vec_math
Class HarmonicFit

java.lang.Object
  util.PropertyContainer
      util.PropertyResources
          util.PropertyBundles
              vec_math.AbstractFit
                  vec_math.HarmonicFit

All Implemented Interfaces:

Cloneable, Initializable, LocalizedSupplying, PropertySupplying, ResourceSupplying, ModelFitting

public class HarmonicFit
extends AbstractFit

A fit to a cosine wave with phase shift, variable period to the input data. If writtn as

   y_fit=c_0+a_0*cos(ωt)+b_0*sin(ωt),
   

the fitting function y_fit is linear in its three parameters a_0, b_0, and c_0 and only non-linear in ω. Nevertheless, this non-linearity renders this fit much more demanding then the pure linear fit PhaseRegression, where the period is held fixed. In applications, where the period is known a priori, this latter class should be used for fitting. This fitter should be used mainly for sparse data, to improve a vaguely defined period. We assign variable names according to OFFSET, AMPLITUDE, and T0, where t0 and amplitude are calculated from the linear parameters as

   amplitude²=a_0²+b_0²
   tan(ωt_0)=b_0/a_0;
   

Nested Class Summary

private static class

HarmonicFit.HarmonicModel Our data model.

Nested classes/interfaces inherited from class util.PropertyResources

PropertyResources.URLResource

Field Summary

static String	AMPLITUDE The name of the amplitude constant.
private static int	DEFTINDEX Default time index.
private static String	DEFUNITAMPLITUDE Default units of the parameters.
private static String	DEFUNITOFFSET Default units of the parameters.
private static String	DEFUNITPERIOD Default units of the parameters.
private static String	DEFUNITPHASE Default units of the parameters.
private static int	DEFYINDEX Default y index.
private List<Variable>	fitted The fitted values to C+A*cos(2pi/P*t+PHI).
static String	KEY_EPSILON Default improvement in chi-2 to induce terminating loop.
static String	KEY_EXTERNALERROR Default external error.
static String	KEY_ITER Default number of maximum iteration in levenberg-marquardt.
static String	KEY_LAMBDA Default starting value for the 'fudge factor' boosting hessian.
static String	KEY_PERIOD This is the main fitting parameter.
static String	KEY_TERMINATE Default number of maximum improvements, if epsilon is reached.
static String	KEY_TINDEX The index of the time, defaults to zero.
static String	KEY_UNITAMPLITUDE The units of the parameters.
static String	KEY_UNITOFFSET The units of the parameters.
static String	KEY_UNITPERIOD The units of the parameters.
static String	KEY_UNITPHASE The units of the parameters.
static String	KEY_YINDEX The index of the measure, defaults to one.
static String	OFFSET The name of the offset constant.
static String	PERIOD period constant.
private HarmonicFit.HarmonicModel	phasemodel The model.
static String	T0 The name of the phase constant.

Fields inherited from class vec_math.AbstractFit

KEY_DEFAULTERROR, KEY_DEFAULTFORMAT, KEY_ERRORFORMAT, KEY_PARAMETERFORMAT

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

HarmonicFit(Map<String,String> prop)
Constructs a new regression analyser.

Method Summary

List<Variable>	fit() We fit the amplitude and phase plus mgnitude offset only, the period stays constant.
DataModel	getDataModel() Returns the phase model.
List<Variable>	getFittedParameters() Returns the fitted parameters.
DataModel	prepareFit(VectorG[] in) Visualization means performing a linear Regression using GeneralRegression#harmonic.
boolean	setInitialCondition(Variable p) We need the period as an initial condition.

Methods inherited from class vec_math.AbstractFit

formatError, formatValue, getChi2, getModelParameterErrors, getModelParameterValues, getR2, getRms, init, qualityOfFit, setConstant

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, 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

Field Detail

PERIOD

public static final String PERIOD

period constant.

See Also:

Constant Field Values

AMPLITUDE

public static final String AMPLITUDE

The name of the amplitude constant.

See Also:

Constant Field Values

OFFSET

public static final String OFFSET

The name of the offset constant.

See Also:

Constant Field Values

T0

public static final String T0

The name of the phase constant.

