Exploration of variable time steps in the simulation of the coupled reactions `2 S <-> U` and `S <-> X`¶

Both mostly forward. 1st-order kinetics throughout.

Based on the reactions and initial conditions of the experiment up_regulate_3

LAST REVISED: Mar. 2, 2023

In [1]:

# Extend the sys.path variable, to contain the project's root directory
import set_path
set_path.add_ancestor_dir_to_syspath(2)  # The number of levels to go up 
                                         # to reach the project's home, from the folder containing this notebook

Added 'D:\Docs\- MY CODE\BioSimulations\life123-Win7' to sys.path

In [2]:

from experiments.get_notebook_info import get_notebook_basename

from src.modules.reactions.reaction_data import ReactionData as chem
from src.modules.reactions.reaction_dynamics import ReactionDynamics

import numpy as np
import plotly.express as px
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 'variable_steps_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 `variable_steps_1.log.htm`]

Set the initial concentrations of all the chemicals¶

In [5]:

dynamics = ReactionDynamics(reaction_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=2., 
                                  variable_steps=True, thresholds={"low": 0.5, "high": 0.8})

df = dynamics.get_history()
df

reaction_step_orchestrator(): entering WHILE loop at System Time=0 with delta_time_full=0.01
EXAMINING CONCENTRATION CHANGES at System Time 0 from the upcoming single step (for all rxns):
    Baseline:  [ 50. 100.   0.]
    Deltas:    [-1. -3.  5.]
    Adjusted L2 norm:    1.9720265943665387
The current time step (0.01) leads to an 'L2 rate' (1.972) that is higher than the specified HIGH threshold (1.2):
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
EXAMINING CONCENTRATION CHANGES at System Time 0 from the upcoming single step (for all rxns):
    Baseline:  [ 50. 100.   0.]
    Deltas:    [-0.5 -1.5  2.5]
    Adjusted L2 norm:    0.9860132971832694
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.986) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.005 from the upcoming single step (for all rxns):
    Baseline:  [49.5 98.5  2.5]
    Deltas:    [-0.1975  -0.70125  1.09625]
    Adjusted L2 norm:    0.43875098923598516
NOTICE: The chosen time step (0.0025) results in an 'L2 rate' (0.4388) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.0075 from the upcoming single step (for all rxns):
    Baseline:  [49.3025  97.79875  3.59625]
    Deltas:    [-0.349175   -1.35909375  2.05744375]
    Adjusted L2 norm:    0.830136119114619
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.8301) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.0125 from the upcoming single step (for all rxns):
    Baseline:  [48.953325   96.43965625  5.65369375]
    Deltas:    [-0.13169275 -0.63849202  0.90187752]
    Adjusted L2 norm:    0.37094445340529236
NOTICE: The chosen time step (0.0025) results in an 'L2 rate' (0.3709) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.015 from the upcoming single step (for all rxns):
    Baseline:  [48.82163225 95.80116423  6.55557127]
    Deltas:    [-0.22599347 -1.24035033  1.69233727]
    Adjusted L2 norm:    0.7034476536211219
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.7034) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.02 from the upcoming single step (for all rxns):
    Baseline:  [48.59563878 94.56081391  8.24790853]
    Deltas:    [-0.15604005 -1.17097495  1.48305505]
    Adjusted L2 norm:    0.6320146889296034
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.632) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.025 from the upcoming single step (for all rxns):
    Baseline:  [48.43959873 93.38983896  9.73096358]
    Deltas:    [-0.09515744 -1.10891868  1.29923357]
    Adjusted L2 norm:    0.5702595342894922
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.5703) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.03 from the upcoming single step (for all rxns):
    Baseline:  [48.34444129 92.28092028 11.03019715]
    Deltas:    [-0.04223653 -1.05330789  1.13778094]
    Adjusted L2 norm:    0.5170199771979221
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.517) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.035 from the upcoming single step (for all rxns):
    Baseline:  [48.30220476 91.22761239 12.16797809]
    Deltas:    [ 0.00369708 -1.00337484  0.99598069]
    Adjusted L2 norm:    0.47125745282035797
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.4713) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.04 from the upcoming single step (for all rxns):
    Baseline:  [48.30590184 90.22423755 13.16395878]
    Deltas:    [ 0.08699867 -1.9168896   1.74289227]
    Adjusted L2 norm:    0.8640799836300542
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.8641) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.05 from the upcoming single step (for all rxns):
    Baseline:  [48.3929005  88.30734795 14.90685105]
    Deltas:    [ 0.11234504 -0.87740469  0.65271461]
    Adjusted L2 norm:    0.3664388323328886
NOTICE: The chosen time step (0.005) results in an 'L2 rate' (0.3664) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.055 from the upcoming single step (for all rxns):
    Baseline:  [48.50524554 87.42994326 15.55956566]
    Deltas:    [ 0.27466034 -1.68932436  1.14000367]
    Adjusted L2 norm:    0.685473353555872
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.6855) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.065 from the upcoming single step (for all rxns):
    Baseline:  [48.77990588 85.7406189  16.69956934]
    Deltas:    [ 0.36036743 -1.57024441  0.84950955]
    Adjusted L2 norm:    0.6071059448138537
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.6071) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.075 from the upcoming single step (for all rxns):
    Baseline:  [49.14027331 84.17037449 17.54907888]
