public class AlgebraicRule extends Rule
The rule type AlgebraicRule
is derived from the parent class Rule
. It
is used to express equations that are neither assignments of model
variables nor rates of change. AlgebraicRule
does not add any
attributes to the basic Rule
its role is simply to distinguish this
case from the other cases.
In the context of a simulation, algebraic rules are in effect at all times, t ≥ 0. For purposes of evaluating expressions that involve the delay 'csymbol' (see the SBML specification), algebraic rules are considered to apply also at t ≤ 0. Please consult the relevant SBML specification for additional information about the semantics of assignments, rules, and entity values for simulation time t ≤ 0.
An SBML model must not be overdetermined. The ability to define
arbitrary algebraic expressions in an SBML model introduces the
possibility that a model is mathematically overdetermined by the overall
system of equations constructed from its rules, reactions and events.
Therefore, if an algebraic rule is introduced in a model, for at least
one of the entities referenced in the rule's 'math' element the value of
that entity must not be completely determined by other constructs in the
model. This means that at least this entity must not have the attribute
'constant'=true
and there must also not be a rate rule or assignment
rule for it. Furthermore, if the entity is a Species
object, its value
must not be determined by reactions, which means that it must either
have the attribute 'boundaryCondition'=true
or else not be involved
in any reaction at all. These restrictions are explained in more detail
in the SBML specification documents.
In SBML Levels 2 and 3, Reaction
object identifiers can be
referenced in the 'math' expression of an algebraic rule, but reaction
rates can never be determined by algebraic rules. This is true
even when a reaction does not contain a KineticLaw
object. (In such cases of missing
kinetic law definitions, the model is valid but incomplete the rates of
reactions lacking kinetic laws are simply undefined, and not determined by
the algebraic rule.)
In SBML Level 3 as well as Level 2, rules are separated into three subclasses for the benefit of model analysis software. The three subclasses are based on the following three different possible functional forms (where x is a variable, f is some arbitrary function returning a numerical result, V is a vector of variables that does not include x, and W is a vector of variables that may include x):
Algebraic: | left-hand side is zero | 0 = f(W) |
Assignment: | left-hand side is a scalar: | x = f(V) |
Rate: | left-hand side is a rate-of-change: | dx/dt = f(W) |
In their general form given above, there is little to distinguish between assignment and algebraic rules. They are treated as separate cases for the following reasons:
InitialAssignment
.)
The approach taken to covering these cases in SBML is to define an
abstract Rule
structure containing a subelement, 'math', to hold the
right-hand side expression, then to derive subtypes of Rule
that add
attributes to distinguish the cases of algebraic, assignment and rate
rules. The 'math' subelement must contain a MathML expression defining the
mathematical formula of the rule. This MathML formula must return a
numerical value. The formula can be an arbitrary expression referencing
the variables and other entities in an SBML model.
Each of the three subclasses of Rule
(AssignmentRule, AlgebraicRule
,
RateRule
) inherit the the 'math' subelement and other fields from SBase
.
The AssignmentRule
and RateRule
classes add an additional attribute,
'variable'. See the definitions of AssignmentRule
, AlgebraicRule
and
RateRule
for details about the structure and interpretation of each one.
An important design goal of SBML rule semantics is to ensure that a model's simulation and analysis results will not be dependent on when or how often rules are evaluated. To achieve this, SBML needs to place two restrictions on rule use. The first concerns algebraic loops in the system of assignments in a model, and the second concerns overdetermined systems.
The combined set of InitialAssignment
, AssignmentRule
and KineticLaw
objects in a model constitute a set of assignment statements that should be
considered as a whole. (A KineticLaw
object is counted as an assignment
because it assigns a value to the symbol contained in the 'id' attribute of
the Reaction
object in which it is defined.) This combined set of
assignment statements must not contain algebraic loops&mdashdependency
chains between these statements must terminate. To put this more formally,
consider a directed graph in which nodes are assignment statements and
directed arcs exist for each occurrence of an SBML species, compartment or
parameter symbol in an assignment statement's 'math' subelement. Let the
directed arcs point from the statement assigning the symbol to the
statements that contain the symbol in their 'math' subelement expressions.
This graph must be acyclic.
