parse_and_graph.py

import pandas as pd
import graphviz as gv


def main(SUBPATH, INPUTDIR = 'input/', OUTPUTDIR = 'output/'):

    raw_df = pd.DataFrame.from_csv(INPUTDIR + SUBPATH, header=1)
    melted_df = pd.melt(raw_df.reset_index(), id_vars=['index']).dropna()
    strings_df = melted_df.applymap(str)

    graph = gv.Graph()
    graph_renaming = {'index':'tail_name','variable':'head_name','value':'rank'}
    for edge in strings_df.rename(columns=graph_renaming).to_dict('records'):
        graph.node(edge['tail_name'], fillcolor='lightblue', style='filled')
        graph.edge(**edge)
    graph.engine = 'circo'
    graph.format = 'pdf'
    graph.graph_attr['overlap'] = 'false'
    graph.render(OUTPUTDIR + SUBPATH + '.gv', view=True)

    # calculate probability
    """

    p = number of people
    s = distinct strengths
    t = distinct possible strengths
    d = depth (number of top strengths per person)


    pvalue_for_s_strengths = ways_with_s_strengths / ways_with_t_strengths

    ---

    ways_with_t_strengths = ncr(t, d) ** p

    ---

    ways_with_s_strengths

    Underestimate
    # undercounts distinct ways to pick set S out of T

        ways_with_s_strengths >= ncr(s, d) ** p

    Overestimate
    # overcounts situations where p people don't use all s strengths

        ways_with_s_strengths <= ncr(s, d) ** p * ncr(t, s)

    It would be good to incorporate actual distributions:
    https://drive.google.com/file/d/0B9GCEaVaZ_FLZDM0bk9Dckc2Sms/view

    """

    p = melted_df.index.nunique()
    s = melted_df.variable.nunique()

    import ncr

    def underestimate(t=34, d=5, p=p, s=s):
        return ncr.Fraction(ncr.ncr(s,d),ncr.ncr(t, d)) ** p

    def overestimate(t=34, d=5, p=p, s=s):
        return underestimate(t, d, p, s) * ncr.ncr(t,s)

    # would prefer to add these to the graph instead of printing
    under = underestimate()
    print("\nUnderestimate:")
    print(under)
    print(float(under))

    over = overestimate()
    print("\nOverestimate:")
    print(over)
    print(float(over))

if __name__ == "__main__":
    import sys
    main(*sys.argv[1:])