vec_math
Class LeastFourier

java.lang.Object
  util.PropertyContainer
      util.PropertyResources
          util.PropertyBundles
              vec_math.AbstractAnalyser
                  vec_math.LeastFourier

All Implemented Interfaces:

Cloneable, Initializable, LocalizedSupplying, PropertySupplying, ResourceSupplying, Analyser

public class LeastFourier
extends AbstractAnalyser

This analyser recursively fits fourier series like

   F_M = ΣMA_k*cos(2πf·k·t)+B_k*sin(2πf·k·t)
   

for increasing M to the data. It starts with the frequency estimated specified by the key KEY_FREQUENCY, or, if not given, tries to estimate the highest frequency from a CleanFourier periodogram focused on the highest peak. The order of the (partial) Fourier series fitted is either determined by KEY_ORDER, or by the stability criterium KEY_CONVERGENCE, which is the relative change in frequency for the step from M-1 to M. If the frequency change drops below this value, the order is reached.

Nested Class Summary

static class	LeastFourier.File Use the fourier least-squares on file data.
protected class	LeastFourier.FourierAmoeba An amoeba for solving least-squares to fourier series.

Nested classes/interfaces inherited from class util.PropertyResources

PropertyResources.URLResource

Field Summary

static double	DEFCONVERGENCE Default frequency convergence criterium.
private static boolean	DEFVISUALIZEALL Default visualize all/
static String	KEY_CONVERGENCE If frequency is stable to this number, series stop.
static String	KEY_FREQUENCY The key for the principal frequency, no default.
static String	KEY_ORDER The key for the maximum Fourier series order, no default
static String	KEY_VISUALIZEALL If true return all residuals, not just highest order.
private List<VectorG>	valid The solutions, ordered for increasing order in the series.

Fields inherited from class util.PropertyBundles

KEY_LOCALECOUNTRY, KEY_LOCALELANGUAGE, KEY_RESOURCEBUNDLES

Fields inherited from class util.PropertyResources

KEY_NOINITONCREATE, localurl, locate, POSTFIX_DIR, POSTFIX_EXT, POSTFIX_FILE, POSTFIX_LIST, POSTFIX_URL, urlset

Fields inherited from class util.PropertyContainer

KEY_LISTSEPARATOR, KEY_MAPKEYVALUECHAR, KEY_MAPSEPARATOR

Fields inherited from interface util.ResourceSupplying

KEY_URLRESOURCES, KEY_URLUSECONFIG, KEY_URLUSECURRENT, KEY_URLUSEHOME

Fields inherited from interface util.PropertySupplying

CONFIG, KEY_CLASS

Constructor Summary

LeastFourier(Map<String,String> prop)
Creates a new phase dispersion minimizer.

Method Summary

long[]	functionCalls(VectorG[] in) No estimate possible.
Object[]	metadata(VectorG[] in, VectorG[] allfits, VectorG[] p) Metadata are the fitting Fouries plus RMS in the following sense.
VectorG[]	process(VectorG[] in) Processes the data until we reach either KEY_ORDER in the Fouriere series expansion, or the frequency is stable to KEY_CONVERGENCE.
double	significance(double f, VectorG[] data, VectorG[] fit, VectorG[] residual) No significance yet.
VectorG[]	visualize(VectorG[] in, VectorG[] allfits) Visualized data is the original data minus the highest-order Fourier fit.

Methods inherited from class vec_math.AbstractAnalyser

getBootstrapData, getBootstrapData, getDiminishedData, getDiminishedData, getSyntheticData, getSyntheticData, reset, runningAverage

Methods inherited from class util.PropertyBundles

clone, getLocalized, getLocalized, getLocalizedString, getLocalizedString, loadResource

Methods inherited from class util.PropertyResources

createFrom, createFrom, createFrom, getApplet, getAsResources, getLocalClassLoader, getPropertiesToKey, getPropertiesToKey, getResource, getResourceAsStream, getResourceFromKey, getResources, init, keyCreate, keyCreate, reload, setApplet

Methods inherited from class util.PropertyContainer

augment, augment, augment, defaultBoolean, defaultChar, defaultDouble, defaultFloat, defaultInt, defaultLong, defaultObject, defaultObject, defaultProperties, defaultProperty, getAsBoolean, getAsChar, getAsDouble, getAsEnums, getAsFloat, getAsInt, getAsList, getAsLong, getAsMap, getAsMap, getAsObject, getAsObject, getProperties, getProperty, has, isNew, parseObject, reload, removeProperty, rescanned, setObject, setProperties, setProperty, stringProperties, toString

