.56825 (rel. to baseline of 73.3303) for the conc. of `X`: abs(-0.775%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.155 from the upcoming single step (for all rxns):
    Baseline:  [54.31836472 73.91559242 17.44767814]
    Deltas:    [ 0.31893399 -1.15355183  0.51568386]
    Adjusted L2 norm:    0.18870339626754337
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.1887) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.02) at the next round! [The current step started at System Time: 0.155, and will continue to 0.165]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.165 with delta_time_full=0.02. Processing interval [0.165 - 0.185]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -1.3773 (rel. to baseline of 17.9634) for the conc. of `S`: abs(-7.67%) > (100% /1)
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.165
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.175
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.61754 (rel. to baseline of 17.6911) for the conc. of `S`: abs(-3.49%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -1.0882 (rel. to baseline of 71.657) for the conc. of `X`: abs(-1.52%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.165 from the upcoming single step (for all rxns):
    Baseline:  [54.63729871 72.76204059 17.963362  ]
    Deltas:    [ 1.34174043 -2.19330116 -0.4901797 ]
    Adjusted L2 norm:    0.7612348313580994
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.7612) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to 0.01) at the next round! [The current step started at System Time: 0.165, and will continue to 0.185]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.185 with delta_time_full=0.01. Processing interval [0.185 - 0.195]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.185
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.19
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 left tagged as 'S', based on a change of [ 0.147988   -0.29597601] (rel. to baseline of [56.11817604 17.72924412]) :
        elements of abs([ 0.26370779 -1.6694226 ]%) are all < (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.51864 (rel. to baseline of 70.0344) for the conc. of `X`: abs(-0.741%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.185 from the upcoming single step (for all rxns):
    Baseline:  [55.97903913 70.56873943 17.4731823 ]
    Deltas:    [ 0.28712491 -1.05297436  0.47872455]
    Adjusted L2 norm:    0.15781921064614185
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.1578) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.02) at the next round! [The current step started at System Time: 0.185, and will continue to 0.195]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.195 with delta_time_full=0.02. Processing interval [0.195 - 0.215]
    * SLOW REACTIONS: [0]
    Processing SLOW reactions
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -1.2433 (rel. to baseline of 17.9519) for the conc. of `S`: abs(-6.93%) > (100% /1)
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.195
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.205
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.5592 (rel. to baseline of 17.7169) for the conc. of `S`: abs(-3.16%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.99221 (rel. to baseline of 68.5074) for the conc. of `X`: abs(-1.45%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.195 from the upcoming single step (for all rxns):
    Baseline:  [56.26616404 69.51576507 17.95190685]
    Deltas:    [ 1.21208721 -2.00056384 -0.42361059]
    Adjusted L2 norm:    0.6278730022554321
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.6279) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.195, and will continue to 0.215]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.215 with delta_time_full=0.02. Processing interval [0.215 - 0.235]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.215
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.225
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.57023 (rel. to baseline of 17.9967) for the conc. of `S`: abs(-3.17%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.91644 (rel. to baseline of 66.5414) for the conc. of `X`: abs(-1.38%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.215 from the upcoming single step (for all rxns):
    Baseline:  [57.47825125 67.51520124 17.52829625]
