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. 6, 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"]  # Uncomment for debug data

dynamics.single_compartment_react(time_step=0.01, stop_time=2.0, 
                                  variable_steps=True, thresholds={"low": 0.25, "high": 0.64})

df = dynamics.get_history()
df

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	L2	action	step_factor
0	0.0000	-1.000000	-3.000000	5.000000	3.888889	ABORT	0.5
1	0.0000	-0.500000	-1.500000	2.500000	0.972222	OK	0.5
2	0.0050	-0.197500	-0.701250	1.096250	0.192502	OK	2.0
3	0.0075	-0.349175	-1.359094	2.057444	0.689126	OK	0.5
4	0.0125	-0.131693	-0.638492	0.901878	0.137600	OK	2.0
5	0.0150	-0.225993	-1.240350	1.692337	0.494839	OK	1.0
6	0.0200	-0.156040	-1.170975	1.483055	0.399443	OK	1.0
7	0.0250	-0.095157	-1.108919	1.299234	0.325196	OK	1.0
8	0.0300	-0.042237	-1.053308	1.137781	0.267310	OK	1.0
9	0.0350	0.003697	-1.003375	0.995981	0.222084	OK	2.0
10	0.0400	0.086999	-1.916890	1.742892	0.746634	OK	0.5
11	0.0500	0.112345	-0.877405	0.652715	0.134277	OK	2.0
12	0.0550	0.274660	-1.689324	1.140004	0.469874	OK	1.0
13	0.0650	0.360367	-1.570244	0.849510	0.368578	OK	1.0
14	0.0750	0.421121	-1.472167	0.629925	0.304602	OK	1.0
15	0.0850	0.463092	-1.390206	0.464021	0.262494	OK	1.0
16	0.0950	0.490952	-1.320659	0.338754	0.233325	OK	2.0
17	0.1050	1.016467	-2.521427	0.488493	0.847714	OK	0.5
18	0.1250	0.526984	-1.155761	0.101794	0.180429	OK	2.0
19	0.1350	1.049175	-2.229961	0.131612	0.676758	OK	0.5
20	0.1550	0.514133	-1.040185	0.011919	0.149607	OK	2.0
21	0.1650	1.009608	-2.016529	-0.002686	0.565078	OK	1.0
22	0.1850	0.968793	-1.895860	-0.041727	0.503843	OK	1.0
23	0.2050	0.923365	-1.787115	-0.059615	0.449993	OK	1.0
24	0.2250	0.876892	-1.687042	-0.066742	0.402167	OK	1.0
25	0.2450	0.831138	-1.593829	-0.068447	0.359529	OK	1.0
26	0.2650	0.786941	-1.506413	-0.067469	0.321456	OK	1.0
27	0.2850	0.744668	-1.424124	-0.065212	0.287435	OK	1.0
28	0.3050	0.704447	-1.346502	-0.062393	0.257023	OK	1.0
29	0.3250	0.666287	-1.273199	-0.059374	0.229833	OK	2.0
30	0.3450	1.260271	-2.407864	-0.112677	0.822088	OK	0.5
31	0.3850	0.561696	-1.072982	-0.050411	0.163259	OK	2.0
32	0.4050	1.062325	-2.029304	-0.095347	0.583967	OK	1.0
33	0.4450	0.946828	-1.808671	-0.084986	0.463888	OK	1.0
34	0.4850	0.843887	-1.612027	-0.075746	0.368501	OK	1.0
35	0.5250	0.752137	-1.436763	-0.067511	0.292728	OK	1.0
36	0.5650	0.670362	-1.280554	-0.060171	0.232536	OK	2.0
37	0.6050	1.194957	-2.282657	-0.107258	0.738883	OK	0.5
38	0.6850	0.467560	-0.893151	-0.041968	0.113121	OK	2.0
39	0.7250	0.833450	-1.592091	-0.074810	0.359443	OK	1.0
40	0.8050	0.652220	-1.245898	-0.058543	0.220120	OK	2.0
41	0.8850	1.020795	-1.949965	-0.091625	0.539198	OK	1.0
42	1.0450	0.576860	-1.101942	-0.051778	0.172192	OK	2.0
43	1.2050	0.651978	-1.245434	-0.058521	0.219956	OK	2.0
44	1.5250	0.169798	-0.324354	-0.015241	0.014919	OK	2.0

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

In [19]:

dynamics.get_diagnostic_delta_data_alt()      # TODO: OBSOLETE!

Out[19]:

	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 [20]:

dynamics.get_diagnostic_L2_data()      # TODO: OBSOLETE!

