DampedSinusoidFit

java.lang.Object
- xal.extension.fit.DampedSinusoidFit

```
public final class DampedSinusoidFit
extends java.lang.Object
```
DampedSinusoid provides an exact closed form solution for fitting a waveform to a damped sinusoid of the form q = Ae^γtsin(μt + φ) + C which is adapted for efficient fitting in the presence of noise. The fits for frequency, offset and growth rate are good in the presence of relatively small noise. However, the estimation of phase and amplitude are relatively poor in the presence of noise. Also, the estimation breaks down when the frequency is near an integer or half integer.

Constructor Summary

Constructors
Constructor and Description
`DampedSinusoidFit(double[] waveform)` Constructor accepting the entire waveform
`DampedSinusoidFit(double[] waveform, int count)` Primary Constructor

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`calculateFittedWaveform(double[] positions, double[] waveform)` Convenience method to calculate the fitted waveform over the specified positions
`double`	`estimateInitialFrequencyVariance(double signalVariance)` get an estimate of the initial frequency's variance
`double`	`estimateInitialGrowthRateVariance(double signalVariance)` get an estimate of the initial growth rate's variance
`double`	`estimateInitialOffsetVariance(double signalVariance)` get an estimate of the initial offset's variance
`double`	`getAmplitude()` Get the optimized sine-like amplitude
`double`	`getCosineLikePhase()` Get the optimized cosine-like phase (equivalent phase if the fitted equation were of the form of A * damping * cos( mu + phase ) ).
`double[]`	`getFittedWaveform(double[] positions)` Convenience method to calculate the fitted waveform over the specified positions
`double`	`getFrequency()` get the optimized frequency
`double`	`getGrowthRate()` get the optimized growth rate
`double`	`getInitialAmplitude()` Get the sine-like amplitude calculating it if necessary.
`double`	`getInitialCosineLikePhase()` Get the cosine-like phase calculating it if necessary.
`double`	`getInitialFrequency()` get the fitted frequency calculating it if necessary
`double`	`getInitialFrequencyVariance()` get the variance in the initial frequency estimate using the initial estimate of the signal variance
`double`	`getInitialGrowthRate()` get the fitted growth rate calculating it if necessary
`double`	`getInitialGrowthRateVariance()` get the variance in the initial growth rate estimate using the initial estimate of the signal variance
`double`	`getInitialOffset()` get the fitted offset calculating it if necessary
`double`	`getInitialOffsetVariance()` get the variance in the initial offset estimate using the initial estimate of the signal variance
`double`	`getInitialPhase()` Get the sine-like phase estimation calculating it if necessary.
`double`	`getInitialSignalVariance()` get the initial estimat of the signal variance
`double`	`getInitialSineLikePhase()` Get the sine-like phase calculating it if necessary.
`double[]`	`getInitialWaveformError()` get the initial waveform error calculating it if necessary
`double`	`getInitialWaveformRMSError()` get the initial RMS error
`static DampedSinusoidFit`	`getInstance(double[] waveform)` Get a new instance of the damped sinusoid using the entire waveform
`static DampedSinusoidFit`	`getInstance(double[] waveform, int count)` Get a new instance of the damped sinusoid
`double`	`getOffset()` get the optimized offset
`double`	`getPhase()` get the optimized phase
`double`	`getSignalVariance()` get the optimized estimate of the signal variance
`double`	`getSineLikePhase()` Get the optimized sine-like phase.
`double[]`	`getWaveformError()` get the waveform error
`double`	`getWaveformRMSError()` get the initial RMS error
`void`	`solve(double noiseLevel, Stopper stopper)` Run the solver to find the best fit
`void`	`solveWithNoise(double noiseLevel)` Run the solver to find the best fit
`void`	`solveWithNoiseMaxEvaluations(double noiseLevel, int maxEvaluations)` Run the solver to find the best fit
`void`	`solveWithNoiseMaxEvaluationsSatisfaction(double noiseLevel, int maxEvaluations, double satisfaction)` Run the solver to find the best fit
`void`	`solveWithNoiseMaxTime(double noiseLevel, double maxTime)` Run the solver to find the best fit
`void`	`solveWithNoiseMaxTimeSatisfaction(double noiseLevel, double maxTime, double satisfaction)` Run the solver to find the best fit

