Module ij
Package ij.measure

Class CurveFitter

java.lang.Object
ij.measure.CurveFitter
All Implemented Interfaces:
UserFunction

public class CurveFitter extends 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 final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final String[]
    Names of the built-in fit functions
    static final String[]
    Equations of the built-in fit functions
    static final String[]
    ImageJ Macro language code for the built-in functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Deprecated.
    now in the Minimizer class (since ImageJ 1.46f).
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int
    Constants for the built-in fit functions
    static final int[]
    Nicer sequence of the built-in function types
    static final int
    Constants for the built-in fit functions
  • Constructor Summary

    Constructors
    Constructor
    Description
    CurveFitter(double[] xData, double[] yData)
    Construct a new CurveFitter.
  • Method Summary

    Modifier and Type
    Method
    Description
    void
    doCustomFit(UserFunction userFunction, int numParams, 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(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.
    final double
    f(double x)
    Returns the formula value for parameters 'p' at 'x'.
    final 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
    returns the code of the fit type of the fit performed
    static int
    getFitCode(String fitName)
    Returns the code for a fit with given name as defined in fitList, or -1 if not found
    double
    Get a measure of "goodness of fit" where 1.0 is best.
    returns a String with the formula of the fit function used
    int
    Get number of iterations performed.
    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
    Get maximum number of iterations allowed (sum of iteration count for all restarts)
    Returns a reference to the Minimizer used, for accessing Minimizer methods directly.
    returns the name of the fit function of the fit performed
    int
    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(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[]
    Get the result of fitting, i.e.
     
    getPlot(int points)
     
    double[]
    Returns residuals array, i.e., differences between data and curve.
    int
    Get maximum number of simplex restarts to do.
    Get a string with detailed description of the curve fitting results (several lines, including the fit parameters).
    double
    Returns R^2, where 1.0 is best.
    double
    Returns the standard deviation of the residuals.
    static String[]
    Returns an array of fit names with nicer sorting
    int
     
    Get a short text with a short description of the status.
    double
    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[]
    returns the array with the x data
    double[]
    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(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.
    final 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 Details

    • STRAIGHT_LINE

      public static final int STRAIGHT_LINE
      Constants for the built-in fit functions
      See Also:
    • POLY2

      public static final int POLY2
      Constants for the built-in fit functions
      See Also:
    • POLY3

      public static final int POLY3
      Constants for the built-in fit functions
      See Also:
    • POLY4

      public static final int POLY4
      Constants for the built-in fit functions
      See Also:
    • EXPONENTIAL

      public static final int EXPONENTIAL
      Constants for the built-in fit functions
      See Also:
    • POWER

      public static final int POWER
      Constants for the built-in fit functions
      See Also:
    • LOG

      public static final int LOG
      Constants for the built-in fit functions
      See Also:
    • RODBARD

      public static final int RODBARD
      Constants for the built-in fit functions
      See Also:
    • GAMMA_VARIATE

      public static final int GAMMA_VARIATE
      Constants for the built-in fit functions
      See Also:
    • LOG2

      public static final int LOG2
      Constants for the built-in fit functions
      See Also:
    • RODBARD2

      public static final int RODBARD2
      Constants for the built-in fit functions
      See Also:
    • EXP_WITH_OFFSET

      public static final int EXP_WITH_OFFSET
      Constants for the built-in fit functions
      See Also:
    • GAUSSIAN

      public static final int GAUSSIAN
      Constants for the built-in fit functions
      See Also:
    • EXP_RECOVERY

      public static final int EXP_RECOVERY
      Constants for the built-in fit functions
      See Also:
    • INV_RODBARD

      public static final int INV_RODBARD
      Constants for the built-in fit functions
      See Also:
    • EXP_REGRESSION

      public static final int EXP_REGRESSION
      Constants for the built-in fit functions
      See Also:
    • POWER_REGRESSION

      public static final int POWER_REGRESSION
      Constants for the built-in fit functions
      See Also:
    • POLY5

      public static final int POLY5
      Constants for the built-in fit functions
      See Also:
    • POLY6

      public static final int POLY6
      Constants for the built-in fit functions
      See Also:
    • POLY7

      public static final int POLY7
      Constants for the built-in fit functions
      See Also:
    • POLY8

      public static final int POLY8
      Constants for the built-in fit functions
      See Also:
    • GAUSSIAN_NOOFFSET

      public static final int GAUSSIAN_NOOFFSET
      Constants for the built-in fit functions
      See Also:
    • EXP_RECOVERY_NOOFFSET

      public static final int EXP_RECOVERY_NOOFFSET
      Constants for the built-in fit functions
      See Also:
    • CHAPMAN

      public static final int CHAPMAN
      Constants for the built-in fit functions
      See Also:
    • ERF

      public static final int ERF
      Constants for the built-in fit functions
      See Also:
    • sortedTypes

      public static final int[] sortedTypes
      Nicer sequence of the built-in function types
    • fitList

      public static final String[] fitList
      Names of the built-in fit functions
    • fList

      public static final String[] fList
      Equations of the built-in fit functions
    • fMacro

      public static final 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:
  • Constructor Details

    • CurveFitter

      public CurveFitter(double[] xData, double[] yData)
      Construct a new CurveFitter.
  • Method Details

    • 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(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, 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(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 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 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(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 String getName()
      returns the name of the fit function of the fit performed
    • getFormula

      public String getFormula()
      returns a String with the formula of the fit function used
    • getMacroCode

      public 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 String[] getSortedFitList()
      Returns an array of fit names with nicer sorting
    • getFitCode

      public static int getFitCode(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)