Package com.imsl.math

Class Spline

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 \(k \times (n-1)\) 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 \(\xi\) 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:

  • Field Summary

    Fields
    Modifier and Type
    Field
    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 final double
    EPSILON_LARGE
    The largest relative spacing for double.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Spline()
     

  • Method Summary

    Modifier and Type
    Method
    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 Details

    • 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]).

    • breakPoint

      protected double[] breakPoint
      The breakpoint array of length n, where n is the number of piecewise polynomials.

    • EPSILON_LARGE

      protected static final double EPSILON_LARGE
      The largest relative spacing for double.
      See Also:

  • Constructor Details

    • Spline

      public Spline()

  • Method Details

    • 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.

    • 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

    • 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 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

    • 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

    • 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

    • 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