    Deltas:    [ 0.53781225 -1.89020212  0.81457762]
    Adjusted L2 norm:    0.5028491972762104
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.5028) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.215, and will continue to 0.235]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.235 with delta_time_full=0.02. Processing interval [0.235 - 0.255]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.235
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.245
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.64257 (rel. to baseline of 18.5968) for the conc. of `S`: abs(-3.46%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.82689 (rel. to baseline of 64.7568) for the conc. of `X`: abs(-1.28%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.235 from the upcoming single step (for all rxns):
    Baseline:  [58.0160635  65.62499911 18.34287388]
    Deltas:    [ 0.62839193 -1.69507214  0.43828828]
    Adjusted L2 norm:    0.38447139938108577
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.3845) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.235, and will continue to 0.255]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.255 with delta_time_full=0.02. Processing interval [0.255 - 0.275]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.255
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.265
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.66711 (rel. to baseline of 18.913) for the conc. of `S`: abs(-3.53%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.75939 (rel. to baseline of 63.1389) for the conc. of `X`: abs(-1.2%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.255 from the upcoming single step (for all rxns):
    Baseline:  [58.64445543 63.92992697 18.78116216]
    Deltas:    [ 0.66316128 -1.5504161   0.22409354]
    Adjusted L2 norm:    0.32153231844307784
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.3215) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.255, and will continue to 0.275]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.275 with delta_time_full=0.02. Processing interval [0.275 - 0.295]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.275
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.285
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.66517 (rel. to baseline of 19.0678) for the conc. of `S`: abs(-3.49%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.70539 (rel. to baseline of 61.6484) for the conc. of `X`: abs(-1.14%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.275 from the upcoming single step (for all rxns):
    Baseline:  [59.30761671 62.37951088 19.0052557 ]
    Deltas:    [ 0.66685358 -1.43645585  0.10274869]
    Adjusted L2 norm:    0.2798507093514281
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.2799) that leads to the following:
ACTION: COMPLETE NORMALLY - we're inside the target range.  No change to step size. [The current step started at System Time: 0.275, and will continue to 0.295]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.295 with delta_time_full=0.02. Processing interval [0.295 - 0.315]
    There are NO SLOW reactions
    * FAST REACTIONS: [0, 1]
    - SUBSTEP: 0 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.295
        Skipping evaluation of rxn speed for all reactions because NOT at last substep (substep_number = 0, time_subdivision = 2)
    - SUBSTEP: 1 (in processing of FAST reactions, i.e. [0, 1]).  'Local' system time: 0.305
      (tentatively tagging rxn #0 as 'S')
        For Rxn # 0, checking concentrations of chems: {0, 2}
        Rxn # 0 FLIPPED TAG to 'F', based on a change of -0.6489 (rel. to baseline of 19.1315) for the conc. of `S`: abs(-3.39%) > (100% /2)
      (tentatively tagging rxn #1 as 'S')
        For Rxn # 1, checking concentrations of chems: {1, 2}
        Rxn # 1 FLIPPED TAG to 'F', based on a change of -0.65995 (rel. to baseline of 60.2612) for the conc. of `X`: abs(-1.1%) > (100% /2)
EXAMINING CONCENTRATION CHANGES at System Time 0.295 from the upcoming single step (for all rxns):
    Baseline:  [59.97447029 60.94305503 19.10800438]
    Deltas:    [ 0.65359963 -1.34175786  0.0345586 ]
    Adjusted L2 norm:    0.24763343791989711
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.2476) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.04) at the next round! [The current step started at System Time: 0.295, and will continue to 0.315]
28 total step(s) taken