    Deltas:    [ 0.42112084 -1.4721665   0.62992481]
    Adjusted L2 norm:    0.551908028188212
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.5519) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.085 from the upcoming single step (for all rxns):
    Baseline:  [49.56139416 82.69820799 18.1790037 ]
    Deltas:    [ 0.46309241 -1.39020602  0.46402119]
    Adjusted L2 norm:    0.512341359965445
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.5123) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.095 from the upcoming single step (for all rxns):
    Baseline:  [50.02448657 81.30800197 18.64302489]
    Deltas:    [ 0.49095226 -1.32065857  0.33875405]
    Adjusted L2 norm:    0.4830375500460132
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.483) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.105 from the upcoming single step (for all rxns):
    Baseline:  [50.51543883 79.98734341 18.98177894]
    Deltas:    [ 1.01646708 -2.52142713  0.48849298]
    Adjusted L2 norm:    0.920713822793345
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.9207) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.125 from the upcoming single step (for all rxns):
    Baseline:  [51.5319059  77.46591628 19.47027191]
    Deltas:    [ 0.52698364 -1.15576117  0.1017939 ]
    Adjusted L2 norm:    0.424768909765701
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.4248) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.135 from the upcoming single step (for all rxns):
    Baseline:  [52.05888954 76.3101551  19.57206582]
    Deltas:    [ 1.04917495 -2.22996141  0.13161151]
    Adjusted L2 norm:    0.8226527244153111
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.8227) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.155 from the upcoming single step (for all rxns):
    Baseline:  [53.10806449 74.08019369 19.70367733]
    Deltas:    [ 0.5141329  -1.04018517  0.01191938]
    Adjusted L2 norm:    0.386790195376169
NOTICE: The chosen time step (0.01) results in an 'L2 rate' (0.3868) 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
EXAMINING CONCENTRATION CHANGES at System Time 0.165 from the upcoming single step (for all rxns):
    Baseline:  [53.62219739 73.04000852 19.71559671]
    Deltas:    [ 1.00960758 -2.01652891 -0.00268625]
    Adjusted L2 norm:    0.751716813419431
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.7517) 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: 0.165, and will continue to 0.185]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.185 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.185 from the upcoming single step (for all rxns):
    Baseline:  [54.63180496 71.02347962 19.71291046]
    Deltas:    [ 0.96879347 -1.89585952 -0.04172743]
    Adjusted L2 norm:    0.7098188581459898
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.7098) 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: 0.185, and will continue to 0.205]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.205 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.205 from the upcoming single step (for all rxns):
    Baseline:  [55.60059844 69.12762009 19.67118303]
    Deltas:    [ 0.92336535 -1.78711524 -0.05961545]
    Adjusted L2 norm:    0.6708152962620689
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.6708) 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: 0.205, and will continue to 0.225]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.225 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.225 from the upcoming single step (for all rxns):
    Baseline:  [56.52396378 67.34050485 19.61156758]
    Deltas:    [ 0.87689226 -1.68704218 -0.06674234]
    Adjusted L2 norm:    0.6341666360749514
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.6342) 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: 0.225, and will continue to 0.245]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.245 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.245 from the upcoming single step (for all rxns):
    Baseline:  [57.40085605 65.65346267 19.54482524]
    Deltas:    [ 0.8311378  -1.59382873 -0.06844686]
    Adjusted L2 norm:    0.5996077454037625
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.5996) 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: 0.245, and will continue to 0.265]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.265 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.265 from the upcoming single step (for all rxns):
    Baseline:  [58.23199384 64.05963394 19.47637838]
    Deltas:    [ 0.78694079 -1.50641263 -0.06746894]
    Adjusted L2 norm:    0.5669711804381353
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.567) 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: 0.265, and will continue to 0.285]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.285 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.285 from the upcoming single step (for all rxns):
    Baseline:  [59.01893463 62.55322131 19.40890943]
    Deltas:    [ 0.74466812 -1.42412415 -0.0652121 ]
    Adjusted L2 norm:    0.5361294223890068
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.5361) 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: 0.285, and will continue to 0.305]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.305 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.305 from the upcoming single step (for all rxns):
    Baseline:  [59.76360275 61.12909716 19.34369733]
    Deltas:    [ 0.70444746 -1.34650215 -0.06239278]
    Adjusted L2 norm:    0.5069743721586161
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.507) 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: 0.305, and will continue to 0.325]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.325 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.325 from the upcoming single step (for all rxns):
    Baseline:  [60.46805022 59.78259501 19.28130456]
