java.lang.Object
- ij.measure.CurveFitter

All Implemented Interfaces:: UserFunction

public class CurveFitter
extends java.lang.Object
implements UserFunction

Curve fitting class based on the Simplex method in the Minimizer class Notes on fitting polynomial functions: (i) The range of x values should not be too far from 0, especially for higher-order polynomials. For polynomials of 4th order, the average x value should fulfill |xMean|

Field Summary

Fields
Modifier and Type	Field	Description
`static int`	`CHAPMAN`	Constants for the built-in fit functions
`static int`	`ERF`	Constants for the built-in fit functions
`static int`	`EXP_RECOVERY`	Constants for the built-in fit functions
`static int`	`EXP_RECOVERY_NOOFFSET`	Constants for the built-in fit functions
`static int`	`EXP_REGRESSION`	Constants for the built-in fit functions
`static int`	`EXP_WITH_OFFSET`	Constants for the built-in fit functions
`static int`	`EXPONENTIAL`	Constants for the built-in fit functions
`static java.lang.String[]`	`fitList`	Names of the built-in fit functions
`static java.lang.String[]`	`fList`	Equations of the built-in fit functions
`static java.lang.String[]`	`fMacro`	ImageJ Macro language code for the built-in functions
`static int`	`GAMMA_VARIATE`	Constants for the built-in fit functions
`static int`	`GAUSSIAN`	Constants for the built-in fit functions
`static int`	`GAUSSIAN_NOOFFSET`	Constants for the built-in fit functions
`static int`	`INV_RODBARD`	Constants for the built-in fit functions
`static int`	`IterFactor`	Deprecated. now in the Minimizer class (since ImageJ 1.46f).
`static int`	`LOG`	Constants for the built-in fit functions
`static int`	`LOG2`	Constants for the built-in fit functions
`static int`	`POLY2`	Constants for the built-in fit functions
`static int`	`POLY3`	Constants for the built-in fit functions
`static int`	`POLY4`	Constants for the built-in fit functions
`static int`	`POLY5`	Constants for the built-in fit functions
`static int`	`POLY6`	Constants for the built-in fit functions
`static int`	`POLY7`	Constants for the built-in fit functions
`static int`	`POLY8`	Constants for the built-in fit functions
`static int`	`POWER`	Constants for the built-in fit functions
`static int`	`POWER_REGRESSION`	Constants for the built-in fit functions
`static int`	`RODBARD`	Constants for the built-in fit functions
`static int`	`RODBARD2`	Constants for the built-in fit functions
`static int[]`	`sortedTypes`	Nicer sequence of the built-in function types
`static int`	`STRAIGHT_LINE`	Constants for the built-in fit functions

