org.apache.commons.math3.analysis.interpolation

Class BicubicSplineInterpolatingFunction

java.lang.Object

org.apache.commons.math3.analysis.interpolation.BicubicSplineInterpolatingFunction

All Implemented Interfaces:

BivariateFunction

public class BicubicSplineInterpolatingFunction
extends java.lang.Object
implements BivariateFunction

Function that implements the bicubic spline interpolation.

Since:

2.1

Version:

$Id: BicubicSplineInterpolatingFunction.java 1379904 2012-09-01 23:54:52Z erans $

Field Summary

Fields

Modifier and Type	Field and Description
private static double[][]	AINV Matrix to compute the spline coefficients from the function values and function derivatives values
private BivariateFunction[][][]	partialDerivatives Partial derivatives The value of the first index determines the kind of derivatives: 0 = first partial derivatives wrt x 1 = first partial derivatives wrt y 2 = second partial derivatives wrt x 3 = second partial derivatives wrt y 4 = cross partial derivatives
private BicubicSplineFunction[][]	splines Set of cubic splines patching the whole data grid
private double[]	xval Samples x-coordinates
private double[]	yval Samples y-coordinates

Constructor Summary

Constructors

Constructor and Description
BicubicSplineInterpolatingFunction(double[] x, double[] y, double[][] f, double[][] dFdX, double[][] dFdY, double[][] d2FdXdY)

Method Summary

Methods

Modifier and Type	Method and Description
private void	computePartialDerivatives() Compute all partial derivatives.
private double[]	computeSplineCoefficients(double[] beta) Compute the spline coefficients from the list of function values and function partial derivatives values at the four corners of a grid element.
private double	partialDerivative(int which, double x, double y)
double	partialDerivativeX(double x, double y)
double	partialDerivativeXX(double x, double y)
double	partialDerivativeXY(double x, double y)
double	partialDerivativeY(double x, double y)
double	partialDerivativeYY(double x, double y)
private int	searchIndex(double c, double[] val)
double	value(double x, double y) Compute the value for the function.

Methods inherited from class java.lang.Object

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

Field Detail

AINV

private static final double[][] AINV

Matrix to compute the spline coefficients from the function values and function derivatives values

xval

private final double[] xval

Samples x-coordinates

yval

private final double[] yval

Samples y-coordinates

splines

private final BicubicSplineFunction[][] splines

Set of cubic splines patching the whole data grid

partialDerivatives

private BivariateFunction[][][] partialDerivatives

Partial derivatives The value of the first index determines the kind of derivatives: 0 = first partial derivatives wrt x 1 = first partial derivatives wrt y 2 = second partial derivatives wrt x 3 = second partial derivatives wrt y 4 = cross partial derivatives

Constructor Detail

BicubicSplineInterpolatingFunction

public BicubicSplineInterpolatingFunction(double[] x,
                                  double[] y,
                                  double[][] f,
                                  double[][] dFdX,
                                  double[][] dFdY,
                                  double[][] d2FdXdY)
                                   throws DimensionMismatchException,
                                          NoDataException,
                                          NonMonotonicSequenceException

Parameters:

x - Sample values of the x-coordinate, in increasing order.

y - Sample values of the y-coordinate, in increasing order.

f - Values of the function on every grid point.

dFdX - Values of the partial derivative of function with respect to x on every grid point.

dFdY - Values of the partial derivative of function with respect to y on every grid point.

d2FdXdY - Values of the cross partial derivative of function on every grid point.

Throws:

DimensionMismatchException - if the various arrays do not contain the expected number of elements.

NonMonotonicSequenceException - if x or y are not strictly increasing.

NoDataException - if any of the arrays has zero length.

Method Detail

value

public double value(double x,
           double y)
             throws OutOfRangeException

Compute the value for the function.

Specified by:

value in interface BivariateFunction

Parameters:

x - Abscissa for which the function value should be computed.

y - Ordinate for which the function value should be computed.

Returns:

the value.

Throws:

OutOfRangeException

partialDerivativeX

public double partialDerivativeX(double x,
                        double y)
                          throws OutOfRangeException

Parameters:

x - x-coordinate.

y - y-coordinate.

Returns:

the value at point (x, y) of the first partial derivative with respect to x.

Throws:

OutOfRangeException - if x (resp. y) is outside the range defined by the boundary values of xval (resp. yval).

partialDerivativeY

public double partialDerivativeY(double x,
                        double y)
                          throws OutOfRangeException

Parameters:

x - x-coordinate.

y - y-coordinate.

Returns:

the value at point (x, y) of the first partial derivative with respect to y.

Throws:

OutOfRangeException - if x (resp. y) is outside the range defined by the boundary values of xval (resp. yval).

partialDerivativeXX

public double partialDerivativeXX(double x,
                         double y)
                           throws OutOfRangeException

Parameters:

x - x-coordinate.

y - y-coordinate.

Returns:

the value at point (x, y) of the second partial derivative with respect to x.

Throws:

OutOfRangeException - if x (resp. y) is outside the range defined by the boundary values of xval (resp. yval).

partialDerivativeYY

public double partialDerivativeYY(double x,
                         double y)
                           throws OutOfRangeException

Parameters:

x - x-coordinate.

y - y-coordinate.

Returns:

the value at point (x, y) of the second partial derivative with respect to y.

Throws:

OutOfRangeException - if x (resp. y) is outside the range defined by the boundary values of xval (resp. yval).

partialDerivativeXY

public double partialDerivativeXY(double x,
                         double y)
                           throws OutOfRangeException

Parameters:

x - x-coordinate.

y - y-coordinate.

Returns:

the value at point (x, y) of the second partial cross-derivative.

Throws:

OutOfRangeException - if x (resp. y) is outside the range defined by the boundary values of xval (resp. yval).

partialDerivative

private double partialDerivative(int which,
                       double x,
                       double y)
                          throws OutOfRangeException

Parameters:

which - First index in partialDerivatives.

x - x-coordinate.

y - y-coordinate.

Returns:

the value at point (x, y) of the selected partial derivative.

Throws:

OutOfRangeException - if x (resp. y) is outside the range defined by the boundary values of xval (resp. yval).

computePartialDerivatives

private void computePartialDerivatives()

Compute all partial derivatives.

searchIndex

private int searchIndex(double c,
              double[] val)

Parameters:

c - Coordinate.

val - Coordinate samples.

Returns:

the index in val corresponding to the interval containing c, or -1 if c is out of the range defined by the boundary values of val.

computeSplineCoefficients

private double[] computeSplineCoefficients(double[] beta)

Compute the spline coefficients from the list of function values and function partial derivatives values at the four corners of a grid element. They must be specified in the following order:

• f(0,0)
• f(1,0)
• f(0,1)
• f(1,1)
• f_x(0,0)
• f_x(1,0)
• f_x(0,1)
• f_x(1,1)
• f_y(0,0)
• f_y(1,0)
• f_y(0,1)
• f_y(1,1)
• f_xy(0,0)
• f_xy(1,0)
• f_xy(0,1)
• f_xy(1,1)

where the subscripts indicate the partial derivative with respect to the corresponding variable(s).

Parameters:

beta - List of function values and function partial derivatives values.

Returns:

the spline coefficients.