See Also:

Constant Field Values

KEY_UNITAMPLITUDE

public static final String KEY_UNITAMPLITUDE

The units of the parameters.

See Also:

Constant Field Values

KEY_UNITPHASE

public static final String KEY_UNITPHASE

The units of the parameters.

See Also:

Constant Field Values

KEY_UNITPERIOD

public static final String KEY_UNITPERIOD

The units of the parameters.

See Also:

Constant Field Values

KEY_UNITOFFSET

public static final String KEY_UNITOFFSET

The units of the parameters.

See Also:

Constant Field Values

KEY_PERIOD

public static final String KEY_PERIOD

This is the main fitting parameter.

See Also:

Constant Field Values

KEY_TINDEX

public static final String KEY_TINDEX

The index of the time, defaults to zero.

See Also:

Constant Field Values

KEY_YINDEX

public static final String KEY_YINDEX

The index of the measure, defaults to one.

See Also:

Constant Field Values

KEY_ITER

public static final String KEY_ITER

Default number of maximum iteration in levenberg-marquardt.

See Also:

Constant Field Values

KEY_TERMINATE

public static final String KEY_TERMINATE

Default number of maximum improvements, if epsilon is reached.

See Also:

Constant Field Values

KEY_EPSILON

public static final String KEY_EPSILON

Default improvement in chi-2 to induce terminating loop.

See Also:

Constant Field Values

KEY_LAMBDA

public static final String KEY_LAMBDA

Default starting value for the 'fudge factor' boosting hessian.

See Also:

Constant Field Values

KEY_EXTERNALERROR

public static final String KEY_EXTERNALERROR

Default external error.

See Also:

Constant Field Values

DEFTINDEX

private static final int DEFTINDEX

Default time index.

See Also:

Constant Field Values

DEFYINDEX

private static final int DEFYINDEX

Default y index.

See Also:

Constant Field Values

DEFUNITPERIOD

private static final String DEFUNITPERIOD

Default units of the parameters.

See Also:

Constant Field Values

DEFUNITAMPLITUDE

private static final String DEFUNITAMPLITUDE

Default units of the parameters.

See Also:

Constant Field Values

DEFUNITPHASE

private static final String DEFUNITPHASE

Default units of the parameters.

See Also:

Constant Field Values

DEFUNITOFFSET

private static final String DEFUNITOFFSET

Default units of the parameters.

See Also:

Constant Field Values

fitted

private List<Variable> fitted

The fitted values to C+A*cos(2pi/P*t+PHI).

phasemodel

private HarmonicFit.HarmonicModel phasemodel

The model.

Constructor Detail

HarmonicFit

public HarmonicFit(Map<String,String> prop)

Constructs a new regression analyser.

Method Detail

setInitialCondition

public boolean setInitialCondition(Variable p)

We need the period as an initial condition.

Specified by:

setInitialCondition in interface ModelFitting

Overrides:

setInitialCondition in class AbstractFit

Returns:

false, if the initial condition does not apply to this model.

prepareFit

public DataModel prepareFit(VectorG[] in)

Visualization means performing a linear Regression using GeneralRegression#harmonic. The three linear parameters are fit into three fitting parameters OFFSET, AMPLITUDE, and #PHASE, where phase and amplitude are calculated from the linear parameters as

       amplitude²=a_0²+b_0²
       tan(ωt_0)=b_0/a_0;
       

The order of the returned array is at index zero amplitude, sigma amplitude, at index one, offset plus sigma, and at index two phase plus sigma.

Parameters:

in - An array of measurements. Each vector contains dependant and independant variables and eventually their errors.

Returns:

A three dimensional array of Vector2D.

fit

public List<Variable> fit()

We fit the amplitude and phase plus mgnitude offset only, the period stays constant. Thus, we return three parameters. For fitting the period starting with an intial condition, see PhaseFit. This fit has the advantage that by transforming the amplitude, phase function into a sin and cosine wave, we get a pure linear regression. This is done here, the result is transformed back to match the original (non-linear) model (holds also for parameter errors).

Returns:

Non-null, if a fit could be obtained.

getDataModel

public DataModel getDataModel()

Returns the phase model.

getFittedParameters

public List<Variable> getFittedParameters()

Returns the fitted parameters.