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

- Constructor Detail
  - DampedSinusoidFit
```
public DampedSinusoidFit(double[] waveform,
                         int count)
```
    Primary Constructor
    
    Parameters:
    
    waveform - data to fit
    
    count - starting from the beginning of the waveform, the number of items in the waveform to use in the fit
  - DampedSinusoidFit
```
public DampedSinusoidFit(double[] waveform)
```
    Constructor accepting the entire waveform
    
    Parameters:
    
    waveform - data to fit
- Method Detail
  - getInstance
```
public static DampedSinusoidFit getInstance(double[] waveform,
                                            int count)
```
    Get a new instance of the damped sinusoid
    
    Parameters:
    
    waveform - data to fit
    
    count - starting from the beginning of the waveform, the number of items in the waveform to use in the fit
  - getInstance
```
public static DampedSinusoidFit getInstance(double[] waveform)
```
    Get a new instance of the damped sinusoid using the entire waveform
    
    Parameters:
    
    waveform - data to fit
  - solveWithNoise
```
public void solveWithNoise(double noiseLevel)
```
    Run the solver to find the best fit
    
    Parameters:
    
    noiseLevel - estimate of the expected noise
  - solveWithNoiseMaxEvaluations
```
public void solveWithNoiseMaxEvaluations(double noiseLevel,
                                         int maxEvaluations)
```
    Run the solver to find the best fit
    
    Parameters:
    
    noiseLevel - estimate of the expected noise
    
    maxEvaluations - the maximum number of evaluations to perform
  - solveWithNoiseMaxEvaluationsSatisfaction
```
public void solveWithNoiseMaxEvaluationsSatisfaction(double noiseLevel,
                                                     int maxEvaluations,
                                                     double satisfaction)
```
    Run the solver to find the best fit
    
    Parameters:
    
    noiseLevel - estimate of the expected noise
    
    maxEvaluations - the maximum number of evaluations to perform
    
    satisfaction - the satisfaction target to reach before stopping
  - solveWithNoiseMaxTime
```
public void solveWithNoiseMaxTime(double noiseLevel,
                                  double maxTime)
```
    Run the solver to find the best fit
    
    Parameters:
    
    noiseLevel - estimate of the expected noise
    
    maxTime - the maximum time to wait for the solution
  - solveWithNoiseMaxTimeSatisfaction
```
public void solveWithNoiseMaxTimeSatisfaction(double noiseLevel,
                                              double maxTime,
                                              double satisfaction)
```
    Run the solver to find the best fit
    
    Parameters:
    
    noiseLevel - estimate of the expected noise
    
    maxTime - the maximum time to wait for the solution
    
    satisfaction - the satisfaction target to reach before stopping
  - solve
```
public void solve(double noiseLevel,
                  Stopper stopper)
```
    Run the solver to find the best fit
    
    Parameters:
    
    noiseLevel - the noise level used to estimate the error bounds and provide a measure for satisfaction
    
