com.imsl.math

Class BsInterpolate

java.lang.Object

com.imsl.math.BSpline

com.imsl.math.BsInterpolate

All Implemented Interfaces:

Serializable, Cloneable

public class BsInterpolate
extends BSpline

Extension of the BSpline class to interpolate data points.

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:

Example, Serialized Form

Field Summary

Fields inherited from class com.imsl.math.BSpline

coef, knot, order

Constructor Summary

Constructors

Constructor and Description
BsInterpolate(double[] xData, double[] yData) Constructs a B-spline that interpolates the given data points.
BsInterpolate(double[] xData, double[] yData, int order) Constructs a B-spline that interpolates the given data points and order, using a default "not-a-knot" spline knot sequence.
BsInterpolate(double[] xData, double[] yData, int order, double[] knot) Constructs a B-spline that interpolates the given data points, using the specified order and knots.

Method Summary

Methods inherited from class com.imsl.math.BSpline

derivative, derivative, derivative, getKnots, getSpline, integral, value, value

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BsInterpolate

public BsInterpolate(double[] xData,
                     double[] yData)

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.

Parameters:

xData - A double array containing the x-coordinates of the data. Values must be distinct.

yData - A double array containing the y-coordinates of the data. The arrays xData and yData must have the same length.

BsInterpolate

public BsInterpolate(double[] xData,
                     double[] yData,
                     int order)

Constructs a B-spline that interpolates the given data points and order, using a default "not-a-knot" spline knot sequence.

Parameters:

xData - A double array containing the x-coordinates of the data. Values must be distinct.

yData - A double array containing the y-coordinates of the data.The arrays xData and yData must have the same length.

order - An int denoting the order of the B-spline.

BsInterpolate

public BsInterpolate(double[] xData,
                     double[] yData,
                     int order,
                     double[] knot)

Constructs a B-spline that interpolates the given data points, using the specified order and knots.

Parameters:

xData - A double array containing the x-coordinates of the data. Values must be distinct.

yData - A double array containing the y-coordinates of the data.The arrays xData and yData must have the same length.

order - An int denoting the order of the spline.

knot - A double array containing the knot sequence for the B-spline.