17.1.9. cobra.util

Submodules

• cobra.util.array
• cobra.util.context
• cobra.util.process_pool
• cobra.util.solver
• cobra.util.util

Package Contents

Classes

HistoryManager	Define a base context manager.
Components	Define an object for adding absolute expressions.
AutoVivification	Implementation of Perl's autovivification feature.
ProcessPool	Define a process pool that handles the Windows platform specially.

Functions

create_stoichiometric_matrix(→ Union[numpy.ndarray, ...)	Return a stoichiometric array representation of the given model.
nullspace(→ numpy.ndarray)	Compute an approximate basis for the nullspace of A.
constraint_matrices(→ NamedTuple)	Create a matrix representation of the problem.
get_context(→ Optional[HistoryManager])	Search for a context manager.
resettable(→ Callable[[Any], Any])	Simplify the context management of simple object attributes.
get_context(→ Optional[HistoryManager])	Search for a context manager.
linear_reaction_coefficients(→ Dict[cobra.Reaction, float])	Retrieve coefficient for the reactions in a linear objective.
_valid_atoms(→ bool)	Check whether a sympy expression references the correct variables.
set_objective(→ None)	Set the model objective.
interface_to_str(→ str)	Give a string representation for an optlang interface.
get_solver_name(→ str)	Select a solver for a given optimization problem.
choose_solver(→ types.ModuleType)	Choose a solver given a solver name and model.
check_solver(obj)	Check whether the chosen solver is valid.
add_cons_vars_to_problem(→ None)	Add variables and constraints to a model's solver object.
remove_cons_vars_from_problem(→ None)	Remove variables and constraints from a model's solver object.
add_absolute_expression(→ Components)	Add the absolute value of an expression to the model.
fix_objective_as_constraint(→ float)	Fix current objective as an additional constraint.
check_solver_status(→ None)	Perform standard checks on a solver's status.
assert_optimal(→ None)	Assert model solver status is optimal.
add_lp_feasibility(→ None)	Add a new objective and variables to ensure a feasible solution.
add_lexicographic_constraints(→ pandas.Series)	Successively optimize separate targets in a specific order.
format_long_string(→ str)	Shorten long string into a small string with ellipsis.
show_versions(→ None)	Print dependency information.

Attributes

OPTLANG_TO_EXCEPTIONS_DICT
CONS_VARS
logger
solvers
qp_solvers
has_primals

cobra.util.create_stoichiometric_matrix(model: cobra.Model, array_type: str = 'dense', dtype: Optional[numpy.dtype] = None) → Union[numpy.ndarray, scipy.sparse.dok_matrix, scipy.sparse.lil_matrix, pandas.DataFrame]

Return a stoichiometric array representation of the given model.

The the columns represent the reactions and rows represent metabolites. S[i,j] therefore contains the quantity of metabolite i produced (negative for consumed) by reaction j.

Parameters

• model (cobra.Model) – The cobra model to construct the matrix for.

• array_type ({"dense", "dok", "lil", "DataFrame"}) – The type of array to construct. “dense” will return a standard numpy.ndarray. “dok”, or “lil” will construct a sparse array using scipy of the corresponding type. “DataFrame” will give a pandas.DataFrame with metabolite as indices and reaction as columns.

• dtype (numpy.dtype, optional) – The desired numpy data type for the array (default numpy.float64).

Returns

The stoichiometric matrix for the given model.

Return type

matrix of class dtype

Raises

• ValueError – If sparse matrix is used and scipy is not installed.

• .. deprecated: – 0.18.1: “DataFrame” option for array_type will be replaced with “frame” in future versions.

cobra.util.nullspace(A: numpy.ndarray, atol: float = 1e-13, rtol: float = 0.0) → numpy.ndarray

Compute an approximate basis for the nullspace of A.

The algorithm used by this function is based on the Singular Value Decomposition (SVD) of A.