    Deltas:    [ 0.66628672 -1.27319915 -0.05937429]
    Adjusted L2 norm:    0.47940928759927104
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.4794) 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: 0.325, and will continue to 0.345]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.345 with delta_time_full=0.04
EXAMINING CONCENTRATION CHANGES at System Time 0.345 from the upcoming single step (for all rxns):
    Baseline:  [61.13433694 58.50939586 19.22193027]
    Deltas:    [ 1.26027073 -2.40786424 -0.11267722]
    Adjusted L2 norm:    0.9066904814971378
NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.9067) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.02) at the next round! [The current step started at System Time: 0.345, and will continue to 0.385]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.385 with delta_time_full=0.02
EXAMINING CONCENTRATION CHANGES at System Time 0.385 from the upcoming single step (for all rxns):
    Baseline:  [62.39460767 56.10153162 19.10925305]
    Deltas:    [ 0.56169618 -1.07298153 -0.05041083]
    Adjusted L2 norm:    0.40405351934013756
NOTICE: The chosen time step (0.02) results in an 'L2 rate' (0.4041) 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: 0.385, and will continue to 0.405]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.405 with delta_time_full=0.04
EXAMINING CONCENTRATION CHANGES at System Time 0.405 from the upcoming single step (for all rxns):
    Baseline:  [62.95630385 55.02855009 19.05884222]
    Deltas:    [ 1.0623252  -2.02930388 -0.09534652]
    Adjusted L2 norm:    0.764177119158623
NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.7642) 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: 0.405, and will continue to 0.445]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.445 with delta_time_full=0.04
EXAMINING CONCENTRATION CHANGES at System Time 0.445 from the upcoming single step (for all rxns):
    Baseline:  [64.01862905 52.99924621 18.96349569]
    Deltas:    [ 0.9468283  -1.80867058 -0.08498602]
    Adjusted L2 norm:    0.6810935415626411
NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.6811) 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: 0.445, and will continue to 0.485]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.485 with delta_time_full=0.04
EXAMINING CONCENTRATION CHANGES at System Time 0.485 from the upcoming single step (for all rxns):
    Baseline:  [64.96545735 51.19057563 18.87850968]
    Deltas:    [ 0.84388651 -1.61202675 -0.07574626]
    Adjusted L2 norm:    0.6070431239872686
NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.607) 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: 0.485, and will continue to 0.525]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.525 with delta_time_full=0.04
EXAMINING CONCENTRATION CHANGES at System Time 0.525 from the upcoming single step (for all rxns):
    Baseline:  [65.80934386 49.57854888 18.80276341]
    Deltas:    [ 0.75213678 -1.43676265 -0.06751092]
    Adjusted L2 norm:    0.5410436794042834
NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.541) 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: 0.525, and will continue to 0.565]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.565 with delta_time_full=0.04
EXAMINING CONCENTRATION CHANGES at System Time 0.565 from the upcoming single step (for all rxns):
    Baseline:  [66.56148064 48.14178623 18.73525249]
    Deltas:    [ 0.67036235 -1.28055375 -0.06017094]
    Adjusted L2 norm:    0.4822198810778668
NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.4822) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.08) at the next round! [The current step started at System Time: 0.565, and will continue to 0.605]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.605 with delta_time_full=0.08
EXAMINING CONCENTRATION CHANGES at System Time 0.605 from the upcoming single step (for all rxns):
    Baseline:  [67.23184299 46.86123248 18.67508155]
    Deltas:    [ 1.19495731 -2.28265665 -0.10725798]
    Adjusted L2 norm:    0.8595831447977756
NOTICE: The chosen time step (0.08) results in an 'L2 rate' (0.8596) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER by a factor 2.0 (set to (0.04) at the next round! [The current step started at System Time: 0.605, and will continue to 0.685]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.685 with delta_time_full=0.04
EXAMINING CONCENTRATION CHANGES at System Time 0.685 from the upcoming single step (for all rxns):
    Baseline:  [68.4268003  44.57857583 18.56782357]
    Deltas:    [ 0.46755952 -0.89315144 -0.0419676 ]
    Adjusted L2 norm:    0.3363352629038791
NOTICE: The chosen time step (0.04) results in an 'L2 rate' (0.3363) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.08) at the next round! [The current step started at System Time: 0.685, and will continue to 0.725]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.725 with delta_time_full=0.08
EXAMINING CONCENTRATION CHANGES at System Time 0.725 from the upcoming single step (for all rxns):
    Baseline:  [68.89435982 43.68542439 18.52585598]
    Deltas:    [ 0.83345025 -1.59209098 -0.07480952]
    Adjusted L2 norm:    0.5995358846406782
NOTICE: The chosen time step (0.08) results in an 'L2 rate' (0.5995) 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: 0.725, and will continue to 0.805]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.805 with delta_time_full=0.08
EXAMINING CONCENTRATION CHANGES at System Time 0.805 from the upcoming single step (for all rxns):
    Baseline:  [69.72781007 42.0933334  18.45104645]
    Deltas:    [ 0.65222012 -1.24589772 -0.05854252]
    Adjusted L2 norm:    0.4691694121768126
NOTICE: The chosen time step (0.08) results in an 'L2 rate' (0.4692) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.16) at the next round! [The current step started at System Time: 0.805, and will continue to 0.885]