Constructor Summary

Constructors
Constructor Description

CurveFitter(double[] xData, double[] yData)
Construct a new CurveFitter.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`void`	`doCustomFit(UserFunction userFunction, int numParams, java.lang.String formula, double[] initialParams, double[] initialParamVariations, boolean showSettings)`	Fit a function defined in a user plugin implementing the UserFunction interface Use getStatus() and/or getStatusString() to see whether fitting was (probably) successful and getParams() to access the result.
`int`	`doCustomFit(java.lang.String equation, double[] initialParams, boolean showSettings)`	Fit a function defined as a macro String like "y = a + bx + cx*x".
`void`	`doFit(int fitType)`	Perform curve fitting with one of the built-in functions doFit(fitType) does the fit quietly Use getStatus() and/or getStatusString() to see whether fitting was (probably) successful and getParams() to access the result.
`void`	`doFit(int fitType, boolean showSettings)`	Perform curve fitting with one of the built-in functions doFit(fitType, true) pops up a dialog allowing the user to set the initial fit parameters and various numbers controlling the Minimizer Use getStatus() and/or getStatusString() to see whether fitting was (probably) successful and getParams() to access the result.
`double`	`f(double x)`	Returns the formula value for parameters 'p' at 'x'.
`double`	`f(double[] p, double x)`	Returns the formula value for parameters 'p' at 'x'.
`static double`	`f(int fitType, double[] p, double x)`	Returns value of built-in 'fitType' formula value for parameters "p" at "x"
`int`	`getFit()`	returns the code of the fit type of the fit performed
`static int`	`getFitCode(java.lang.String fitName)`	Returns the code for a fit with given name as defined in fitList, or -1 if not found
`double`	`getFitGoodness()`	Get a measure of "goodness of fit" where 1.0 is best.
`java.lang.String`	`getFormula()`	returns a String with the formula of the fit function used
`int`	`getIterations()`	Get number of iterations performed.
`java.lang.String`	`getMacroCode()`	Returns macro code of the form "y = ...x" for the fit function used.
`static int`	`getMax(double[] array)`	Gets index of highest value in an array.
`int`	`getMaxIterations()`	Get maximum number of iterations allowed (sum of iteration count for all restarts)
`Minimizer`	`getMinimizer()`	Returns a reference to the Minimizer used, for accessing Minimizer methods directly.
`java.lang.String`	`getName()`	returns the name of the fit function of the fit performed
`int`	`getNumParams()`	Get number of parameters for current fit formula Do not use before 'doFit', because the fit function would be undefined.
`static int`	`getNumParams(int fitType)`	Returns the number of parameters for a given fit type, except for the 'custom' fit, where the number of parameters is given by the equation: see getNumParams(String)
`static int`	`getNumParams(java.lang.String customFormula)`	Returns the number of parameters for a custom equation given as a macro String, like "y = a + bx + cx*x" .
`double[]`	`getParams()`	Get the result of fitting, i.e.
`Plot`	`getPlot()`
`Plot`	`getPlot(int points)`
`double[]`	`getResiduals()`	Returns residuals array, i.e., differences between data and curve.
`int`	`getRestarts()`	Get maximum number of simplex restarts to do.
`java.lang.String`	`getResultString()`	Get a string with detailed description of the curve fitting results (several lines, including the fit parameters).
`double`	`getRSquared()`	Returns R^2, where 1.0 is best.
`double`	`getSD()`	Returns the standard deviation of the residuals.
`static java.lang.String[]`	`getSortedFitList()`	Returns an array of fit names with nicer sorting
`int`	`getStatus()`
`java.lang.String`	`getStatusString()`	Get a short text with a short description of the status.
`double`	`getSumResidualsSqr()`	Returns the sum of the residuals (may be NaN if the minimizer could not start properly i.e., if getStatus() returns Minimizer.INITILIZATION_FAILURE).
`double[]`	`getXPoints()`	returns the array with the x data
`double[]`	`getYPoints()`	returns the array with the y data
`void`	`setInitialParameters(double[] initialParams)`	Sets the initial parameters, which override the default initial parameters.
`void`	`setMaxError(double maxRelError)`	Set the maximum error.
`void`	`setMaxIterations(int maxIter)`	Set maximum number of iterations allowed (sum of iteration count for all restarts)
`void`	`setOffsetMultiplySlopeParams(int offsetParam, int multiplyParam, int slopeParam)`	For improved fitting performance when using a custom fit formula, one may specify parameters that can be calculated directly by linear regression.
`void`	`setRestarts(int maxRestarts)`	Set maximum number of simplex restarts to do.
`void`	`setStatusAndEsc(java.lang.String ijStatusString, boolean checkEscape)`	Create output on the number of iterations in the ImageJ Status line, e.g.
`void`	`setWeights(double[] weights)`	Sets weights of the data points.
`double`	`userFunction(double[] params, double dummy)`	This function is called by the Minimizer and calculates the sum of squared residuals for given parameters.

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

- Field Detail
  - STRAIGHT_LINE
```
public static final int STRAIGHT_LINE
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POLY2
```
public static final int POLY2
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POLY3
```
public static final int POLY3
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POLY4
```
public static final int POLY4
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - EXPONENTIAL
```
public static final int EXPONENTIAL
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POWER
```
public static final int POWER
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - LOG
```
public static final int LOG
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - RODBARD
```
public static final int RODBARD
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - GAMMA_VARIATE
```
public static final int GAMMA_VARIATE
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - LOG2
```
public static final int LOG2
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - RODBARD2
```
public static final int RODBARD2
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - EXP_WITH_OFFSET
```
public static final int EXP_WITH_OFFSET
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - GAUSSIAN
```
public static final int GAUSSIAN
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - EXP_RECOVERY
```
public static final int EXP_RECOVERY
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - INV_RODBARD
```
public static final int INV_RODBARD
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - EXP_REGRESSION
```
public static final int EXP_REGRESSION
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POWER_REGRESSION
```
public static final int POWER_REGRESSION
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POLY5
```
public static final int POLY5
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POLY6
```
public static final int POLY6
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POLY7
```
public static final int POLY7
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - POLY8
```
public static final int POLY8
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - GAUSSIAN_NOOFFSET
```
public static final int GAUSSIAN_NOOFFSET
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - EXP_RECOVERY_NOOFFSET
```
public static final int EXP_RECOVERY_NOOFFSET
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - CHAPMAN
```
public static final int CHAPMAN
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - ERF
```
public static final int ERF
```
    Constants for the built-in fit functions
    