Parameters

• A (numpy.ndarray) – A should be at most 2-D. 1-D array with length k will be treated as a 2-D with shape (1, k).

• atol (float, optional) – The absolute tolerance for a zero singular value. Singular values smaller than atol are considered to be zero (default 1e-13).

• rtol (float, optional) – The relative tolerance. Singular values less than rtol * smax are considered to be zero, where smax is the largest singular value (default 0.0).

Returns

If A is an array with shape (m, k), then ns will be an array with shape (k, n), where n is the estimated dimension of the nullspace of A. The columns of ns are a basis for the nullspace; each element in numpy.dot(A, ns) will be approximately zero.

Return type

numpy.ndarray

Notes

This is taken from the numpy cookbook.

If both atol and rtol are positive, the combined tolerance is the maximum of the two; that is:

\[\mathtt{tol} = \max(\mathtt{atol}, \mathtt{rtol} * \mathtt{smax})\]

Singular values smaller than tol are considered to be zero.

cobra.util.constraint_matrices(model: cobra.Model, array_type: str = 'dense', zero_tol: float = 1e-06) → NamedTuple

Create a matrix representation of the problem.

This is used for alternative solution approaches that do not use “optlang”. The function will construct the equality matrix, inequality matrix and bounds for the complete problem.

Parameters

• model (cobra.Model) – The model from which to obtain the LP problem.

• array_type ({"dense", "dok", "lil", "DataFrame"}) – The type of array to construct. “dense” will return a standard numpy.ndarray. “dok”, or “lil” will construct a sparse array using scipy of the corresponding type. “DataFrame” will give a pandas.DataFrame with metabolite as indices and reaction as columns.

• zero_tol (float, optional) – The zero tolerance used to judge whether two bounds are the same (default 1e-6).

Returns

A named tuple consisting of 6 matrices and 2 vectors: - “equalities” is a matrix S such that S * vars = b. It

includes a row for each constraint and one column for each variable.

• ”b” is the right side of the equality equation such that S * vars = b.

• ”inequalities” is a matrix M such that lb <= M * vars <= ub. It contains a row for each inequality and as many columns as variables.

• ”bounds” is a compound matrix [lb ub] containing the lower and upper bounds for the inequality constraints in M.

• ”variable_fixed” is a boolean vector indicating whether the variable at that index is fixed (lower bound == upper_bound) and is thus bounded by an equality constraint.

• ”variable_bounds” is a compound matrix [lb ub] containing the lower and upper bounds for all variables.

Return type

NamedTuple

Notes

To accomodate non-zero equalities, the problem will add the variable “const_one” which is a variable that equals one.

Deprecated since version 0.18.1: “DataFrame” option for array_type will be replaced with “frame” in future versions.

class cobra.util.HistoryManager(**kwargs)

Define a base context manager.

It records a list of actions to be taken at a later time. This is used to implement context managers that allow temporary changes to a cobra.core.Model.

__call__(operation: Callable[[Any], Any]) → None

Add the corresponding operation to the history stack.

Parameters

operation (callable) – A function to be called at a later time.

reset() → None

Trigger executions for all items in the stack in reverse order.

size() → int

Calculate number of operations on the stack.

cobra.util.get_context(obj: cobra.Object) → Optional[HistoryManager]

Search for a context manager.

Parameters

obj (cobra.Object) – The cobra.Object for which to search context manager.

Returns

HistoryManager instance, or None if no context manager is found.

Return type

HistoryManager or None

Raises

• AttributeError – If no context manager is found.

• IndexError – If no context manager is found.

cobra.util.resettable(func: Callable[[Any], Any]) → Callable[[Any], Any]

Simplify the context management of simple object attributes.

It gets the value of the attribute prior to setting it, and stores a function to set the value to the old value in the cobra.util.HistoryManager.

Parameters

func (callable) – The function to decorate.

Returns

The decorated function.