Out[6]:

	SYSTEM TIME	U	X	S	caption
0	0.00000	50.000000	100.000000	0.000000	Initial state
1	0.00500	49.500000	98.500000	2.500000	Interm. step, due to the fast rxns: [0, 1]
2	0.00250	49.750000	99.250000	1.250000	Interm. step, due to the fast rxns: [0, 1]
3	0.00500	49.526250	98.524375	2.423125
4	0.00625	49.426666	98.173082	2.973587	Interm. step, due to the fast rxns: [1]
5	0.00750	49.327081	97.827235	3.518603
6	0.01250	48.974555	96.465384	5.585506
7	0.01375	48.907973	96.145531	6.038523	Interm. step, due to the fast rxns: [1]
8	0.01500	48.841392	95.830274	6.486942
9	0.02000	48.612456	94.587428	8.187661
10	0.02250	48.533147	94.000837	8.932870	Interm. step, due to the fast rxns: [1]
11	0.02500	48.453838	93.429824	9.662501
12	0.02750	48.404818	92.874038	10.316326	Interm. step, due to the fast rxns: [1]
13	0.03000	48.355799	92.332227	10.956174
14	0.03250	48.333144	91.804078	11.529634	Interm. step, due to the fast rxns: [1]
15	0.03500	48.310488	91.288492	12.090531
16	0.03750	48.310746	90.785186	12.593321	Interm. step, due to the fast rxns: [1]
17	0.04000	48.311005	90.293197	13.084794
18	0.05000	48.391568	88.369489	14.847375
19	0.05250	48.446558	87.929428	15.177456	Interm. step, due to the fast rxns: [1]
20	0.05500	48.501547	87.497620	15.499286
21	0.06500	48.771459	85.802648	16.654433
22	0.07000	48.949922	85.015241	17.084915	Interm. step, due to the fast rxns: [1]
23	0.07500	49.128385	84.252560	17.490670
24	0.08000	49.336728	83.513492	17.813053	Interm. step, due to the fast rxns: [1]
25	0.08500	49.545071	82.795181	18.114678
26	0.09000	49.774207	82.096694	18.354892	Interm. step, due to the fast rxns: [1]
27	0.09500	50.003343	81.415890	18.577423
28	0.10000	50.246407	80.751974	18.755212	Interm. step, due to the fast rxns: [1]
29	0.10500	50.489470	80.103351	18.917708
30	0.11500	51.496725	78.835313	18.171237	Interm. step, due to the fast rxns: [0, 1]
31	0.12500	52.424117	77.560528	17.591239
32	0.13000	52.603525	76.924857	17.868093	Interm. step, due to the fast rxns: [0, 1]
33	0.13500	52.792213	76.307027	18.108546
34	0.14500	53.577892	75.104329	17.739886	Interm. step, due to the fast rxns: [0, 1]
35	0.15500	54.318365	73.915592	17.447678
36	0.16000	54.473088	73.330289	17.723535	Interm. step, due to the fast rxns: [0, 1]
37	0.16500	54.637299	72.762041	17.963362
38	0.17500	55.325945	71.656981	17.691130	Interm. step, due to the fast rxns: [0, 1]
39	0.18500	55.979039	70.568739	17.473182
40	0.19000	56.118176	70.034404	17.729244	Interm. step, due to the fast rxns: [0, 1]
41	0.19500	56.266164	69.515765	17.951907
42	0.20500	56.887823	68.507407	17.716948	Interm. step, due to the fast rxns: [0, 1]
43	0.21500	57.478251	67.515201	17.528296
44	0.22500	57.730950	66.541443	17.996657	Interm. step, due to the fast rxns: [0, 1]
45	0.23500	58.016064	65.624999	18.342874
46	0.24500	58.323172	64.756822	18.596834	Interm. step, due to the fast rxns: [0, 1]
47	0.25500	58.644455	63.929927	18.781162
48	0.26500	58.974059	63.138899	18.912983	Interm. step, due to the fast rxns: [0, 1]
49	0.27500	59.307617	62.379511	19.005256
50	0.28500	59.641885	61.648441	19.067789	Interm. step, due to the fast rxns: [0, 1]
51	0.29500	59.974470	60.943055	19.108004
52	0.30500	60.303621	60.261244	19.131514	Interm. step, due to the fast rxns: [0, 1]
53	0.31500	60.628070	59.601297	19.142563

In [7]:

(transition_times, step_sizes) = dynamics.explain_time_advance(return_times=True)

From time 0 to 0.005, in 1 reduced step of 0.005 (1/2 of requested step)
From time 0.005 to 0.0025, in 1 reduced step of -0.0025 (1/-2 of requested step)
From time 0.0025 to 0.005, in 1 reduced step of 0.0025 (1/4 of requested step)
From time 0.005 to 0.0075, in 2 reduced step of 0.00125 (each 1/2 of requested step)
From time 0.0075 to 0.0125, in 1 FULL step of 0.005
From time 0.0125 to 0.015, in 2 reduced step of 0.00125 (each 1/2 of requested step)
From time 0.015 to 0.02, in 1 FULL step of 0.005
From time 0.02 to 0.04, in 8 reduced step of 0.0025 (each 1/2 of requested step)
From time 0.04 to 0.05, in 1 FULL step of 0.01
From time 0.05 to 0.055, in 2 reduced step of 0.0025 (each 1/2 of requested step)
From time 0.055 to 0.065, in 1 FULL step of 0.01
From time 0.065 to 0.105, in 8 reduced step of 0.005 (each 1/2 of requested step)
From time 0.105 to 0.125, in 2 reduced step of 0.01 (each 1/2 of requested step)
From time 0.125 to 0.135, in 2 reduced step of 0.005 (each 1/2 of requested step)
From time 0.135 to 0.155, in 2 reduced step of 0.01 (each 1/2 of requested step)
From time 0.155 to 0.165, in 2 reduced step of 0.005 (each 1/2 of requested step)
From time 0.165 to 0.185, in 2 reduced step of 0.01 (each 1/2 of requested step)
From time 0.185 to 0.195, in 2 reduced step of 0.005 (each 1/2 of requested step)
From time 0.195 to 0.315, in 12 reduced step of 0.01 (each 1/2 of requested step)

