CsPeriodic (JMSL Numerical Library)

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JMSL^TM Numerical Library 6.1

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com.imsl.math
Class CsPeriodic

java.lang.Object
  com.imsl.math.Spline
      com.imsl.math.CsPeriodic

All Implemented Interfaces:: Serializable, Cloneable

public class CsPeriodic
extends Spline
extends Spline

Extension of the Spline class to interpolate data points with periodic boundary conditions.

Class CsPeriodic computes a cubic spline interpolant to a set of data points for . The breakpoints of the spline are the abscissas. The program enforces periodic endpoint conditions. This means that the spline s satisfies s(a) = s(b), , and , where a is the leftmost abscissa and b is the rightmost abscissa. If the ordinate values corresponding to a and b are not equal, then a warning message is issued. The ordinate value at b is set equal to the ordinate value at a and the interpolant is computed.

If the data points arise from the values of a smooth (say ) periodic function f, i.e. , then the error will behave in a predictable fashion. Let be the breakpoint vector for the above spline interpolant. Then, the maximum absolute error satisfies

$|f-s|_{[xi_0,xi_{n-1}]} le C |f^{(4)}|_{[{xi_0 ,xi_{n-1} }]} |xi|^4$

where

$|xi|;: = max_{i=1,ldots,n-1} |xi_i - xi_{i - 1} |$

For more details, see de Boor (1978, pages 320-322).

See Also:: Example, Serialized Form

Field Summary

Fields inherited from class com.imsl.math.Spline
`breakPoint, coef, EPSILON_LARGE`

Constructor Summary
`CsPeriodic(double[] xData, double[] yData)` Constructs a cubic spline that interpolates the given data points with periodic boundary conditions.

Method Summary

Methods inherited from class com.imsl.math.Spline
`copyAndSortData, copyAndSortData, derivative, derivative, derivative, getBreakpoints, integral, value, value`

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

CsPeriodic

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

Constructs a cubic spline that interpolates the given data points with periodic boundary conditions.

Parameters:: xData - A double array containing the x-coordinates of the data. There must be at least 4 data points and 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.