reaction_step_orchestrator(): entering WHILE loop at System Time=0.885 with delta_time_full=0.16
EXAMINING CONCENTRATION CHANGES at System Time 0.885 from the upcoming single step (for all rxns):
    Baseline:  [70.38003019 40.84743568 18.39250394]
    Deltas:    [ 1.02079538 -1.94996535 -0.0916254 ]
    Adjusted L2 norm:    0.7343011251253482
NOTICE: The chosen time step (0.16) results in an 'L2 rate' (0.7343) 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: 0.885, and will continue to 1.045]

reaction_step_orchestrator(): entering WHILE loop at System Time=1.045 with delta_time_full=0.16
EXAMINING CONCENTRATION CHANGES at System Time 1.045 from the upcoming single step (for all rxns):
    Baseline:  [71.40082557 38.89747033 18.30087853]
    Deltas:    [ 0.57686034 -1.10194237 -0.05177831]
    Adjusted L2 norm:    0.4149599485210064
NOTICE: The chosen time step (0.16) results in an 'L2 rate' (0.415) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.32) at the next round! [The current step started at System Time: 1.045, and will continue to 1.205]

reaction_step_orchestrator(): entering WHILE loop at System Time=1.205 with delta_time_full=0.32
EXAMINING CONCENTRATION CHANGES at System Time 1.205 from the upcoming single step (for all rxns):
    Baseline:  [71.97768591 37.79552796 18.24910022]
    Deltas:    [ 0.65197758 -1.24543442 -0.05852075]
    Adjusted L2 norm:    0.46899494767126315
NOTICE: The chosen time step (0.32) results in an 'L2 rate' (0.469) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 0.64) at the next round! [The current step started at System Time: 1.205, and will continue to 1.525]

reaction_step_orchestrator(): entering WHILE loop at System Time=1.525 with delta_time_full=0.64
EXAMINING CONCENTRATION CHANGES at System Time 1.525 from the upcoming single step (for all rxns):
    Baseline:  [72.62966349 36.55009354 18.19057947]
    Deltas:    [ 0.16979763 -0.32435443 -0.01524084]
    Adjusted L2 norm:    0.12214259081733582
NOTICE: The chosen time step (0.64) results in an 'L2 rate' (0.1221) that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER by a factor 2 (set to 1.28) at the next round! [The current step started at System Time: 1.525, and will continue to 2.165]
44 total step(s) taken

Out[6]:

	SYSTEM TIME	U	X	S	caption
0	0.0000	50.000000	100.000000	0.000000	Initial state
1	0.0050	49.500000	98.500000	2.500000
2	0.0075	49.302500	97.798750	3.596250
3	0.0125	48.953325	96.439656	5.653694
4	0.0150	48.821632	95.801164	6.555571
5	0.0200	48.595639	94.560814	8.247909
6	0.0250	48.439599	93.389839	9.730964
7	0.0300	48.344441	92.280920	11.030197
8	0.0350	48.302205	91.227612	12.167978
9	0.0400	48.305902	90.224238	13.163959
10	0.0500	48.392901	88.307348	14.906851
11	0.0550	48.505246	87.429943	15.559566
12	0.0650	48.779906	85.740619	16.699569
13	0.0750	49.140273	84.170374	17.549079
14	0.0850	49.561394	82.698208	18.179004
15	0.0950	50.024487	81.308002	18.643025
16	0.1050	50.515439	79.987343	18.981779
17	0.1250	51.531906	77.465916	19.470272
18	0.1350	52.058890	76.310155	19.572066
19	0.1550	53.108064	74.080194	19.703677
20	0.1650	53.622197	73.040009	19.715597
21	0.1850	54.631805	71.023480	19.712910
22	0.2050	55.600598	69.127620	19.671183
23	0.2250	56.523964	67.340505	19.611568
24	0.2450	57.400856	65.653463	19.544825
25	0.2650	58.231994	64.059634	19.476378
26	0.2850	59.018935	62.553221	19.408909
27	0.3050	59.763603	61.129097	19.343697
28	0.3250	60.468050	59.782595	19.281305
29	0.3450	61.134337	58.509396	19.221930
30	0.3850	62.394608	56.101532	19.109253
31	0.4050	62.956304	55.028550	19.058842
32	0.4450	64.018629	52.999246	18.963496
33	0.4850	64.965457	51.190576	18.878510
34	0.5250	65.809344	49.578549	18.802763
35	0.5650	66.561481	48.141786	18.735252
36	0.6050	67.231843	46.861232	18.675082
37	0.6850	68.426800	44.578576	18.567824
38	0.7250	68.894360	43.685424	18.525856
39	0.8050	69.727810	42.093333	18.451046
40	0.8850	70.380030	40.847436	18.392504
41	1.0450	71.400826	38.897470	18.300879
42	1.2050	71.977686	37.795528	18.249100
43	1.5250	72.629663	36.550094	18.190579
44	2.1650	72.799461	36.225739	18.175339

