def removal_effects(df, conversion_rate):
    removal_effects_dict = {}
    channels = [channel for channel in df.columns if channel not in ['Start',
                                                                     'Null',
                                                                     'Activation']]
    for channel in channels:
        removal_df = df.drop(channel, axis=1).drop(channel, axis=0)
        for column in removal_df.columns:
            row_sum = np.sum(list(removal_df.loc[column]))
            null_pct = float(1) - row_sum
            if null_pct != 0:
                removal_df.loc[column]['Null'] = null_pct
            removal_df.loc['Null']['Null'] = 1.0

        R = removal_df[
            ['Null', 'Activation']].drop(['Null', 'Activation'], axis=0)
        
        Q = removal_df.drop(
            ['Null', 'Activation'], axis=1).drop(['Null', 'Activation'], axis=0)
        
        I = np.identity(len(Q.columns))

        N = np.linalg.inv(
            I - Q.to_numpy()
        )
        
        removal_dot_prod = np.dot(N, R.to_numpy())
        removal_cvr = pd.DataFrame(removal_dot_prod,
                                   index=R.index)[[1]].loc['Start'].values[0]
        removal_effect = 1 - removal_cvr / conversion_rate
        removal_effects_dict[channel] = removal_effect

    return removal_effects_dict


removal_effects_dict = removal_effects(trans_matrix, activation_rate)

def removal_effect_pct(removal_effects, total_activations):
    re_sum = np.sum(list(removal_effects.values()))

    return {k: (v / re_sum) * total_activations for k, v in removal_effects.items()}


attributions = removal_effect_pct(removal_effects_dict, total_activations)