com.imsl.math
Class CsPeriodic
java.lang.Object
com.imsl.math.Spline
com.imsl.math.CsPeriodic
- All Implemented Interfaces:
- Cloneable, Serializable
- public class CsPeriodic
- 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](eqn_0715.png)
where

For more details, see de Boor (1978, pages 320-322).
- See Also:
- Example,
Serialized Form
Constructor Summary |
CsPeriodic(double[] xData,
double[] yData)
Constructs a cubic spline that interpolates the given
data points with periodic boundary conditions. |
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
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.
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Built June 1 2006.