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
This experiment gets repeated, with very fine fixed steps (as a proxy for the "exact value"), in variable_steps_2
LAST REVISED: June 4, 2023
In [1]:
import set_path # Importing this module will add the project's home directory to sys.path
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 ChemData 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()
# All of these settings are currently close to the default values... but subject to change; set for repeatability
dynamics.set_thresholds(norm="norm_A", low=0.25, high=0.64, abort=1.44)
dynamics.set_thresholds(norm="norm_B") # We are disabling norm_B (to conform to the original run)
dynamics.set_step_factors(upshift=2.0, downshift=0.5, abort=0.5) # Note: upshift=2.0 seems to often be excessive. About 1.4 is currently recommended
dynamics.set_error_step_factor(0.5)
dynamics.single_compartment_react(initial_step=0.01, target_end_time=2.0,
variable_steps=True, explain_variable_steps=True)
(STEP 0) ANALYSIS: Examining Conc. Changes from System Time 0 due to tentative single step of 0.01:
Baseline: [ 50. 100. 0.]
Deltas: [-1. -3. 5.]
Relative Deltas: [-0.02 -0.03 inf]
Norms: {'norm_A': 3.888888888888889}
Thresholds:
norm_A : low 0.25 | high 0.64 | abort 1.44 | (VALUE 3.8889)
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: abort (with step size factor of 0.5)
INFO: the tentative time step (0.01) leads to a least one norm value > its ABORT threshold:
-> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.005) [Step started at t=0, and will rewind there]
(STEP 0) ANALYSIS: Examining Conc. Changes from System Time 0 due to tentative single step of 0.005:
Baseline: [ 50. 100. 0.]
Deltas: [-0.5 -1.5 2.5]
Relative Deltas: [-0.01 -0.015 inf]
Norms: {'norm_A': 0.9722222222222222}
Thresholds:
norm_A : low 0.25 | high 0.64 | (VALUE 0.97222) | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: high (with step size factor of 0.5)
NOTICE: the tentative time step (0.005) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER, multiplied by 0.5 (set to 0.0025) at the next round, because at least one norm is high
[The current step started at System Time: 0, and will continue to 0.005]
(STEP 1) ANALYSIS: Examining Conc. Changes from System Time 0.005 due to tentative single step of 0.0025:
Baseline: [49.5 98.5 2.5]
Deltas: [-0.1975 -0.70125 1.09625]
Relative Deltas: [-0.0039899 -0.00711929 0.4385 ]
Norms: {'norm_A': 0.19250243055555555}
Thresholds:
norm_A : (VALUE 0.1925) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.0025) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.005) at the next round, because all norms are low
[The current step started at System Time: 0.005, and will continue to 0.0075]
(STEP 2) ANALYSIS: Examining Conc. Changes from System Time 0.0075 due to tentative single step of 0.005:
Baseline: [49.3025 97.79875 3.59625]
Deltas: [-0.349175 -1.35909375 2.05744375]
Relative Deltas: [-0.0070823 -0.01389684 0.5721081 ]
Norms: {'norm_A': 0.6891259762586809}
Thresholds:
norm_A : low 0.25 | high 0.64 | (VALUE 0.68913) | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: high (with step size factor of 0.5)
NOTICE: the tentative time step (0.005) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER, multiplied by 0.5 (set to 0.0025) at the next round, because at least one norm is high
[The current step started at System Time: 0.0075, and will continue to 0.0125]
(STEP 3) ANALYSIS: Examining Conc. Changes from System Time 0.0125 due to tentative single step of 0.0025:
Baseline: [48.953325 96.43965625 5.65369375]
Deltas: [-0.13169275 -0.63849202 0.90187752]
Relative Deltas: [-0.00269017 -0.00662064 0.15952005]
Norms: {'norm_A': 0.1375997875121511}
Thresholds:
norm_A : (VALUE 0.1376) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.0025) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.005) at the next round, because all norms are low
[The current step started at System Time: 0.0125, and will continue to 0.015]
(STEP 4) ANALYSIS: Examining Conc. Changes from System Time 0.015 due to tentative single step of 0.005:
Baseline: [48.82163225 95.80116423 6.55557127]
Deltas: [-0.22599347 -1.24035033 1.69233727]
Relative Deltas: [-0.00462896 -0.01294713 0.25815252]
Norms: {'norm_A': 0.494838601385062}
Thresholds:
norm_A : low 0.25 | (VALUE 0.49484) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.005) results in norm values 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]
(STEP 5) ANALYSIS: Examining Conc. Changes from System Time 0.02 due to tentative single step of 0.005:
Baseline: [48.59563878 94.56081391 8.24790853]
Deltas: [-0.15604005 -1.17097495 1.48305505]
