Element
Smallest unit of representation of a min-plus algebra function. Can be either a Point or a Segment.
public abstract class Element : IToCodeString, Unipi.Nancy.Utility.IStableHashCode
Inheritance Object → Element
Implements IToCodeString, IStableHashCode
Properties
Type
Type identification property for JSON (de)serialization.
public abstract string Type { get; }
Property Value
StartTime
Left endpoint of the support of the element. If the element is a Segment, it is exclusive and strictly lower than EndTime. If the element is a Point, it is inclusive and equal to EndTime.
public abstract Rational StartTime { get; }
Property Value
EndTime
Right endpoint of the support of the element. If the element is a Segment, it is exclusive and strictly greater than StartTime. If the element is a Point, it is inclusive and equal to StartTime.
public abstract Rational EndTime { get; }
Property Value
Length
Length in time of the element. If the element is a Segment, it is strictly greater than 0. If the element is a Point, it is equal to 0.
public Rational Length { get; }
Property Value
IsInfinite
True if the element has plus/minus infinite value.
public abstract bool IsInfinite { get; }
Property Value
IsPlusInfinite
True if the element has plus infinite value.
public abstract bool IsPlusInfinite { get; }
Property Value
IsMinusInfinite
True if the element has minus infinite value.
public abstract bool IsMinusInfinite { get; }
Property Value
IsFinite
True if the element has finite value.
public bool IsFinite { get; }
Property Value
IsZero
True if the element has 0 value. If the element is a Segment, this must be true for all its support.
public abstract bool IsZero { get; }
Property Value
Methods
ValueAt(Rational)
Computes the value of the element at the given time.
public abstract Rational ValueAt(Rational time)
Parameters
time Rational
The time of sampling.
Returns
Rational
Value of the element at the given time or if outside definition bounds.
IsDefinedFor(Rational)
True if given time is between the element's definition bounds.
public abstract bool IsDefinedFor(Rational time)
Parameters
time Rational
Returns
ToString()
Returns string serialization in Json format.
public string ToString()
Returns
FromJson(String)
Deserializes an Element.
public static Element FromJson(string json)
Parameters
json String
Returns
ToCodeString(Boolean, Int32)
Returns a string containing C# code to create this Element. Useful to copy and paste from a debugger into another test or notebook for further investigation.
public abstract string ToCodeString(bool formatted, int indentation)
Parameters
formatted Boolean
indentation Int32
Returns
GetStableHashCode()
A stable hashcode.
public abstract int GetStableHashCode()
Returns
Scale(Rational)
Scales the element by a multiplicative factor.
public abstract Element Scale(Rational scaling)
Parameters
scaling Rational
Returns
Delay(Rational)
Translates forwards the support by the given time quantity.
public abstract Element Delay(Rational delay)
Parameters
delay Rational
Returns
Anticipate(Rational)
Translates backwards the support by the given time quantity.
public abstract Element Anticipate(Rational time)
Parameters
time Rational
Returns
VerticalShift(Rational)
Shifts the element vertically by an additive factor.
public abstract Element VerticalShift(Rational shift)
Parameters
shift Rational
Returns
Negate()
Returns the opposite element, .
public abstract Element Negate()
Returns
Inverse()
Compute the inverse function,
public abstract Element Inverse()
Returns
Exceptions
If the element is non-bijective, i.e. a constant segment.
Addition(Element)
Sums two elements over their overlapping part.
public abstract Element Addition(Element element)
Parameters
element Element
Second operand.
Returns
Element
The element resulting from the sum.
Exceptions
ArgumentException
Thown if the two elements do not overlap.
Addition(Element, Element)
Sums two elements over their overlapping part.
public static Element Addition(Element a, Element b)
Parameters
a Element
b Element
Returns
Element
The element resulting from the sum.
Exceptions
ArgumentException
Thown if the two elements do not overlap.
Addition(IEnumerable<Element>)
Sums a set of elements over their overlapping part.
public static Element Addition(IEnumerable<Element> elements)
Parameters
elements IEnumerable<Element>
The elements to be summed.
Returns
Element
The result of the overall sum.
Exceptions
ArgumentException
Thrown if the elements do not overlap.
InvalidOperationException
Thrown if the set of elements is empty.
Subtraction(Element)
Subtracts two elements over their overlapping part.
The operation does not enforce non-negative values.
public abstract Element Subtraction(Element element)
Parameters
element Element
Second operand.
Returns
Element
The element resulting from the subtraction.
Exceptions
ArgumentException
Thown if the two elements do not overlap.
Subtraction(Element, Element)
Subtracts two elements over their overlapping part.
The operation does not enforce non-negative values.
public static Element Subtraction(Element a, Element b)
Parameters
a Element
b Element
Returns
Element
The element resulting from the subtraction.
Exceptions
ArgumentException
Thown if the two elements do not overlap.
Subtraction(IEnumerable<Element>)
Subtracts a set of elements over their overlapping part.
The operation does not enforce non-negative values. As subtraction is not commutative, beware of the order of the operands.
public static Element Subtraction(IEnumerable<Element> elements)
Parameters
elements IEnumerable<Element>
The elements to be summed.
Returns
Element
The result of the overall subtraction.
Exceptions
ArgumentException
Thrown if the elements do not overlap.
InvalidOperationException
Thrown if the set of elements is empty.
Minimum(Element)
Computes the minimum of two elements over their overlapping part. The result is either a point, a segment or a segment-point-segment sequence.
public abstract List<Element> Minimum(Element element)
Parameters
element Element
Second operand.
