ReciprocalFunction

FunctionWithCachingFunctionReferences
[IoId("00000000-9E93-447C-A4AA-E575275ACDA7")] public class ReciprocalFunction : FunctionWithCaching
Represents an immutable reciprocal equation in the form y = 1/((x - b)^p) + c, however with fixed signs to allow for fractional exponents and negative numbers.

Constructors

ReciprocalFunction

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public ReciprocalFunction(double b, double c, double p)
Create a new reciprocal equation from variables.
Parameters:
b (double)Horizontal offset.
c (double)Vertical offset..
p (double)Exponent of reciprocal.

ReciprocalFunction

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public ReciprocalFunction(IReader reader)
Parameters:
reader (IReader)

Properties

Derivative

public sealed override Function Derivative { get; }
Gets a function which is the derivative of this function. The returned function may be either analytic or approximate.
inherited fromFunctionWithCaching
Overrides: Function.Derivative

Integral

public sealed override Function Integral { get; }
Gets a function which is the indefinite integral of this function. The returned function may be analytic or approximate. Note that numeric approximation of indefinite integrals is a slow and not particularly high quality process.
inherited fromFunctionWithCaching
Overrides: Function.Integral

Nomen

public sealed override Nomen Nomen { get; }
Gets a description of this function.
inherited fromFunctionWithCaching
Overrides: Function.Nomen

Notation

public override string Notation { get; }
Gets the notation for this function. Notation is aimed at humans and does not need to return a parseable string.
inherited fromFunctionWithCaching
Overrides: Function.Notation

Ui

public virtual FunctionUi Ui { get; }
Gets a UI object for modifying this function. This property may return null, not all functions must be editable.
inherited fromFunction

Methods

Asymptotes

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public override Line[] Asymptotes()
Returns an array of *all* the non-vertical asymptotes for this function. This property may return both null and empty arrays, implying no asymptotes. Due to the nature of non-vertical asymptotes, there can only be a finite amount of them.
Overrides: Function.Asymptotes

AutoCoDomain

protected void AutoCoDomain(double x0, double x1, out double y0, out double y1, int samples = 100)
Compute the automatic codomain for a given domain.
inherited fromFunction
Parameters:
x0 (double)Domain start.
x1 (double)Domain end.
y0 (out double)Lowest value in codomain.
y1 (out double)Highest value in codomain.
samples (int = 100)Samples.

DomainEstimate

public virtual void DomainEstimate(out double x0, out double x1, out double y0, out double y1)
Return an estimate of the interesting part of a function. Each function may choose how to answer this question individually.
inherited fromFunction
Parameters:
x0 (out double)Lowest x coordinate of interest.
x1 (out double)Highest x coordinate of interest.
y0 (out double)Lowest y coordinate of interest.
y1 (out double)Highest y coordinate of interest.

EmitDerivative

protected virtual Function EmitDerivative()
Override this method to provide an analytic derivative.
inherited fromFunctionWithCaching

EmitIntegral

protected virtual Function EmitIntegral()
Override this method to provide an analytic indefinite integral.
inherited fromFunctionWithCaching

FromInput

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public static ReciprocalFunction FromInput(Point2d focus, double power)
Create a reciprocal equation from inputs.
Parameters:
focus (Point2d)
power (double)

Holes

public virtual Interval[] Holes(double x0, double x1)
Returns a collection of domains for which this function is not defined. This method may return null or an empty array, implying no undefined domains. This method may also return domains outside of the specified interval.
inherited fromFunction
Parameters:
x0 (double)Lower limit of query domain.
x1 (double)Upper limit of query domain.

Integrate

public virtual double Integrate(double x0, double x1)
Evaluate the definite integral between two parameters. Unless a function specifically implements an analytic integral, this value will be approximate. Note to implementer: if you provide an analytic integral via the Function.Integral property, that function will be used to compute an analytic result. There is typically no reason to override this method.
inherited fromFunction
Parameters:
x0 (double)Integral start.
x1 (double)Integral end.
Returns: Definite integral from x0 to x1.

Poles

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public override Pole[] Poles(double x0, double x1)
Returns an array of all the poles (i.e. vertical asymptotes) within a domain. This method may return both null and empty arrays, implying no poles. Furthermore this method may choose to return poles which fall outside of the given domain.
Parameters:
x0 (double)Lower limit of query domain.
x1 (double)Upper limit of query domain.
Overrides: Function.Poles

Store

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public override void Store(IWriter writer)
Parameters:
writer (IWriter)
Overrides: FunctionWithCaching.Store

Y

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public override double Y(double x)
Parameters:
x (double)
Overrides: Function.Y

YYYY

public double[] YYYY(double[] x)
Evaluate a large amount of values. Functions may choose to use multiple threads to perform this calculation. This method should not throw, instead every failed evaluation will be represented by a NaN value.
inherited fromFunction
Parameters:
x (double[])Value to evaluate.
Returns: Evaluation results. Array will contain double.NaN entries for failed evaluations.