Relative Deltas: [-0.00321099 -0.0123833 0.17980983]
Norms: {'norm_A': 0.3994425670227834}
Thresholds:
norm_A : low 0.25 | (VALUE 0.39944) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.005) results in norm values 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]
(STEP 6) ANALYSIS: Examining Conc. Changes from System Time 0.025 due to tentative single step of 0.005:
Baseline: [48.43959873 93.38983896 9.73096358]
Deltas: [-0.09515744 -1.10891868 1.29923357]
Relative Deltas: [-0.00196446 -0.01187408 0.13351541]
Norms: {'norm_A': 0.32519593644806855}
Thresholds:
norm_A : low 0.25 | (VALUE 0.3252) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.005) results in norm values 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]
(STEP 7) ANALYSIS: Examining Conc. Changes from System Time 0.03 due to tentative single step of 0.005:
Baseline: [48.34444129 92.28092028 11.03019715]
Deltas: [-0.04223653 -1.05330789 1.13778094]
Relative Deltas: [-0.00087366 -0.01141415 0.10315146]
Norms: {'norm_A': 0.2673096568217399}
Thresholds:
norm_A : low 0.25 | (VALUE 0.26731) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.005) results in norm values 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]
(STEP 8) ANALYSIS: Examining Conc. Changes from System Time 0.035 due to tentative single step of 0.005:
Baseline: [48.30220476 91.22761239 12.16797809]
Deltas: [ 0.00369708 -1.00337484 0.99598069]
Relative Deltas: [ 7.65405221e-05 -1.09985871e-02 8.18526039e-02]
Norms: {'norm_A': 0.22208358683873192}
Thresholds:
norm_A : (VALUE 0.22208) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.005) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.01) at the next round, because all norms are low
[The current step started at System Time: 0.035, and will continue to 0.04]
(STEP 9) ANALYSIS: Examining Conc. Changes from System Time 0.04 due to tentative single step of 0.01:
Baseline: [48.30590184 90.22423755 13.16395878]
Deltas: [ 0.08699867 -1.9168896 1.74289227]
Relative Deltas: [ 0.00180099 -0.02124584 0.13239879]
Norms: {'norm_A': 0.7466342181101149}
Thresholds:
norm_A : low 0.25 | high 0.64 | (VALUE 0.74663) | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: high (with step size factor of 0.5)
NOTICE: the tentative time step (0.01) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER, multiplied by 0.5 (set to 0.005) at the next round, because at least one norm is high
[The current step started at System Time: 0.04, and will continue to 0.05]
(STEP 10) ANALYSIS: Examining Conc. Changes from System Time 0.05 due to tentative single step of 0.005:
Baseline: [48.3929005 88.30734795 14.90685105]
Deltas: [ 0.11234504 -0.87740469 0.65271461]
Relative Deltas: [ 0.00232152 -0.00993581 0.04378622]
Norms: {'norm_A': 0.13427741784149083}
Thresholds:
norm_A : (VALUE 0.13428) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.005) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.01) at the next round, because all norms are low
[The current step started at System Time: 0.05, and will continue to 0.055]
(STEP 11) ANALYSIS: Examining Conc. Changes from System Time 0.055 due to tentative single step of 0.01:
Baseline: [48.50524554 87.42994326 15.55956566]
Deltas: [ 0.27466034 -1.68932436 1.14000367]
Relative Deltas: [ 0.00566249 -0.01932203 0.07326706]
Norms: {'norm_A': 0.4698737184351335}
Thresholds:
norm_A : low 0.25 | (VALUE 0.46987) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.01) results in norm values 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]
(STEP 12) ANALYSIS: Examining Conc. Changes from System Time 0.065 due to tentative single step of 0.01:
Baseline: [48.77990588 85.7406189 16.69956934]
Deltas: [ 0.36036743 -1.57024441 0.84950955]
Relative Deltas: [ 0.00738762 -0.01831389 0.05087015]
Norms: {'norm_A': 0.3685776282283221}
Thresholds:
norm_A : low 0.25 | (VALUE 0.36858) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.01) results in norm values 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]
(STEP 13) ANALYSIS: Examining Conc. Changes from System Time 0.075 due to tentative single step of 0.01:
Baseline: [49.14027331 84.17037449 17.54907888]
Deltas: [ 0.42112084 -1.4721665 0.62992481]
Relative Deltas: [ 0.00856977 -0.01749032 0.03589504]
Norms: {'norm_A': 0.3046024715786003}
Thresholds:
norm_A : low 0.25 | (VALUE 0.3046) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.01) results in norm values 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]
(STEP 14) ANALYSIS: Examining Conc. Changes from System Time 0.085 due to tentative single step of 0.01:
Baseline: [49.56139416 82.69820799 18.1790037 ]
Deltas: [ 0.46309241 -1.39020602 0.46402119]
Relative Deltas: [ 0.00934381 -0.01681059 0.02552512]