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 0.0075, in 1 FULL step of 0.0025
From time 0.0075 to 0.0125, in 1 FULL step of 0.005
From time 0.0125 to 0.015, in 1 FULL step of 0.0025
From time 0.015 to 0.04, in 5 FULL steps of 0.005
From time 0.04 to 0.05, in 1 FULL step of 0.01
From time 0.05 to 0.055, in 1 FULL step of 0.005
From time 0.055 to 0.105, in 5 FULL steps of 0.01
From time 0.105 to 0.125, in 1 FULL step of 0.02
From time 0.125 to 0.135, in 1 FULL step of 0.01
From time 0.135 to 0.155, in 1 FULL step of 0.02
From time 0.155 to 0.165, in 1 FULL step of 0.01
From time 0.165 to 0.345, in 9 FULL steps of 0.02
From time 0.345 to 0.385, in 1 FULL step of 0.04
From time 0.385 to 0.405, in 1 FULL step of 0.02
From time 0.405 to 0.605, in 5 FULL steps of 0.04
From time 0.605 to 0.685, in 1 FULL step of 0.08
From time 0.685 to 0.725, in 1 FULL step of 0.04
From time 0.725 to 0.885, in 2 FULL steps of 0.08
From time 0.885 to 1.205, in 2 FULL steps of 0.16
From time 1.205 to 1.525, in 1 FULL step of 0.32
From time 1.525 to 2.165, in 1 FULL step of 0.64

In [8]:

np.array(step_sizes)

Out[8]:

array([0.005 , 0.0025, 0.005 , 0.0025, 0.005 , 0.01  , 0.005 , 0.01  ,
       0.02  , 0.01  , 0.02  , 0.01  , 0.02  , 0.04  , 0.02  , 0.04  ,
       0.08  , 0.04  , 0.08  , 0.16  , 0.32  , 0.64  ])

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 , 0.0075, 0.0125, 0.015 , 0.04  , 0.05  , 0.055 ,
       0.105 , 0.125 , 0.135 , 0.155 , 0.165 , 0.345 , 0.385 , 0.405 ,
       0.605 , 0.685 , 0.725 , 0.885 , 1.205 , 1.525 , 2.165 ])

Plots of changes of concentration with time¶

In [10]:

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

In [11]:

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

In [12]:

# Show the "critical values", i.e. times when the step size changes
dynamics.plot_curves(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.is_in_equilibrium()

2 S <-> U
Final concentrations:  [U] = 72.8 ; [S] = 18.18
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.0054
    Formula used:  [U] / [S]
2. Ratio of forward/reverse reaction rates: 4.0
Discrepancy between the two values: 0.1349 %
Reaction IS in equilibrium (within 1% tolerance)

S <-> X
Final concentrations:  [X] = 36.23 ; [S] = 18.18
1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99313
    Formula used:  [X] / [S]
2. Ratio of forward/reverse reaction rates: 2.0
Discrepancy between the two values: 0.3437 %
Reaction IS in equilibrium (within 1% tolerance)

Out[14]:

True

In [15]:

dynamics.get_diagnostic_rxn_data(rxn_index=0)

Reaction:  2 S <-> U

Out[15]:

	TIME	Delta U	Delta S	time_subdivision	delta_time
0	0.0000	-1.000000	2.000000	1	0.0100
1	0.0000	-0.500000	1.000000	1	0.0050
2	0.0050	-0.197500	0.395000	1	0.0025
3	0.0075	-0.349175	0.698350	1	0.0050
4	0.0125	-0.131693	0.263385	1	0.0025
5	0.0150	-0.225993	0.451987	1	0.0050
6	0.0200	-0.156040	0.312080	1	0.0050
7	0.0250	-0.095157	0.190315	1	0.0050
8	0.0300	-0.042237	0.084473	1	0.0050
9	0.0350	0.003697	-0.007394	1	0.0050
10	0.0400	0.086999	-0.173997	1	0.0100
11	0.0500	0.112345	-0.224690	1	0.0050
12	0.0550	0.274660	-0.549321	1	0.0100
13	0.0650	0.360367	-0.720735	1	0.0100
14	0.0750	0.421121	-0.842242	1	0.0100
15	0.0850	0.463092	-0.926185	1	0.0100
16	0.0950	0.490952	-0.981905	1	0.0100
17	0.1050	1.016467	-2.032934	1	0.0200
18	0.1250	0.526984	-1.053967	1	0.0100
19	0.1350	1.049175	-2.098350	1	0.0200
20	0.1550	0.514133	-1.028266	1	0.0100
21	0.1650	1.009608	-2.019215	1	0.0200
22	0.1850	0.968793	-1.937587	1	0.0200
23	0.2050	0.923365	-1.846731	1	0.0200
24	0.2250	0.876892	-1.753785	1	0.0200
25	0.2450	0.831138	-1.662276	1	0.0200
26	0.2650	0.786941	-1.573882	1	0.0200
27	0.2850	0.744668	-1.489336	1	0.0200
28	0.3050	0.704447	-1.408895	1	0.0200
29	0.3250	0.666287	-1.332573	1	0.0200
30	0.3450	1.260271	-2.520541	1	0.0400
31	0.3850	0.561696	-1.123392	1	0.0200
32	0.4050	1.062325	-2.124650	1	0.0400
33	0.4450	0.946828	-1.893657	1	0.0400
34	0.4850	0.843887	-1.687773	1	0.0400
35	0.5250	0.752137	-1.504274	1	0.0400
36	0.5650	0.670362	-1.340725	1	0.0400
37	0.6050	1.194957	-2.389915	1	0.0800
38	0.6850	0.467560	-0.935119	1	0.0400
39	0.7250	0.833450	-1.666901	1	0.0800
40	0.8050	0.652220	-1.304440	1	0.0800
41	0.8850	1.020795	-2.041591	1	0.1600
42	1.0450	0.576860	-1.153721	1	0.1600
43	1.2050	0.651978	-1.303955	1	0.3200
44	1.5250	0.169798	-0.339595	1	0.6400

