vectorized fast implementation of PMI contextual discounting in pandas+numpy

pmi_discount

def pmi_discount(df):
    """ Turney and Pantel (2010)
    From Frequency to Meaning: Vector Space Models of Semantics 
    arXiv:1003.1141 [cs.CL] https://arxiv.org/abs/1003.1141
    p. 158 "contextual discounting" extension of PMI 
        rc_min = min(rowsum, colsum)
        l = cell / (cell + 1) * rc_min / (rc_min + 1)
        newpmi = pmi * l
        
    in: pmi pandas df 
    out: modified df
    """
    
    colsum = df.sum(axis=0)
    rowsum = df.sum(axis=1)
    # broadcast rowsum into a matrix of repeated cols, and 
    # colsum into a matrix of repeated rows, 
    # then compare the 2 resulting matrices (no data copying overhead)
    rowcol_min = np.minimum(rowsum[:, None], colsum[None, :])
    l = df / (df + 1) * rowcol_min / (rowcol_min + 1)
    return df*l

# very very slow traversal version, but it's easier to see what's happening
def pmi_discount_slow(df):
    colsum = df.sum(axis=0)
    rowsum = df.sum(axis=1)
    for i in range(0, df.shape[0]):
        for j in range(0, df.shape[1]):
            cell = df.iloc[i,j] 
            rc_min = min(rowsum[i], colsum[j])
            l = cell / (cell + 1) * rc_min / (rc_min + 1)
            df.iloc[i,j] = cell*l
    return df