In [8]:

np.array(step_sizes)

Out[8]:

array([0.005  , 0.0025 , 0.00125, 0.005  , 0.00125, 0.005  , 0.0025 ,
       0.01   , 0.0025 , 0.01   , 0.005  , 0.01   , 0.005  , 0.01   ,
       0.005  , 0.01   , 0.005  , 0.01   ])

In [9]:

np.array(transition_times)    # Note: there will be one more transition time (the end time) than step sizes

Out[9]:

array([0.    , 0.005 , 0.005 , 0.0075, 0.0125, 0.015 , 0.02  , 0.04  ,
       0.05  , 0.055 , 0.065 , 0.105 , 0.125 , 0.135 , 0.155 , 0.165 ,
       0.185 , 0.195 , 0.315 ])

Plots of changes of concentration with time¶

In [10]:

dynamics.plot_history(colors=['green', 'orange', 'blue'])

Notice the irregular "bumpiness" on the plot of S. See comments at very end.¶

In [11]:

dynamics.plot_history(colors=['green', 'orange', 'blue'], show_intervals=True)

In [12]:

# Show the "critical values", i.e. times when the step size changes
dynamics.plot_history(colors=['green', 'orange', 'blue'], vertical_lines=transition_times,
                      title="Critical values of time-step changes for reactions `2 S <-> U` and `S <-> X`")

Note: the dashed lines in the plots immediatly above and below are NOT the steps; they are the "critical values", i.e. times when the step size changes.¶

The time steps were shown in an earlier plots

In [13]:

dynamics.plot_step_sizes(show_intervals=True)

In [14]:

dynamics.get_diagnostic_rxn_data(rxn_index=0)

Reaction:  2 S <-> U

Out[14]:

	TIME	Delta U	Delta S	substep	time_subdivision	delta_time
0	0.0000	-0.500000	1.000000	0	2	0.0050
1	0.0050	-0.395000	0.790000	1	2	0.0050
2	0.0000	-0.250000	0.500000	0	2	0.0025
3	0.0025	-0.223750	0.447500	1	2	0.0025
4	0.0050	-0.199169	0.398337	0	1	0.0025
5	0.0075	-0.352527	0.705053	0	1	0.0050
6	0.0125	-0.133163	0.266325	0	1	0.0025
7	0.0150	-0.228936	0.457872	0	1	0.0050
8	0.0200	-0.158618	0.317236	0	1	0.0050
9	0.0250	-0.098038	0.196077	0	1	0.0050
10	0.0300	-0.045311	0.090622	0	1	0.0050
11	0.0350	0.000516	-0.001033	0	1	0.0050
12	0.0400	0.080563	-0.161127	0	1	0.0100
13	0.0500	0.109979	-0.219959	0	1	0.0050
14	0.0550	0.269912	-0.539824	0	1	0.0100
15	0.0650	0.356925	-0.713851	0	1	0.0100
16	0.0750	0.416686	-0.833372	0	1	0.0100
17	0.0850	0.458273	-0.916546	0	1	0.0100
18	0.0950	0.486127	-0.972254	0	1	0.0100
19	0.1050	1.007254	-2.014509	0	1	0.0200
20	0.1050	0.503627	-1.007254	0	2	0.0100
21	0.1150	0.423764	-0.847529	1	2	0.0100
22	0.1250	0.179408	-0.358817	0	2	0.0050
23	0.1300	0.188688	-0.377377	1	2	0.0050
24	0.1350	0.785679	-1.571358	0	1	0.0200
25	0.1350	0.392839	-0.785679	0	2	0.0100
26	0.1450	0.347633	-0.695266	1	2	0.0100
27	0.1550	0.154723	-0.309447	0	2	0.0050
28	0.1600	0.164211	-0.328421	1	2	0.0050
29	0.1650	0.688646	-1.377292	0	1	0.0200
30	0.1650	0.344323	-0.688646	0	2	0.0100
31	0.1750	0.308771	-0.617543	1	2	0.0100
32	0.1850	0.139137	-0.278274	0	2	0.0050
33	0.1900	0.147988	-0.295976	1	2	0.0050
34	0.1950	0.621659	-1.243317	0	1	0.0200
35	0.1950	0.310829	-0.621659	0	2	0.0100
36	0.2050	0.279599	-0.559199	1	2	0.0100
37	0.2150	0.252699	-0.505397	0	2	0.0100
38	0.2250	0.285114	-0.570227	1	2	0.0100
39	0.2350	0.307109	-0.614217	0	2	0.0100
40	0.2450	0.321283	-0.642567	1	2	0.0100
41	0.2550	0.329604	-0.659208	0	2	0.0100
42	0.2650	0.333557	-0.667115	1	2	0.0100
43	0.2750	0.334268	-0.668536	0	2	0.0100
44	0.2850	0.332585	-0.665171	1	2	0.0100
45	0.2950	0.329151	-0.658302	0	2	0.0100
46	0.3050	0.324449	-0.648897	1	2	0.0100

