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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def ctmc(data, numstates, transintv=1.0, toltime=1e-8, debug=False):
 """ Continous Time Markov Chain Parameters data : list of lists A python list of N examples (e.g. rating histories of N companies, the event data of N basketball games, etc.). The i-th example consist of one list with M_i encoded state labels and M_i the durations or time periods the state lasted since the recording started. numstates : int number of unique states transintv : float The time interval toltime : float (If debug=True) Will throw an exception if the aggregated state duration or aggregated time periods of any state is smaller than toltime. debug : bool (Default: False) If True run the ctmc.datacheck function. Enable this flag if you to check if your 'data' variable has been processed correctly. Returns ------- transmat : ndarray The estimated transition/stochastic matrix. genmat : ndarray The estimated generator matrix transcount : ndarray statetime : ndarray Errors: ------- - ctmc assumes a clean data object and does not autocorrect any errors as result of it The main error sources are - transitions counting (e.g. two consequtive states has not been aggregated, only one distinct state reported) and - a state is modeled ore required that does not occur in the dataset (e.g. you a certain scale in mind and just assume it's in the data) or resp. involved in any transition (e.g. an example with just one state) You can enable error checking and exceptions by setting debug=True. You should do this for the first run on a smaller dataset. Example: -------- Use `datacheck` to check during preprocessing the dataset ctmc.datacheck(data, numstates, toltime) Disable checks in `ctmc` transmat, genmat, transcount, statetime = ctmc.ctmc( data, numstates, toltime, checks=False) Check aftwards if there has been an error ctmc.errorcheck(transcount, statetime, toltime) """

    # raise an exception if the data format is wrong
    if debug:
        datacheck(data, numstates, toltime)

    # aggregate event data
    transcount, statetime = aggregateevents(data, numstates)

    # raise an exception if the event data aggregation failed
    if debug:
        errorcheck(transcount, statetime, toltime)

    # create generator matrix
    genmat = generatormatrix(transcount, statetime)

    # compute matrix exponential of the generator matrix
    transmat = scipy.linalg.expm(genmat * transintv)

    # done
    return transmat, genmat, transcount, statetime