Levenberg-Marquardt Plugin

The Levenberg-Marquardt plugin is used to ”fit” a SBML models parameters to experimental data, i.e. find parameter values that causes the model output most closely resembles experimental data.

The plugin has numerous properties to allow the user full control over the internal fitting
engine, as well as access to generated fitted data after a minimization session.

In addition,various statistical properties, such as standardized residuals, Q-Q data, ChiSquare and reduced ChiSquare are made accessible to the user. The resulting parameter values do also come with estimated confidence limits.

The plugin implements the Levenberg-Marquardt method using code (Licensed under FreeBSD) developed by Joachim Wuttke.
The following code shows simple usage of the plugin.

from telplugins import *

# Load Plugins
chiPlugin       = Plugin("tel_chisquare")
lm              = Plugin("tel_levenberg_marquardt")
modelPlugin     = Plugin("tel_test_model")
addNoisePlugin  = Plugin("tel_add_noise")

try:    
    #========== EVENT FUNCTION SETUP ===========================
    def myEvent(dummy): #We are not capturing any data from the plugin, so just pass a dummy
        print 'Iteration, Norm = ' + `lm.getProperty("NrOfIter")`  + ', ' + `lm.getProperty("Norm")`

    #Setup progress event function
    progressEvent =  NotifyEventEx(myEvent)     
    assignOnProgressEvent(lm.plugin, progressEvent)
    #============================================================

    #Create model data, with and without noise using the test_model plugin
    modelPlugin.execute()     

    #Setup lmfit properties.
    lm.SBML             = modelPlugin.Model 
    lm.ExperimentalData = modelPlugin.TestDataWithNoise

    # Add the parameters that we're going to fit and an initial 'start' value
    lm.setProperty("InputParameterList", ["k1", .3])
    lm.setProperty("FittedDataSelectionList", "[S1] [S2]")
    lm.setProperty("ExperimentalDataSelectionList", "[S1] [S2]")

    # Start minimization
    lm.execute()

    print 'Minimization finished. \n==== Result ===='    
    print 'Fit engine status: ' + `lm.getProperty('StatusMessage')`

    print 'Hessian Matrix'
    print lm.getProperty("Hessian")

    print 'Covariance  Matrix'
    print lm.getProperty("CovarianceMatrix")

    print 'ChiSquare = '            + `lm.getProperty("ChiSquare")`
    print 'Reduced ChiSquare = '    + `lm.getProperty("ReducedChiSquare")`

    #This is a list of parameters
    parameters = tpc.getPluginProperty (lm.plugin, "OutputParameterList")
    confLimits = tpc.getPluginProperty (lm.plugin, "ConfidenceLimits")    

    #Iterate trough list of parameters and confidence limits
    para  = getFirstProperty(parameters)
    limit = getFirstProperty(confLimits)     
    while para and limit:           
        print getPropertyName(para) + ' = ' + `getPropertyValue(para)` + ' +/- ' + `getPropertyValue(limit)`
        para  = getNextProperty(parameters)
        limit = getNextProperty(confLimits)                        

    # Get the fitted and residual data
    fittedData = lm.getProperty ("FittedData").toNumpy
    residuals  = lm.getProperty ("Residuals").toNumpy

    # Get the experimental data as a numpy array
    experimentalData = modelPlugin.TestDataWithNoise.toNumpy

    telplugins.plot(fittedData         [:,[0,1]], "blue", "-",    "",    "S1 Fitted")
    telplugins.plot(fittedData         [:,[0,2]], "blue", "-",    "",    "S2 Fitted")
    telplugins.plot(residuals          [:,[0,1]], "blue", "None", "x",   "S1 Residual")
    telplugins.plot(residuals          [:,[0,2]], "red",  "None", "x",   "S2 Residual")
    telplugins.plot(experimentalData   [:,[0,1]], "red",  "",     "*",   "S1 Data")
    telplugins.plot(experimentalData   [:,[0,2]], "blue", "",     "*",   "S2 Data")
    telplugins.plt.show()

    #Finally, view the manual and version
    lm.viewManual()    
    print 'Plugin version: ' + `lm.getVersion()`

except Exception as e:
    print 'Problem.. ' + `e`

The following screen shots shows the plot output from the script above.

More information can be found in the embedded Plugin Document, available here: levenberg_marquardt

Current Version: 1.0.0 (2014-03-09)