cosapp.core.numerics.basics

Classes

MathematicalProblem(name, context)

Container object for unknowns and equations.

SolverResults()

Storage class for solver solution

WeakDeferredResidue(deferred, weak)

class cosapp.core.numerics.basics.MathematicalProblem(name: str, context: Optional[cosapp.systems.System])[source]

Bases: object

Container object for unknowns and equations.

Parameters

  • name (str) – Name of the mathematical problem

  • context (cosapp.systems.System) – Context in which the mathematical problem will be evaluated.

activate_targets() → None[source]

Activate deferred residues (targets) and incorporate them in the mathematical problem residue list. Warning: This operation is irreversible, as targets are purged.

add_equation(equation: Union[str, Iterable[Union[dict, str, Tuple[str, str]]]], name: Optional[str] = None, reference: Union[numbers.Number, numpy.ndarray, str] = 1) → cosapp.core.numerics.basics.MathematicalProblem[source]

Add residue equation.

You can add residue equation one by one or provide a list of dictionary to add multiple equation at once. The dictionary key are the arguments of this method.

Parameters

  • equation (str or Iterable of str of the kind 'lhs == rhs') – Equation or list of equations to add

  • name (str, optional) – Name of the equation; default None => ‘lhs == rhs’

  • reference (Number, numpy.ndarray or "norm", optional) – Reference value(s) used to normalize the equation; default is 1. If value is “norm”, actual reference value is estimated from order of magnitude.

Returns

The modified MathematicalSystem

Return type

MathematicalProblem

add_rate(name: str, source: Any, initial_value: Optional[Any] = None) → cosapp.core.numerics.basics.MathematicalProblem[source]

Add a time derivative.

Parameters

  • name (str) – Name of the new time-dependent (transient) variable

  • source (Any) – Name of the variable or evaluable expression whose time derivative will be computed

Returns

The modified MathematicalSystem

Return type

MathematicalProblem

add_target(expression: Union[str, Iterable[str]], reference: Union[numbers.Number, numpy.ndarray, str] = 1, weak=False) → cosapp.core.numerics.basics.MathematicalProblem[source]

Add deferred equation.

Parameters

  • expression (str) – Targetted expression

  • reference (Number, numpy.ndarray or "norm", optional) – Reference value(s) used to normalize the (deferred) equation; default is 1. If value is “norm”, actual reference value is estimated from order of magnitude.

  • weak (bool, optional) – If True, the target is disregarded if the corresponding variable is connected; default is False.

Returns

The modified MathematicalSystem

Return type

MathematicalProblem

add_transient(name: str, der: Any, max_time_step: Union[numbers.Number, str] = inf, max_abs_step: Union[numbers.Number, str] = inf, pulled_from: Optional[cosapp.core.variableref.VariableReference] = None) → cosapp.core.numerics.basics.MathematicalProblem[source]

Add a time-dependent unknown.

Parameters

  • name (str) – Name of the new time-dependent (transient) variable

  • der (Any) – Name of the variable or evaluable expression defining the time derivative of transient variable

  • max_time_step (Number or evaluable expression (str), optional) – Maximal time step for the time integration of the transient variable; numpy.inf by default.

  • max_abs_step (Number or evaluable expression compatible with transient variable, optional) – Maximum variable step admissible over one time step; numpy.inf by default.

  • pulled_from (VariableReference, optional) – Original time unknown before pulling; None by default.

Returns

The modified MathematicalSystem

Return type

MathematicalProblem

add_unknown(name: Union[str, Iterable[Union[dict, str, cosapp.core.numerics.boundary.Unknown]]], max_abs_step: numbers.Number = inf, max_rel_step: numbers.Number = inf, lower_bound: numbers.Number = - inf, upper_bound: numbers.Number = inf, mask: Optional[numpy.ndarray] = None) → cosapp.core.numerics.basics.MathematicalProblem[source]

Add unknown variables.

You can set variable one by one or provide a list of dictionary to set multiple variable at once. The dictionary key are the arguments of this method.

Parameters

  • name (str or Iterable of dictionary or str) – Name of the variable or list of variable to add

  • max_rel_step (float, optional) – Maximal relative step by which the variable can be modified by the numerical solver; default numpy.inf

  • max_abs_step (float, optional) – Maximal absolute step by which the variable can be modified by the numerical solver; default numpy.inf

  • lower_bound (float, optional) – Lower bound on which the solver solution is saturated; default -numpy.inf

  • upper_bound (float, optional) – Upper bound on which the solver solution is saturated; default numpy.inf

  • mask (numpy.ndarray or None) – Mask of unknown values in the vector variable

Returns

The modified MathematicalSystem

Return type

MathematicalProblem

clear() → None[source]

Clear all mathematical elements in this problem.

property context

Context in which the mathematical system is evaluated.

