Opens the PottersWheel equalizer to change and to analyze
 characteristics of the current fitting assembly.



 The equalizer comprises several views:

 - Sliders
 - Plotting (Pl)
 - Phase space (PS)
 - Sensitivities
 - Fitting (FV)
 - Fit sequence analysis (N)
 - Single fit analysis (1)



 Eight pairs of sliders are available in th slider view to tune
 selected parameters, with the left slider changing the
 mantissa (fine tuning) and the right slider changing the
 order of magnitude (coarse tuning).  A parameter value can also be
 entered directly into the textbox below the sliders.

 The slider-pair on the left will be visible in each Equalizer view.

 In order to keep parameters at a certain relationship, e.g.
 a constant fraction of 3.0, a parameter equation can be applied, e.g.
  kon = 3.0 * koff
 If koff is changed, the value for kon is updated automatically and the
 corresponding slider is set to its proper value. Please insert one equation
 per line into the textbox on the right. To temporarilly turn off the
 parameter equations, uncheck "Apply parameter equations".



 The plotting view allows to show and hide a subset of variable of each
 class u (driving inputs), x (dynamic variables), y (observables),
 z (derived variables), and 'a' (algebraic expressions).
 Please select a couple and variable class. The use the arrow buttons
 between the listboxes "Visible" and "Invisible" to shift the selected
 variables between the two sets.

 It is often useful to plot several species into one subplot, e.g. to
 directly compare their absolute values over time. This can be done by
 creating variable groups. Afer selecting the species of interest click
 on 'Create group' and provide an optional group name to identify the group
 in the list of groups on the right and to specify the subplot header.

 If the fitted model complies to the PottersWheel naming convention,
 groups can be generated automatically by selecting the action
 'Automatic group creation for basic species' and pressing 'Start action'.
 Especially in large models the information content of the plotted
 trajectories benefits from hiding all single variables and plotting only
 grouped ones.

 In order to save or load a reasonable visualization setting select the
 corresponding action and press 'Start action'. The generated file can
 be copy-pasted into an existing model definition file in order to
 start with a predefined visualization scheme from the beginning.

 Not only variables but also stimuli can be made visible or invisible

 Changes to the visualization setting take effect replotting the figures.


Phase space

 The phase space view allows to create pairs of two variables which will
 be plotted against each other, i.e. in a so-called phase space diagramm.
 The pairs are defined separately for each combined couple.



 This view allows to plot the derivative of one variable x to a parameter k,
 i.e. the sensitivity of x on k. This dependency is time-dependent and is
 either approximated numerically or calculated during model integration by
 suitable integrators based on analytical expressions. The latter approach
 requires the CVODES integrator, the symbolic math toolbox, and the setting

  config.integration.calcSensitivities = true


Fitting view

 The fitting view allows to select an optimization strategy in normal
 or logarithmic parameter space. The latter is recommended if you expect
 model parameter to vary of orders of magnitude between each other or/and
 during parameter calibration.

 A single fit calibrates all non-fixed start values x0, dynamic parameters k,
 and scaling (or observation) parameters s. Shortcut buttons exist to fit
 only parameters from one of the three classes labeled 'x0', 'k', and 's'.
 Fit sequences F2 and F3 with a specified number of fits 'n' and disturbance
 strength 'd' can be run directly from the fitting view interface.
 In this case calculation is accelerated by unchecking "Show fitting"
 in order to avoid repetitive plotting of each fit.
 Compare pwF2 and pwF3.

 The boosted fit combines the trust region optimization with simulated
 annealing in logarithmic and linear parameter space. This strategy is
 a good starting point for a completely uncalibrated model. See pwFitBoost
 for further information.

 Which parameters are calibrated or stay fixed is usually defined in the
 model definition files or the fit settings dialog. Temporarilly, parameters
 may be fixed using the 'Set fixed pars' button.

 Pressing the disturb button or running a fit sequence leads to varied
 and refitted parameter values. The button 'Set disturbed pars.' allows
 to define which parameters are disturbed. Compare pwDisturb and

 A user-defined optimization function can be employed instead of the default
 PottersWheel optimization strategy. This is done using the function
 pwOptimizationSetUserFunction. By unchecking 'User fun', the user
 optimization function may be quickly
 turned off and on.

 The following lists are used for fit-based analyses:

 - Fit groups
 - Fit sequences
 - All fits
 - Fits of analysis


Fit groups

 Each fit is characterized by a fit group ID which represents
 the fitted model-data-couples and set of calibrated parameters.
 Additional fits under the same settings will receive the same
 fit group ID. The list of fit groups displays the number of fits
 in each group and their group ID. The function pwFitHistoryGetFits
 may be used to access the fits group programmatically or to plot
 an overview.


Fit sequences

 Fits belonging to the same fit sequence are listed here characterized
 by the time when the fit sequence started together with the number
 of fits in the sequence.