Norms: {'norm_A': 0.2624936691312418}
Thresholds:
norm_A : low 0.25 | (VALUE 0.26249) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.01) results in norm values 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]
(STEP 15) ANALYSIS: Examining Conc. Changes from System Time 0.095 due to tentative single step of 0.01:
Baseline: [50.02448657 81.30800197 18.64302489]
Deltas: [ 0.49095226 -1.32065857 0.33875405]
Relative Deltas: [ 0.00981424 -0.01624266 0.01817055]
Norms: {'norm_A': 0.23332527475445466}
Thresholds:
norm_A : (VALUE 0.23333) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.01) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.02) at the next round, because all norms are low
[The current step started at System Time: 0.095, and will continue to 0.105]
(STEP 16) ANALYSIS: Examining Conc. Changes from System Time 0.105 due to tentative single step of 0.02:
Baseline: [50.51543883 79.98734341 18.98177894]
Deltas: [ 1.01646708 -2.52142713 0.48849298]
Relative Deltas: [ 0.02012191 -0.03152283 0.02573484]
Norms: {'norm_A': 0.847713943482735}
Thresholds:
norm_A : low 0.25 | high 0.64 | (VALUE 0.84771) | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: high (with step size factor of 0.5)
NOTICE: the tentative time step (0.02) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER, multiplied by 0.5 (set to 0.01) at the next round, because at least one norm is high
[The current step started at System Time: 0.105, and will continue to 0.125]
(STEP 17) ANALYSIS: Examining Conc. Changes from System Time 0.125 due to tentative single step of 0.01:
Baseline: [51.5319059 77.46591628 19.47027191]
Deltas: [ 0.52698364 -1.15576117 0.1017939 ]
Relative Deltas: [ 0.01022636 -0.01491961 0.00522817]
Norms: {'norm_A': 0.18042862670354223}
Thresholds:
norm_A : (VALUE 0.18043) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.01) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.02) at the next round, because all norms are low
[The current step started at System Time: 0.125, and will continue to 0.135]
(STEP 18) ANALYSIS: Examining Conc. Changes from System Time 0.135 due to tentative single step of 0.02:
Baseline: [52.05888954 76.3101551 19.57206582]
Deltas: [ 1.04917495 -2.22996141 0.13161151]
Relative Deltas: [ 0.02015362 -0.02922234 0.00672446]
Norms: {'norm_A': 0.676757504987934}
Thresholds:
norm_A : low 0.25 | high 0.64 | (VALUE 0.67676) | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: high (with step size factor of 0.5)
NOTICE: the tentative time step (0.02) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER, multiplied by 0.5 (set to 0.01) at the next round, because at least one norm is high
[The current step started at System Time: 0.135, and will continue to 0.155]
(STEP 19) ANALYSIS: Examining Conc. Changes from System Time 0.155 due to tentative single step of 0.01:
Baseline: [53.10806449 74.08019369 19.70367733]
Deltas: [ 0.5141329 -1.04018517 0.01191938]
Relative Deltas: [ 0.00968088 -0.01404134 0.00060493]
Norms: {'norm_A': 0.149606655239135}
Thresholds:
norm_A : (VALUE 0.14961) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.01) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.02) at the next round, because all norms are low
[The current step started at System Time: 0.155, and will continue to 0.165]
(STEP 20) ANALYSIS: Examining Conc. Changes from System Time 0.165 due to tentative single step of 0.02:
Baseline: [53.62219739 73.04000852 19.71559671]
Deltas: [ 1.00960758 -2.01652891 -0.00268625]
Relative Deltas: [ 0.01882816 -0.02760855 -0.00013625]
Norms: {'norm_A': 0.5650781675774635}
Thresholds:
norm_A : low 0.25 | (VALUE 0.56508) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 21) ANALYSIS: Examining Conc. Changes from System Time 0.185 due to tentative single step of 0.02:
Baseline: [54.63180496 71.02347962 19.71291046]
Deltas: [ 0.96879347 -1.89585952 -0.04172743]
Relative Deltas: [ 0.01773314 -0.02669342 -0.00211676]
Norms: {'norm_A': 0.5038428113796767}
Thresholds:
norm_A : low 0.25 | (VALUE 0.50384) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 22) ANALYSIS: Examining Conc. Changes from System Time 0.205 due to tentative single step of 0.02:
Baseline: [55.60059844 69.12762009 19.67118303]
Deltas: [ 0.92336535 -1.78711524 -0.05961545]
Relative Deltas: [ 0.01660711 -0.02585241 -0.0030306 ]
Norms: {'norm_A': 0.4499931616991674}
Thresholds:
norm_A : low 0.25 | (VALUE 0.44999) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 23) ANALYSIS: Examining Conc. Changes from System Time 0.225 due to tentative single step of 0.02:
Baseline: [56.52396378 67.34050485 19.61156758]
Deltas: [ 0.87689226 -1.68704218 -0.06674234]