In [15]:

dynamics.get_diagnostic_rxn_data(rxn_index=1)

Reaction:  S <-> X

Out[15]:

	TIME	Delta X	Delta S	reaction	substep	time_subdivision	delta_time
0	0.00000	-1.500000	1.500000	1	0	2	0.00500
1	0.00500	-1.402500	1.402500	1	1	2	0.00500
2	0.00000	-0.750000	0.750000	1	0	2	0.00250
3	0.00250	-0.725625	0.725625	1	1	2	0.00250
4	0.00500	-0.351293	0.351293	1	0	2	0.00125
5	0.00625	-0.345847	0.345847	1	1	2	0.00125
6	0.00750	-1.361850	1.361850	1	0	1	0.00500
7	0.01250	-0.319854	0.319854	1	0	2	0.00125
8	0.01375	-0.315257	0.315257	1	1	2	0.00125
9	0.01500	-1.242846	1.242846	1	0	1	0.00500
10	0.02000	-0.586591	0.586591	1	0	2	0.00250
11	0.02250	-0.571013	0.571013	1	1	2	0.00250
12	0.02500	-0.555786	0.555786	1	0	2	0.00250
13	0.02750	-0.541810	0.541810	1	1	2	0.00250
14	0.03000	-0.528149	0.528149	1	0	2	0.00250
15	0.03250	-0.515586	0.515586	1	1	2	0.00250
16	0.03500	-0.503306	0.503306	1	0	2	0.00250
17	0.03750	-0.491989	0.491989	1	1	2	0.00250
18	0.04000	-1.923708	1.923708	1	0	1	0.01000
19	0.05000	-0.440061	0.440061	1	0	2	0.00250
20	0.05250	-0.431809	0.431809	1	1	2	0.00250
21	0.05500	-1.694971	1.694971	1	0	1	0.01000
22	0.06500	-0.787407	0.787407	1	0	2	0.00500
23	0.07000	-0.762681	0.762681	1	1	2	0.00500
24	0.07500	-0.739068	0.739068	1	0	2	0.00500
25	0.08000	-0.718311	0.718311	1	1	2	0.00500
26	0.08500	-0.698487	0.698487	1	0	2	0.00500
27	0.09000	-0.680804	0.680804	1	1	2	0.00500
28	0.09500	-0.663916	0.663916	1	0	2	0.00500
29	0.10000	-0.648623	0.648623	1	1	2	0.00500
30	0.10500	-1.268038	1.268038	1	0	2	0.01000
31	0.11500	-1.274785	1.274785	1	1	2	0.01000
32	0.12500	-0.635671	0.635671	1	0	2	0.00500
33	0.13000	-0.617830	0.617830	1	1	2	0.00500
34	0.13500	-1.202698	1.202698	1	0	2	0.01000
35	0.14500	-1.188737	1.188737	1	1	2	0.01000
36	0.15500	-0.585304	0.585304	1	0	2	0.00500
37	0.16000	-0.568248	0.568248	1	1	2	0.00500
38	0.16500	-1.105059	1.105059	1	0	2	0.01000
39	0.17500	-1.088242	1.088242	1	1	2	0.01000
40	0.18500	-0.534336	0.534336	1	0	2	0.00500
41	0.19000	-0.518639	0.518639	1	1	2	0.00500
42	0.19500	-1.008359	1.008359	1	0	2	0.01000
43	0.20500	-0.992205	0.992205	1	1	2	0.01000
44	0.21500	-0.973758	0.973758	1	0	2	0.01000
45	0.22500	-0.916444	0.916444	1	1	2	0.01000
46	0.23500	-0.868178	0.868178	1	0	2	0.01000
47	0.24500	-0.826895	0.826895	1	1	2	0.01000
48	0.25500	-0.791028	0.791028	1	0	2	0.01000
49	0.26500	-0.759388	0.759388	1	1	2	0.01000
50	0.27500	-0.731070	0.731070	1	0	2	0.01000
51	0.28500	-0.705386	0.705386	1	1	2	0.01000
52	0.29500	-0.681811	0.681811	1	0	2	0.01000
53	0.30500	-0.659946	0.659946	1	1	2	0.01000