SBML does not specify when or how often rules should be evaluated. Eliminating algebraic loops ensures that assignment statements can be evaluated any number of times without the result of those evaluations changing. As an example, consider the set of equations x = x + 1, y = z + 200 and z = y + 100. If this set of equations were interpreted as a set of assignment statements, it would be invalid because the rule for x refers to x (exhibiting one type of loop), and the rule for y refers to z while the rule for z refers back to y (exhibiting another type of loop). Conversely, the following set of equations would constitute a valid set of assignment statements: x = 10, y = z + 200, and z = x + 100.
An SBML model must not be overdetermined that is, a model must not
define more equations than there are unknowns in a model. An SBML model
that does not contain AlgebraicRule
structures cannot be overdetermined.
LibSBML implements the static analysis procedure described in Appendix B of the SBML Level 3 Version 1 Core specification for assessing whether a model is overdetermined.
(In summary, assessing whether a given continuous, deterministic, mathematical model is overdetermined does not require dynamic analysis it can be done by analyzing the system of equations created from the model. One approach is to construct a bipartite graph in which one set of vertices represents the variables and the other the set of vertices represents the equations. Place edges between vertices such that variables in the system are linked to the equations that determine them. For algebraic equations, there will be edges between the equation and each variable occurring in the equation. For ordinary differential equations (such as those defined by rate rules or implied by the reaction rate definitions), there will be a single edge between the equation and the variable determined by that differential equation. A mathematical model is overdetermined if the maximal matchings of the bipartite graph contain disconnected vertexes representing equations. If one maximal matching has this property, then all the maximal matchings will have this property i.e., it is only necessary to find one maximal matching.)
SBML Level 1 uses a different scheme than SBML Level 2 and Level 3 for distinguishing rules specifically, it uses an attribute whose value is drawn from an enumeration of 3 values. LibSBML supports this using methods that work with the enumeration values listed below.
RULE_TYPE_RATE
: Indicates
the rule is a 'rate' rule.
RULE_TYPE_SCALAR
:
Indicates the rule is a 'scalar' rule.
RULE_TYPE_INVALID
:
Indicates the rule type is unknown or not yet set.
Constructor and Description |
---|
AlgebraicRule(long level,
long version)
|
AlgebraicRule(SBMLNamespaces sbmlns)
|
Modifier and Type | Method and Description |
---|---|
AlgebraicRule |
cloneObject()
Creates and returns a deep copy of this
AlgebraicRule object. |
void |
delete()
Explicitly deletes the underlying native object.
|
boolean |
hasRequiredAttributes()
Predicate returning
true if all the required attributes for this
AlgebraicRule object have been set. |
containsUndeclaredUnits, getDerivedUnitDefinition, getElementName, getFormula, getL1TypeCode, getMath, getType, getTypeCode, getUnits, getVariable, hasRequiredElements, isAlgebraic, isAssignment, isCompartmentVolume, isParameter, isRate, isScalar, isSetFormula, isSetMath, isSetUnits, isSetVariable, isSpeciesConcentration, renameSIdRefs, renameUnitSIdRefs, setFormula, setL1TypeCode, setMath, setUnits, setVariable, unsetUnits, unsetVariable
addCVTerm, addCVTerm, appendAnnotation, appendAnnotation, appendNotes, appendNotes, connectToChild, deleteDisabledPlugins, deleteDisabledPlugins, disablePackage, enablePackage, equals, getAncestorOfType, getAncestorOfType, getAnnotation, getAnnotationString, getColumn, getCVTerm, getCVTerms, getDisabledPlugin, getElementByMetaId, getElementBySId, getLevel, getLine, getListOfAllElements, getListOfAllElements, getListOfAllElementsFromPlugins, getListOfAllElementsFromPlugins, getMetaId, getModel, getModelHistory, getNamespaces, getNotes, getNotesString, getNumCVTerms, getNumDisabledPlugins, getNumPlugins, getPackageName, getPackageVersion, getParentSBMLObject, getPlugin, getPlugin, getPrefix, getResourceBiologicalQualifier, getResourceModelQualifier, getSBMLDocument, getSBOTerm, getSBOTermAsURL, getSBOTermID, getURI, getVersion, hashCode, hasValidLevelVersionNamespaceCombination, isPackageEnabled, isPackageURIEnabled, isPkgEnabled, isPkgURIEnabled, isSetAnnotation, isSetMetaId, isSetModelHistory, isSetNotes, isSetSBOTerm, isSetUserData, matchesRequiredSBMLNamespacesForAddition, matchesSBMLNamespaces, removeFromParentAndDelete, removeTopLevelAnnotationElement, removeTopLevelAnnotationElement, removeTopLevelAnnotationElement, renameMetaIdRefs, replaceTopLevelAnnotationElement, replaceTopLevelAnnotationElement, setAnnotation, setAnnotation, setMetaId, setModelHistory, setNamespaces, setNotes, setNotes, setNotes, setSBOTerm, setSBOTerm, toSBML, toXMLNode, unsetAnnotation, unsetCVTerms, unsetId, unsetMetaId, unsetModelHistory, unsetName, unsetNotes, unsetSBOTerm, unsetUserData
public AlgebraicRule(long level, long version) throws SBMLConstructorException
level
- the SBML Level to assign to this AlgebraicRule
object.
