Spline Class

Spline Class

Spline represents and evaluates univariate piecewise polynomial splines.

Inheritance Hierarchy

SystemObject
Imsl.MathSpline
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Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public abstract class Spline

<SerializableAttribute>
Public MustInherit Class Spline

[SerializableAttribute]
public ref class Spline abstract

[<AbstractClassAttribute>]
[<SerializableAttribute>]
type Spline =  class end

The Spline type exposes the following members.

Constructors

	Name	Description
	Spline	Initializes a new instance of the Spline class

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Methods

	Name	Description
	Derivative(Double)	Returns the value of the first derivative of the spline at a point.
	Derivative(Double, Int32)	Returns the value of the derivative of the spline at a point.
	Derivative(Double, Int32)	Returns the value of the derivative of the spline at each point of an array.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Eval(Double)	Returns the value of the spline at a point.
	Eval(Double)	Returns the value of the spline at each point of an array.
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetBreakpoints	Returns a copy of the breakpoints.
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Integral	Returns the value of an integral of the spline.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Remarks

A univariate piecewise polynomial (function) p(x) is specified by giving its breakpoint sequence breakPoint[]= $\xi \in {\bf R}^n$ , the order k (degree k-1) of its polynomial pieces,and the $k \times (n-1)$ matrix coef=c of its local polynomial coefficients. In terms of this information, the piecewise polynomial (ppoly) function is given by

$p(x) = \sum_{j=1}^k c_{ji} \frac{(x-\xi_i)^{j-1}}{(j-1)!} \;\;{\rm for}\; \xi_i \le x \le \xi_{i+1}$

The breakpoint sequence $\xi$ is assumed to be strictly increasing, and we extend the ppoly function to the entire real axis by extrapolation from the first and last intervals.

Reference

Imsl.Math Namespace

Other Resources

Akima Example

Interpolate Example

Periodic Example

Shape Preserving Example

Smoothing Example 1

Smoothing Example 2

Inheritance Hierarchy

SystemObject
  Imsl.MathSpline
    Imsl.MathCsAkima
    Imsl.MathCsInterpolate
    Imsl.MathCsPeriodic
    Imsl.MathCsShape
    Imsl.MathCsSmooth
    Imsl.MathCsSmoothC2
    Imsl.MathCsTCB