BsInterpolate Class

BsInterpolate Class

Extension of the BSpline class to interpolate data points.

Inheritance Hierarchy

SystemObject
Imsl.MathBSpline
Imsl.MathBsInterpolate

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

Syntax

C++

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[SerializableAttribute]
public class BsInterpolate : BSpline

<SerializableAttribute>
Public Class BsInterpolate
	Inherits BSpline

[SerializableAttribute]
public ref class BsInterpolate : public BSpline

[<SerializableAttribute>]
type BsInterpolate =  
    class
        inherit BSpline
    end

The BsInterpolate type exposes the following members.

Constructors

	Name	Description
	BsInterpolate(Double, Double)	Constructs a B-spline that interpolates the given data points. The computed B-spline will be order 4 (cubic) and have a default "not-a-knot" spline knot sequence.
	BsInterpolate(Double, Double, Int32)	Constructs a B-spline that interpolates the given data points and order, using a default "not-a-knot" spline knot sequence.
	BsInterpolate(Double, Double, Int32, Double)	Constructs a B-spline that interpolates the given data points, using the specified order and knots.

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Methods

	Name	Description
	Derivative(Double)	Returns the value of the first derivative of the B-spline at a point. (Inherited from BSpline.)
	Derivative(Double, Int32)	Returns the value of the derivative of the B-spline at a point. (Inherited from BSpline.)
	Derivative(Double, Int32)	Returns the value of the derivative of the B-spline at each point of an array. (Inherited from BSpline.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Eval(Double)	Returns the value of the B-spline at a point. (Inherited from BSpline.)
	Eval(Double)	Returns the value of the B-spline at each point of an array. (Inherited from BSpline.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetKnots	Returns a copy of the knot sequence. (Inherited from BSpline.)
	GetSpline	Returns a Spline representation of the B-spline. (Inherited from BSpline.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Integral	Returns the value of an integral of the B-spline. (Inherited from BSpline.)
	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

Given the data points x = xData, f = yData, and n the number of elements in xData and yData, the default action of BsInterpolate computes a cubic (order = 4) spline interpolant s to the data using a default "not-a-knot" knot sequence. Constructors are also provided that allow the order and knot sequence to be specified. This algorithm is based on the routine SPLINT by de Boor (1978, p. 204).

First, the xData vector is sorted and the result is stored in x. The elements of yData are permuted appropriately and stored in f, yielding the equivalent data for i = 0 to n-1. The following preliminary checks are performed on the data, with k = order. We verify that

$x_i \lt x_{i+1}\mbox{ for }i=0,\ldots,n-2$

${\bf t}_i \lt {\bf t}_{i+k}\mbox{ for }i=0,\ldots,n-1$

${\bf t}_i \lt {\bf t}_{i+1}\mbox{ for }i=0,\ldots,n+k-2$

The first test checks to see that the abscissas are distinct. The second and third inequalities verify that a valid knot sequence has been specified.

In order for the interpolation matrix to be nonsingular, we also check ${\bf t}_{k-1} \leq x_i \leq {\bf t}_n$ for i = 0 to n-1. This first inequality in the last check is necessary since the method used to generate the entries of the interpolation matrix requires that the k possibly nonzero B-splines at , $B_{j-k+1}, ..., B_j$ where j satisfies ${\bf t}_j \leq x_i \lt {\bf t}_{j+1}$ be well-defined (that is, $j-k+1 \geq 0$ ).

Reference

Imsl.Math Namespace

Other Resources

Example