    See Also:
    
    Constant Field Values
  - sortedTypes
```
public static final int[] sortedTypes
```
    Nicer sequence of the built-in function types
  - fitList
```
public static final java.lang.String[] fitList
```
    Names of the built-in fit functions
  - fList
```
public static final java.lang.String[] fList
```
    Equations of the built-in fit functions
  - fMacro
```
public static final java.lang.String[] fMacro
```
    ImageJ Macro language code for the built-in functions
  - IterFactor
```
public static final int IterFactor
```
    Deprecated.
    now in the Minimizer class (since ImageJ 1.46f). (probably of not much value for anyone anyhow?)
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - CurveFitter
```
public CurveFitter(double[] xData,
                   double[] yData)
```
    Construct a new CurveFitter.
- Method Detail
  - doFit
```
public void doFit(int fitType)
```
    Perform curve fitting with one of the built-in functions doFit(fitType) does the fit quietly Use getStatus() and/or getStatusString() to see whether fitting was (probably) successful and getParams() to access the result.
  - doFit
```
public void doFit(int fitType,
                  boolean showSettings)
```
    Perform curve fitting with one of the built-in functions doFit(fitType, true) pops up a dialog allowing the user to set the initial fit parameters and various numbers controlling the Minimizer Use getStatus() and/or getStatusString() to see whether fitting was (probably) successful and getParams() to access the result.
  - doCustomFit
```
public int doCustomFit(java.lang.String equation,
                       double[] initialParams,
                       boolean showSettings)
```
    Fit a function defined as a macro String like "y = a + b*x + c*x*x". When showSettings is true, pops up a dialog allowing the user to set the initial fit parameters and various numbers controlling the Minimizer Returns the number of parameters, or 0 in case of a macro syntax error. Use getStatus() and/or getStatusString() to see whether fitting was (probably) successful and getParams() to access the result. For complicated fits and good performance, it is advisable to use the doCustomFit method with a (java) UserFunction, which also has more options.
  - doCustomFit
```
public void doCustomFit(UserFunction userFunction,
                        int numParams,
                        java.lang.String formula,
                        double[] initialParams,
                        double[] initialParamVariations,
                        boolean showSettings)
```
    Fit a function defined in a user plugin implementing the UserFunction interface Use getStatus() and/or getStatusString() to see whether fitting was (probably) successful and getParams() to access the result. For getter performance, if possible it is advisable to first call setOffsetMultiplySlopeParams, to avoid searching for one or two parameters that can be calculated directly by linear regression.
    
    Parameters:
    
    userFunction - A class instance implementing the userFunction interface. There, the fit function hould be defined by the method userFunction(params, x). This function must allow simultaneous calls in multiple threads.
    
    numParams - Number of parameters of the fit function.
    
    formula - A String describing the fit formula, may be null.
    
    initialParams - Starting point for the parameters; the fit function with these parameters must not return NaN for any of the data points given in the constructor (xData). initialParams may be null, then random values are used, with repeated tries if the userFunction returns NaN.
    
    initialParamVariations - Each parameter is initially varied by up to +/- this value. If not given (null), initial variations are taken as 10% of initial parameter value or 0.01 for parameters that are zero. When this array is given, all elements must be positive (nonzero). See Minimizer.minimize for details. Providing this array is especially valuable if one or more initial parameters have a value of 0.
    
    showSettings - Displays a popup dialog for modifying the initial parameters and a few numbers controlling the minimizer.
  - setInitialParameters
```
public void setInitialParameters(double[] initialParams)
```
    Sets the initial parameters, which override the default initial parameters.
  - setWeights
```
public void setWeights(double[] weights)
```
    Sets weights of the data points. The 'weights' array must have the same length as the data arrays passed with the constructor. If the error bars of the data points are known, the weights should be proportional to 1/error^2. When weights are specified, note that 'getSumResidualsSqr' will return the weighted sum.
  - getMinimizer
```
public Minimizer getMinimizer()
```
    Returns a reference to the Minimizer used, for accessing Minimizer methods directly. Note that no Minimizer is used if fitType is any of STRAIGHT_LINE, EXP_REGRESSION, and POWER_REGRESSION.
  - setOffsetMultiplySlopeParams
```
public void setOffsetMultiplySlopeParams(int offsetParam,
                                         int multiplyParam,
                                         int slopeParam)
```
    For improved fitting performance when using a custom fit formula, one may specify parameters that can be calculated directly by linear regression. For values not used, set the index to -1
    
    Parameters:
    
    offsetParam - Index of a parameter that is a pure offset: E.g. '0' if f(p0, p1, p2...) = p0 + function(p1, p2, ...).
    