In [16]:

dynamics.get_diagnostic_conc_data()

Out[16]:

	TIME	U	X	S	is_primary	primary_timestep	n_substeps	substep_number
0	0.00000	50.000000	100.000000	0.000000	True	0.0100	2	0
1	0.00500	49.500000	98.500000	2.500000	False	0.0100	2	1
2	0.00250	49.750000	99.250000	1.250000	False	0.0050	2	1
3	0.00500	49.526250	98.524375	2.423125	True	0.0100	2	0
4	0.00625	49.426666	98.173082	2.973587	False	0.0025	2	1
5	0.00750	49.327081	97.827235	3.518603	True	0.0025	2	0
6	0.01250	48.974555	96.465384	5.585506	True	0.0050	2	0
7	0.01375	48.907973	96.145531	6.038523	False	0.0025	2	1
8	0.01500	48.841392	95.830274	6.486942	True	0.0025	2	0
9	0.02000	48.612456	94.587428	8.187661	True	0.0050	2	0
10	0.02250	48.533147	94.000837	8.932870	False	0.0050	2	1
11	0.02500	48.453838	93.429824	9.662501	True	0.0050	2	0
12	0.02750	48.404818	92.874038	10.316326	False	0.0050	2	1
13	0.03000	48.355799	92.332227	10.956174	True	0.0050	2	0
14	0.03250	48.333144	91.804078	11.529634	False	0.0050	2	1
15	0.03500	48.310488	91.288492	12.090531	True	0.0050	2	0
16	0.03750	48.310746	90.785186	12.593321	False	0.0050	2	1
17	0.04000	48.311005	90.293197	13.084794	True	0.0050	2	0
18	0.05000	48.391568	88.369489	14.847375	True	0.0100	2	0
19	0.05250	48.446558	87.929428	15.177456	False	0.0050	2	1
20	0.05500	48.501547	87.497620	15.499286	True	0.0050	2	0
21	0.06500	48.771459	85.802648	16.654433	True	0.0100	2	0
22	0.07000	48.949922	85.015241	17.084915	False	0.0100	2	1
23	0.07500	49.128385	84.252560	17.490670	True	0.0100	2	0
24	0.08000	49.336728	83.513492	17.813053	False	0.0100	2	1
25	0.08500	49.545071	82.795181	18.114678	True	0.0100	2	0
26	0.09000	49.774207	82.096694	18.354892	False	0.0100	2	1
27	0.09500	50.003343	81.415890	18.577423	True	0.0100	2	0
28	0.10000	50.246407	80.751974	18.755212	False	0.0100	2	1
29	0.10500	50.489470	80.103351	18.917708	True	0.0100	2	0
30	0.11500	51.496725	78.835313	18.171237	False	0.0200	2	1
31	0.12500	52.424117	77.560528	17.591239	True	0.0200	2	0
32	0.13000	52.603525	76.924857	17.868093	False	0.0100	2	1
33	0.13500	52.792213	76.307027	18.108546	True	0.0100	2	0
34	0.14500	53.577892	75.104329	17.739886	False	0.0200	2	1
35	0.15500	54.318365	73.915592	17.447678	True	0.0200	2	0
36	0.16000	54.473088	73.330289	17.723535	False	0.0100	2	1
37	0.16500	54.637299	72.762041	17.963362	True	0.0100	2	0
38	0.17500	55.325945	71.656981	17.691130	False	0.0200	2	1
39	0.18500	55.979039	70.568739	17.473182	True	0.0200	2	0
40	0.19000	56.118176	70.034404	17.729244	False	0.0100	2	1
41	0.19500	56.266164	69.515765	17.951907	True	0.0100	2	0
42	0.20500	56.887823	68.507407	17.716948	False	0.0200	2	1
43	0.21500	57.478251	67.515201	17.528296	True	0.0200	2	0
44	0.22500	57.730950	66.541443	17.996657	False	0.0200	2	1
45	0.23500	58.016064	65.624999	18.342874	True	0.0200	2	0
46	0.24500	58.323172	64.756822	18.596834	False	0.0200	2	1
47	0.25500	58.644455	63.929927	18.781162	True	0.0200	2	0
48	0.26500	58.974059	63.138899	18.912983	False	0.0200	2	1
49	0.27500	59.307617	62.379511	19.005256	True	0.0200	2	0
50	0.28500	59.641885	61.648441	19.067789	False	0.0200	2	1
51	0.29500	59.974470	60.943055	19.108004	True	0.0200	2	0
52	0.30500	60.303621	60.261244	19.131514	False	0.0200	2	1
53	0.31500	60.628070	59.601297	19.142563	True	0.0200	2	0

