Package org.apache.commons.math3.analysis.interpolation

Class TricubicInterpolatingFunction

java.lang.Object

org.apache.commons.math3.analysis.interpolation.TricubicInterpolatingFunction

All Implemented Interfaces:

TrivariateFunction

public class TricubicInterpolatingFunction
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. Eng 2005; 63:455-471

Since:

3.4.

Field Summary

Fields

Modifier and Type	Field	Description
private static final double[][]	AINV	Matrix to compute the spline coefficients from the function values and function derivatives values
private final TricubicFunction[][][]	splines	Set of cubic splines patching the whole data grid
private final double[]	xval	Samples x-coordinates
private final double[]	yval	Samples y-coordinates
private final double[]	zval	Samples z-coordinates

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
private double[]	computeCoefficients(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.
boolean	isValidPoint(double x, double y, double z)	Indicates whether a point is within the interpolation range.
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 Details

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 TricubicFunction[][][] splines

Set of cubic splines patching the whole data grid

Constructor Details

TricubicInterpolatingFunction

public TricubicInterpolatingFunction(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 Details

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.

isValidPoint

public boolean isValidPoint(double x,
 double y,
 double z)

Indicates whether a point is within the interpolation range.

Parameters:

x - First coordinate.

y - Second coordinate.

z - Third coordinate.

Returns:

true if (x, y, z) is a valid point.

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.

computeCoefficients

private double[] computeCoefficients(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.