org.esa.beam.util.math
Class FXYSum

java.lang.Object
  org.esa.beam.util.math.FXYSum

Direct Known Subclasses:

FXYSum.BiCubic, FXYSum.BiLinear, FXYSum.BiQuadric, FXYSum.Cubic, FXYSum.Linear, FXYSum.Quadric

public class FXYSum
extends Object

The class FXYSum represents a sum of function terms sum(c[i] * f[i](x,y), i=0, n-1) where the vector c is a double array of constant coefficients and the vector f is an array of functions of type FXY in x and y.

The vector c of constants is set by the approximate(double[][], int[]) method.

After vector c is set, the actual function values z(x,y) are retrieved using the computeZ(double, double) method.

Version:

$Revision$ $Date$

Author:

Norman Fomferra

Nested Class Summary

static class	FXYSum.BiCubic Provides an optimized computeZ method for bi-cubic polynomials (order = 3+3).
static class	FXYSum.BiLinear Provides an optimized computeZ method for bi-linear polynomials (order = 1+1).
static class	FXYSum.BiQuadric Provides an optimized computeZ method for bi-quadric polynomials (order = 2+2).
static class	FXYSum.Cubic Provides an optimized computeZ method for cubic polynomials (order = 3).
static class	FXYSum.Linear Provides an optimized computeZ method for linear polynomials (order = 1).
static class	FXYSum.Quadric Provides an optimized computeZ method for quadric polynomials (order = 2).

Field Summary

static FXY[]	FXY_4TH
static FXY[]	FXY_BI_4TH
static FXY[]	FXY_BI_CUBIC
static FXY[]	FXY_BI_LINEAR
static FXY[]	FXY_BI_QUADRATIC
static FXY[]	FXY_CUBIC
static FXY[]	FXY_LINEAR
static FXY[]	FXY_QUADRATIC

Constructor Summary

FXYSum(FXY[] functions)
Constructs a new sum of terms sum(c[i] * f[i](x,y), i=0, n-1) for the given vector of functions.

FXYSum(FXY[] functions, int order)
Constructs a new sum of terms sum(c[i] * f[i](x,y), i=0, n-1) for the given vector of functions and a polynomial order.

FXYSum(FXY[] functions, int order, double[] coefficients)
Constructs a new sum of terms sum(c[i] * f[i](x,y), i=0, n-1) for the given vector of functions and a polynomial order.

Method Summary

protected void	appendCFunctionCodeBody(String fname, String x, String y, StringBuffer sb)
protected void	appendCFunctionCodeEnd(String fname, String x, String y, StringBuffer sb)
protected void	appendCFunctionCodePart(StringBuffer sb, String part, String x, String y)
protected void	appendCFunctionCodeStart(String fname, String x, String y, StringBuffer sb)
void	approximate(double[][] data, int[] indices) Approximates the given data points x,y,z by this sum of function terms so that z ~ sum(c[i] * f[i](x,y), i=0, n-1).
double	computeZ(double x, double y) Computes this sum of function terms z(x,y) = sum(c[i] * f[i](x,y), i=0, n-1).
static double	computeZ(FXY[] f, double[] c, double x, double y) Computes z(x,y) = sum(c[i] * f[i](x,y), i = 0, n - 1).
String	createCFunctionCode(String fname, String x, String y) Returns this sum of function terms as human-readable C-code.
static FXYSum	createCopy(FXYSum fxySum) Creates a copy of the given fxySum.
static FXYSum	createFXYSum(int order, double[] coefficients) Creates a FXYSum by the given order and coefficients.
double[]	getCoefficients() Gets the vector c of coefficient elements c[i].
FXY[]	getFunctions() Gets the vector f of functions elements f[i](x,y).
double	getMaxError() Gets the maximum, absolute error of the approximation.
int	getNumTerms() Gets the number n of terms c[i] * f[i](x,y).
int	getOrder() Gets the polynomial order, if any.
double	getRootMeanSquareError() Gets the root mean square error.

Methods inherited from class java.lang.Object

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

Field Detail

FXY_LINEAR

public static final FXY[] FXY_LINEAR

FXY_BI_LINEAR

public static final FXY[] FXY_BI_LINEAR

FXY_QUADRATIC

public static final FXY[] FXY_QUADRATIC

FXY_BI_QUADRATIC

public static final FXY[] FXY_BI_QUADRATIC

FXY_CUBIC

public static final FXY[] FXY_CUBIC

FXY_BI_CUBIC

public static final FXY[] FXY_BI_CUBIC

FXY_4TH

public static final FXY[] FXY_4TH

FXY_BI_4TH

public static final FXY[] FXY_BI_4TH

Constructor Detail

FXYSum

public FXYSum(FXY[] functions)

Constructs a new sum of terms sum(c[i] * f[i](x,y), i=0, n-1) for the given vector of functions. The vector c is initally set to zero and will remeain zero until the method approximate(double[][], int[]) is performed with given data on this function sum.

