pg_utils.pg_model.expansion.SystemEquations

class pg_utils.pg_model.expansion.SystemEquations(names: List[str], expansion_recipe: ExpansionRecipe, **fields)

Bases: LabeledCollection

The top-level class for system of equations to be solved The equations are always assumed to be written in the first-order form in time, i.e. LHS = d()/dt

Variables:

expansion_recipe (ExpansionRecipe) – expansion recipe used for the eq

__init__(names: List[str], expansion_recipe: ExpansionRecipe, **fields) → None

Initialization

Methods

__init__(names, expansion_recipe, **fields)	Initialization
apply(fun[, inplace, metadata])	Apply a function iteratively to all collection items
as_empty()	Overriding base.LabeledCollection.as_empty
collect_matrices([factor_lhs, factor_rhs])	Collect the coefficient matrices of the equations
copy()	Overriding base.LabeledCollection.copy
deserialize(obj[, parser])	Deserialize an object
generate_collection(index_array)	Generate a new collection based on indices
load_json(fp[, parser])	Load LabeledCollection object from json
save_json(fp[, serializer])	Serialize the object in string format and save to json file
serialize([serializer])	Serialize the object
subs(sub_map[, inplace])	Substitute variables iteratively in all fields.
to_fourier_domain([inplace])	Convert expression into Fourier domain
to_inner_product([factor_lhs, factor_rhs, ...])	Collect the radial equations to inner product form
to_radial([inplace])	Introduce radial expansion to the equations.

Attributes

iter_filter	iter_filter: bool determines whether None fields are skipped.
iter_name	iter_name: bool determines whether the string of the field is also returned.

apply(fun: Callable[[...], Any], inplace: bool = False, metadata: bool = False) → LabeledCollection

Apply a function iteratively to all collection items

Parameters:

• fun (Callable) – determines how the collection entries are processed. The signature of the function should take the form fun(type(self[i])) when metadata is False, and the form fun(str, type(self[i])) when metadata is True

• inplace (bool) – whether to write changes in situ.

• metadata (bool) – whether to pass field name to the function

Returns:

Updated object. If inplace, then the current object itself is returned.

Return type:

LabeledCollection

as_empty()

Overriding base.LabeledCollection.as_empty

collect_matrices(factor_lhs: Expr = 1, factor_rhs: Expr = 1) → List[SystemMatrix]

Collect the coefficient matrices of the equations

Parameters:

• factor_lhs (sympy.Expr) – sympy.Expr, allows the user to choose which factor should be moved out of the inner product on LHS

• factor_rhs – ditto, but for RHS

copy()

Overriding base.LabeledCollection.copy

static deserialize(obj: ~typing.List[tuple], parser: ~typing.Callable[[str], ~typing.Any] = <function LabeledCollection.<lambda>>) → LabeledCollection

Deserialize an object

Parameters:

• obj (List[tuple]) – a serialized object of LabeledCollection

• parser (Callable[[str], Any]) – a parser that defines how each string can be parsed into meaningful objects

Returns:

LabeledCollection, that is deserialized from the input object

Warning

Sanitized input needed. Unexpected behaviour if input is not a legitimate serialized object

generate_collection(index_array: List[bool]) → LabeledCollection

Generate a new collection based on indices

Parameters:

index_array (List[bool]) – array of booleans indicating whether a field is to be included in the new collection

Returns:

new collection with elements specified by index_array

property iter_filter

iter_filter: bool determines whether None fields are skipped.

property iter_name

iter_name: bool determines whether the string of the field is also returned.

static load_json(fp: ~typing.TextIO, parser: ~typing.Callable[[str], ~typing.Any] = <function LabeledCollection.<lambda>>) → LabeledCollection

Load LabeledCollection object from json

convenient wrapper for deserialize

save_json(fp: ~typing.TextIO, serializer: ~typing.Callable[[~typing.Any], str] = <class 'str'>) → None

Serialize the object in string format and save to json file

Parameters:

• fp (TextIO) – file handle of the output file

• serializer (Callable[[Any], str]) – a callable that maps an element to a string. Default is the str method.

serialize(serializer: ~typing.Callable[[~typing.Any], str] = <class 'str'>) → List[tuple]

Serialize the object

Parameters:

serializer (Callable[[Any],str]) – a callable that maps an element to a string. Default is the str method.

Returns:

a list of serialized objects, in the format [(fname_1, serialized_element_1), (fname_2, serialized_element_2), …]

subs(sub_map: dict, inplace: bool = False)

Substitute variables iteratively in all fields. This utility is for collections with sympy.Expr elements. See warning below.

Parameters:

• sub_map (dict) – a substitution map

• inplace (bool) – whether the change is made in place; default is False

Warning

To use this method, all elements in the collection need to have implemented the subs method. This is intended for a collection of which all elements are sympy.Expr type. Then, this method calls apply internally to substitute all the variables.

to_fourier_domain(inplace: bool = False) → SystemEquations

Convert expression into Fourier domain

Uses the bases and coefficients defined in recipe.fourier_ansatz

Parameters:

inplace (bool) – whether the operation is made in situ

to_inner_product(factor_lhs: Expr = 1, factor_rhs: Expr = 1, inplace: bool = False) → SystemEquations

Collect the radial equations to inner product form

Parameters:

• factor_lhs (sympy.Expr) – allows the user to choose which factor should be moved out of the inner product on LHS

• factor_rhs – ditto, but for RHS

• inplace (bool) – whether the operation is made in situ

Warning

Functions/fields that are not expanded with an coefficient (elements from recipe.rad_xpd.coeffs) will no longer be collected properly and may be lost in linear system formation!

to_radial(inplace: bool = False) → SystemEquations

Introduce radial expansion to the equations.

Parameters:

inplace (bool) – whether the operation is made in situ