Class SimpleGaussianOptimizationFunction

java.lang.Object
  ScalableGaussianOptimizationFunction
      SimpleGaussianOptimizationFunction

All Implemented Interfaces:

edu.stanford.rsl.jpop.GradientOptimizableFunction, edu.stanford.rsl.jpop.OptimizableFunction, GaussianOptimizationFunction

public class SimpleGaussianOptimizationFunction
extends ScalableGaussianOptimizationFunction

This class provides an optimization function for the JPOP framework (http://www5.cs.fau.de/research/software/java-parallel-optimization-package/ or http://peaks.informatik.uni-erlangen.de/jpop-api/overview-summary.html.

The goal is to model a given set of values with a sum of three Gaussian functions and optimize the parameters of these Gaussian functions via the sum of squared differences. The following parameters are optimized: Mean (\mu_i), standard deviation (\sigma_i).

Formula: Sum of three Gaussians (in latex):
g(x) = \sum_{k=1}^{3} \mathcal{N}(x; \mu_k, \sigma_k)
Formula: Optimization function:
h(\theta) = \sum_{i = 1}^{N} (f(x_i)-g_s(x_i))^2 --> minimum
with \theta = (\mu_1, \sigma_1, \mu_2, \sigma_2, \mu_3, \sigma_3)

Except not noted otherwise in the method description, these parameters must have the same order as shown in the line above and will have the same order in the array that contains the final result of the optimization process.

Note: For further information please refer to the superclass ScalableGaussianOptimizationFunction. This implementation is strongly based on the superclass - for the variable scaling factors a constant value of 1 is passed.

Constructor Summary

SimpleGaussianOptimizationFunction(double[] xvalues, double[] yvalues)

Method Summary

double	evaluate(double[] params, int block) Unscaled version.
double	evaluateBasisFunction(double x, double[] params) Evaluates the function g_s (see class description) at position x.
double[]	gradient(double[] params, int block) Computes the Gradient at position x.

Methods inherited from class ScalableGaussianOptimizationFunction

getNumberOfProcessingBlocks, setNumberOfProcessingBlocks

Methods inherited from class java.lang.Object

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

Constructor Detail

SimpleGaussianOptimizationFunction

public SimpleGaussianOptimizationFunction(double[] xvalues,
                                          double[] yvalues)

See Also:

ScalableGaussianOptimizationFunction

Method Detail

evaluate

public double evaluate(double[] params,
                       int block)

Unscaled version.

Specified by:

evaluate in interface edu.stanford.rsl.jpop.OptimizableFunction

Overrides:

evaluate in class ScalableGaussianOptimizationFunction

Parameters:

params - = {\mu_1, \sigma_1, \mu_2, \sigma_2, \mu_3, \sigma_3}

block -

Returns:

the function value at x

gradient

public double[] gradient(double[] params,
                         int block)

Description copied from interface: edu.stanford.rsl.jpop.GradientOptimizableFunction

Computes the Gradient at position x. (Note that x is a Fortran Array which starts at 1.)

Specified by:

gradient in interface edu.stanford.rsl.jpop.GradientOptimizableFunction

Overrides:

gradient in class ScalableGaussianOptimizationFunction

Parameters:

params - the position

block - the block identifier. First block is 0. block is < getNumberOfProcessingBlocks().

Returns:

the gradient at x. (In Fortran Style)

evaluateBasisFunction

public double evaluateBasisFunction(double x,
                                    double[] params)

Description copied from class: ScalableGaussianOptimizationFunction

Evaluates the function g_s (see class description) at position x.

Specified by:

evaluateBasisFunction in interface GaussianOptimizationFunction

Overrides:

evaluateBasisFunction in class ScalableGaussianOptimizationFunction

params - The parameters for the three Gaussians. params = {\mu_1, \sigma_1, \mu_2, \sigma_2, \mu_3, \sigma_3, \alpha_1, \alpha_2, \alpha_3}