    stopper - the stopper which determines when to stop the solver
  - getInitialOffset
```
public double getInitialOffset()
```
    get the fitted offset calculating it if necessary
  - getInitialOffsetVariance
```
public double getInitialOffsetVariance()
```
    get the variance in the initial offset estimate using the initial estimate of the signal variance
  - getInitialSignalVariance
```
public double getInitialSignalVariance()
```
    get the initial estimat of the signal variance
  - estimateInitialOffsetVariance
```
public double estimateInitialOffsetVariance(double signalVariance)
```
    get an estimate of the initial offset's variance
  - getOffset
```
public double getOffset()
```
    get the optimized offset
  - getSignalVariance
```
public double getSignalVariance()
```
    get the optimized estimate of the signal variance
  - getInitialGrowthRate
```
public double getInitialGrowthRate()
```
    get the fitted growth rate calculating it if necessary
  - getInitialGrowthRateVariance
```
public double getInitialGrowthRateVariance()
```
    get the variance in the initial growth rate estimate using the initial estimate of the signal variance
  - estimateInitialGrowthRateVariance
```
public double estimateInitialGrowthRateVariance(double signalVariance)
```
    get an estimate of the initial growth rate's variance
  - getInitialWaveformError
```
public double[] getInitialWaveformError()
```
    get the initial waveform error calculating it if necessary
  - getInitialWaveformRMSError
```
public double getInitialWaveformRMSError()
```
    get the initial RMS error
  - getGrowthRate
```
public double getGrowthRate()
```
    get the optimized growth rate
  - getInitialFrequency
```
public double getInitialFrequency()
```
    get the fitted frequency calculating it if necessary
  - getInitialFrequencyVariance
```
public double getInitialFrequencyVariance()
```
    get the variance in the initial frequency estimate using the initial estimate of the signal variance
  - estimateInitialFrequencyVariance
```
public double estimateInitialFrequencyVariance(double signalVariance)
```
    get an estimate of the initial frequency's variance
  - getFrequency
```
public double getFrequency()
```
    get the optimized frequency
  - getInitialPhase
```
public double getInitialPhase()
```
    Get the sine-like phase estimation calculating it if necessary. Note that this estimation is relatively poor.
  - getPhase
```
public double getPhase()
```
    get the optimized phase
  - getSineLikePhase
```
public double getSineLikePhase()
```
    Get the optimized sine-like phase.
  - getCosineLikePhase
```
public double getCosineLikePhase()
```
    Get the optimized cosine-like phase (equivalent phase if the fitted equation were of the form of A * damping * cos( mu + phase ) ).
  - getWaveformError
```
public double[] getWaveformError()
```
    get the waveform error
  - getWaveformRMSError
```
public double getWaveformRMSError()
```
    get the initial RMS error
  - getInitialSineLikePhase
```
public double getInitialSineLikePhase()
```
    Get the sine-like phase calculating it if necessary. Note that this estimation is relatively poor.
  - getInitialCosineLikePhase
```
public double getInitialCosineLikePhase()
```
    Get the cosine-like phase calculating it if necessary. Note that this estimation is relatively poor.
  - getInitialAmplitude
```
public double getInitialAmplitude()
```
    Get the sine-like amplitude calculating it if necessary. Note that this estimation is relatively poor.
  - getAmplitude
```
public double getAmplitude()
```
    Get the optimized sine-like amplitude
  - getFittedWaveform
```
public double[] getFittedWaveform(double[] positions)
```
    Convenience method to calculate the fitted waveform over the specified positions
    
    Parameters:
    
    positions - array of positions over which to calculate the waveform
    
    Returns:
    
    array holding the calculated waveform over each of the positions
  - calculateFittedWaveform
```
public void calculateFittedWaveform(double[] positions,
                                    double[] waveform)
```
    Convenience method to calculate the fitted waveform over the specified positions
    
    Parameters:
    
    positions - array of positions over which to calculate the waveform
    
    array - big enough to hold the calculated waveform over each of the positions

Class DampedSinusoidFit

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

DampedSinusoidFit

DampedSinusoidFit

Method Detail

getInstance

getInstance

solveWithNoise

solveWithNoiseMaxEvaluations

solveWithNoiseMaxEvaluationsSatisfaction

solveWithNoiseMaxTime

solveWithNoiseMaxTimeSatisfaction

solve

getInitialOffset

getInitialOffsetVariance

getInitialSignalVariance

estimateInitialOffsetVariance

getOffset

getSignalVariance

getInitialGrowthRate

getInitialGrowthRateVariance

estimateInitialGrowthRateVariance

getInitialWaveformError

getInitialWaveformRMSError

getGrowthRate

getInitialFrequency

getInitialFrequencyVariance

estimateInitialFrequencyVariance

getFrequency

getInitialPhase

getPhase

getSineLikePhase

getCosineLikePhase

getWaveformError

getWaveformRMSError

getInitialSineLikePhase

getInitialCosineLikePhase

getInitialAmplitude

getAmplitude

getFittedWaveform

calculateFittedWaveform