Return type

callable

cobra.util.OPTLANG_TO_EXCEPTIONS_DICT

exception cobra.util.OptimizationError(message)

Bases: Exception

Exception for Optimization issues.

exception cobra.util.SolverNotFound

Bases: Exception

A simple Exception when a solver can not be found.

cobra.util.get_context(obj: cobra.Object) → Optional[HistoryManager]

Search for a context manager.

Parameters

obj (cobra.Object) – The cobra.Object for which to search context manager.

Returns

HistoryManager instance, or None if no context manager is found.

Return type

HistoryManager or None

Raises

• AttributeError – If no context manager is found.

• IndexError – If no context manager is found.

cobra.util.CONS_VARS

cobra.util.logger

cobra.util.solvers

cobra.util.qp_solvers = ['cplex', 'gurobi', 'osqp']

cobra.util.has_primals

class cobra.util.Components

Bases: NamedTuple

Define an object for adding absolute expressions.

variable: optlang.interface.Variable

upper_constraint: optlang.interface.Constraint

lower_constraint: optlang.interface.Constraint

cobra.util.linear_reaction_coefficients(model: cobra.Model, reactions: Optional[List[cobra.Reaction]] = None) → Dict[cobra.Reaction, float]

Retrieve coefficient for the reactions in a linear objective.

Parameters

• model (cobra.Model) – The cobra model defining the linear objective.

• reactions (list of cobra.Reaction, optional) – An optional list of the reactions to get the coefficients for. By default, all reactions are considered (default None).

Returns

A dictionary where the keys are the reaction objects and the values are the corresponding coefficient. Empty dictionary if there are no linear terms in the objective.

Return type

dict

cobra.util._valid_atoms(model: cobra.Model, expression: optlang.symbolics.Basic) → bool

Check whether a sympy expression references the correct variables.

Parameters

• model (cobra.Model) – The model in which to check for variables.

• expression (sympy.Basic) – A sympy expression.

Returns

True if all referenced variables are contained in model, False otherwise.

Return type

bool

cobra.util.set_objective(model: cobra.Model, value: Union[optlang.interface.Objective, optlang.symbolics.Basic, Dict[cobra.Reaction, float]], additive: bool = False) → None

Set the model objective.

Parameters

• model (cobra.Model) – The model to set the objective for.

• value (optlang.interface.Objective, optlang.symbolics.Basic, dict) – If the model objective is linear, then the value can be a new optlang.interface.Objective or a dictionary with linear coefficients where each key is a reaction and the corresponding value is the new coefficient (float). If the objective is non-linear and additive is True, then only values of class optlang.interface.Objective, are accepted.

• additive (bool) – If True, add the terms to the current objective, otherwise start with an empty objective.

Raises

• ValueError – If model objective is non-linear and the value is a dict.

• TypeError – If the type of value is not one of the accepted ones.

cobra.util.interface_to_str(interface: Union[str, types.ModuleType]) → str

Give a string representation for an optlang interface.

Parameters

interface (str, ModuleType) – Full name of the interface in optlang or cobra representation. For instance, ‘optlang.glpk_interface’ or ‘optlang-glpk’.

Returns

The name of the interface as a string.

Return type

str

cobra.util.get_solver_name(mip: bool = False, qp: bool = False) → str

Select a solver for a given optimization problem.

Parameters

• mip (bool) – True if the solver requires mixed integer linear programming capabilities.

• qp (bool) – True if the solver requires quadratic programming capabilities.

Returns

The name of the feasible solver.

Return type

str

Raises

SolverNotFound – If no suitable solver could be found.

cobra.util.choose_solver(model: cobra.Model, solver: Optional[str] = None, qp: bool = False) → types.ModuleType

Choose a solver given a solver name and model.

This will choose a solver compatible with the model and required capabilities. Also respects model.solver where it can.

Parameters

• model (cobra.Model) – The model for which to choose the solver.

• solver (str, optional) – The name of the solver to be used (default None).

• qp (boolean, optional) – True if the solver needs quadratic programming capabilities (default False).