Parameters:

functions - the vector F of functions

FXYSum

public FXYSum(FXY[] functions,
              int order)

Constructs a new sum of terms sum(c[i] * f[i](x,y), i=0, n-1) for the given vector of functions and a polynomial order. The vector c is initally set to zero and will remeain zero until the method approximate(double[][], int[]) is performed with given data on this function sum.

Parameters:

functions - the vector F of functions

order - the polynomial order (for descriptive purpose only), -1 if unknown

FXYSum

public FXYSum(FXY[] functions,
              int order,
              double[] coefficients)

Constructs a new sum of terms sum(c[i] * f[i](x,y), i=0, n-1) for the given vector of functions and a polynomial order. The vector c is set by the coefficients parameter. The coefficients will be recalculated if the method approximate(double[][], int[]) is called.

Parameters:

functions - the vector F of functions

order - the polynomial order (for descriptive purpose only), -1 if unknown

coefficients - the vector c

Method Detail

createFXYSum

public static FXYSum createFXYSum(int order,
                                  double[] coefficients)

Creates a FXYSum by the given order and coefficients.

Note: This factory method supprots only the creation of instances of the following FXYSum classes:

• FXYSum.Linear - order = 1 ; number of coefficients = 3
• FXYSum.BiLinear - order = 2 ; number of coefficients = 4
• FXYSum.Quadric - order = 2 ; number of coefficients = 6
• FXYSum.BiQuadric - order = 4 ; number of coefficients = 9
• FXYSum.Cubic - order = 3 ; number of coefficients = 10
• FXYSum.BiCubic - order = 6 ; number of coefficients = 16

Parameters:

order - the order of the sum

coefficients - the coefficients

Returns:

returns a FXYSum instance, or null if the resulting instance is one of the supported.

createCopy

public static FXYSum createCopy(FXYSum fxySum)

Creates a copy of the given fxySum.

Parameters:

fxySum - the FXYSum to copy

Returns:

a copy of the given FXYSum

getNumTerms

public final int getNumTerms()

Gets the number n of terms c[i] * f[i](x,y).

Returns:

the number of function terms

getFunctions

public final FXY[] getFunctions()

Gets the vector f of functions elements f[i](x,y).

Returns:

the vector F of functions

getCoefficients

public final double[] getCoefficients()

Gets the vector c of coefficient elements c[i].

Returns:

the vector F of functions

getOrder

public int getOrder()

Gets the polynomial order, if any.

Returns:

the polynomial order or -1 if unknown

getRootMeanSquareError

public double getRootMeanSquareError()

Gets the root mean square error.

Returns:

the root mean square error

getMaxError

public double getMaxError()

Gets the maximum, absolute error of the approximation.

Returns:

the maximum, absolute error

computeZ

public double computeZ(double x,
                       double y)

Computes this sum of function terms z(x,y) = sum(c[i] * f[i](x,y), i=0, n-1). The method will return zero unless the approximate(double[][], int[]) is called in order to set the coefficient vector c.

Parameters:

x - the x value

y - the y value

Returns:

the z value

See Also:

computeZ(FXY[], double[], double, double)

computeZ

public static double computeZ(FXY[] f,
                              double[] c,
                              double x,
                              double y)

Computes z(x,y) = sum(c[i] * f[i](x,y), i = 0, n - 1).

Parameters:

f - the function vector

c - the coeffcient vector

x - the x value

y - the y value

Returns:

the z value

approximate

public void approximate(double[][] data,
                        int[] indices)

Approximates the given data points x,y,z by this sum of function terms so that z ~ sum(c[i] * f[i](x,y), i=0, n-1). The method also sets the error statistics which can then be retrieved by the getRootMeanSquareError() and getMaxError() methods.

Parameters:

data - an array of values of the form {{x1,y1,z1}, {x2,y2,z2}, {x3,y3,z3}, ...}

indices - an array of coordinate indices, determining the indices of x, y and z within a data element. If null then indices defaults to the array {0, 1, 2}.

See Also:

Approximator.approximateFXY(double[][], int[], FXY[], double[]), Approximator.computeErrorStatistics(double[][], int[], FXY[], double[]), computeZ(double, double)

createCFunctionCode

public String createCFunctionCode(String fname,
                                  String x,
                                  String y)

Returns this sum of function terms as human-readable C-code.

Parameters:

fname - the name of the function z(x,y) = sum(C[i]*F[i](x,y), i, n)

x - the name of the x variable

y - the name of the y variable

Returns:

the C-code

appendCFunctionCodeStart

protected void appendCFunctionCodeStart(String fname,
                                        String x,
                                        String y,
                                        StringBuffer sb)

appendCFunctionCodeBody

protected void appendCFunctionCodeBody(String fname,
                                       String x,
                                       String y,
                                       StringBuffer sb)

appendCFunctionCodeEnd

protected void appendCFunctionCodeEnd(String fname,
                                      String x,
                                      String y,
                                      StringBuffer sb)

appendCFunctionCodePart

protected void appendCFunctionCodePart(StringBuffer sb,
                                       String part,
                                       String x,
                                       String y)