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BsInterpolate Class
Extension of the BSpline class to interpolate data points.
Inheritance Hierarchy

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
[SerializableAttribute]
public class BsInterpolate : BSpline

The BsInterpolate type exposes the following members.

Constructors
Methods
  NameDescription
Public methodDerivative(Double)
Returns the value of the first derivative of the B-spline at a point.
(Inherited from BSpline.)
Public methodDerivative(Double, Int32)
Returns the value of the derivative of the B-spline at a point.
(Inherited from BSpline.)
Public methodDerivative(Double, Int32)
Returns the value of the derivative of the B-spline at each point of an array.
(Inherited from BSpline.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodEval(Double)
Returns the value of the B-spline at a point.
(Inherited from BSpline.)
Public methodEval(Double)
Returns the value of the B-spline at each point of an array.
(Inherited from BSpline.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetKnots
Returns a copy of the knot sequence.
(Inherited from BSpline.)
Public methodGetSpline
Returns a Spline representation of the B-spline.
(Inherited from BSpline.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodIntegral
Returns the value of an integral of the B-spline.
(Inherited from BSpline.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodToString
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 (x_i, f_i) 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 x_i, 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).

See Also

Reference

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