    multiplyParam - Index of a parameter that is purely multiplicative. E.g. multiplyParams=1 if f(p0, p1, p2, p3...) can be expressed as p1*func(p0, p2, p3, ...) or p0 +p1*func(p0, p2, p3, ...) with '0' being the offsetparam.
    
    slopeParam - Index of a parameter that is multiplied with x and then summed to the function. E.g. '1' for f(p0, p1, p2, p3...) = p1*x + func(p0, p2, p3, ...) Only one, multiplyParam and slopeParam can be used (ie.e, the other should be set to -1)
  - getNumParams
```
public int getNumParams()
```
    Get number of parameters for current fit formula Do not use before 'doFit', because the fit function would be undefined.
  - getNumParams
```
public static int getNumParams(int fitType)
```
    Returns the number of parameters for a given fit type, except for the 'custom' fit, where the number of parameters is given by the equation: see getNumParams(String)
  - getNumParams
```
public static int getNumParams(java.lang.String customFormula)
```
    Returns the number of parameters for a custom equation given as a macro String, like "y = a + b*x + c*x*x" . Restricted to 6 parameters "a" ... "f" (fitting more parameters is not likely to yield an accurate result anyhow). Returns 0 if a very basic check does not find a formula of this type.
  - f
```
public final double f(double x)
```
    Returns the formula value for parameters 'p' at 'x'. Do not use before 'doFit', because the fit function would be undefined.
  - f
```
public final double f(double[] p,
                      double x)
```
    Returns the formula value for parameters 'p' at 'x'. Do not use before 'doFit', because the fit function would be undefined.
  - f
```
public static double f(int fitType,
                       double[] p,
                       double x)
```
    Returns value of built-in 'fitType' formula value for parameters "p" at "x"
  - getParams
```
public double[] getParams()
```
    Get the result of fitting, i.e. the set of parameter values for the best fit. Note that the array returned may have more elements than numParams; ignore the rest. May return an array with only NaN values if the minimizer could not start properly, i.e., if getStatus() returns Minimizer.INITILIZATION_FAILURE. See Minimizer.getParams() for details.
  - getResiduals
```
public double[] getResiduals()
```
    Returns residuals array, i.e., differences between data and curve. The residuals are with respect to the real data, also for fit types where the data are modified before fitting (power&exp fit by linear regression, 'Rodbard NIH Image' ). This is in contrast to sum of squared residuals, which is for the fit that was actually done.
  - getSumResidualsSqr
```
public double getSumResidualsSqr()
```
    Returns the sum of the residuals (may be NaN if the minimizer could not start properly i.e., if getStatus() returns Minimizer.INITILIZATION_FAILURE). If weights have been specified, each of the residuals is multiplied by the corresponding weight before summing.
  - getSD
```
public double getSD()
```
    Returns the standard deviation of the residuals. Here, the standard deviation is defined here as the root-mean-square of the residuals times sqrt(n/(n-1)); where n is the number of points. If weights are provided, the standard deviation does not take the weights into account. With weights, the standard deviation and getSumResidualsSqr (which uses weights) are not related the usual way.
  - getRSquared
```
public double getRSquared()
```
    Returns R^2, where 1.0 is best. For unweighted data,
    r^2 = 1 - SSE/SSD where: SSE = sum of the squared errors SSD = sum of the squared deviations about the mean.
    For power, exp by linear regression and 'Rodbard NIH Image', this is calculated for the fit actually done, not for the residuals of the original data.
  - getFitGoodness
```
public double getFitGoodness()
```
    Get a measure of "goodness of fit" where 1.0 is best. Approaches R^2 if the number of points is much larger than the number of fit parameters. Assumes that the data points are independent (i.e., each point having a different x value). For power, exp by linear regression and 'Rodbard NIH Image', this is calculated for the fit actually done, not for the residuals of the original data.
  - getStatus
```
public int getStatus()
```
  - getStatusString
```
public java.lang.String getStatusString()
```
    Get a short text with a short description of the status. Should be preferred over Minimizer.STATUS_STRING[getMinimizer().getStatus()] because getStatusString() better explains the problem in some cases of initialization failure (data not compatible with the fit function chosen)
  - getResultString
```
public java.lang.String getResultString()
```
    Get a string with detailed description of the curve fitting results (several lines, including the fit parameters).
  - setRestarts
```
public void setRestarts(int maxRestarts)
```
    Set maximum number of simplex restarts to do. See Minimizer.setMaxRestarts for details.
  - setMaxError
```
public void setMaxError(double maxRelError)
```
    Set the maximum error. by which the sum of residuals may deviate from the true value (relative w.r.t. full sum of rediduals). Possible range: 0.1 ... 10^-16
  - setStatusAndEsc
```
public void setStatusAndEsc(java.lang.String ijStatusString,
                            boolean checkEscape)
```
    Create output on the number of iterations in the ImageJ Status line, e.g. " 50 (max 750); ESC to stop"
    