In [17]:

dynamics.get_diagnostic_decisions_data()

Out[17]:

	TIME	Delta U	Delta X	Delta S	L2	action	step_factor
0	0.0000	-0.500000	-1.500000	2.500000	NaN	NaN	NaN
1	0.0000	-0.895000	-2.902500	4.692500	3.471676	ABORT	0.5
2	0.0000	-0.250000	-0.750000	1.250000	NaN	NaN	NaN
3	0.0000	-0.473750	-1.475625	2.423125	0.919271	OK	0.5
4	0.0050	0.000000	-0.351293	0.351293	NaN	NaN	NaN
5	0.0050	-0.199169	-0.697140	1.095478	0.191749	OK	2.0
6	0.0075	-0.352527	-1.361850	2.066904	0.694556	OK	0.5
7	0.0125	0.000000	-0.319854	0.319854	NaN	NaN	NaN
8	0.0125	-0.133163	-0.635111	0.901436	0.137076	OK	2.0
9	0.0150	-0.228936	-1.242846	1.700718	0.498836	OK	1.0
10	0.0200	0.000000	-0.586591	0.586591	NaN	NaN	NaN
11	0.0200	-0.158618	-1.157604	1.474840	0.393373	OK	1.0
12	0.0250	0.000000	-0.555786	0.555786	NaN	NaN	NaN
13	0.0250	-0.098038	-1.097597	1.293673	0.320880	OK	1.0
14	0.0300	0.000000	-0.528149	0.528149	NaN	NaN	NaN
15	0.0300	-0.045311	-1.043735	1.134357	0.264245	OK	1.0
16	0.0350	0.000000	-0.503306	0.503306	NaN	NaN	NaN
17	0.0350	0.000516	-0.995295	0.994262	0.219908	OK	2.0
18	0.0400	0.080563	-1.923708	1.762582	0.757093	OK	0.5
19	0.0500	0.000000	-0.440061	0.440061	NaN	NaN	NaN
20	0.0500	0.109979	-0.871869	0.651911	0.133027	OK	2.0
21	0.0550	0.269912	-1.694971	1.155148	0.475572	OK	1.0
22	0.0650	0.000000	-0.787407	0.787407	NaN	NaN	NaN
23	0.0650	0.356925	-1.550088	0.836237	0.358829	OK	1.0
24	0.0750	0.000000	-0.739068	0.739068	NaN	NaN	NaN
25	0.0750	0.416686	-1.457379	0.624007	0.298552	OK	1.0
26	0.0850	0.000000	-0.698487	0.698487	NaN	NaN	NaN
27	0.0850	0.458273	-1.379291	0.462745	0.258510	OK	1.0
28	0.0950	0.000000	-0.663916	0.663916	NaN	NaN	NaN
29	0.0950	0.486127	-1.312539	0.340285	0.230541	OK	2.0
30	0.1050	0.503627	-1.268038	0.260784	NaN	NaN	NaN
31	0.1050	1.934646	-2.542823	-1.326469	1.329814	OK	0.5
32	0.1250	0.179408	-0.635671	0.276854	NaN	NaN	NaN
33	0.1250	0.368097	-1.253501	0.517307	0.219374	OK	2.0
34	0.1350	0.392839	-1.202698	0.417019	NaN	NaN	NaN
35	0.1350	1.526151	-2.391435	-0.660868	0.942760	OK	0.5
36	0.1550	0.154723	-0.585304	0.275857	NaN	NaN	NaN
37	0.1550	0.318934	-1.153552	0.515684	0.188703	OK	2.0
38	0.1650	0.344323	-1.105059	0.416414	NaN	NaN	NaN
39	0.1650	1.341740	-2.193301	-0.490180	0.761235	OK	0.5
40	0.1850	0.139137	-0.534336	0.256062	NaN	NaN	NaN
41	0.1850	0.287125	-1.052974	0.478725	0.157819	OK	2.0
42	0.1950	0.310829	-1.008359	0.386700	NaN	NaN	NaN
43	0.1950	1.212087	-2.000564	-0.423611	0.627873	OK	1.0
44	0.2150	0.252699	-0.973758	0.468361	NaN	NaN	NaN
45	0.2150	0.537812	-1.890202	0.814578	0.502849	OK	1.0
46	0.2350	0.307109	-0.868178	0.253960	NaN	NaN	NaN
47	0.2350	0.628392	-1.695072	0.438288	0.384471	OK	1.0
48	0.2550	0.329604	-0.791028	0.131820	NaN	NaN	NaN
49	0.2550	0.663161	-1.550416	0.224094	0.321532	OK	1.0
50	0.2750	0.334268	-0.731070	0.062534	NaN	NaN	NaN
51	0.2750	0.666854	-1.436456	0.102749	0.279851	OK	1.0
52	0.2950	0.329151	-0.681811	0.023509	NaN	NaN	NaN
53	0.2950	0.653600	-1.341758	0.034559	0.247633	OK	2.0