In [16]:

dynamics.get_diagnostic_rxn_data(rxn_index=1)

Reaction:  S <-> X

Out[16]:

	TIME	Delta X	Delta S	reaction	time_subdivision	delta_time
0	0.0000	-3.000000	3.000000	1	1	0.0100
1	0.0000	-1.500000	1.500000	1	1	0.0050
2	0.0050	-0.701250	0.701250	1	1	0.0025
3	0.0075	-1.359094	1.359094	1	1	0.0050
4	0.0125	-0.638492	0.638492	1	1	0.0025
5	0.0150	-1.240350	1.240350	1	1	0.0050
6	0.0200	-1.170975	1.170975	1	1	0.0050
7	0.0250	-1.108919	1.108919	1	1	0.0050
8	0.0300	-1.053308	1.053308	1	1	0.0050
9	0.0350	-1.003375	1.003375	1	1	0.0050
10	0.0400	-1.916890	1.916890	1	1	0.0100
11	0.0500	-0.877405	0.877405	1	1	0.0050
12	0.0550	-1.689324	1.689324	1	1	0.0100
13	0.0650	-1.570244	1.570244	1	1	0.0100
14	0.0750	-1.472167	1.472167	1	1	0.0100
15	0.0850	-1.390206	1.390206	1	1	0.0100
16	0.0950	-1.320659	1.320659	1	1	0.0100
17	0.1050	-2.521427	2.521427	1	1	0.0200
18	0.1250	-1.155761	1.155761	1	1	0.0100
19	0.1350	-2.229961	2.229961	1	1	0.0200
20	0.1550	-1.040185	1.040185	1	1	0.0100
21	0.1650	-2.016529	2.016529	1	1	0.0200
22	0.1850	-1.895860	1.895860	1	1	0.0200
23	0.2050	-1.787115	1.787115	1	1	0.0200
24	0.2250	-1.687042	1.687042	1	1	0.0200
25	0.2450	-1.593829	1.593829	1	1	0.0200
26	0.2650	-1.506413	1.506413	1	1	0.0200
27	0.2850	-1.424124	1.424124	1	1	0.0200
28	0.3050	-1.346502	1.346502	1	1	0.0200
29	0.3250	-1.273199	1.273199	1	1	0.0200
30	0.3450	-2.407864	2.407864	1	1	0.0400
31	0.3850	-1.072982	1.072982	1	1	0.0200
32	0.4050	-2.029304	2.029304	1	1	0.0400
33	0.4450	-1.808671	1.808671	1	1	0.0400
34	0.4850	-1.612027	1.612027	1	1	0.0400
35	0.5250	-1.436763	1.436763	1	1	0.0400
36	0.5650	-1.280554	1.280554	1	1	0.0400
37	0.6050	-2.282657	2.282657	1	1	0.0800
38	0.6850	-0.893151	0.893151	1	1	0.0400
39	0.7250	-1.592091	1.592091	1	1	0.0800
40	0.8050	-1.245898	1.245898	1	1	0.0800
41	0.8850	-1.949965	1.949965	1	1	0.1600
42	1.0450	-1.101942	1.101942	1	1	0.1600
43	1.2050	-1.245434	1.245434	1	1	0.3200
44	1.5250	-0.324354	0.324354	1	1	0.6400

In [17]:

dynamics.get_diagnostic_conc_data()

Out[17]:

