Spline (JMSL Numerical Library)

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

All Implemented Interfaces:

Serializable, Cloneable

Direct Known Subclasses:

CsAkima, CsInterpolate, CsPeriodic, CsShape, CsSmooth, CsSmoothC2, CsTCB
```
public abstract class Spline
extends Object
implements Serializable, Cloneable
```
Spline represents and evaluates univariate piecewise polynomial splines.
A univariate piecewise polynomial (function) p(x) is specified by giving its breakpoint sequence $xi in {bf R}^n$ , the order k (degree k-1) of its polynomial pieces, and the matrix c of its local polynomial coefficients. In terms of this information, the piecewise polynomial (ppoly) function is given by
$p(x) = sum_{j=1}^k c_{ji} frac{(x-xi_i)^{j-1}}{(j-1)!} ;;{rm for}; xi_i le x le xi_{i+1}$
The breakpoint sequence is assumed to be strictly increasing, and we extend the ppoly function to the entire real axis by extrapolation from the first and last intervals.

See Also:
Akima Example, Interpolate Example, Periodic Example, Shape Preserving Example, Smoothing Example 1, Smoothing Example 2, Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`protected double[]`	`breakPoint` The breakpoint array of length n, where n is the number of piecewise polynomials.
`protected double[][]`	`coef` Coefficients of the piecewise polynomials.
`protected static double`	`EPSILON_LARGE` The largest relative spacing for double.

Constructor Summary

Constructors
Constructor and Description

Spline()

Constructors
Constructor and Description
`Spline()`

Method Summary

Methods
Modifier and Type	Method and Description
`protected void`	`copyAndSortData(double[] xData, double[] yData)` Copy and sort xData into breakPoint and yData into the first column of coef.
`protected void`	`copyAndSortData(double[] xData, double[] yData, double[] weight)` Copy and sort xData into breakPoint and yData into the first column of coef.
`double`	`derivative(double x)` Returns the value of the first derivative of the spline at a point.
`double[]`	`derivative(double[] x, int ideriv)` Returns the value of the derivative of the spline at each point of an array.
`double`	`derivative(double x, int ideriv)` Returns the value of the derivative of the spline at a point.
`double[]`	`getBreakpoints()` Returns a copy of the breakpoints.
`double`	`integral(double a, double b)` Returns the value of an integral of the spline.
`double`	`value(double x)` Returns the value of the spline at a point.
`double[]`	`value(double[] x)` Returns the value of the spline at each point of an array.

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

- Field Detail
  - breakPoint
```
protected double[] breakPoint
```
    The breakpoint array of length n, where n is the number of piecewise polynomials.
  - coef
```
protected double[][] coef
```
    Coefficients of the piecewise polynomials. This is an n by k array, where n is the number of piecewise polynomials and k is the order (degree+1) of the piecewise polynomials.
    coef[i] contains the coefficients for the piecewise polynomial valid in the interval [x[k],x[k+1]).
  - EPSILON_LARGE
```
protected static final double EPSILON_LARGE
```
    The largest relative spacing for double.
    
    See Also:
    Constant Field Values
- Constructor Detail
  - Spline
```
public Spline()
```
- Method Detail
  - copyAndSortData
```
protected void copyAndSortData(double[] xData,
                   double[] yData)
```
    Copy and sort xData into breakPoint and yData into the first column of coef.
  - copyAndSortData
```
protected void copyAndSortData(double[] xData,
                   double[] yData,
                   double[] weight)
```
    Copy and sort xData into breakPoint and yData into the first column of coef.
  - derivative
```
public double derivative(double x)
```
    Returns the value of the first derivative of the spline at a point.
    
    Parameters:
    x - a double, the point at which the derivative is to be evaluated
    
    Returns:
    a double containing the value of the first derivative of the spline at the point x
  - derivative
```
public double[] derivative(double[] x,
                  int ideriv)
```
    Returns the value of the derivative of the spline at each point of an array.
    
    Parameters:
    x - a double array of points at which the derivative is to be evaluated
    ideriv - an int specifying the derivative to be computed. If zero, the function value is returned. If one, the first derivative is returned, etc.
    
    Returns:
    a double array containing the value of the derivative of the spline at each point of the array x
  - derivative
```
public double derivative(double x,
                int ideriv)
```
    Returns the value of the derivative of the spline at a point.
    
    Parameters:
    x - a double, the point at which the derivative is to be evaluated
    ideriv - an int specifying the derivative to be computed. If zero, the function value is returned. If one, the first derivative is returned, etc.
    
    Returns:
    a double containing the value of the derivative of the spline at the point x
  - getBreakpoints
```
public double[] getBreakpoints()
```
    Returns a copy of the breakpoints.
    
    Returns:
    a double array containing a copy of the breakpoints
  - integral
```
public double integral(double a,
              double b)
```
    Returns the value of an integral of the spline.
    
    Parameters:
    a - a double specifying the lower limit of integration
    b - a double specifying the upper limit of integration
    
    Returns:
    a double, the integral of the spline from a to b
  - value
```
public double value(double x)
```
    Returns the value of the spline at a point.
    
    Parameters:
    x - a double, the point at which the spline is to be evaluated
    
    Returns:
    a double giving the value of the spline at the point x
  - value
```
public double[] value(double[] x)
```
    Returns the value of the spline at each point of an array.
    
    Parameters:
    x - a double array of points at which the spline is to be evaluated
    
    Returns:
    a double array containing the value of the spline at each point of the array x

Class Spline

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

breakPoint

coef

EPSILON_LARGE

Constructor Detail

Spline

Method Detail

copyAndSortData

copyAndSortData

derivative

derivative

derivative

getBreakpoints

integral

value

value