version
- the SBML Version to assign to this AlgebraicRule
object.
SBMLConstructorException
- Thrown if the given level
and version
combination are invalid
or if this object is incompatible with the given level and version.
SBMLDocument
having a different
combination of SBML Level, Version and XML namespaces than the object
itself will result in an error at the time a caller attempts to make the
addition. A parent object must have compatible Level, Version and XML
namespaces. (Strictly speaking, a parent may also have more XML
namespaces than a child, but the reverse is not permitted.) The
restriction is necessary to ensure that an SBML model has a consistent
overall structure. This requires callers to manage their objects
carefully, but the benefit is increased flexibility in how models can be
created by permitting callers to create objects bottom-up if desired. In
situations where objects are not yet attached to parents (e.g.,
SBMLDocument
), knowledge of the intented SBML Level and Version help
libSBML determine such things as whether it is valid to assign a
particular value to an attribute.public AlgebraicRule(SBMLNamespaces sbmlns) throws SBMLConstructorException
AlgebraicRule
object using the given SBMLNamespaces
object
sbmlns
.
The SBMLNamespaces
object encapsulates SBML Level/Version/namespaces
information. It is used to communicate the SBML Level, Version, and (in
Level 3) packages used in addition to SBML Level 3 Core. A
common approach to using libSBML's SBMLNamespaces
facilities is to create an
SBMLNamespaces
object somewhere in a program once, then hand that object
as needed to object constructors that accept SBMLNamespaces
as arguments.
sbmlns
- an SBMLNamespaces
object.
SBMLConstructorException
- Thrown if the given sbmlns
is inconsistent or incompatible
with this object.
SBMLDocument
having a different
combination of SBML Level, Version and XML namespaces than the object
itself will result in an error at the time a caller attempts to make the
addition. A parent object must have compatible Level, Version and XML
namespaces. (Strictly speaking, a parent may also have more XML
namespaces than a child, but the reverse is not permitted.) The
restriction is necessary to ensure that an SBML model has a consistent
overall structure. This requires callers to manage their objects
carefully, but the benefit is increased flexibility in how models can be
created by permitting callers to create objects bottom-up if desired. In
situations where objects are not yet attached to parents (e.g.,
SBMLDocument
), knowledge of the intented SBML Level and Version help
libSBML determine such things as whether it is valid to assign a
particular value to an attribute.public void delete()
In general, application software will not need to call this method directly. The Java language binding for libSBML is implemented as a language wrapper that provides a Java interface to libSBML's underlying C++/C code. Some of the Java methods return objects that are linked to objects created not by Java code, but by C++ code. The Java objects wrapped around them will be deleted when the garbage collector invokes the corresponding C++ finalize()
methods for the objects. The finalize()
methods in turn call the AlgebraicRule.delete()
method on the libSBML object.
This method is exposed in case calling programs want to ensure that the underlying object is freed immediately, and not at some arbitrary time determined by the Java garbage collector. In normal usage, callers do not need to invoke AlgebraicRule.delete()
themselves.
public AlgebraicRule cloneObject()
AlgebraicRule
object.
cloneObject
 in class Rule
Rule
object.public boolean hasRequiredAttributes()
true
if all the required attributes for this
AlgebraicRule
object have been set.
In SBML Levels 2&ndash3, there is no required attribute
for an AlgebraicRule
object. For Level 1, the only required
attribute is 'formula'.
hasRequiredAttributes
 in class Rule
true
if the required attributes have been set, false
otherwise.