Module ij
Package ij.measure

Class 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| < 2*(xMax-xMin). For polynomials of 5th order or higher, the x range should encompass x=0; and for 7th and 8th order it is desirable to have x=0 near the center of the x range. (ii) In contrast to some fitting algorithms using the normal equations and matrix inversion, the simplex algorithm used here can cope with parameters having very different orders of magnitude, as long as the coefficients of the polynomial are within a reasonable range (say, 1e-80 to 1e80). Thus, it is usually not needed to scale the x values, even for high-order polynomials. Version history: 2008-01-21: Modified to do Gaussian fitting by Stefan Woerz (s.woerz at dkfz.de). 2012-01-30: Modified for external Minimizer class and UserFunction fit by Michael Schmid. - Also fixed incorrect equation string for 'Gamma Variate' & 'Rodbard (NIH Image)', - Added 'Inverse Rodbard', 'Exponential (linear regression)', 'Power (linear regression)' functions and polynomials of order 5-8. Added 'nicely' sorted list of types. - Added absolute error for minimizer to avoid endless minimization if exact fit is possible. - Added 'initialParamVariations' (order of magnitude if parameter variations) - this is important for safer and better convergence. - Linear regression for up to 2 linear parameters, reduces the number of parameters handled by the simplex Minimizer and improves convergence. These parameters can be an offset and either a linear slope or a factor that the full function is multiplied with. 2012-10-07: added GAUSSIAN_NOOFFSET fit type 2012-11-20: Bugfix: exception on Gaussian&Rodbard with initial params, bad initial params for Gaussian 2013-09-24: Added "Exponential Recovery (no offset)" and "Chapman-Richards" (3-parameter; used e.g. to describe forest growth) fit types. 2013-10-11: bugfixes, added setStatusAndEsc to show iterations and enable abort by ESC 2015-03-26: bugfix, did not use linear regression for RODBARD 2016-11-28: added static getNumParams methods 2018-03-23: fixes NullPointerException for custom fit without initialParamVariations 2018-07-19: added error function erf (=integral over Gaussian) 2021-04-30: data points can have weights
    • 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 + b*x + c*x*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 + b*x + c*x*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)