Returns

Valid solver for the problem.

Return type

optlang.interface

Raises

SolverNotFound – If no suitable solver could be found.

cobra.util.check_solver(obj)

Check whether the chosen solver is valid.

Check whether chosen solver is valid and also warn when using a specialized solver. Will return the optlang interface for the requested solver.

Parameters

obj (str or optlang.interface or optlang.interface.Model) – The chosen solver.

Raises

SolverNotFound – If the solver is not valid.

cobra.util.add_cons_vars_to_problem(model: cobra.Model, what: Union[List[CONS_VARS], Tuple[CONS_VARS], Components], **kwargs) → None

Add variables and constraints to a model’s solver object.

Useful for variables and constraints that can not be expressed with reactions and lower/upper bounds. It will integrate with the model’s context manager in order to revert changes upon leaving the context.

Parameters

• model (cobra.Model) – The model to which to add the variables and constraints.

• what (list or tuple of optlang.interface.Variable or) – optlang.interface.Constraint The variables and constraints to add to the model.

• **kwargs (keyword arguments) – Keyword arguments passed to solver’s add() method.

cobra.util.remove_cons_vars_from_problem(model: cobra.Model, what: Union[List[CONS_VARS], Tuple[CONS_VARS], Components]) → None

Remove variables and constraints from a model’s solver object.

Useful to temporarily remove variables and constraints from a model’s solver object.

Parameters

• model (cobra.Model) – The model from which to remove the variables and constraints.

• what (list or tuple of optlang.interface.Variable or) – optlang.interface.Constraint The variables and constraints to remove from the model.

cobra.util.add_absolute_expression(model: cobra.Model, expression: str, name: str = 'abs_var', ub: Optional[float] = None, difference: float = 0.0, add: bool = True) → Components

Add the absolute value of an expression to the model.

Also defines a variable for the absolute value that can be used in other objectives or constraints.

Parameters

• model (cobra.Model) – The model to which to add the absolute expression.

• expression (str) – Must be a valid symbolic expression within the model’s solver object. The absolute value is applied automatically on the expression.

• name (str, optional) – The name of the newly created variable (default “abs_var”).

• ub (positive float, optional) – The upper bound for the variable (default None).

• difference (positive float, optional) – The difference between the expression and the variable (default 0.0).

• add (bool, optional) – Whether to add the variable to the model at once (default True).

Returns

A named tuple with variable and two constraints (upper_constraint, lower_constraint) describing the new variable and the constraints that assign the absolute value of the expression to it.

Return type

Components

cobra.util.fix_objective_as_constraint(model: cobra.Model, fraction: float = 1.0, bound: Optional[float] = None, name: str = 'fixed_objective_{}') → float

Fix current objective as an additional constraint.

When adding constraints to a model, such as done in pFBA which minimizes total flux, these constraints can become too powerful, resulting in solutions that satisfy optimality but sacrifices too much for the original objective function. To avoid that, we can fix the current objective value as a constraint to ignore solutions that give a lower (or higher depending on the optimization direction) objective value than the original model.

When done with the model as a context, the modification to the objective will be reverted when exiting that context.

Parameters

• model (cobra.Model) – The model to operate on.

• fraction (float, optional) – The fraction of the optimum the objective is allowed to reach (default 1.0).

• bound (float, optional) – The bound to use instead of fraction of maximum optimal value. If not None, fraction is ignored (default None).

• name (str, optional) – Name of the objective. May contain one “{}” placeholder which is filled with the name of the old objective (default “fixed_objective_{}”).

Returns

The value of the optimized objective * fraction

Return type

float

cobra.util.check_solver_status(status: str = None, raise_error: bool = False) → None

Perform standard checks on a solver’s status.

Parameters

• status (str, optional) – The status string obtained from the solver (default None).

• raise_error (bool, optional) – If True, raise error or display warning if False (default False).