All fits

 To access an individual fit the list of all fits can be used.
 Next to the start time of each fit, its chi-square value (CS)
 is printed. One or more fits may be selected. When check-marking
 the fields 'Direct plot' or 'Direct info', the system trajectories
 or information of the fit are drawn or displayed, respectively,
 when the fit gets selected.


Fits of analysis

 When an analysis is carried out, e.g. a fit-sequence analysis
 based on the best 50% of the fits with a minimum p-value of 0.01,
 the resulting fits are displayed in the 'fits of analysis' list.
 They can be saved into an xls or txt file using the menu
 'Parameters | Save fits of analysis to file...'.
 In the same fashion a set of fits may be loaded from a file
 into the same list using the menu
 'Parameters | Load fits of analysis from file...'.


Fit sequence analysis (N)

 Several analyses exist to characterize subset of fit sequences:

 - Linear fit sequence analysis
 - Nonlinear Mean Optimal Transformation Approach (MOTA) analysis
 - Scatter plots
 - Multi-trajectories

 Each analysis is applied to a subset of fits based on:

 - Last fit sequence
 - Selected fit sequence
 - Selected fit group
 - Selected fits
 - Fits of (last) analysis

 The subset is further constrained by

 - Percentage of best fits
 - A minimum p-value
 - Percentage of included outliers

 The subset of fits is ordered by the fit chi-square value.
 By specifying a percentage of fits below 100, fits with the worst
 fit quality are neglected.

 A p-value is determined for each fit using a chi-square test for
 N-#p degrees of freedom, where N is the number of fitted data points
 and #p the number of calibrated parameters. All fits below the minimum
 p-value are omitted.

 It may be reasonable to determine the region in parameter
 space where most of the fits are lying. Fits far away from this region,
 i.e. outliers, should be excluded even if they have a similiar chi-square


Linear fit sequence analysis

 Compare pwFitSequenceAnalysis.


Nonlinear MOTA analysis

 Compare pwMota.


Scatter plots

 Compare pwScatterPlots.



 The trajectories are displayed for each fit. Using the setting
  config.optimization.levelOfHistoryStorage = 3;
 when applying a fit allows to plot the saved trajectories
 instead of fresh calculation. This is especially useful, if the
 model trajectories are computationally expensive to be calculated.

 Compare pwTrajectoriesOfManyParameterSettings.


Single fit analysis

 Available analyses based on a single fit are:

 - Single fit analysis (to be renamed (TODO))
   Compare pwCovarianceMatrixOfJacobian and pwSingleSimFitAnalysis
 - Residuals based analyses:
   Compare pwAnalysisOfResiduals.
   - Residuals against time
   - Residuals embedded
   - ACF
   - Histogram
   - QQ-Plot
   - Residuals against predicted values
   - Predicted against observed values
 - Standard deviation analysis
   Compare pwAnalysisOfStandardDeviations.
 - Chi-square landscape for two parameters
   Compare pwShowChisqLandscape.
 - Chi-square Iso surfaces for three parameters
   Compare pwChiSquareIsoSurfaces3D.
 - Estimation of the Profile Likelihood (PLE)
   Compare pwPleInit.



 The toolbar comprises the following buttons:
pwOpen the PottersWheel main user interface
AToggles to show or hide trajectories for algebraic expressions
UToggles to show or hide trajectories for driving input functions
XToggles to show or hide trajectories for dynamic variables
YToggles to show or hide trajectories for observables
ZToggles to show or hide trajectories for derived variables
SiToggles to combine all trajectories of one variable class into one subplot
BrushDraws the trajectories
ArrangeArranges all trajectory-figures
SlidersOpens the slider view
PlOpens the plotting view
PSOpens the phase space view
FVOpens the fitting view
1Opens the single fit analysis view
NOpens the fit sequence analysis view
PlayStart a fit. Compare pwFit.
StopStops the current fit. Else, use Strg+C if fitting is not stopped.
LightingDisturbes the parameters. Compare pwDisturb.
ResetResets the parameter values. Compare pwReset.
P-SaveSaves the current parameter settings as a manual fit.
OvToggles between overwritten trajectories or overlayed ones
SiSSaves parameter values in order to simulate synthetic data. Compare pwSim.
DFgDisplays all current figures.
F-SaveSave all current figures. Compare pwSaveFigures.
(i)Displays information about the last fit. Compare pwInfo.
InDOpens the driving input designer. Compare pwInputDesigner.

Fitting information

 The header of the PottersWheel equalizer displays information about the
 current fit:
NNumber of fitted data points.
ChisqCurrent chi-square value. Compare pwGoodnessOfFit.
Chisq/NChi-square value divided by N. Should be lower than 1 for a good fit.
DMeasure of deviation between true and fitted parameter values.
Only applies to fitting of simulated synthetic data.
Compare pwFitDeviation.

See also