Out[20]:

	TIME	Delta U	Delta X	Delta S	L2	action	step_factor	L2_computed	actions_computed	step_factors_computed
0	0.0000	-1.000000	-3.000000	5.000000	3.888889	ABORT	0.5	3.888889	ABORT	0.5
1	0.0000	-0.500000	-1.500000	2.500000	0.972222	OK	0.5	0.972222	OK	0.5
2	0.0050	-0.197500	-0.701250	1.096250	0.192502	OK	2.0	0.192502	OK	2.0
3	0.0075	-0.349175	-1.359094	2.057444	0.689126	OK	0.5	0.689126	OK	0.5
4	0.0125	-0.131693	-0.638492	0.901878	0.137600	OK	2.0	0.137600	OK	2.0
5	0.0150	-0.225993	-1.240350	1.692337	0.494839	OK	1.0	0.494839	OK	1.0
6	0.0200	-0.156040	-1.170975	1.483055	0.399443	OK	1.0	0.399443	OK	1.0
7	0.0250	-0.095157	-1.108919	1.299234	0.325196	OK	1.0	0.325196	OK	1.0
8	0.0300	-0.042237	-1.053308	1.137781	0.267310	OK	1.0	0.267310	OK	1.0
9	0.0350	0.003697	-1.003375	0.995981	0.222084	OK	2.0	0.222084	OK	2.0
10	0.0400	0.086999	-1.916890	1.742892	0.746634	OK	0.5	0.746634	OK	0.5
11	0.0500	0.112345	-0.877405	0.652715	0.134277	OK	2.0	0.134277	OK	2.0
12	0.0550	0.274660	-1.689324	1.140004	0.469874	OK	1.0	0.469874	OK	1.0
13	0.0650	0.360367	-1.570244	0.849510	0.368578	OK	1.0	0.368578	OK	1.0
14	0.0750	0.421121	-1.472167	0.629925	0.304602	OK	1.0	0.304602	OK	1.0
15	0.0850	0.463092	-1.390206	0.464021	0.262494	OK	1.0	0.262494	OK	1.0
16	0.0950	0.490952	-1.320659	0.338754	0.233325	OK	2.0	0.233325	OK	2.0
17	0.1050	1.016467	-2.521427	0.488493	0.847714	OK	0.5	0.847714	OK	0.5
18	0.1250	0.526984	-1.155761	0.101794	0.180429	OK	2.0	0.180429	OK	2.0
19	0.1350	1.049175	-2.229961	0.131612	0.676758	OK	0.5	0.676758	OK	0.5
20	0.1550	0.514133	-1.040185	0.011919	0.149607	OK	2.0	0.149607	OK	2.0
21	0.1650	1.009608	-2.016529	-0.002686	0.565078	OK	1.0	0.565078	OK	1.0
22	0.1850	0.968793	-1.895860	-0.041727	0.503843	OK	1.0	0.503843	OK	1.0
23	0.2050	0.923365	-1.787115	-0.059615	0.449993	OK	1.0	0.449993	OK	1.0
24	0.2250	0.876892	-1.687042	-0.066742	0.402167	OK	1.0	0.402167	OK	1.0
25	0.2450	0.831138	-1.593829	-0.068447	0.359529	OK	1.0	0.359529	OK	1.0
26	0.2650	0.786941	-1.506413	-0.067469	0.321456	OK	1.0	0.321456	OK	1.0
27	0.2850	0.744668	-1.424124	-0.065212	0.287435	OK	1.0	0.287435	OK	1.0
28	0.3050	0.704447	-1.346502	-0.062393	0.257023	OK	1.0	0.257023	OK	1.0
29	0.3250	0.666287	-1.273199	-0.059374	0.229833	OK	2.0	0.229833	OK	2.0
30	0.3450	1.260271	-2.407864	-0.112677	0.822088	OK	0.5	0.822088	OK	0.5
31	0.3850	0.561696	-1.072982	-0.050411	0.163259	OK	2.0	0.163259	OK	2.0
32	0.4050	1.062325	-2.029304	-0.095347	0.583967	OK	1.0	0.583967	OK	1.0
33	0.4450	0.946828	-1.808671	-0.084986	0.463888	OK	1.0	0.463888	OK	1.0
34	0.4850	0.843887	-1.612027	-0.075746	0.368501	OK	1.0	0.368501	OK	1.0
35	0.5250	0.752137	-1.436763	-0.067511	0.292728	OK	1.0	0.292728	OK	1.0
36	0.5650	0.670362	-1.280554	-0.060171	0.232536	OK	2.0	0.232536	OK	2.0
37	0.6050	1.194957	-2.282657	-0.107258	0.738883	OK	0.5	0.738883	OK	0.5
38	0.6850	0.467560	-0.893151	-0.041968	0.113121	OK	2.0	0.113121	OK	2.0
39	0.7250	0.833450	-1.592091	-0.074810	0.359443	OK	1.0	0.359443	OK	1.0
40	0.8050	0.652220	-1.245898	-0.058543	0.220120	OK	2.0	0.220120	OK	2.0
41	0.8850	1.020795	-1.949965	-0.091625	0.539198	OK	1.0	0.539198	OK	1.0
42	1.0450	0.576860	-1.101942	-0.051778	0.172192	OK	2.0	0.172192	OK	2.0
43	1.2050	0.651978	-1.245434	-0.058521	0.219956	OK	2.0	0.219956	OK	2.0
44	1.5250	0.169798	-0.324354	-0.015241	0.014919	OK	2.0	0.014919	OK	2.0

In [ ]:

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