Relative Deltas: [ 0.01551364 -0.02505241 -0.00340321]
Norms: {'norm_A': 0.4021673223106198}
Thresholds:
norm_A : low 0.25 | (VALUE 0.40217) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 24) ANALYSIS: Examining Conc. Changes from System Time 0.245 due to tentative single step of 0.02:
Baseline: [57.40085605 65.65346267 19.54482524]
Deltas: [ 0.8311378 -1.59382873 -0.06844686]
Relative Deltas: [ 0.01447954 -0.02427638 -0.00350205]
Norms: {'norm_A': 0.3595294483481833}
Thresholds:
norm_A : low 0.25 | (VALUE 0.35953) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 25) ANALYSIS: Examining Conc. Changes from System Time 0.265 due to tentative single step of 0.02:
Baseline: [58.23199384 64.05963394 19.47637838]
Deltas: [ 0.78694079 -1.50641263 -0.06746894]
Relative Deltas: [ 0.01351389 -0.02351579 -0.00346414]
Norms: {'norm_A': 0.32145631944741265}
Thresholds:
norm_A : low 0.25 | (VALUE 0.32146) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 26) ANALYSIS: Examining Conc. Changes from System Time 0.285 due to tentative single step of 0.02:
Baseline: [59.01893463 62.55322131 19.40890943]
Deltas: [ 0.74466812 -1.42412415 -0.0652121 ]
Relative Deltas: [ 0.01261744 -0.0227666 -0.00335991]
Norms: {'norm_A': 0.2874347575511702}
Thresholds:
norm_A : low 0.25 | (VALUE 0.28743) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 27) ANALYSIS: Examining Conc. Changes from System Time 0.305 due to tentative single step of 0.02:
Baseline: [59.76360275 61.12909716 19.34369733]
Deltas: [ 0.70444746 -1.34650215 -0.06239278]
Relative Deltas: [ 0.01178723 -0.02202719 -0.00322548]
Norms: {'norm_A': 0.25702301402562294}
Thresholds:
norm_A : low 0.25 | (VALUE 0.25702) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.02) results in norm values 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]
(STEP 28) ANALYSIS: Examining Conc. Changes from System Time 0.325 due to tentative single step of 0.02:
Baseline: [60.46805022 59.78259501 19.28130456]
Deltas: [ 0.66628672 -1.27319915 -0.05937429]
Relative Deltas: [ 0.01101882 -0.02129715 -0.00307937]
Norms: {'norm_A': 0.22983326503644058}
Thresholds:
norm_A : (VALUE 0.22983) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.02) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.04) at the next round, because all norms are low
[The current step started at System Time: 0.325, and will continue to 0.345]
(STEP 29) ANALYSIS: Examining Conc. Changes from System Time 0.345 due to tentative single step of 0.04:
Baseline: [61.13433694 58.50939586 19.22193027]
Deltas: [ 1.26027073 -2.40786424 -0.11267722]
Relative Deltas: [ 0.02061478 -0.04115346 -0.00586191]
Norms: {'norm_A': 0.8220876292375117}
Thresholds:
norm_A : low 0.25 | high 0.64 | (VALUE 0.82209) | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: high (with step size factor of 0.5)
NOTICE: the tentative time step (0.04) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER, multiplied by 0.5 (set to 0.02) at the next round, because at least one norm is high
[The current step started at System Time: 0.345, and will continue to 0.385]
(STEP 30) ANALYSIS: Examining Conc. Changes from System Time 0.385 due to tentative single step of 0.02:
Baseline: [62.39460767 56.10153162 19.10925305]
Deltas: [ 0.56169618 -1.07298153 -0.05041083]
Relative Deltas: [ 0.00900232 -0.01912571 -0.00263803]
Norms: {'norm_A': 0.16325924649115092}
Thresholds:
norm_A : (VALUE 0.16326) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.02) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.04) at the next round, because all norms are low
[The current step started at System Time: 0.385, and will continue to 0.405]
(STEP 31) ANALYSIS: Examining Conc. Changes from System Time 0.405 due to tentative single step of 0.04:
Baseline: [62.95630385 55.02855009 19.05884222]
Deltas: [ 1.0623252 -2.02930388 -0.09534652]
Relative Deltas: [ 0.01687401 -0.03687729 -0.00500274]
Norms: {'norm_A': 0.5839666694455721}
Thresholds:
norm_A : low 0.25 | (VALUE 0.58397) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.04) results in norm values 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]
(STEP 32) ANALYSIS: Examining Conc. Changes from System Time 0.445 due to tentative single step of 0.04:
Baseline: [64.01862905 52.99924621 18.96349569]
Deltas: [ 0.9468283 -1.80867058 -0.08498602]
Relative Deltas: [ 0.01478989 -0.03412635 -0.00448156]
Norms: {'norm_A': 0.4638884123583411}
Thresholds:
norm_A : low 0.25 | (VALUE 0.46389) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.04) results in norm values 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]
(STEP 33) ANALYSIS: Examining Conc. Changes from System Time 0.485 due to tentative single step of 0.04:
Baseline: [64.96545735 51.19057563 18.87850968]
Deltas: [ 0.84388651 -1.61202675 -0.07574626]
Relative Deltas: [ 0.01298977 -0.03149069 -0.0040123 ]
Norms: {'norm_A': 0.36850135438022225}
Thresholds:
norm_A : low 0.25 | (VALUE 0.3685) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.04) results in norm values 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]
(STEP 34) ANALYSIS: Examining Conc. Changes from System Time 0.525 due to tentative single step of 0.04:
Baseline: [65.80934386 49.57854888 18.80276341]
Deltas: [ 0.75213678 -1.43676265 -0.06751092]
Relative Deltas: [ 0.01142903 -0.02897952 -0.00359048]
Norms: {'norm_A': 0.29272826302332505}
Thresholds:
norm_A : low 0.25 | (VALUE 0.29273) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.04) results in norm values 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]
(STEP 35) ANALYSIS: Examining Conc. Changes from System Time 0.565 due to tentative single step of 0.04:
Baseline: [66.56148064 48.14178623 18.73525249]
Deltas: [ 0.67036235 -1.28055375 -0.06017094]
Relative Deltas: [ 0.01007133 -0.02659963 -0.00321164]
Norms: {'norm_A': 0.23253601370675195}
Thresholds:
norm_A : (VALUE 0.23254) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.04) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.08) at the next round, because all norms are low
[The current step started at System Time: 0.565, and will continue to 0.605]
(STEP 36) ANALYSIS: Examining Conc. Changes from System Time 0.605 due to tentative single step of 0.08:
Baseline: [67.23184299 46.86123248 18.67508155]
Deltas: [ 1.19495731 -2.28265665 -0.10725798]
Relative Deltas: [ 0.01777368 -0.04871098 -0.00574337]
Norms: {'norm_A': 0.7388831828204337}
Thresholds:
norm_A : low 0.25 | high 0.64 | (VALUE 0.73888) | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: high (with step size factor of 0.5)
NOTICE: the tentative time step (0.08) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL SMALLER, multiplied by 0.5 (set to 0.04) at the next round, because at least one norm is high
[The current step started at System Time: 0.605, and will continue to 0.685]
(STEP 37) ANALYSIS: Examining Conc. Changes from System Time 0.685 due to tentative single step of 0.04:
Baseline: [68.4268003 44.57857583 18.56782357]
Deltas: [ 0.46755952 -0.89315144 -0.0419676 ]
Relative Deltas: [ 0.00683299 -0.02003544 -0.00226023]
Norms: {'norm_A': 0.11312140907262146}
Thresholds:
norm_A : (VALUE 0.11312) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.04) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.08) at the next round, because all norms are low
[The current step started at System Time: 0.685, and will continue to 0.725]
(STEP 38) ANALYSIS: Examining Conc. Changes from System Time 0.725 due to tentative single step of 0.08:
Baseline: [68.89435982 43.68542439 18.52585598]
Deltas: [ 0.83345025 -1.59209098 -0.07480952]
Relative Deltas: [ 0.01209751 -0.03644444 -0.00403811]
Norms: {'norm_A': 0.3594432769718806}
Thresholds:
norm_A : low 0.25 | (VALUE 0.35944) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.08) results in norm values 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]
(STEP 39) ANALYSIS: Examining Conc. Changes from System Time 0.805 due to tentative single step of 0.08:
Baseline: [69.72781007 42.0933334 18.45104645]
Deltas: [ 0.65222012 -1.24589772 -0.05854252]
Relative Deltas: [ 0.0093538 -0.02959846 -0.00317286]
Norms: {'norm_A': 0.2201199373223358}
Thresholds:
norm_A : (VALUE 0.22012) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.08) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.16) at the next round, because all norms are low
[The current step started at System Time: 0.805, and will continue to 0.885]
(STEP 40) ANALYSIS: Examining Conc. Changes from System Time 0.885 due to tentative single step of 0.16:
Baseline: [70.38003019 40.84743568 18.39250394]
Deltas: [ 1.02079538 -1.94996535 -0.0916254 ]
Relative Deltas: [ 0.01450405 -0.04773777 -0.00498167]
Norms: {'norm_A': 0.5391981423603522}
Thresholds:
norm_A : low 0.25 | (VALUE 0.5392) | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: stay (with step size factor of 1)
NOTICE: the tentative time step (0.16) results in norm values 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]
(STEP 41) ANALYSIS: Examining Conc. Changes from System Time 1.045 due to tentative single step of 0.16:
Baseline: [71.40082557 38.89747033 18.30087853]
Deltas: [ 0.57686034 -1.10194237 -0.05177831]
Relative Deltas: [ 0.00807918 -0.02832941 -0.00282928]
Norms: {'norm_A': 0.17219175887655633}
Thresholds:
