def bolliger_band(df):

    df['mean'] = df['close'].rolling(20).mean()
    df['std'] = df['close'].rolling(20).std()

    df['upperband'] = df['mean'] + (df['std'] * 2)
    df['lowerband'] = df['mean'] - (df['std'] * 2)
    df = df.drop(['mean', 'std'], axis=1)
    return df


def macd(df):
	df['12_ema'] = df['close'].ewm(span=12, adjust=False).mean()
	df['26_ema'] = df['close'].ewm(span=26, adjust=False).mean()
	df['macd_line'] = df['12_ema'] - df['26_ema']	 # MACD Line: (12-day EMA - 26-day EMA)
	df['single_line'] = df['macd_line'].ewm(span=9, adjust=False).mean() # Signal Line: 9-day EMA of MACD Line
	df['macd_hist']	= df['macd_line'] - df['single_line'] # MACD Histogram: MACD Line - Signal Line
	return df

def rsi(df, period):
	df['pnl'] = df['close'].diff()
	df.loc[df['pnl'] >= 0, 'gain'] = df['pnl']
	df['gain'].fillna(value=0, inplace=True)
	df.loc[df['pnl'] < 0, 'loss'] = df['pnl'].abs()
	df['loss'].fillna(value=0, inplace=True)
	df['average_gain'] = df['gain'].ewm(com = period-1, min_periods=period).mean()
	df['average_loss'] = df['loss'].ewm(com = period-1, min_periods=period).mean()
	df['rs'] = df['average_gain'] / df['average_loss']
	df['rsi'] = 100 - (100/(1+df['rs']))
	return df