LinearRegressionFitter (math 8.1.4 API)

java.lang.Object
- de.gsi.math.fitter.LinearRegressionFitter

```
public class LinearRegressionFitter
extends Object
```
Simple linear regression fitter The fit is based on a local gradient matrix that is computed using the supplied function. This fit works fine for polyonimal function or other functions where scale-type factors need to be fitted For non-linear fits (e.g. Gaussian, etc. ), please use 'NonLinearRegressionFitter'

Author:

rstein last modified: 2011-07-25 exported fitted parameter values, errors, added Tikhonov regularisation, expanded/generalised interface

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class LinearRegressionFitter.REG_METHOD

Nested Classes
Modifier and Type	Class and Description
`static class`	`LinearRegressionFitter.REG_METHOD`

Field Summary

Fields
Modifier and Type Field and Description

static boolean USE_SVD

Fields
Modifier and Type	Field and Description
`static boolean`	`USE_SVD`

Constructor Summary

Constructors
Constructor and Description

LinearRegressionFitter()

Constructors
Constructor and Description
`LinearRegressionFitter()`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double[][]`	`fit(Function func, double[] xValues, double[] yValues)` Local linear regression fitter using standard SVD-type or Tikhonov regularisation The linear gradient matrix is calculated using the provided @param func function template and for the given @param xValues vector.
`void`	`fit(Function func, Function returnFunction, double[] xValues, double[] yValues)` Local linear regression fitter using standard SVD-type or Tikhonov regularisation The linear gradient matrix is calculated using the provided @param func function template and for the given @param xValues vector.
`double[]`	`getBestEstimates()` Get the best estimates of the unknown parameters.
`double[]`	`getBestEstimatesErrors()` Get the estimates of the standard deviations of the best estimates of the unknown parameters.
`double`	`getChiSquared()`
`long`	`getLastFitDuration()`
`long`	`getLastPrepareDuration()`
`double`	`getParameter(int index)` Value of fitted parameter.
`double`	`getParError(int index)` Error estimate of fitted parameter N.B.
`LinearRegressionFitter.REG_METHOD`	`getRegularisationMethod()`
`double`	`getSVDCutOff()`
`double`	`getTikhonovRegularisation()` 1/lambda_i -> lambda_i/(lambda_i^2+mu^2) for \|1/lambda_i\| > 1e-16 1/lambda_i -> 0 (for numerical stability)
`boolean`	`isConverged()`
`boolean`	`isErrorWeighting()`
`boolean`	`isSilent()` Fitter verbosity (local print-out) is enabled...
`static void`	`main(String[] args)`
`void`	`setErrorWeighting(boolean state)`
`void`	`setRegularisationMethod(LinearRegressionFitter.REG_METHOD method)` KStandard: standard SVD-type cut 1/lambda_i -> 1/lambda_i for (\|lambda_i/lambda_0\| > getSVDCutOff & \|1/lambda_i\| > 1e-16 1/lambda_i -> 0 otherwise (numerical stability) Tikhonov type regularisation: 1/lambda_i -> lambda_i/(lambda_i^2+mu^2) for \|1/lambda_i\| > 1e-16 1/lambda_i
`void`	`setSVDCutOff(double cutOff)` SVD cut off threshold for ill-conditioned systems, default: 1e-16
`void`	`setTikhonovRegularisation(double cutOff)` Tikhonov regularisation parameter mu, default: 1.0 1/lambda_i -> lambda_i/(lambda_i^2+mu^2) for \|1/lambda_i\| > 1e-16 1/lambda_i -> 0 (for numerical stability)
`void`	`setVerbosity(boolean state)` Fitter verbosity (local print-out) is enabled...

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - USE_SVD
```
public static boolean USE_SVD
```
- Constructor Detail
  - LinearRegressionFitter
```
public LinearRegressionFitter()
```
- Method Detail
  - fit
```
public double[][] fit(Function func,
                      double[] xValues,
                      double[] yValues)
```
    Local linear regression fitter using standard SVD-type or Tikhonov regularisation The linear gradient matrix is calculated using the provided @param func function template and for the given @param xValues vector. (Near-) Singular values are rejected using a standard SVD-type regularisation (default) of setting the inverse of near or singular eigenvalues of the gradient matrix to zero or using a Tikhonov based approach (aka. Wiener filter) of reducing the weight of near-singular values.
    
    Parameters:
    
    func - the prototype function to fit the data to
    
    xValues - horizontal data coordinates
    
    yValues - vertical data coordinates
    
    Returns:
    
    matrix three component vector containing matrix[0]: a copy of xValues matrix[1]: a computed estimate of the fitted yValues matrix[2]: a computed estimate of the fitted yValues errors
  - fit
```
public void fit(Function func,
                Function returnFunction,
                double[] xValues,
                double[] yValues)
```
    Local linear regression fitter using standard SVD-type or Tikhonov regularisation The linear gradient matrix is calculated using the provided @param func function template and for the given @param xValues vector. (Near-) Singular values are rejected using a standard SVD-type regularisation (default) of setting the inverse of near or singular eigenvalues of the gradient matrix to zero or using a Tikhonov based approach (aka. Wiener filter) of reducing the weight of near-singular values.
    