	TIME	U	X	S	is_primary	primary_timestep	n_substeps
0	0.0000	50.000000	100.000000	0.000000	True	0.0100	1
1	0.0050	49.500000	98.500000	2.500000	True	0.0100	1
2	0.0075	49.302500	97.798750	3.596250	True	0.0025	1
3	0.0125	48.953325	96.439656	5.653694	True	0.0050	1
4	0.0150	48.821632	95.801164	6.555571	True	0.0025	1
5	0.0200	48.595639	94.560814	8.247909	True	0.0050	1
6	0.0250	48.439599	93.389839	9.730964	True	0.0050	1
7	0.0300	48.344441	92.280920	11.030197	True	0.0050	1
8	0.0350	48.302205	91.227612	12.167978	True	0.0050	1
9	0.0400	48.305902	90.224238	13.163959	True	0.0050	1
10	0.0500	48.392901	88.307348	14.906851	True	0.0100	1
11	0.0550	48.505246	87.429943	15.559566	True	0.0050	1
12	0.0650	48.779906	85.740619	16.699569	True	0.0100	1
13	0.0750	49.140273	84.170374	17.549079	True	0.0100	1
14	0.0850	49.561394	82.698208	18.179004	True	0.0100	1
15	0.0950	50.024487	81.308002	18.643025	True	0.0100	1
16	0.1050	50.515439	79.987343	18.981779	True	0.0100	1
17	0.1250	51.531906	77.465916	19.470272	True	0.0200	1
18	0.1350	52.058890	76.310155	19.572066	True	0.0100	1
19	0.1550	53.108064	74.080194	19.703677	True	0.0200	1
20	0.1650	53.622197	73.040009	19.715597	True	0.0100	1
21	0.1850	54.631805	71.023480	19.712910	True	0.0200	1
22	0.2050	55.600598	69.127620	19.671183	True	0.0200	1
23	0.2250	56.523964	67.340505	19.611568	True	0.0200	1
24	0.2450	57.400856	65.653463	19.544825	True	0.0200	1
25	0.2650	58.231994	64.059634	19.476378	True	0.0200	1
26	0.2850	59.018935	62.553221	19.408909	True	0.0200	1
27	0.3050	59.763603	61.129097	19.343697	True	0.0200	1
28	0.3250	60.468050	59.782595	19.281305	True	0.0200	1
29	0.3450	61.134337	58.509396	19.221930	True	0.0200	1
30	0.3850	62.394608	56.101532	19.109253	True	0.0400	1
31	0.4050	62.956304	55.028550	19.058842	True	0.0200	1
32	0.4450	64.018629	52.999246	18.963496	True	0.0400	1
33	0.4850	64.965457	51.190576	18.878510	True	0.0400	1
34	0.5250	65.809344	49.578549	18.802763	True	0.0400	1
35	0.5650	66.561481	48.141786	18.735252	True	0.0400	1
36	0.6050	67.231843	46.861232	18.675082	True	0.0400	1
37	0.6850	68.426800	44.578576	18.567824	True	0.0800	1
38	0.7250	68.894360	43.685424	18.525856	True	0.0400	1
39	0.8050	69.727810	42.093333	18.451046	True	0.0800	1
40	0.8850	70.380030	40.847436	18.392504	True	0.0800	1
41	1.0450	71.400826	38.897470	18.300879	True	0.1600	1
42	1.2050	71.977686	37.795528	18.249100	True	0.1600	1
43	1.5250	72.629663	36.550094	18.190579	True	0.3200	1
44	2.1650	72.799461	36.225739	18.175339	True	0.6400	1

In [18]:

dynamics.get_diagnostic_delta_data()

Out[18]:

	TIME	Delta U	Delta X	Delta S
0	0.0000	-1.000000	-3.000000	5.000000
1	0.0000	-0.500000	-1.500000	2.500000
2	0.0050	-0.197500	-0.701250	1.096250
3	0.0075	-0.349175	-1.359094	2.057444
4	0.0125	-0.131693	-0.638492	0.901878
5	0.0150	-0.225993	-1.240350	1.692337
6	0.0200	-0.156040	-1.170975	1.483055
7	0.0250	-0.095157	-1.108919	1.299234
8	0.0300	-0.042237	-1.053308	1.137781
9	0.0350	0.003697	-1.003375	0.995981
10	0.0400	0.086999	-1.916890	1.742892
11	0.0500	0.112345	-0.877405	0.652715
12	0.0550	0.274660	-1.689324	1.140004
13	0.0650	0.360367	-1.570244	0.849510
14	0.0750	0.421121	-1.472167	0.629925
15	0.0850	0.463092	-1.390206	0.464021
16	0.0950	0.490952	-1.320659	0.338754
17	0.1050	1.016467	-2.521427	0.488493
18	0.1250	0.526984	-1.155761	0.101794
19	0.1350	1.049175	-2.229961	0.131612
20	0.1550	0.514133	-1.040185	0.011919
21	0.1650	1.009608	-2.016529	-0.002686
22	0.1850	0.968793	-1.895860	-0.041727
23	0.2050	0.923365	-1.787115	-0.059615
24	0.2250	0.876892	-1.687042	-0.066742
25	0.2450	0.831138	-1.593829	-0.068447
26	0.2650	0.786941	-1.506413	-0.067469
27	0.2850	0.744668	-1.424124	-0.065212
28	0.3050	0.704447	-1.346502	-0.062393
29	0.3250	0.666287	-1.273199	-0.059374
30	0.3450	1.260271	-2.407864	-0.112677
31	0.3850	0.561696	-1.072982	-0.050411
32	0.4050	1.062325	-2.029304	-0.095347
33	0.4450	0.946828	-1.808671	-0.084986
34	0.4850	0.843887	-1.612027	-0.075746
35	0.5250	0.752137	-1.436763	-0.067511
36	0.5650	0.670362	-1.280554	-0.060171
37	0.6050	1.194957	-2.282657	-0.107258
38	0.6850	0.467560	-0.893151	-0.041968
39	0.7250	0.833450	-1.592091	-0.074810
40	0.8050	0.652220	-1.245898	-0.058543
41	0.8850	1.020795	-1.949965	-0.091625
42	1.0450	0.576860	-1.101942	-0.051778
43	1.2050	0.651978	-1.245434	-0.058521
44	1.5250	0.169798	-0.324354	-0.015241

