atropy¶

Submodules¶

atropy.src

Classes¶

`Model`	Represent model for reaction system.
`Partitioning`	Generate partitioning for the reaction system.

Functions¶

`species`(symbol_string)	Generate sympy variables for species.
`run`(partitioning, output, tau, tfinal[, snapshot, ...])	Run the low rank simulation.

Package Contents¶

atropy.species(symbol_string: str)¶

Generate sympy variables for species.

The species of a rection network can be defined as sympy variables, which is needed for model generation. The type of output is dependent on the properties of input arguments.

Parameters¶

symbol_stringstr: Names of species inside a string, seperated by a comma.

Examples¶

>>> from atropy import species
>>> S0, S1, S2, S3, S4 = species("S0, S1, S2, S3, S4")

class atropy.Model(_species)¶

Represent model for reaction system.

For a reaction system we can set up the model. Before initialization, the species need to be defined using atropy.species.

Parameters¶

_speciestuple: Species from atropy.species.

Returns¶

Model: Model for the reaction system.

Examples¶

>>> from atropy import Model
>>> model = Model((S0, S1, S2, S3, S4))

reactions = []¶

species¶

add_reaction(reactants, products, propensities)¶

Add single reaction to Model.

For translating a single chemical reaction to implementation.

Parameters¶

reactants: Sympy equation of reactants.
products: Sympy equation of products.
propensitiesdict, float or int: Propensity for specific reaction. Type of float or int can only be used if propensity described by mass action.

Examples¶

>>> from atropy import Model
>>> model = Model((S0, S1, S2, S3, S4))

Adding a reaction using a dictionary for propensity:

>>> model.add_reaction(0, S1, {S0: 0.6 / (0.6 + S0), S4: 1.0 + S4})

Adding a reaction using a float value for propensity:

>>> model.add_reaction(S0, 0, 0.0025)

add_reactions(reactants_list, products_list, propensities_list)¶

Add multiple reactions to Model.

For translating multiple chemical reactions to implementation.

Parameters¶

reactants_listlist: List of Sympy equations of reactants.
products_listlist: List of Sympy equations of products.
propensities_listlist of dict, list of float or list of int: List of propensities for specific reactions. Type of list of float or list of int can only be used if propensities described by mass action.

Examples¶

>>> from atropy import Model
>>> model = Model((S0, S1, S2, S3, S4))
>>> model.add_reactions([S0, S1], [0, 0], [0.0025, 0.0007])

generate_reaction_system()¶

Generate the reaction system.

After the Model was initialized and the reactions were added using atropy.Model.add_reaction, the reaction system can be generated.

Examples¶

>>> from atropy import Model
>>> model = Model((S0, S1, S2, S3, S4))
>>> model.add_reaction(S0, 0, 0.0025)
>>> model.generate_reaction_system()

class atropy.Partitioning(_partition: str, _r: numpy.ndarray, _model: Model)¶

Generate partitioning for the reaction system.

To reduce computational complexity of the low rank solver a good partition is needed. Note that cuts should be chosen in a way that tightly coupled species are together in the same partition.

Parameters¶

_partitionstr: Partitioning of the species. Each partition is inside a set of brackets.
_rnumpy.ndarray: Ranks for each level of the partitioning.
_modelatropy.Model: Model for the reaction system.

Examples¶

>>> from atropy import Model, Partitioning

Set up the parameters (for model reactions can be added using atropy.Model.add_reaction):

>>> model = Model((S0, S1, S2, S3, S4))
>>> r = np.array([5, 4])
>>> p0 = "(S0 S1)((S2 S3)(S4))"

Initialize the partitioning:

>>> partitioning = Partitioning(p0, r, model)

r¶

model¶

partition¶

add_grid_params(n: numpy.ndarray, binsize: numpy.ndarray, liml: numpy.ndarray)¶

Add grid parameters to Partitioning.

Parameters¶

nnumpy.ndarray: Amount of gridpoints for each species.

binsize : numpy.ndarray

limlnumpy.ndarray: Lower limits of the population numbers.

Examples¶

>>> from atropy import Partitioning
>>> partitioning = Partitioning(p0, r, model)

Define parameters and add grid parameters:

>>> n = np.array([16, 41, 11, 11, 11])
>>> d = n.size
>>> binsize = np.ones(d, dtype=int)
>>> liml = np.zeros(d)
>>> partitioning.add_grid_params(n, binsize, liml)

generate_tree()¶

Generate tree structure for reaction system.

The tree should be generated after setting up the Model and adding the grid parameters to the Partitioning.

Examples¶

>>> from atropy import Partitioning
>>> partitioning = Partitioning(p0, r, model)
>>> partitioning.add_grid_params(n, binsize, liml)

Generate the tree structure:

>>> partitioning.generate_tree()

generate_initial_condition(n_basisfunctions: numpy.ndarray)¶

Initialize the initial condition.

Parameters¶

n_basisfunctionsnumpy.ndarray: Number of basis functions.

Examples¶

>>> from atropy import Partitioning
>>> partitioning = Partitioning(p0, r, model)
>>> partitioning.add_grid_params(n, binsize, liml)
>>> partitioning.generate_tree()

Initialize the initial condition:

>>> partitioning.generate_initial_condition(r)

set_initial_condition(polynomials_dict)¶

Set values for inital condition.

Only possible for rank 1 inital condition, which can be split into a product of functions, each depending only on one species

Parameters¶

polynomials_dictdict: Dictionary containing a function for each species.

Examples¶

>>> from atropy import Partitioning
>>> partitioning = Partitioning(p0, r, model)
>>> partitioning.add_grid_params(n, binsize, liml)
>>> partitioning.generate_tree()
>>> partitioning.generate_initial_condition(n_basisfunctions)

Assign a function to each species:

>>> polynomials_dict = {
...     S0: sp.exp(-S0**2),
...     S1: sp.exp(-S1**2),
...     S2: sp.exp(-S2**2),
...     S3: sp.exp(-S3**2),
...     S4: sp.exp(-S4**2),
... }

Set values for the initial condition:

>>> partitioning.set_initial_condition(polynomials_dict)

atropy.run(partitioning: Partitioning, output: str, tau: float, tfinal: float | int, snapshot: int = 2, substeps: int = 1, method: str = 'RK4')¶

Run the low rank simulation.

Generate multiple NetCDF output files, which simulate the reaction system described in partitioning.

Parameters¶

partitioningPartitioning: Partitioning of the reaction system.
outputstr: Name of the generated output files.
taufloat: Timestep size for the simulation.
tfinal: float or int: Final time for the simulation.
snapshotint, default 2: Number of generated output files.

substeps : int, default 1

methodstr, default “RK4”: Time integration method for the simulation. The 4 possible values are: “implicit_Euler”, “explicit_Euler”, “Crank_Nicolson” and “RK4”.

Examples¶

After setting up Model and Partitioning one can run the simulation:

>>> run(partitioning, "output", 1e-3, 10, snapshot=10, method="implicit_Euler")

atropy¶

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