norm_A : (VALUE 0.17219) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.16) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.32) at the next round, because all norms are low
[The current step started at System Time: 1.045, and will continue to 1.205]
(STEP 42) ANALYSIS: Examining Conc. Changes from System Time 1.205 due to tentative single step of 0.32:
Baseline: [71.97768591 37.79552796 18.24910022]
Deltas: [ 0.65197758 -1.24543442 -0.05852075]
Relative Deltas: [ 0.00905805 -0.0329519 -0.00320677]
Norms: {'norm_A': 0.21995626094117085}
Thresholds:
norm_A : (VALUE 0.21996) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.32) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 0.64) at the next round, because all norms are low
[The current step started at System Time: 1.205, and will continue to 1.525]
(STEP 43) ANALYSIS: Examining Conc. Changes from System Time 1.525 due to tentative single step of 0.64:
Baseline: [72.62966349 36.55009354 18.19057947]
Deltas: [ 0.16979763 -0.32435443 -0.01524084]
Relative Deltas: [ 0.00233786 -0.00887424 -0.00083784]
Norms: {'norm_A': 0.01491881249157113}
Thresholds:
norm_A : (VALUE 0.014919) | low 0.25 | high 0.64 | abort 1.44
Step Factors: {'upshift': 2.0, 'downshift': 0.5, 'abort': 0.5}
=> Action: low (with step size factor of 2.0)
NOTICE: the tentative time step (0.64) results in norm values that leads to the following:
ACTION: COMPLETE STEP NORMALLY and MAKE THE INTERVAL LARGER, multiplied by 2.0 (set to 1.28) at the next round, because all norms are low
[The current step started at System Time: 1.525, and will continue to 2.165]
44 total step(s) taken
In [7]:
dynamics.get_history()
Out[7]:
| 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 [8]:
(transition_times, step_sizes) = dynamics.explain_time_advance(return_times=True)
From time 0 to 0.005, in 1 step of 0.005 From time 0.005 to 0.0075, in 1 step of 0.0025 From time 0.0075 to 0.0125, in 1 step of 0.005 From time 0.0125 to 0.015, in 1 step of 0.0025 From time 0.015 to 0.04, in 5 steps of 0.005 From time 0.04 to 0.05, in 1 step of 0.01 From time 0.05 to 0.055, in 1 step of 0.005 From time 0.055 to 0.105, in 5 steps of 0.01 From time 0.105 to 0.125, in 1 step of 0.02 From time 0.125 to 0.135, in 1 step of 0.01 From time 0.135 to 0.155, in 1 step of 0.02 From time 0.155 to 0.165, in 1 step of 0.01 From time 0.165 to 0.345, in 9 steps of 0.02 From time 0.345 to 0.385, in 1 step of 0.04 From time 0.385 to 0.405, in 1 step of 0.02 From time 0.405 to 0.605, in 5 steps of 0.04 From time 0.605 to 0.685, in 1 step of 0.08 From time 0.685 to 0.725, in 1 step of 0.04 From time 0.725 to 0.885, in 2 steps of 0.08 From time 0.885 to 1.205, in 2 steps of 0.16 From time 1.205 to 1.525, in 1 step of 0.32 From time 1.525 to 2.165, in 1 step of 0.64 (44 steps total)
In [9]:
np.array(step_sizes)
Out[9]:
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 [10]:
np.array(transition_times) # Note: there will be one more transition time (the end time) than step sizes
Out[10]:
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 [11]:
dynamics.plot_curves(colors=['green', 'orange', 'blue'])
In [12]:
dynamics.curve_intersection("U", "X", t_start=0.3, t_end=0.35) # Compare with the value from experiment "variable_steps_2"
Min abs distance found at data row: 28
Out[12]:
(0.3183157284824908, 60.23261431038145)
In [13]:
dynamics.plot_curves(colors=['green', 'orange', 'blue'], show_intervals=True)
In [14]:
# 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 [15]:
dynamics.plot_step_sizes(show_intervals=True)
In [16]:
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[16]:
True
In [17]:
dynamics.get_diagnostic_rxn_data(rxn_index=0)
Reaction: 2 S <-> U
Out[17]:
| START_TIME | Delta U | Delta X | Delta S | time_step | caption | |
|---|---|---|---|---|---|---|
| 0 | 0.0000 | -1.000000 | 0.0 | 2.000000 | 0.0100 | aborted: excessive norm value(s) |
| 1 | 0.0000 | -0.500000 | 0.0 | 1.000000 | 0.0050 | |
| 2 | 0.0050 | -0.197500 | 0.0 | 0.395000 | 0.0025 | |
| 3 | 0.0075 | -0.349175 | 0.0 | 0.698350 | 0.0050 | |
| 4 | 0.0125 | -0.131693 | 0.0 | 0.263385 | 0.0025 | |
| 5 | 0.0150 | -0.225993 | 0.0 | 0.451987 | 0.0050 | |
| 6 | 0.0200 | -0.156040 | 0.0 | 0.312080 | 0.0050 | |
| 7 | 0.0250 | -0.095157 | 0.0 | 0.190315 | 0.0050 | |
| 8 | 0.0300 | -0.042237 | 0.0 | 0.084473 | 0.0050 | |
| 9 | 0.0350 | 0.003697 | 0.0 | -0.007394 | 0.0050 | |
| 10 | 0.0400 | 0.086999 | 0.0 | -0.173997 | 0.0100 | |
| 11 | 0.0500 | 0.112345 | 0.0 | -0.224690 | 0.0050 | |
| 12 | 0.0550 | 0.274660 | 0.0 | -0.549321 | 0.0100 | |
| 13 | 0.0650 | 0.360367 | 0.0 | -0.720735 | 0.0100 | |
| 14 | 0.0750 | 0.421121 | 0.0 | -0.842242 | 0.0100 | |
| 15 | 0.0850 | 0.463092 | 0.0 | -0.926185 | 0.0100 | |
| 16 | 0.0950 | 0.490952 | 0.0 | -0.981905 | 0.0100 | |
