def scale_df(df,axis=0):
    return (df - df.mean(axis=axis)) / df.std(axis=axis)

def plot_hmap(df, ix=None, cmap='bwr'):
    if ix is None:
        ix = np.arange(df.shape[0])
    plt.imshow(df.iloc[ix,:], cmap=cmap)
    plt.colorbar(fraction=0.03)
    plt.yticks(np.arange(df.shape[0]), df.index[ix])
    plt.xticks(np.arange(df.shape[1]))
    plt.grid(False)
    plt.show()

def scale_and_plot(df, ix = None):
    df_marginal_scaled = scale_df(df.T).T
    if ix is None:
        ix = AC(4).fit(df_marginal_scaled).labels_.argsort() # a trick to make better heatmaps
    cap = np.min([np.max(df_marginal_scaled.as_matrix()), np.abs(np.min(df_marginal_scaled.as_matrix()))])
    df_marginal_scaled = np.clip(df_marginal_scaled, -1*cap, cap)
    plot_hmap(df_marginal_scaled, ix=ix)

def normalize(df):
    result = df.copy()
    for feature_name in df.columns:
        max_value = df[feature_name].max()
        min_value = df[feature_name].min()
        result[feature_name] = (df[feature_name] - min_value) / (max_value - min_value)
    return result

dayofweek_by_location = df.pivot_table(values='ID', index='Location.Description', columns=df.index.dayofweek, aggfunc=np.size).fillna(0)
dayofweek_by_type = df.pivot_table(values='ID', index='Primary.Type', columns=df.index.dayofweek, aggfunc=np.size).fillna(0)
location_by_type  = df.pivot_table(values='ID', index='Location.Description', columns='Primary.Type', aggfunc=np.size).fillna(0)

from sklearn.cluster import AgglomerativeClustering as AC

plt.figure(figsize=(17,17))
scale_and_plot(dayofweek_by_type)