In [19]:

dynamics.get_diagnostic_L2_data()

Out[19]:

	TIME	Delta U	Delta X	Delta S	L2	actions	step_factors
0	0.0000	-1.000000	-3.000000	5.000000	1.972027	ABORT	0.5
1	0.0000	-0.500000	-1.500000	2.500000	0.986013	OK	0.5
2	0.0050	-0.197500	-0.701250	1.096250	0.438751	OK	2.0
3	0.0075	-0.349175	-1.359094	2.057444	0.830136	OK	0.5
4	0.0125	-0.131693	-0.638492	0.901878	0.370944	OK	2.0
5	0.0150	-0.225993	-1.240350	1.692337	0.703448	OK	1.0
6	0.0200	-0.156040	-1.170975	1.483055	0.632015	OK	1.0
7	0.0250	-0.095157	-1.108919	1.299234	0.570260	OK	1.0
8	0.0300	-0.042237	-1.053308	1.137781	0.517020	OK	1.0
9	0.0350	0.003697	-1.003375	0.995981	0.471257	OK	2.0
10	0.0400	0.086999	-1.916890	1.742892	0.864080	OK	0.5
11	0.0500	0.112345	-0.877405	0.652715	0.366439	OK	2.0
12	0.0550	0.274660	-1.689324	1.140004	0.685473	OK	1.0
13	0.0650	0.360367	-1.570244	0.849510	0.607106	OK	1.0
14	0.0750	0.421121	-1.472167	0.629925	0.551908	OK	1.0
15	0.0850	0.463092	-1.390206	0.464021	0.512341	OK	1.0
16	0.0950	0.490952	-1.320659	0.338754	0.483038	OK	2.0
17	0.1050	1.016467	-2.521427	0.488493	0.920714	OK	0.5
18	0.1250	0.526984	-1.155761	0.101794	0.424769	OK	2.0
19	0.1350	1.049175	-2.229961	0.131612	0.822653	OK	0.5
20	0.1550	0.514133	-1.040185	0.011919	0.386790	OK	2.0
21	0.1650	1.009608	-2.016529	-0.002686	0.751717	OK	1.0
22	0.1850	0.968793	-1.895860	-0.041727	0.709819	OK	1.0
23	0.2050	0.923365	-1.787115	-0.059615	0.670815	OK	1.0
24	0.2250	0.876892	-1.687042	-0.066742	0.634167	OK	1.0
25	0.2450	0.831138	-1.593829	-0.068447	0.599608	OK	1.0
26	0.2650	0.786941	-1.506413	-0.067469	0.566971	OK	1.0
27	0.2850	0.744668	-1.424124	-0.065212	0.536129	OK	1.0
28	0.3050	0.704447	-1.346502	-0.062393	0.506974	OK	1.0
29	0.3250	0.666287	-1.273199	-0.059374	0.479409	OK	2.0
30	0.3450	1.260271	-2.407864	-0.112677	0.906690	OK	0.5
31	0.3850	0.561696	-1.072982	-0.050411	0.404054	OK	2.0
32	0.4050	1.062325	-2.029304	-0.095347	0.764177	OK	1.0
33	0.4450	0.946828	-1.808671	-0.084986	0.681094	OK	1.0
34	0.4850	0.843887	-1.612027	-0.075746	0.607043	OK	1.0
35	0.5250	0.752137	-1.436763	-0.067511	0.541044	OK	1.0
36	0.5650	0.670362	-1.280554	-0.060171	0.482220	OK	2.0
37	0.6050	1.194957	-2.282657	-0.107258	0.859583	OK	0.5
38	0.6850	0.467560	-0.893151	-0.041968	0.336335	OK	2.0
39	0.7250	0.833450	-1.592091	-0.074810	0.599536	OK	1.0
40	0.8050	0.652220	-1.245898	-0.058543	0.469169	OK	2.0
41	0.8850	1.020795	-1.949965	-0.091625	0.734301	OK	1.0
42	1.0450	0.576860	-1.101942	-0.051778	0.414960	OK	2.0
43	1.2050	0.651978	-1.245434	-0.058521	0.468995	OK	2.0
44	1.5250	0.169798	-0.324354	-0.015241	0.122143	OK	2.0

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

In [ ]:

Exploration of variable time steps in the simulation of the coupled reactions 2 S <-> U and S <-> X¶