    Parameters:
    
    func - the prototype function to fit the data to
    
    xValues - horizontal data coordinates
    
    yValues - vertical data coordinates
    
    returnFunction - copy with the adjusted fitted parameter function
  - getBestEstimates
```
public double[] getBestEstimates()
```
    Get the best estimates of the unknown parameters.
    
    Returns:
    
    best estimate value
  - getBestEstimatesErrors
```
public double[] getBestEstimatesErrors()
```
    Get the estimates of the standard deviations of the best estimates of the unknown parameters.
    
    Returns:
    
    parameter best estimates error
  - getChiSquared
```
public double getChiSquared()
```
    Returns:
    
    the \chi^2 value of the last fit
  - getLastFitDuration
```
public long getLastFitDuration()
```
    Returns:
    
    last fitting execution time [ms]
  - getLastPrepareDuration
```
public long getLastPrepareDuration()
```
    Returns:
    
    last fitting execution time including preparation [ms]
  - getParameter
```
public double getParameter(int index)
```
    Value of fitted parameter.
    
    Parameters:
    
    index - of parameter
    
    Returns:
    
    parameter value
  - getParError
```
public double getParError(int index)
```
    Error estimate of fitted parameter N.B. estimate based on assumption that measurement errors are uncorrelated
    
    Parameters:
    
    index - of parameter
    
    Returns:
    
    parameter error estimation value
  - getRegularisationMethod
```
public LinearRegressionFitter.REG_METHOD getRegularisationMethod()
```
    Returns:
    
    kStandard: standard SVD-type cut
    1/lambda_i -> 1/lambda_i
    for (|lambda_i/lambda_0| > getSVDCutOff & |1/lambda_i| > 1e-16 1/lambda_i -> 0
    otherwise (numerical stability) Tikhonov type regularisation:
    1/lambda_i -> lambda_i/(lambda_i^2+mu^2) for |1/lambda_i| > 1e-16 1/lambda_i
    the paramater mu can be read set via function getTikhonovRegularisationParameter, or function setTikhonovRegularisationParameter
  - getSVDCutOff
```
public double getSVDCutOff()
```
    Returns:
    
    SVD cut off threshold for ill-conditioned systems, default: 1e-16
  - getTikhonovRegularisation
```
public double getTikhonovRegularisation()
```
    1/lambda_i -> lambda_i/(lambda_i^2+mu^2) for |1/lambda_i| > 1e-16
    1/lambda_i -> 0 (for numerical stability)
    
    Returns:
    
    Tikhonov regularisation parameter mu, default: 1.0
  - isConverged
```
public boolean isConverged()
```
    Returns:
    
    last fit converged successfully
  - isErrorWeighting
```
public boolean isErrorWeighting()
```
    Returns:
    
    true: errors are used as fitting weights
  - isSilent
```
public boolean isSilent()
```
    Fitter verbosity (local print-out) is enabled... for debugging purposes
    
    Returns:
    
    whether fitter is silent (ie. not outputting debugging/info messages
  - setErrorWeighting
```
public void setErrorWeighting(boolean state)
```
    Parameters:
    
    state - true: use errors as fitting weights
  - setRegularisationMethod
```
public void setRegularisationMethod(LinearRegressionFitter.REG_METHOD method)
```
    KStandard: standard SVD-type cut
    1/lambda_i -> 1/lambda_i
    for (|lambda_i/lambda_0| > getSVDCutOff & |1/lambda_i| > 1e-16 1/lambda_i -> 0
    otherwise (numerical stability) Tikhonov type regularisation:
    1/lambda_i -> lambda_i/(lambda_i^2+mu^2) for |1/lambda_i| > 1e-16 1/lambda_i
    
    Parameters:
    
    method - regularisation method to be used the paramater mu can be read set via function getTikhonovRegularisationParameter, or function setTikhonovRegularisationParameter
  - setSVDCutOff
```
public void setSVDCutOff(double cutOff)
```
    SVD cut off threshold for ill-conditioned systems, default: 1e-16
    
    Parameters:
    
    cutOff - minimum eigenvalue cut-off
  - setTikhonovRegularisation
```
public void setTikhonovRegularisation(double cutOff)
```
    Tikhonov regularisation parameter mu, default:
    1.0 1/lambda_i -> lambda_i/(lambda_i^2+mu^2) for |1/lambda_i| > 1e-16 1/lambda_i -> 0 (for numerical stability)
    
    Parameters:
    
    cutOff - minimum eigenvalue cutt-off
  - setVerbosity
```
public void setVerbosity(boolean state)
```
    Fitter verbosity (local print-out) is enabled... for debugging purposes
    
    Parameters:
    
    state - true <-> 'on', false <-> 'off'
  - main
```
public static void main(String[] args)
```

Class LinearRegressionFitter

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

USE_SVD

Constructor Detail

LinearRegressionFitter

Method Detail

fit

fit

getBestEstimates

getBestEstimatesErrors

getChiSquared

getLastFitDuration

getLastPrepareDuration

getParameter

getParError

getRegularisationMethod

getSVDCutOff

getTikhonovRegularisation

isConverged

isErrorWeighting

isSilent

setErrorWeighting

setRegularisationMethod

setSVDCutOff

setTikhonovRegularisation

setVerbosity

main