Methods inherited from class java.lang.Object

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

Methods inherited from interface util.ResourceSupplying

getResource, getResourceAsStream, getResources

Methods inherited from interface util.PropertySupplying

defaultBoolean, defaultChar, defaultDouble, defaultFloat, defaultInt, defaultLong, defaultObject, defaultObject, defaultProperties, defaultProperty, getAsBoolean, getAsChar, getAsDouble, getAsFloat, getAsInt, getAsList, getAsLong, getAsMap, getAsObject, getAsObject, getProperties, getProperty, has, parseObject, removeProperty, setObject, setProperty, stringProperties

Methods inherited from interface util.Initializable

init

Field Detail

KEY_FREQUENCY

public static final String KEY_FREQUENCY

The key for the principal frequency, no default.

See Also:

Constant Field Values

KEY_ORDER

public static final String KEY_ORDER

The key for the maximum Fourier series order, no default

See Also:

Constant Field Values

KEY_CONVERGENCE

public static final String KEY_CONVERGENCE

If frequency is stable to this number, series stop.

See Also:

Constant Field Values

KEY_VISUALIZEALL

public static final String KEY_VISUALIZEALL

If true return all residuals, not just highest order.

See Also:

Constant Field Values

DEFCONVERGENCE

public static final double DEFCONVERGENCE

Default frequency convergence criterium.

See Also:

Constant Field Values

DEFVISUALIZEALL

private static final boolean DEFVISUALIZEALL

Default visualize all/

See Also:

Constant Field Values

valid

private List<VectorG> valid

The solutions, ordered for increasing order in the series.

Constructor Detail

LeastFourier

public LeastFourier(Map<String,String> prop)

Creates a new phase dispersion minimizer.

Method Detail

process

public VectorG[] process(VectorG[] in)

Processes the data until we reach either KEY_ORDER in the Fouriere series expansion, or the frequency is stable to KEY_CONVERGENCE. Each iteration produces a fit in the resulting data vector, so the dimension of the processed VectorG is 1+order. The original data is not part of the processed data.

Parameters:

in - The measured data.

Returns:

Processed data of the same length as input data.

functionCalls

public long[] functionCalls(VectorG[] in)

No estimate possible.

Returns:

null If unknown.

visualize

public VectorG[] visualize(VectorG[] in,
                           VectorG[] allfits)

Visualized data is the original data minus the highest-order Fourier fit. If the KEY_VISUALIZEALL is set to true, we return all fits.

Specified by:

visualize in interface Analyser

Overrides:

visualize in class AbstractAnalyser

Parameters:

in - The measured data.

allfits - The processed data from Analyser.process(vec_math.VectorG[]).

Returns:

Visualizable data derived from processed one.

metadata

public Object[] metadata(VectorG[] in,
                         VectorG[] allfits,
                         VectorG[] p)

Metadata are the fitting Fouries plus RMS in the following sense. We return an VectorG array with a vector for each series solution. Each solution vector has the data RMS (measured-model fit) in the zeroth coordinate, the frequency on index one, followed by the amplitudes, first to the cosines, then sines. For ease of printout, all returned $x\_\{\backslash mathrm\{rms\}\}\; =\; \backslash sqrt\; \{\{1\; \backslash over\; n\}\; \backslash sum\_\{i=1\}^\{n\}\; x\_i^2\}\; =\; \backslash sqrt\; \{\{x\_1^2\; +\; x\_2^2\; +\; \backslash cdots\; +\; x\_n^2\}\; \backslash over\; n\}$ vectors are augmented to have the dimensionality of 2*order+2.

Parameters:

in - The original data, before process.

allfits - The processed data from Analyser.process(vec_math.VectorG[]).

p - The visualized data from Analyser.visualize(vec_math.VectorG[], vec_math.VectorG[]).

significance

public double significance(double f,
                           VectorG[] data,
                           VectorG[] fit,
                           VectorG[] residual)

No significance yet.

Parameters:

f - The value whose significance is to be probed.

data - The original data, before process.

fit - The processed data from Analyser.process(vec_math.VectorG[]).

residual - The visualized data from Analyser.visualize(vec_math.VectorG[], vec_math.VectorG[]).

Returns:

A significance, 1-false-Alarm probability