Returns
List<Element>
The set of segments resulting from the minimum.
Minimum(Element, Element)
Computes the minimum of two elements over their overlapping part. The result is either a point, a segment or a segment-point-segment sequence.
public static List<Element> Minimum(Element a, Element b)
Parameters
a Element
b Element
Returns
List<Element>
The set of segments resulting from the minimum.
Minimum(IReadOnlyList<Element>)
Computes the minimum of a set of elements over their overlapping part.
public static List<Element> Minimum(IReadOnlyList<Element> elements)
Parameters
elements IReadOnlyList<Element>
Elements of which the minimum has to be computed.
Returns
List<Element>
The result of the overall minimum.
Exceptions
ArgumentException
Thrown if the elements do not overlap.
InvalidOperationException
Thrown if the set of elements is empty.
Maximum(Element)
Computes the maximum of two elements over their overlapping part. The result is either a point, a segment or a segment-point-segment sequence.
public abstract List<Element> Maximum(Element element)
Parameters
element Element
Second operand.
Returns
List<Element>
The set of segments resulting from the maximum.
Maximum(Element, Element)
Computes the maximum of two elements over their overlapping part. The result is either a point, a segment or a segment-point-segment sequence.
public static List<Element> Maximum(Element a, Element b)
Parameters
a Element
b Element
Returns
List<Element>
The set of segments resulting from the maximum.
Maximum(IReadOnlyList<Element>)
Computes the maximum of a set of elements over their overlapping part.
public static List<Element> Maximum(IReadOnlyList<Element> elements)
Parameters
elements IReadOnlyList<Element>
Elements of which the maximum has to be computed.
Returns
List<Element>
The result of the overall maximum.
Exceptions
ArgumentException
Thrown if the elements do not overlap.
InvalidOperationException
Thrown if the set of elements is empty.
Convolution(Element, Nullable<Rational>, Nullable<Rational>)
Computes the convolution between two Elements.
Described in [BT08] Section 3.2.1
public abstract IEnumerable<Element> Convolution(Element element, Nullable<Rational> cutEnd, Nullable<Rational> cutCeiling)
Parameters
element Element
Second operand.
cutEnd Nullable<Rational>
If defined, computation of convolutions beyond the given limit will be omitted.
cutCeiling Nullable<Rational>
If defined, computation of convolutions beyond the given limit will be omitted.
Returns
IEnumerable<Element>
The set of segments resulting from the convolution.
Convolution(Element, Element, Nullable<Rational>, Nullable<Rational>)
Computes the convolution between two Elements.
Described in [BT08] Section 3.2.1
public static IEnumerable<Element> Convolution(Element a, Element b, Nullable<Rational> cutEnd, Nullable<Rational> cutCeiling)
Parameters
a Element
First operand.
b Element
Second operand.
cutEnd Nullable<Rational>
If defined, computation of convolutions beyond the given limit will be omitted.
cutCeiling Nullable<Rational>
If defined, computation of convolutions beyond the given limit will be omitted.
Returns
IEnumerable<Element>
The set of segments resulting from the convolution.
Deconvolution(Element)
Computes the deconvolution between two Elements.
Described in [BT08] Section 3.2.2
public abstract IEnumerable<Element> Deconvolution(Element element)
Parameters
element Element
Returns
IEnumerable<Element>
The set of segments resulting from the deconvolution.
Deconvolution(Element, Element)
Computes the deconvolution between two Elements.
Described in [BT08] Section 3.2.2
public static IEnumerable<Element> Deconvolution(Element a, Element b)
Parameters
a Element
b Element
Returns
IEnumerable<Element>
The set of segments resulting from the deconvolution.
MaxPlusConvolution(Element, Nullable<Rational>)
Computes the max-plus convolution between two Elements.
Adapted from the min-plus convolution algorithm described in [BT08] Section 3.2.1
public abstract IEnumerable<Element> MaxPlusConvolution(Element element, Nullable<Rational> cutEnd)
Parameters
element Element
Second operand.
cutEnd Nullable<Rational>
If defined, computation of convolutions beyond the given limit will be omitted.
Returns
IEnumerable<Element>
The set of segments resulting from the max-plus convolution.
MaxPlusConvolution(Element, Element, Nullable<Rational>)
Computes the max-plus convolution between two Elements.
Adapted from the min-plus convolution algorithm described in [BT08] Section 3.2.1
public static IEnumerable<Element> MaxPlusConvolution(Element a, Element b, Nullable<Rational> cutEnd)
Parameters
a Element
First operand.
b Element
Second operand.
cutEnd Nullable<Rational>
If defined, computation of convolutions beyond the given limit will be omitted.
Returns
IEnumerable<Element>
The set of segments resulting from the max-plus convolution.
SubAdditiveClosure(ComputationSettings)
Computes the sub-additive closure of the element.
public abstract SubAdditiveCurve SubAdditiveClosure(ComputationSettings settings)
Parameters
settings ComputationSettings
Returns
SubAdditiveClosure(Rational, Rational, ComputationSettings)
Computes the sub-additive closure of the pseudo-periodic element.
public abstract SubAdditiveCurve SubAdditiveClosure(Rational pseudoPeriodLength, Rational pseudoPeriodHeight, ComputationSettings settings)
Parameters
pseudoPeriodLength Rational
Lenght of the pseudo-period
pseudoPeriodHeight Rational
Step gained after each pseudo-period
settings ComputationSettings
Returns
Exceptions
ArgumentException
Thrown if the period is not greater than 0