Type

cosapp.systems.System or None

copy(activate_targets=False) → cosapp.core.numerics.basics.MathematicalProblem[source]

Copy the MathematicalSystem object.

Returns

The duplicated mathematical problem.

Return type

MathematicalProblem

property deferred_residues

Dict of deferred residues defined for this system.

Type

Dict[str, WeakDeferredResidue]

extend(other: cosapp.core.numerics.basics.MathematicalProblem, copy=True, unknowns=True, equations=True, overwrite=False, unknown_wrapper: Optional[Callable[[str], str]] = None, residue_wrapper: Optional[Callable[[str], str]] = None) → cosapp.core.numerics.basics.MathematicalProblem[source]

Extend the current mathematical system with the other one.

Parameters

  • other [MathematicalProblem] (-) – The other mathematical system to add

  • copy [bool (-) – Should the objects be copied; default is True.

  • optional] – Should the objects be copied; default is True.

  • unknowns [bool (-) – If False, unknowns are discarded; default is True.

  • optional] – If False, unknowns are discarded; default is True.

  • equations [bool (-) – If False, equations are discarded; default is True.

  • optional] – If False, equations are discarded; default is True.

  • overwrite [bool (-) – If False (default), common unknowns/equations raise ValueError. If True, attributes are silently overwritten.

  • optional] – If False (default), common unknowns/equations raise ValueError. If True, attributes are silently overwritten.

Returns

The resulting mathematical system

Return type

MathematicalProblem

get_target_equations() → List[str][source]
get_target_residues() → Dict[str, cosapp.core.numerics.residues.Residue][source]
property n_equations

Number of equations (including deferred equations).

Type

int

property n_unknowns

Number of unknowns.

Type

int

property name

Mathematical system name.

Type

str

property rates

Time derivatives computed during system evolution.

Type

Dict[str, TimeDerivative]

property residues

Residue equations.

Type

Dict[str, Residue]

property residues_names

Names of residues, flattened to have the same size as residues_vector.

Type

Tuple[str]

property residues_vector

Vector of residues.

Type

numpy.ndarray

property shape

Number of unknowns and equations.

Type

(int, int)

static target_key(target: str) → str[source]

Returns dict key to be used for targetted quantity target

to_dict() → Dict[str, Any][source]

Returns a JSONable representation of the mathematical problem.

Returns

JSONable representation

Return type

Dict[str, Any]

property transients

Unknown time-dependent numerical features defined for this system.

Type

Dict[str, TimeUnknown]

property unknowns

Unknown numerical features defined for this system.

Type

Dict[str, Unknown]

property unknowns_names

Names of unknowns flatten to have the same size as residues_vector.

Type

Tuple[str]

validate() → None[source]

Verifies that there are as much unknowns as equations defined.

Raises

ArithmeticError – If the mathematical system is not closed.

class cosapp.core.numerics.basics.SolverResults[source]

Bases: object

Storage class for solver solution

x

Solution vector

Type

Sequence[float]

success

Whether or not the solver exited successfully.

Type

bool

message

Description of the cause of the termination.

Type

str

fun

Values of objective function.

Type

ndarray

jac_lup

LU decomposition of Jacobian given as tuple (LU, perm); (None, None) if not available.

Type

(ndarray[float], ndarray[int]), optional

jac

Values of function Jacobian; None if not available.

Type

ndarray, optional

jac_errors

Dictionary with singular Jacobian matrix error indexes

Type

dict, optional

jac_calls

Number of calls to the Jacobian matrix calculation

Type

int

fres_calls

Number of calls to the residues function

Type

int

trace

Resolution history (if requested) with the evolution of x, residues and jacobian

Type

List[Dict[str, Any]]

class cosapp.core.numerics.basics.WeakDeferredResidue(deferred, weak)[source]

Bases: NamedTuple

property context

evaluation context of residue

Type

System

deferred: cosapp.core.numerics.residues.DeferredResidue

Alias for field number 0

equation() → str[source]

Returns target equation with updated lhs value

make_residue(reference=None) → cosapp.core.numerics.residues.Residue[source]

Generates the residue corresponding to equation ‘target == value(target)’

property target

targetted quantity

Type

str

target_value() → Any[source]

Evaluates and returns current value of target

property variables

names of variables involved in residue

Type

Set[str]

weak: bool

Alias for field number 1