org.apache.commons.math3.analysis.interpolation
Class TricubicSplineInterpolatingFunction

java.lang.Object
  org.apache.commons.math3.analysis.interpolation.TricubicSplineInterpolatingFunction

All Implemented Interfaces:

TrivariateFunction

public class TricubicSplineInterpolatingFunction
extends Object
implements TrivariateFunction

Function that implements the tricubic spline interpolation, as proposed in Tricubic interpolation in three dimensions
F. Lekien and J. Marsden
Int. J. Numer. Meth. Engng 2005; 63:455-471

Since:

2.2

Version:

$Id: TricubicSplineInterpolatingFunction.java 1385314 2012-09-16 16:35:49Z tn $

Field Summary

private static double[][]	AINV Matrix to compute the spline coefficients from the function values and function derivatives values
private TricubicSplineFunction[][][]	splines Set of cubic splines pacthing the whole data grid
private double[]	xval Samples x-coordinates
private double[]	yval Samples y-coordinates
private double[]	zval Samples z-coordinates

Constructor Summary

TricubicSplineInterpolatingFunction(double[] x, double[] y, double[] z, double[][][] f, double[][][] dFdX, double[][][] dFdY, double[][][] dFdZ, double[][][] d2FdXdY, double[][][] d2FdXdZ, double[][][] d2FdYdZ, double[][][] d3FdXdYdZ)

Method Summary

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 int	searchIndex(double c, double[] val)
double	value(double x, double y, double z) 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

zval

private final double[] zval

Samples z-coordinates

splines

private final TricubicSplineFunction[][][] splines

Set of cubic splines pacthing the whole data grid

Constructor Detail

TricubicSplineInterpolatingFunction

public TricubicSplineInterpolatingFunction(double[] x,
                                           double[] y,
                                           double[] z,
                                           double[][][] f,
                                           double[][][] dFdX,
                                           double[][][] dFdY,
                                           double[][][] dFdZ,
                                           double[][][] d2FdXdY,
                                           double[][][] d2FdXdZ,
                                           double[][][] d2FdYdZ,
                                           double[][][] d3FdXdYdZ)
                                    throws NoDataException,
                                           DimensionMismatchException,
                                           NonMonotonicSequenceException

Parameters:

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

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

z - 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.

dFdZ - Values of the partial derivative of function with respect to z on every grid point.

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

d2FdXdZ - Values of the cross partial derivative of function on every grid point.

d2FdYdZ - Values of the cross partial derivative of function on every grid point.

d3FdXdYdZ - Values of the cross partial derivative of function on every grid point.

Throws:

NoDataException - if any of the arrays has zero length.

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

NonMonotonicSequenceException - if x, y or z are not strictly increasing.

Method Detail

value

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

Compute the value for the function.

Specified by:

value in interface TrivariateFunction

Parameters:

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

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

z - z-coordinate for which the function value should be computed.

Returns:

the value.

Throws:

OutOfRangeException - if any of the variables is outside its interpolation range.

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 end 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(0,0,0)
• f(1,0,0)
• f(0,1,0)
• f(1,1,0)
• f(0,0,1)
• f(1,0,1)
• f(0,1,1)
• f(1,1,1)
• f_x(0,0,0)
• ... (same order as above)
• f_x(1,1,1)
• f_y(0,0,0)
• ... (same order as above)
• f_y(1,1,1)
• f_z(0,0,0)
• ... (same order as above)
• f_z(1,1,1)
• f_xy(0,0,0)
• ... (same order as above)
• f_xy(1,1,1)
• f_xz(0,0,0)
• ... (same order as above)
• f_xz(1,1,1)
• f_yz(0,0,0)
• ... (same order as above)
• f_yz(1,1,1)
• f_xyz(0,0,0)
• ... (same order as above)
• f_xyz(1,1,1)

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.