Notice how the first step got aborted, and re-run, because of the large adjusted L2 value in the concentrations¶

At time t=0.185 :¶

Data from this simulation (with substeps):¶

[it took 39 computation steps]

In [19]:

df.iloc[39]

Out[19]:

SYSTEM TIME        0.185
U              55.979039
X              70.568739
S              17.473182
caption                 
Name: 39, dtype: object

In [20]:

substep_data = df.iloc[39][['U', 'X', 'S']].to_numpy()
substep_data

Out[20]:

array([55.97903913467732, 70.568739429991, 17.473182300654425],
      dtype=object)

Data from experiment `variable_steps_1` (no substeps, and same main steps as in here):¶

[it took 21 computation steps]

In [21]:

no_substep_data = np.array([54.631805, 71.023480, 19.712910])
no_substep_data

Out[21]:

array([54.631805, 71.02348 , 19.71291 ])

Data from experiment `substeps_2` (with tiny fixed steps, used as a proxy for exact solution):¶

In [22]:

exact_data = np.array([54.529071, 71.351769, 19.590088])
exact_data

Out[22]:

array([54.529071, 71.351769, 19.590088])

Comparing the results:¶

In [23]:

substep_error = abs(substep_data - exact_data)
substep_error

Out[23]:

array([1.44996813467732, 0.7830295700090062, 2.116905699345576],
      dtype=object)

In [24]:

no_substep_error = abs(no_substep_data - exact_data)
no_substep_error

Out[24]:

array([0.102734, 0.328289, 0.122822])

Conclusions:¶

In this scenario, the substeps option made the errors WORSE - in spite of a substantial number of extra steps.
Also, substeps led to irregularies in the plot of the concentrations of S.
At any rates, substeps are far less relevant ever since the introduction of variable (main) step.

=> IMPORTANT: This implementation of substeps was OBSOLETED in release Beta 26.3 - and is no longer used in Life123¶