org.esa.beam.util.math
Class Approximator

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

public class Approximator
extends Object

A utility class which can be used to find approximation functions for a given dataset.

Version:

$Revision$ $Date$

Author:

Norman Fomferra

Constructor Summary

Approximator()

Method Summary

static void	approximateFX(double[][] data, int[] indices, FX[] f, double[] c) Solves a linear equation system with each term having the form c * f(x).
static void	approximateFXY(double[][] data, int[] indices, FXY[] f, double[] c) Solves a linear equation system with each term having the form c * f(x,y).
static double[]	computeErrorStatistics(double[][] data, int[] indices, FXY[] f, double[] c) Returns the root mean square error (RMSE) for the approximation of the given data with a function given by z(x,y) = c[0]*f[0](x,y) + c[1]*f[1](x,y) + c[2]*f[2](x,y) + ... + c[n-1]*f[n-1](x,y).
static double	computeRMSE(double[][] data, int[] indices, FXY[] f, double[] c) Returns the root mean square error (RMSE) for the approximation of the given data with a function given by z(x,y) = c[0]*f[0](x,y) + c[1]*f[1](x,y) + c[2]*f[2](x,y) + ... + c[n-1]*f[n-1](x,y).
static double	computeY(FX[] f, double[] c, double x) Computes y(x) = sum(c[i] * f[i](x), 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).
static double	getRMSE(double[][] data, int[] indices, FX[] f, double[] c) Returns the root mean square error (RMSE) for the approximation of the given data with a function given by y'(x) = c[0]*f[0](x) + c[1]*f[1](x) + c[2]*f[2](x) + ... + c[n-1]*f[n-1](x).
static void	solve1(double[][] a, double[] b, double[] c) Solves the matrix equation A * C = B for given A,B by performing the operation C = A.solve(B).

Methods inherited from class java.lang.Object

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

Constructor Detail

Approximator

public Approximator()

Method Detail

approximateFX

public static void approximateFX(double[][] data,
                                 int[] indices,
                                 FX[] f,
                                 double[] c)

Solves a linear equation system with each term having the form c * f(x). The method finds the coefficients c[0] to c[n-1] with n = f.length for an approximation function y'(x) = c[0]*f[0](x) + c[1]*f[1](x) + c[2]*f[2](x) + ... + c[n-1]*f[n-1](x) which approximates the given data vector x_i=data[i][0], y_i=data[i][1] with i = 0 to data.length-1.

Parameters:

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

indices - the co-ordinate indices vector, determining the indices of x,y within data. If null then indices defaults to {0, 1}.

f - the function vector, each function has the form y=f(x)

c - the resulting coefficient vector, must have the same size as the function vector

approximateFXY

public static void approximateFXY(double[][] data,
                                  int[] indices,
                                  FXY[] f,
                                  double[] c)

Solves a linear equation system with each term having the form c * f(x,y). The method finds the coefficients c[0] to c[n-1] with n = f.length for an approximation function z'(x,y) = c[0]*f[0](x,y) + c[1]*f[1](x,y) + c[2]*f[2](x,y) + ... + c[n-1]*f[n-1](x,y) which approximates the given data vector x_i=data[i][0], y_i=data[i][1], z_i=data[i][2] with i = 0 to data.length-1.

Parameters:

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

indices - the co-ordinate indices vector, determining the indices of x,y,z within data. If null then indices defaults to {0, 1, 2}.

f - the function vector, each function has the form z=f(x,y)

c - the resulting coefficient vector, must have the same size as the function vector

getRMSE

public static double getRMSE(double[][] data,
                             int[] indices,
                             FX[] f,
                             double[] c)

Returns the root mean square error (RMSE) for the approximation of the given data with a function given by y'(x) = c[0]*f[0](x) + c[1]*f[1](x) + c[2]*f[2](x) + ... + c[n-1]*f[n-1](x).

Parameters:

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

indices - the co-ordinate indices vector, determining the indices of x,y within data. If null then indices defaults to {0, 1}.

f - the function vector, each function has the form y=f(x)

c - the coefficient vector, must have the same size as the function vector

computeRMSE

public static double computeRMSE(double[][] data,
                                 int[] indices,
                                 FXY[] f,
                                 double[] c)

Returns the root mean square error (RMSE) for the approximation of the given data with a function given by z(x,y) = c[0]*f[0](x,y) + c[1]*f[1](x,y) + c[2]*f[2](x,y) + ... + c[n-1]*f[n-1](x,y).

Parameters:

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

indices - the co-ordinate indices vector, determining the indices of x,y,z within data. If null then indices defaults to {0, 1, 2}.

f - the function vector, each function has the form z=f(x,y)

c - the coefficient vector, must have the same size as the function vector

computeErrorStatistics

public static double[] computeErrorStatistics(double[][] data,
                                              int[] indices,
                                              FXY[] f,
                                              double[] c)

Returns the root mean square error (RMSE) for the approximation of the given data with a function given by z(x,y) = c[0]*f[0](x,y) + c[1]*f[1](x,y) + c[2]*f[2](x,y) + ... + c[n-1]*f[n-1](x,y).

Parameters:

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

indices - the co-ordinate indices vector, determining the indices of x,y,z within data. If null then indices defaults to {0, 1, 2}.

f - the function vector, each function has the form z=f(x,y)

c - the coefficient vector, must have the same size as the function vector

computeY

public static double computeY(FX[] f,
                              double[] c,
                              double x)

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

Parameters:

f - the function vector

c - the coeffcient vector

x - the x value

Returns:

the y value

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

solve1

public static void solve1(double[][] a,
                          double[] b,
                          double[] c)

Solves the matrix equation A * C = B for given A,B by performing the operation C = A.solve(B).

Parameters:

a - matrix A

b - matrix B

c - result matrix C