    Parameters:
    
    ijStatusString - Displayed in the beginning of the status message. No display if null. E.g. "Curve Fit: Iteration "
    
    checkEscape - When true, the Minimizer stops if escape is pressed and the status becomes ABORTED. Note that checking for ESC does not work in the Event Queue thread.
  - getIterations
```
public int getIterations()
```
    Get number of iterations performed. Returns 1 in case the fit was done by linear regression only.
  - getMaxIterations
```
public int getMaxIterations()
```
    Get maximum number of iterations allowed (sum of iteration count for all restarts)
  - setMaxIterations
```
public void setMaxIterations(int maxIter)
```
    Set maximum number of iterations allowed (sum of iteration count for all restarts)
  - getRestarts
```
public int getRestarts()
```
    Get maximum number of simplex restarts to do. See Minimizer.setMaxRestarts for details.
  - getXPoints
```
public double[] getXPoints()
```
    returns the array with the x data
  - getYPoints
```
public double[] getYPoints()
```
    returns the array with the y data
  - getFit
```
public int getFit()
```
    returns the code of the fit type of the fit performed
  - getName
```
public java.lang.String getName()
```
    returns the name of the fit function of the fit performed
  - getFormula
```
public java.lang.String getFormula()
```
    returns a String with the formula of the fit function used
  - getMacroCode
```
public java.lang.String getMacroCode()
```
    Returns macro code of the form "y = ...x" for the fit function used. Note that this is not neccessarily the equation acutally used for the fit (for the various "linear regression" types and RODBARD2, the fit is done differently). Note that no macro code may be avialable for custom fits using the UserFunction interface.
  - getSortedFitList
```
public static java.lang.String[] getSortedFitList()
```
    Returns an array of fit names with nicer sorting
  - getFitCode
```
public static int getFitCode(java.lang.String fitName)
```
    Returns the code for a fit with given name as defined in fitList, or -1 if not found
  - userFunction
```
public final double userFunction(double[] params,
                                 double dummy)
```
    This function is called by the Minimizer and calculates the sum of squared residuals for given parameters. To improve the efficiency, simple linear dependencies are solved directly by linear regression; in that case the corresponding parameters are modified. This effectively reduces the number of free parameters by one or two and thereby significantly improves the performance of minimization.
    
    Specified by:
    
    userFunction in interface UserFunction
    
    Parameters:
    
    params - When minimizing, array of variables. For curve fit array of fit parameters. The array contents should not be modified. Note that the function can get an array with more elements then needed to specify the parameters. Ignore the rest (and don't modify them).
    
    dummy - For a fit function, the independent variable of the function. Ignore it when using the minimizer.
    
    Returns:
    
    The result of the function.
  - getMax
```
public static int getMax(double[] array)
```
    Gets index of highest value in an array.
    
    Parameters:
    
    array - the array.
    
    Returns:
    
    Index of highest value.
  - getPlot
```
public Plot getPlot()
```
  - getPlot
```
public Plot getPlot(int points)
```

Class CurveFitter

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

STRAIGHT_LINE

POLY2

POLY3

POLY4

EXPONENTIAL

POWER

LOG

RODBARD

GAMMA_VARIATE

LOG2

RODBARD2

EXP_WITH_OFFSET

GAUSSIAN

EXP_RECOVERY

INV_RODBARD

EXP_REGRESSION

POWER_REGRESSION

POLY5

POLY6

POLY7

POLY8

GAUSSIAN_NOOFFSET

EXP_RECOVERY_NOOFFSET

CHAPMAN

ERF

sortedTypes

fitList

fList

fMacro

IterFactor

Constructor Detail

CurveFitter

Method Detail

doFit

doFit

doCustomFit

doCustomFit

setInitialParameters

setWeights

getMinimizer

setOffsetMultiplySlopeParams

getNumParams

getNumParams

getNumParams

f

f

f

getParams

getResiduals

getSumResidualsSqr

getSD

getRSquared

getFitGoodness

getStatus

getStatusString

getResultString

setRestarts

setMaxError

setStatusAndEsc

getIterations

getMaxIterations

setMaxIterations

getRestarts

getXPoints

getYPoints

getFit

getName

getFormula

getMacroCode

getSortedFitList

getFitCode

userFunction

getMax

getPlot