Return type

None

Warns

UserWarning – If status is not optimal and raise_error is set to True.

Raises

OptimizationError – If status is None or is not optimal and raise_error is set to True.

cobra.util.assert_optimal(model: cobra.Model, message: str = 'Optimization failed') → None

Assert model solver status is optimal.

Do nothing if model solver status is optimal, otherwise throw appropriate exception depending on the status.

Parameters

• model (cobra.Model) – The model to check the solver status for.

• message (str, optional) – Message for the exception if solver status is not optimal (default “Optimization failed”).

Return type

None

Raises

OptimizationError – If solver status is not optimal.

cobra.util.add_lp_feasibility(model: cobra.Model) → None

Add a new objective and variables to ensure a feasible solution.

The optimized objective will be zero for a feasible solution and otherwise represent the distance from feasibility (please see [1]_ for more information).

Parameters

model (cobra.Model) – The model whose feasibility is to be tested.

Return type

None

References

1

Gomez, Jose A., Kai Höffner, and Paul I. Barton.

“DFBAlab: A Fast and Reliable MATLAB Code for Dynamic Flux Balance Analysis.” BMC Bioinformatics 15, no. 1 (December 18, 2014): 409. https://doi.org/10.1186/s12859-014-0409-8.

cobra.util.add_lexicographic_constraints(model: cobra.Model, objectives: List[cobra.Reaction], objective_direction: Union[str, List[str]] = 'max') → pandas.Series

Successively optimize separate targets in a specific order.

For each objective, optimize the model and set the optimal value as a constraint. Proceed in the order of the objectives given. Due to the specific order this is called lexicographic FBA [1]_. This procedure is useful for returning unique solutions for a set of important fluxes. Typically this is applied to exchange fluxes.

Parameters

• model (cobra.Model) – The model to be optimized.

• objectives (list of cobra.Reaction) – A list of reactions (or objectives) in the model for which unique fluxes are to be determined.

• objective_direction (str or list of str, optional) – The desired objective direction for each reaction (if a list) or the objective direction to use for all reactions (default “max”).

Returns

A pandas Series containing the optimized fluxes for each of the given reactions in objectives.

Return type

pandas.Series

References

1

Gomez, Jose A., Kai Höffner, and Paul I. Barton.

“DFBAlab: A Fast and Reliable MATLAB Code for Dynamic Flux Balance Analysis.” BMC Bioinformatics 15, no. 1 (December 18, 2014): 409. https://doi.org/10.1186/s12859-014-0409-8.

cobra.util.format_long_string(string: str, max_length: int = 50) → str

Shorten long string into a small string with ellipsis.

Parameters

• string (str) – The long string to shorten.

• max_length (int, optional) – The maximum length after which to append ellipsis (default 50).

Returns

The shortened string.

Return type

str

class cobra.util.AutoVivification

Bases: dict

Implementation of Perl’s autovivification feature.

Notes

For more information, check https://stackoverflow.com/a/652284/280182 .

__getitem__(item: Any) → Any

Retrieve if item is found, else add it.

Parameters

item (Any) – The object to look for.

Returns

The retrieved object.

Return type

Any

cobra.util.show_versions() → None

Print dependency information.

class cobra.util.ProcessPool(processes: Optional[int] = None, initializer: Optional[Callable] = None, initargs: Tuple = (), maxtasksperchild: Optional[int] = None, **kwargs)

Define a process pool that handles the Windows platform specially.

__getattr__(name: str, **kwargs) → Any

Defer attribute access to the pool instance.

__enter__() → ProcessPool

Enable context management.

__exit__(exc_type: Optional[Type[BaseException]], exc_val: Optional[BaseException], exc_tb: Optional[types.TracebackType]) → Optional[bool]

Clean up resources when leaving a context.

close() → None

Close the process pool.

Prevent any more tasks from being submitted to the pool. Once all the tasks have been completed, the worker processes will exit.

_clean_up() → None

Remove the dump file if it exists.