Package org.opensourcephysics.cabrillo.tracker

Class BounceModel

java.lang.Object
org.opensourcephysics.cabrillo.tracker.BounceModel
public class BounceModel extends Object
A LinearModelWithStep maps a parameter vector to a series of data points at equally spaced time intervals. For handling 2D data, the parameters are a num_params x 2 Matrix. This class requires the JAMA matrix package from http://math.nist.gov/javanumerics/jama Mon Oct 31 14:02:07 PDT 2011 Kevin Karplus
Author:
Kevin Karplus

  • Constructor Summary

    Constructors
    Constructor
    Description
    BounceModel(int num_data, int deg, double when_step)
    constructor for n data points using polynomial of degree d plus a Dirac delta in the acceleration (step in velocity) at time s That is, data[t] will be fitted to sum_i<=d param[i]*t**i for t<s sum_i<=d param[i]*t**i + param[d+1]*(t-s) for s<=t If the time of the step is <=0 or >=num_data-1, then it is not possible to fit an extra parameter, so it is omitted from the model, and a pure polynomial is used sum_i<=d param[i]*t**i If the time of the step is Double.NaN, then the step time is unknown and two extra parameters are needed to estimate s, which is assumed to be in range (0.5*num_data-1, 0.5*num_data).

  • Method Summary

    Modifier and Type
    Method
    Description
    double[]
    first_deriv(BounceMatrix model_param, double t)
    return first derivatives at time t The dimensionality of the returned array of doubles is the same as the number of columns in the model_param Matrix (that would be 2 for model_param returned by fit_xy()).
    BounceParameters
    fit_xy(double[] xData, double[] yData, int start, int index_step)
    fit parameters for model to a window of (x,y) points Returned result: fitted paramters returns null if fitting is not possible, which can happen if start, start+index_step, ..., start+(num_data-1)*index_step goes out of range for either data array or xdata or ydata is Double.NaN for one of the specified points Time t=0 corresponds to subscript "start" Time t=1 to start+time_step
    BounceParameters
    fit_xy(double[] xData, double[] yData, int start, int index_step, double initial_step_at, double[] initial_step_size)
    fit parameters for model to a window of (x,y) points, with a specified step to be removed before fitting Returned result: fitted parameters, with record of extra step returns null if fitting is not possible, which can happen if start, start+index_step, ..., start+(num_data-1)*index_step goes out of range for either data array or xdata or ydata is Double.NaN for one of the specified points Time t=0 corresponds to subscript "start" Time t=1 to start+time_step
    double
    getStepAt()
    where is there a step?
    double
    getStepAt(BounceMatrix model_param)
    where is there a step? If there is a step in a model which estimates time as well as size of step, we need the model parameters to say where the step was fitted.
    double[]
    getStepSize(BounceMatrix model_param)
    return step size The dimensionality of the returned array of doubles is the same as the number of columns in the model_param Matrix (that would be 2 for model_param returned by fit_xy()).
    double[]
    second_deriv(BounceMatrix model_param, double t)
    return second derivatives at time t The dimensionality of the returned array of doubles is the same as the number of columns in the model_param Matrix (that would be 2 for model_param returned by fit_xy()).
    boolean
    usesStep()
    return use_step

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • BounceModel

      public BounceModel(int num_data, int deg, double when_step)
      constructor for n data points using polynomial of degree d plus a Dirac delta in the acceleration (step in velocity) at time s That is, data[t] will be fitted to sum_i<=d param[i]*t**i for t<s sum_i<=d param[i]*t**i + param[d+1]*(t-s) for s<=t If the time of the step is <=0 or >=num_data-1, then it is not possible to fit an extra parameter, so it is omitted from the model, and a pure polynomial is used sum_i<=d param[i]*t**i If the time of the step is Double.NaN, then the step time is unknown and two extra parameters are needed to estimate s, which is assumed to be in range (0.5*num_data-1, 0.5*num_data). Other than 0 to turn it off, the step should not be located at an integer.
      Parameters:
      num_data -
      deg -
      when_step - when step in velocity happens

  • Method Details

    • getStepAt

      public double getStepAt()
      where is there a step?
      Returns:
      time of step in velocity

    • getStepAt

      public double getStepAt(BounceMatrix model_param)
      where is there a step? If there is a step in a model which estimates time as well as size of step, we need the model parameters to say where the step was fitted.
      Parameters:
      model_param - parameters from fit
      Returns:
      time of step in velocity

    • fit_xy

      public BounceParameters fit_xy(double[] xData, double[] yData, int start, int index_step)
      fit parameters for model to a window of (x,y) points Returned result: fitted paramters returns null if fitting is not possible, which can happen if start, start+index_step, ..., start+(num_data-1)*index_step goes out of range for either data array or xdata or ydata is Double.NaN for one of the specified points Time t=0 corresponds to subscript "start" Time t=1 to start+time_step
      Parameters:
      xData - array of x values
      yData - array of y values
      start - subscript of first (x,y) pair for window
      index_step - increment between subscripts for subsequent data points
      Returns:
      LinearModelParams containing parameters and residual square error

    • fit_xy

      public BounceParameters fit_xy(double[] xData, double[] yData, int start, int index_step, double initial_step_at, double[] initial_step_size)
      fit parameters for model to a window of (x,y) points, with a specified step to be removed before fitting Returned result: fitted parameters, with record of extra step returns null if fitting is not possible, which can happen if start, start+index_step, ..., start+(num_data-1)*index_step goes out of range for either data array or xdata or ydata is Double.NaN for one of the specified points Time t=0 corresponds to subscript "start" Time t=1 to start+time_step
      Parameters:
      xData - array of x values
      yData - array of y values
      start - subscript of first (x,y) pair for window
      index_step - increment between subscripts for subsequent data points
      initial_step_at - what time the predefined step happens 0<=t<num_data
      initial_step_size -
      Returns:
      LinearModelParams containing parameters and residual square error

    • first_deriv

      public double[] first_deriv(BounceMatrix model_param, double t)
      return first derivatives at time t The dimensionality of the returned array of doubles is the same as the number of columns in the model_param Matrix (that would be 2 for model_param returned by fit_xy()). Time t=0 corresponds to subscript "start" in the fit_xy call Time t=1 to start+time_step in the fit_xy call
      Parameters:
      model_param - parameter matrix as returned by a fit_xy call
      t - what time
      Returns:
      first derivates of x and y at time t

    • second_deriv

      public double[] second_deriv(BounceMatrix model_param, double t)
      return second derivatives at time t The dimensionality of the returned array of doubles is the same as the number of columns in the model_param Matrix (that would be 2 for model_param returned by fit_xy()). The Dirac delta causes some difficulty in expressing the acceleration, and it is replaced in the acceleration output (but not the velocity or data fitting) by a pulse in the interval (s-0.5, s+.5]
      Parameters:
      model_param - parameter matrix as returned by a fit_xy call
      t - what time step (t=0 corresponds to subscript "start" in the fit_xy call
      Returns:
      second derivates of x and y at time t

    • usesStep

      public boolean usesStep()
      return use_step
      Returns:
      true if model uses as step, false if pure polynomial model

    • getStepSize

      public double[] getStepSize(BounceMatrix model_param)
      return step size The dimensionality of the returned array of doubles is the same as the number of columns in the model_param Matrix (that would be 2 for model_param returned by fit_xy()).
      Parameters:
      model_param - parameter matrix as returned by a fit_xy call
      Returns:
      step size (0 if no step)