| 17 | 0.1050 | 1.016467 | 0.0 | -2.032934 | 0.0200 | |
| 18 | 0.1250 | 0.526984 | 0.0 | -1.053967 | 0.0100 | |
| 19 | 0.1350 | 1.049175 | 0.0 | -2.098350 | 0.0200 | |
| 20 | 0.1550 | 0.514133 | 0.0 | -1.028266 | 0.0100 | |
| 21 | 0.1650 | 1.009608 | 0.0 | -2.019215 | 0.0200 | |
| 22 | 0.1850 | 0.968793 | 0.0 | -1.937587 | 0.0200 | |
| 23 | 0.2050 | 0.923365 | 0.0 | -1.846731 | 0.0200 | |
| 24 | 0.2250 | 0.876892 | 0.0 | -1.753785 | 0.0200 | |
| 25 | 0.2450 | 0.831138 | 0.0 | -1.662276 | 0.0200 | |
| 26 | 0.2650 | 0.786941 | 0.0 | -1.573882 | 0.0200 | |
| 27 | 0.2850 | 0.744668 | 0.0 | -1.489336 | 0.0200 | |
| 28 | 0.3050 | 0.704447 | 0.0 | -1.408895 | 0.0200 | |
| 29 | 0.3250 | 0.666287 | 0.0 | -1.332573 | 0.0200 | |
| 30 | 0.3450 | 1.260271 | 0.0 | -2.520541 | 0.0400 | |
| 31 | 0.3850 | 0.561696 | 0.0 | -1.123392 | 0.0200 | |
| 32 | 0.4050 | 1.062325 | 0.0 | -2.124650 | 0.0400 | |
| 33 | 0.4450 | 0.946828 | 0.0 | -1.893657 | 0.0400 | |
| 34 | 0.4850 | 0.843887 | 0.0 | -1.687773 | 0.0400 | |
| 35 | 0.5250 | 0.752137 | 0.0 | -1.504274 | 0.0400 | |
| 36 | 0.5650 | 0.670362 | 0.0 | -1.340725 | 0.0400 | |
| 37 | 0.6050 | 1.194957 | 0.0 | -2.389915 | 0.0800 | |
| 38 | 0.6850 | 0.467560 | 0.0 | -0.935119 | 0.0400 | |
| 39 | 0.7250 | 0.833450 | 0.0 | -1.666901 | 0.0800 | |
| 40 | 0.8050 | 0.652220 | 0.0 | -1.304440 | 0.0800 | |
| 41 | 0.8850 | 1.020795 | 0.0 | -2.041591 | 0.1600 | |
| 42 | 1.0450 | 0.576860 | 0.0 | -1.153721 | 0.1600 | |
| 43 | 1.2050 | 0.651978 | 0.0 | -1.303955 | 0.3200 | |
| 44 | 1.5250 | 0.169798 | 0.0 | -0.339595 | 0.6400 |
In [18]:
dynamics.get_diagnostic_rxn_data(rxn_index=1)
Reaction: S <-> X
Out[18]:
| START_TIME | Delta U | Delta X | Delta S | time_step | caption | |
|---|---|---|---|---|---|---|
| 0 | 0.0000 | 0.0 | -3.000000 | 3.000000 | 0.0100 | aborted: excessive norm value(s) |
| 1 | 0.0000 | 0.0 | -1.500000 | 1.500000 | 0.0050 | |
| 2 | 0.0050 | 0.0 | -0.701250 | 0.701250 | 0.0025 | |
| 3 | 0.0075 | 0.0 | -1.359094 | 1.359094 | 0.0050 | |
| 4 | 0.0125 | 0.0 | -0.638492 | 0.638492 | 0.0025 | |
| 5 | 0.0150 | 0.0 | -1.240350 | 1.240350 | 0.0050 | |
| 6 | 0.0200 | 0.0 | -1.170975 | 1.170975 | 0.0050 | |
| 7 | 0.0250 | 0.0 | -1.108919 | 1.108919 | 0.0050 | |
| 8 | 0.0300 | 0.0 | -1.053308 | 1.053308 | 0.0050 | |
| 9 | 0.0350 | 0.0 | -1.003375 | 1.003375 | 0.0050 | |
| 10 | 0.0400 | 0.0 | -1.916890 | 1.916890 | 0.0100 | |
| 11 | 0.0500 | 0.0 | -0.877405 | 0.877405 | 0.0050 | |
| 12 | 0.0550 | 0.0 | -1.689324 | 1.689324 | 0.0100 | |
| 13 | 0.0650 | 0.0 | -1.570244 | 1.570244 | 0.0100 | |
| 14 | 0.0750 | 0.0 | -1.472167 | 1.472167 | 0.0100 | |
| 15 | 0.0850 | 0.0 | -1.390206 | 1.390206 | 0.0100 | |
| 16 | 0.0950 | 0.0 | -1.320659 | 1.320659 | 0.0100 | |
| 17 | 0.1050 | 0.0 | -2.521427 | 2.521427 | 0.0200 | |
| 18 | 0.1250 | 0.0 | -1.155761 | 1.155761 | 0.0100 | |
| 19 | 0.1350 | 0.0 | -2.229961 | 2.229961 | 0.0200 | |
| 20 | 0.1550 | 0.0 | -1.040185 | 1.040185 | 0.0100 | |
| 21 | 0.1650 | 0.0 | -2.016529 | 2.016529 | 0.0200 | |
| 22 | 0.1850 | 0.0 | -1.895860 | 1.895860 | 0.0200 | |
| 23 | 0.2050 | 0.0 | -1.787115 | 1.787115 | 0.0200 | |
| 24 | 0.2250 | 0.0 | -1.687042 | 1.687042 | 0.0200 | |
| 25 | 0.2450 | 0.0 | -1.593829 | 1.593829 | 0.0200 | |
| 26 | 0.2650 | 0.0 | -1.506413 | 1.506413 | 0.0200 | |
| 27 | 0.2850 | 0.0 | -1.424124 | 1.424124 | 0.0200 | |
| 28 | 0.3050 | 0.0 | -1.346502 | 1.346502 | 0.0200 | |
| 29 | 0.3250 | 0.0 | -1.273199 | 1.273199 | 0.0200 | |
| 30 | 0.3450 | 0.0 | -2.407864 | 2.407864 | 0.0400 | |
| 31 | 0.3850 | 0.0 | -1.072982 | 1.072982 | 0.0200 | |
| 32 | 0.4050 | 0.0 | -2.029304 | 2.029304 | 0.0400 | |
| 33 | 0.4450 | 0.0 | -1.808671 | 1.808671 | 0.0400 | |
| 34 | 0.4850 | 0.0 | -1.612027 | 1.612027 | 0.0400 | |
| 35 | 0.5250 | 0.0 | -1.436763 | 1.436763 | 0.0400 | |
| 36 | 0.5650 | 0.0 | -1.280554 | 1.280554 | 0.0400 | |
| 37 | 0.6050 | 0.0 | -2.282657 | 2.282657 | 0.0800 | |
| 38 | 0.6850 | 0.0 | -0.893151 | 0.893151 | 0.0400 | |
| 39 | 0.7250 | 0.0 | -1.592091 | 1.592091 | 0.0800 | |
| 40 | 0.8050 | 0.0 | -1.245898 | 1.245898 | 0.0800 | |
| 41 | 0.8850 | 0.0 | -1.949965 | 1.949965 | 0.1600 | |
| 42 | 1.0450 | 0.0 | -1.101942 | 1.101942 | 0.1600 | |
| 43 | 1.2050 | 0.0 | -1.245434 | 1.245434 | 0.3200 | |
| 44 | 1.5250 | 0.0 | -0.324354 | 0.324354 | 0.6400 |
In [19]:
dynamics.get_diagnostic_conc_data()
Out[19]:
| TIME | U | X | S | caption | |
|---|---|---|---|---|---|
| 0 | 0.0000 | 50.000000 | 100.000000 | 0.000000 | |
| 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 [20]:
dynamics.get_diagnostic_decisions_data()
Out[20]:
| START_TIME | Delta U | Delta X | Delta S | norm_A | norm_B | action | step_factor | time_step | caption | |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.0000 | -1.000000 | -3.000000 | 5.000000 | 3.888889 | None | ABORT | 0.5 | 0.0100 | excessive norm value(s) |
| 1 | 0.0000 | -0.500000 | -1.500000 | 2.500000 | 0.972222 | None | OK (high) | 0.5 | 0.0050 | |
| 2 | 0.0050 | -0.197500 | -0.701250 | 1.096250 | 0.192502 | None | OK (low) | 2.0 | 0.0025 | |
| 3 | 0.0075 | -0.349175 | -1.359094 | 2.057444 | 0.689126 | None | OK (high) | 0.5 | 0.0050 | |
| 4 | 0.0125 | -0.131693 | -0.638492 | 0.901878 | 0.137600 | None | OK (low) | 2.0 | 0.0025 | |
| 5 | 0.0150 | -0.225993 | -1.240350 | 1.692337 | 0.494839 | None | OK (stay) | 1.0 | 0.0050 | |
| 6 | 0.0200 | -0.156040 | -1.170975 | 1.483055 | 0.399443 | None | OK (stay) | 1.0 | 0.0050 | |
| 7 | 0.0250 | -0.095157 | -1.108919 | 1.299234 | 0.325196 | None | OK (stay) | 1.0 | 0.0050 | |
| 8 | 0.0300 | -0.042237 | -1.053308 | 1.137781 | 0.267310 | None | OK (stay) | 1.0 | 0.0050 | |
| 9 | 0.0350 | 0.003697 | -1.003375 | 0.995981 | 0.222084 | None | OK (low) | 2.0 | 0.0050 | |
| 10 | 0.0400 | 0.086999 | -1.916890 | 1.742892 | 0.746634 | None | OK (high) | 0.5 | 0.0100 | |
| 11 | 0.0500 | 0.112345 | -0.877405 | 0.652715 | 0.134277 | None | OK (low) | 2.0 | 0.0050 | |
| 12 | 0.0550 | 0.274660 | -1.689324 | 1.140004 | 0.469874 | None | OK (stay) | 1.0 | 0.0100 | |
| 13 | 0.0650 | 0.360367 | -1.570244 | 0.849510 | 0.368578 | None | OK (stay) | 1.0 | 0.0100 | |
| 14 | 0.0750 | 0.421121 | -1.472167 | 0.629925 | 0.304602 | None | OK (stay) | 1.0 | 0.0100 | |
| 15 | 0.0850 | 0.463092 | -1.390206 | 0.464021 | 0.262494 | None | OK (stay) | 1.0 | 0.0100 | |
| 16 | 0.0950 | 0.490952 | -1.320659 | 0.338754 | 0.233325 | None | OK (low) | 2.0 | 0.0100 | |
| 17 | 0.1050 | 1.016467 | -2.521427 | 0.488493 | 0.847714 | None | OK (high) | 0.5 | 0.0200 | |
| 18 | 0.1250 | 0.526984 | -1.155761 | 0.101794 | 0.180429 | None | OK (low) | 2.0 | 0.0100 | |
| 19 | 0.1350 | 1.049175 | -2.229961 | 0.131612 | 0.676758 | None | OK (high) | 0.5 | 0.0200 | |
| 20 | 0.1550 | 0.514133 | -1.040185 | 0.011919 | 0.149607 | None | OK (low) | 2.0 | 0.0100 | |
| 21 | 0.1650 | 1.009608 | -2.016529 | -0.002686 | 0.565078 | None | OK (stay) | 1.0 | 0.0200 | |
| 22 | 0.1850 | 0.968793 | -1.895860 | -0.041727 | 0.503843 | None | OK (stay) | 1.0 | 0.0200 | |
| 23 | 0.2050 | 0.923365 | -1.787115 | -0.059615 | 0.449993 | None | OK (stay) | 1.0 | 0.0200 | |
| 24 | 0.2250 | 0.876892 | -1.687042 | -0.066742 | 0.402167 | None | OK (stay) | 1.0 | 0.0200 | |
| 25 | 0.2450 | 0.831138 | -1.593829 | -0.068447 | 0.359529 | None | OK (stay) | 1.0 | 0.0200 | |
| 26 | 0.2650 | 0.786941 | -1.506413 | -0.067469 | 0.321456 | None | OK (stay) | 1.0 | 0.0200 | |
| 27 | 0.2850 | 0.744668 | -1.424124 | -0.065212 | 0.287435 | None | OK (stay) | 1.0 | 0.0200 | |
| 28 | 0.3050 | 0.704447 | -1.346502 | -0.062393 | 0.257023 | None | OK (stay) | 1.0 | 0.0200 | |
| 29 | 0.3250 | 0.666287 | -1.273199 | -0.059374 | 0.229833 | None | OK (low) | 2.0 | 0.0200 | |
| 30 | 0.3450 | 1.260271 | -2.407864 | -0.112677 | 0.822088 | None | OK (high) | 0.5 | 0.0400 | |
| 31 | 0.3850 | 0.561696 | -1.072982 | -0.050411 | 0.163259 | None | OK (low) | 2.0 | 0.0200 | |
| 32 | 0.4050 | 1.062325 | -2.029304 | -0.095347 | 0.583967 | None | OK (stay) | 1.0 | 0.0400 | |
| 33 | 0.4450 | 0.946828 | -1.808671 | -0.084986 | 0.463888 | None | OK (stay) | 1.0 | 0.0400 | |
| 34 | 0.4850 | 0.843887 | -1.612027 | -0.075746 | 0.368501 | None | OK (stay) | 1.0 | 0.0400 | |
| 35 | 0.5250 | 0.752137 | -1.436763 | -0.067511 | 0.292728 | None | OK (stay) | 1.0 | 0.0400 | |
| 36 | 0.5650 | 0.670362 | -1.280554 | -0.060171 | 0.232536 | None | OK (low) | 2.0 | 0.0400 | |
| 37 | 0.6050 | 1.194957 | -2.282657 | -0.107258 | 0.738883 | None | OK (high) | 0.5 | 0.0800 | |
| 38 | 0.6850 | 0.467560 | -0.893151 | -0.041968 | 0.113121 | None | OK (low) | 2.0 | 0.0400 | |
| 39 | 0.7250 | 0.833450 | -1.592091 | -0.074810 | 0.359443 | None | OK (stay) | 1.0 | 0.0800 | |
| 40 | 0.8050 | 0.652220 | -1.245898 | -0.058543 | 0.220120 | None | OK (low) | 2.0 | 0.0800 | |
| 41 | 0.8850 | 1.020795 | -1.949965 | -0.091625 | 0.539198 | None | OK (stay) | 1.0 | 0.1600 | |
| 42 | 1.0450 | 0.576860 | -1.101942 | -0.051778 | 0.172192 | None | OK (low) | 2.0 | 0.1600 | |
| 43 | 1.2050 | 0.651978 | -1.245434 | -0.058521 | 0.219956 | None | OK (low) | 2.0 | 0.3200 | |
| 44 | 1.5250 | 0.169798 | -0.324354 | -0.015241 | 0.014919 | None | OK (low) | 2.0 | 0.6400 |
Notice how the first step got aborted, and re-run, because of the large value of norm_A¶
In [ ]:
In [21]:
dynamics.get_diagnostic_decisions_data_ALT() # TODO: OBSOLETE!
Out[21]:
| START_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 [ ]: