#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# QTPyLib: Quantitative Trading Python Library
# https://github.com/ranaroussi/qtpylib
#
# Copyright 2016-2018 Ran Aroussi
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#

import warnings
import sys
from datetime import datetime, timedelta

import numpy as np
import pandas as pd
from pandas.core.base import PandasObject

# =============================================
# check min, python version
if sys.version_info < (3, 4):
    raise SystemError("QTPyLib requires Python version >= 3.4")

# =============================================
warnings.simplefilter(action="ignore", category=RuntimeWarning)

# =============================================


def numpy_rolling_window(data, window):
    shape = data.shape[:-1] + (data.shape[-1] - window + 1, window)
    strides = data.strides + (data.strides[-1],)
    return np.lib.stride_tricks.as_strided(data, shape=shape, strides=strides)


def numpy_rolling_series(func):
    def func_wrapper(data, window, as_source=False):
        series = data.values if isinstance(data, pd.Series) else data

        new_series = np.empty(len(series)) * np.nan
        calculated = func(series, window)
        new_series[-len(calculated):] = calculated

        if as_source and isinstance(data, pd.Series):
            return pd.Series(index=data.index, data=new_series)

        return new_series

    return func_wrapper


@numpy_rolling_series
def numpy_rolling_mean(data, window, as_source=False):
    return np.mean(numpy_rolling_window(data, window), axis=-1)


@numpy_rolling_series
def numpy_rolling_std(data, window, as_source=False):
    return np.std(numpy_rolling_window(data, window), axis=-1, ddof=1)


# ---------------------------------------------


def session(df, start='17:00', end='16:00'):
    """ remove previous globex day from df """
    if df.empty:
        return df

    # get start/end/now as decimals
    int_start = list(map(int, start.split(':')))
    int_start = (int_start[0] + int_start[1] - 1 / 100) - 0.0001
    int_end = list(map(int, end.split(':')))
    int_end = int_end[0] + int_end[1] / 100
    int_now = (df[-1:].index.hour[0] + (df[:1].index.minute[0]) / 100)

    # same-dat session?
    is_same_day = int_end > int_start

    # set pointers
    curr = prev = df[-1:].index[0].strftime('%Y-%m-%d')

    # globex/forex session
    if not is_same_day:
        prev = (datetime.strptime(curr, '%Y-%m-%d') -
                timedelta(1)).strftime('%Y-%m-%d')

    # slice
    if int_now >= int_start:
        df = df[df.index >= curr + ' ' + start]
    else:
        df = df[df.index >= prev + ' ' + start]

    return df.copy()

# ---------------------------------------------


def heikinashi(bars):
    bars = bars.copy()
    bars['ha_close'] = (bars['open'] + bars['high'] +
                        bars['low'] + bars['close']) / 4

    # ha open
    bars.at[0, 'ha_open'] = (bars.at[0, 'open'] + bars.at[0, 'close']) / 2
    for i in range(1, len(bars)):
        bars.at[i, 'ha_open'] = (bars.at[i - 1, 'ha_open'] + bars.at[i - 1, 'ha_close']) / 2

    bars['ha_high'] = bars.loc[:, ['high', 'ha_open', 'ha_close']].max(axis=1)
    bars['ha_low'] = bars.loc[:, ['low', 'ha_open', 'ha_close']].min(axis=1)

    return pd.DataFrame(index=bars.index,
                        data={'open': bars['ha_open'],
                              'high': bars['ha_high'],
                              'low': bars['ha_low'],
                              'close': bars['ha_close']})

# ---------------------------------------------


def tdi(series, rsi_lookback=13, rsi_smooth_len=2,
        rsi_signal_len=7, bb_lookback=34, bb_std=1.6185):

    rsi_data = rsi(series, rsi_lookback)
    rsi_smooth = sma(rsi_data, rsi_smooth_len)
    rsi_signal = sma(rsi_data, rsi_signal_len)

    bb_series = bollinger_bands(rsi_data, bb_lookback, bb_std)

    return pd.DataFrame(index=series.index, data={
        "rsi": rsi_data,
        "rsi_signal": rsi_signal,
        "rsi_smooth": rsi_smooth,
        "rsi_bb_upper": bb_series['upper'],
        "rsi_bb_lower": bb_series['lower'],
        "rsi_bb_mid": bb_series['mid']
    })

# ---------------------------------------------


def awesome_oscillator(df, weighted=False, fast=5, slow=34):
    midprice = (df['high'] + df['low']) / 2

    if weighted:
        ao = (midprice.ewm(fast).mean() - midprice.ewm(slow).mean()).values
    else:
        ao = numpy_rolling_mean(midprice, fast) - \
            numpy_rolling_mean(midprice, slow)

    return pd.Series(index=df.index, data=ao)


# ---------------------------------------------

def nans(length=1):
    mtx = np.empty(length)
    mtx[:] = np.nan
    return mtx


# ---------------------------------------------

def typical_price(bars):
    res = (bars['high'] + bars['low'] + bars['close']) / 3.
    return pd.Series(index=bars.index, data=res)


# ---------------------------------------------

def mid_price(bars):
    res = (bars['high'] + bars['low']) / 2.
    return pd.Series(index=bars.index, data=res)


# ---------------------------------------------

def ibs(bars):
    """ Internal bar strength """
    res = np.round((bars['close'] - bars['low']) /
                   (bars['high'] - bars['low']), 2)
    return pd.Series(index=bars.index, data=res)


# ---------------------------------------------

def true_range(bars):
    return pd.DataFrame({
        "hl": bars['high'] - bars['low'],
        "hc": abs(bars['high'] - bars['close'].shift(1)),
        "lc": abs(bars['low'] - bars['close'].shift(1))
    }).max(axis=1)


# ---------------------------------------------

def atr(bars, window=14, exp=False):
    tr = true_range(bars)

    if exp:
        res = rolling_weighted_mean(tr, window)
    else:
        res = rolling_mean(tr, window)

    return pd.Series(res)


# ---------------------------------------------

def crossed(series1, series2, direction=None):
    if isinstance(series1, np.ndarray):
        series1 = pd.Series(series1)

    if isinstance(series2, (float, int, np.ndarray)):
        series2 = pd.Series(index=series1.index, data=series2)

    if direction is None or direction == "above":
        above = pd.Series((series1 > series2) & (
            series1.shift(1) <= series2.shift(1)))

    if direction is None or direction == "below":
        below = pd.Series((series1 < series2) & (
            series1.shift(1) >= series2.shift(1)))

    if direction is None:
        return above or below

    return above if direction == "above" else below


def crossed_above(series1, series2):
    return crossed(series1, series2, "above")


def crossed_below(series1, series2):
    return crossed(series1, series2, "below")

# ---------------------------------------------


def rolling_std(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    if min_periods == window and len(series) > window:
        return numpy_rolling_std(series, window, True)
    else:
        try:
            return series.rolling(window=window, min_periods=min_periods).std()
        except Exception as e:  # noqa: F841
            return pd.Series(series).rolling(window=window, min_periods=min_periods).std()

# ---------------------------------------------


def rolling_mean(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    if min_periods == window and len(series) > window:
        return numpy_rolling_mean(series, window, True)
    else:
        try:
            return series.rolling(window=window, min_periods=min_periods).mean()
        except Exception as e:  # noqa: F841
            return pd.Series(series).rolling(window=window, min_periods=min_periods).mean()

# ---------------------------------------------


def rolling_min(series, window=14, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    try:
        return series.rolling(window=window, min_periods=min_periods).min()
    except Exception as e:  # noqa: F841
        return pd.Series(series).rolling(window=window, min_periods=min_periods).min()


# ---------------------------------------------

def rolling_max(series, window=14, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    try:
        return series.rolling(window=window, min_periods=min_periods).max()
    except Exception as e:  # noqa: F841
        return pd.Series(series).rolling(window=window, min_periods=min_periods).max()


# ---------------------------------------------

def rolling_weighted_mean(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    try:
        return series.ewm(span=window, min_periods=min_periods).mean()
    except Exception as e:  # noqa: F841
        return pd.ewma(series, span=window, min_periods=min_periods)


# ---------------------------------------------

def hull_moving_average(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    ma = (2 * rolling_weighted_mean(series, window / 2, min_periods)) - \
        rolling_weighted_mean(series, window, min_periods)
    return rolling_weighted_mean(ma, np.sqrt(window), min_periods)


# ---------------------------------------------

def sma(series, window=200, min_periods=None):
    return rolling_mean(series, window=window, min_periods=min_periods)


# ---------------------------------------------

def wma(series, window=200, min_periods=None):
    return rolling_weighted_mean(series, window=window, min_periods=min_periods)


# ---------------------------------------------

def hma(series, window=200, min_periods=None):
    return hull_moving_average(series, window=window, min_periods=min_periods)


# ---------------------------------------------

def vwap(bars):
    """
    calculate vwap of entire time series
    (input can be pandas series or numpy array)
    bars are usually mid [ (h+l)/2 ] or typical [ (h+l+c)/3 ]
    """
    typical = ((bars['high'] + bars['low'] + bars['close']) / 3).values
    volume = bars['volume'].values

    return pd.Series(index=bars.index,
                     data=np.cumsum(volume * typical) / np.cumsum(volume))


# ---------------------------------------------

def rolling_vwap(bars, window=200, min_periods=None):
    """
    calculate vwap using moving window
    (input can be pandas series or numpy array)
    bars are usually mid [ (h+l)/2 ] or typical [ (h+l+c)/3 ]
    """
    min_periods = window if min_periods is None else min_periods

    typical = ((bars['high'] + bars['low'] + bars['close']) / 3)
    volume = bars['volume']

    left = (volume * typical).rolling(window=window,
                                      min_periods=min_periods).sum()
    right = volume.rolling(window=window, min_periods=min_periods).sum()

    return pd.Series(index=bars.index, data=(left / right)
                     ).replace([np.inf, -np.inf], float('NaN')).ffill()


# ---------------------------------------------

def rsi(series, window=14):
    """
    compute the n period relative strength indicator
    """

    # 100-(100/relative_strength)
    deltas = np.diff(series)
    seed = deltas[:window + 1]

    # default values
    ups = seed[seed > 0].sum() / window
    downs = -seed[seed < 0].sum() / window
    rsival = np.zeros_like(series)
    rsival[:window] = 100. - 100. / (1. + ups / downs)

    # period values
    for i in range(window, len(series)):
        delta = deltas[i - 1]
        if delta > 0:
            upval = delta
            downval = 0
        else:
            upval = 0
            downval = -delta

        ups = (ups * (window - 1) + upval) / window
        downs = (downs * (window - 1.) + downval) / window
        rsival[i] = 100. - 100. / (1. + ups / downs)

    # return rsival
    return pd.Series(index=series.index, data=rsival)


# ---------------------------------------------

def macd(series, fast=3, slow=10, smooth=16):
    """
    compute the MACD (Moving Average Convergence/Divergence)
    using a fast and slow exponential moving avg'
    return value is emaslow, emafast, macd which are len(x) arrays
    """
    macd_line = rolling_weighted_mean(series, window=fast) - \
        rolling_weighted_mean(series, window=slow)
    signal = rolling_weighted_mean(macd_line, window=smooth)
    histogram = macd_line - signal
    # return macd_line, signal, histogram
    return pd.DataFrame(index=series.index, data={
        'macd': macd_line.values,
        'signal': signal.values,
        'histogram': histogram.values
    })


# ---------------------------------------------

def bollinger_bands(series, window=20, stds=2):
    ma = rolling_mean(series, window=window, min_periods=1)
    std = rolling_std(series, window=window, min_periods=1)
    upper = ma + std * stds
    lower = ma - std * stds

    return pd.DataFrame(index=series.index, data={
        'upper': upper,
        'mid': ma,
        'lower': lower
    })


# ---------------------------------------------

def weighted_bollinger_bands(series, window=20, stds=2):
    ema = rolling_weighted_mean(series, window=window)
    std = rolling_std(series, window=window)
    upper = ema + std * stds
    lower = ema - std * stds

    return pd.DataFrame(index=series.index, data={
        'upper': upper.values,
        'mid': ema.values,
        'lower': lower.values
    })


# ---------------------------------------------

def returns(series):
    try:
        res = (series / series.shift(1) -
               1).replace([np.inf, -np.inf], float('NaN'))
    except Exception as e:  # noqa: F841
        res = nans(len(series))

    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def log_returns(series):
    try:
        res = np.log(series / series.shift(1)
                     ).replace([np.inf, -np.inf], float('NaN'))
    except Exception as e:  # noqa: F841
        res = nans(len(series))

    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def implied_volatility(series, window=252):
    try:
        logret = np.log(series / series.shift(1)
                        ).replace([np.inf, -np.inf], float('NaN'))
        res = numpy_rolling_std(logret, window) * np.sqrt(window)
    except Exception as e:  # noqa: F841
        res = nans(len(series))

    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def keltner_channel(bars, window=14, atrs=2):
    typical_mean = rolling_mean(typical_price(bars), window)
    atrval = atr(bars, window) * atrs

    upper = typical_mean + atrval
    lower = typical_mean - atrval

    return pd.DataFrame(index=bars.index, data={
        'upper': upper.values,
        'mid': typical_mean.values,
        'lower': lower.values
    })


# ---------------------------------------------

def roc(series, window=14):
    """
    compute rate of change
    """
    res = (series - series.shift(window)) / series.shift(window)
    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def cci(series, window=14):
    """
    compute commodity channel index
    """
    price = typical_price(series)
    typical_mean = rolling_mean(price, window)
    res = (price - typical_mean) / (.015 * np.std(typical_mean))
    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def stoch(df, window=14, d=3, k=3, fast=False):
    """
    compute the n period relative strength indicator
    http://excelta.blogspot.co.il/2013/09/stochastic-oscillator-technical.html
    """

    my_df = pd.DataFrame(index=df.index)

    my_df['rolling_max'] = df['high'].rolling(window).max()
    my_df['rolling_min'] = df['low'].rolling(window).min()

    my_df['fast_k'] = (
        100 * (df['close'] - my_df['rolling_min']) /
        (my_df['rolling_max'] - my_df['rolling_min'])
    )
    my_df['fast_d'] = my_df['fast_k'].rolling(d).mean()

    if fast:
        return my_df.loc[:, ['fast_k', 'fast_d']]

    my_df['slow_k'] = my_df['fast_k'].rolling(k).mean()
    my_df['slow_d'] = my_df['slow_k'].rolling(d).mean()

    return my_df.loc[:, ['slow_k', 'slow_d']]

# ---------------------------------------------


def zlma(series, window=20, min_periods=None, kind="ema"):
    """
    John Ehlers' Zero lag (exponential) moving average
    https://en.wikipedia.org/wiki/Zero_lag_exponential_moving_average
    """
    min_periods = window if min_periods is None else min_periods

    lag = (window - 1) // 2
    series = 2 * series - series.shift(lag)
    if kind in ['ewm', 'ema']:
        return wma(series, lag, min_periods)
    elif kind == "hma":
        return hma(series, lag, min_periods)
    return sma(series, lag, min_periods)


def zlema(series, window, min_periods=None):
    return zlma(series, window, min_periods, kind="ema")


def zlsma(series, window, min_periods=None):
    return zlma(series, window, min_periods, kind="sma")


def zlhma(series, window, min_periods=None):
    return zlma(series, window, min_periods, kind="hma")

# ---------------------------------------------


def zscore(bars, window=20, stds=1, col='close'):
    """ get zscore of price """
    std = numpy_rolling_std(bars[col], window)
    mean = numpy_rolling_mean(bars[col], window)
    return (bars[col] - mean) / (std * stds)

# ---------------------------------------------


def pvt(bars):
    """ Price Volume Trend """
    trend = ((bars['close'] - bars['close'].shift(1)) /
             bars['close'].shift(1)) * bars['volume']
    return trend.cumsum()


def chopiness(bars, window=14):
    atrsum = true_range(bars).rolling(window).sum()
    highs = bars['high'].rolling(window).max()
    lows = bars['low'].rolling(window).min()
    return 100 * np.log10(atrsum / (highs - lows)) / np.log10(window)


# =============================================


PandasObject.session = session
PandasObject.atr = atr
PandasObject.bollinger_bands = bollinger_bands
PandasObject.cci = cci
PandasObject.crossed = crossed
PandasObject.crossed_above = crossed_above
PandasObject.crossed_below = crossed_below
PandasObject.heikinashi = heikinashi
PandasObject.hull_moving_average = hull_moving_average
PandasObject.ibs = ibs
PandasObject.implied_volatility = implied_volatility
PandasObject.keltner_channel = keltner_channel
PandasObject.log_returns = log_returns
PandasObject.macd = macd
PandasObject.returns = returns
PandasObject.roc = roc
PandasObject.rolling_max = rolling_max
PandasObject.rolling_min = rolling_min
PandasObject.rolling_mean = rolling_mean
PandasObject.rolling_std = rolling_std
PandasObject.rsi = rsi
PandasObject.stoch = stoch
PandasObject.zscore = zscore
PandasObject.pvt = pvt
PandasObject.chopiness = chopiness
PandasObject.tdi = tdi
PandasObject.true_range = true_range
PandasObject.mid_price = mid_price
PandasObject.typical_price = typical_price
PandasObject.vwap = vwap
PandasObject.rolling_vwap = rolling_vwap
PandasObject.weighted_bollinger_bands = weighted_bollinger_bands
PandasObject.rolling_weighted_mean = rolling_weighted_mean

PandasObject.sma = sma
PandasObject.wma = wma
PandasObject.ema = wma
PandasObject.hma = hma

PandasObject.zlsma = zlsma
PandasObject.zlwma = zlema
PandasObject.zlema = zlema
PandasObject.zlhma = zlhma
PandasObject.zlma = zlma

freqtrade/vendor/qtpylib/indicators.py
#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# QTPyLib: Quantitative Trading Python Library
# https://github.com/ranaroussi/qtpylib
#
# Copyright 2016-2018 Ran Aroussi
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#

import warnings
import sys
from datetime import datetime, timedelta

import numpy as np
import pandas as pd
from pandas.core.base import PandasObject

# =============================================
# check min, python version
if sys.version_info < (3, 4):
    raise SystemError("QTPyLib requires Python version >= 3.4")

# =============================================
warnings.simplefilter(action="ignore", category=RuntimeWarning)

# =============================================


def numpy_rolling_window(data, window):
    shape = data.shape[:-1] + (data.shape[-1] - window + 1, window)
    strides = data.strides + (data.strides[-1],)
    return np.lib.stride_tricks.as_strided(data, shape=shape, strides=strides)


def numpy_rolling_series(func):
    def func_wrapper(data, window, as_source=False):
        series = data.values if isinstance(data, pd.Series) else data

        new_series = np.empty(len(series)) * np.nan
        calculated = func(series, window)
        new_series[-len(calculated):] = calculated

        if as_source and isinstance(data, pd.Series):
            return pd.Series(index=data.index, data=new_series)

        return new_series

    return func_wrapper


@numpy_rolling_series
def numpy_rolling_mean(data, window, as_source=False):
    return np.mean(numpy_rolling_window(data, window), axis=-1)


@numpy_rolling_series
def numpy_rolling_std(data, window, as_source=False):
    return np.std(numpy_rolling_window(data, window), axis=-1, ddof=1)


# ---------------------------------------------


def session(df, start='17:00', end='16:00'):
    """ remove previous globex day from df """
    if df.empty:
        return df

    # get start/end/now as decimals
    int_start = list(map(int, start.split(':')))
    int_start = (int_start[0] + int_start[1] - 1 / 100) - 0.0001
    int_end = list(map(int, end.split(':')))
    int_end = int_end[0] + int_end[1] / 100
    int_now = (df[-1:].index.hour[0] + (df[:1].index.minute[0]) / 100)

    # same-dat session?
    is_same_day = int_end > int_start

    # set pointers
    curr = prev = df[-1:].index[0].strftime('%Y-%m-%d')

    # globex/forex session
    if not is_same_day:
        prev = (datetime.strptime(curr, '%Y-%m-%d') -
                timedelta(1)).strftime('%Y-%m-%d')

    # slice
    if int_now >= int_start:
        df = df[df.index >= curr + ' ' + start]
    else:
        df = df[df.index >= prev + ' ' + start]

    return df.copy()

# ---------------------------------------------


def heikinashi(bars):
    bars = bars.copy()
    bars['ha_close'] = (bars['open'] + bars['high'] +
                        bars['low'] + bars['close']) / 4

    # ha open
    bars.at[0, 'ha_open'] = (bars.at[0, 'open'] + bars.at[0, 'close']) / 2
    for i in range(1, len(bars)):
        bars.at[i, 'ha_open'] = (bars.at[i - 1, 'ha_open'] + bars.at[i - 1, 'ha_close']) / 2

    bars['ha_high'] = bars.loc[:, ['high', 'ha_open', 'ha_close']].max(axis=1)
    bars['ha_low'] = bars.loc[:, ['low', 'ha_open', 'ha_close']].min(axis=1)

    return pd.DataFrame(index=bars.index,
                        data={'open': bars['ha_open'],
                              'high': bars['ha_high'],
                              'low': bars['ha_low'],
                              'close': bars['ha_close']})

# ---------------------------------------------


def tdi(series, rsi_lookback=13, rsi_smooth_len=2,
        rsi_signal_len=7, bb_lookback=34, bb_std=1.6185):

    rsi_data = rsi(series, rsi_lookback)
    rsi_smooth = sma(rsi_data, rsi_smooth_len)
    rsi_signal = sma(rsi_data, rsi_signal_len)

    bb_series = bollinger_bands(rsi_data, bb_lookback, bb_std)

    return pd.DataFrame(index=series.index, data={
        "rsi": rsi_data,
        "rsi_signal": rsi_signal,
        "rsi_smooth": rsi_smooth,
        "rsi_bb_upper": bb_series['upper'],
        "rsi_bb_lower": bb_series['lower'],
        "rsi_bb_mid": bb_series['mid']
    })

# ---------------------------------------------


def awesome_oscillator(df, weighted=False, fast=5, slow=34):
    midprice = (df['high'] + df['low']) / 2

    if weighted:
        ao = (midprice.ewm(fast).mean() - midprice.ewm(slow).mean()).values
    else:
        ao = numpy_rolling_mean(midprice, fast) - \
            numpy_rolling_mean(midprice, slow)

    return pd.Series(index=df.index, data=ao)


# ---------------------------------------------

def nans(length=1):
    mtx = np.empty(length)
    mtx[:] = np.nan
    return mtx


# ---------------------------------------------

def typical_price(bars):
    res = (bars['high'] + bars['low'] + bars['close']) / 3.
    return pd.Series(index=bars.index, data=res)


# ---------------------------------------------

def mid_price(bars):
    res = (bars['high'] + bars['low']) / 2.
    return pd.Series(index=bars.index, data=res)


# ---------------------------------------------

def ibs(bars):
    """ Internal bar strength """
    res = np.round((bars['close'] - bars['low']) /
                   (bars['high'] - bars['low']), 2)
    return pd.Series(index=bars.index, data=res)


# ---------------------------------------------

def true_range(bars):
    return pd.DataFrame({
        "hl": bars['high'] - bars['low'],
        "hc": abs(bars['high'] - bars['close'].shift(1)),
        "lc": abs(bars['low'] - bars['close'].shift(1))
    }).max(axis=1)


# ---------------------------------------------

def atr(bars, window=14, exp=False):
    tr = true_range(bars)

    if exp:
        res = rolling_weighted_mean(tr, window)
    else:
        res = rolling_mean(tr, window)

    return pd.Series(res)


# ---------------------------------------------

def crossed(series1, series2, direction=None):
    if isinstance(series1, np.ndarray):
        series1 = pd.Series(series1)

    if isinstance(series2, (float, int, np.ndarray, np.integer, np.floating)):
        series2 = pd.Series(index=series1.index, data=series2)

    if direction is None or direction == "above":
        above = pd.Series((series1 > series2) & (
            series1.shift(1) <= series2.shift(1)))

    if direction is None or direction == "below":
        below = pd.Series((series1 < series2) & (
            series1.shift(1) >= series2.shift(1)))

    if direction is None:
        return above or below

    return above if direction == "above" else below


def crossed_above(series1, series2):
    return crossed(series1, series2, "above")


def crossed_below(series1, series2):
    return crossed(series1, series2, "below")

# ---------------------------------------------


def rolling_std(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    if min_periods == window and len(series) > window:
        return numpy_rolling_std(series, window, True)
    else:
        try:
            return series.rolling(window=window, min_periods=min_periods).std()
        except Exception as e:  # noqa: F841
            return pd.Series(series).rolling(window=window, min_periods=min_periods).std()

# ---------------------------------------------


def rolling_mean(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    if min_periods == window and len(series) > window:
        return numpy_rolling_mean(series, window, True)
    else:
        try:
            return series.rolling(window=window, min_periods=min_periods).mean()
        except Exception as e:  # noqa: F841
            return pd.Series(series).rolling(window=window, min_periods=min_periods).mean()

# ---------------------------------------------


def rolling_min(series, window=14, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    try:
        return series.rolling(window=window, min_periods=min_periods).min()
    except Exception as e:  # noqa: F841
        return pd.Series(series).rolling(window=window, min_periods=min_periods).min()


# ---------------------------------------------

def rolling_max(series, window=14, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    try:
        return series.rolling(window=window, min_periods=min_periods).max()
    except Exception as e:  # noqa: F841
        return pd.Series(series).rolling(window=window, min_periods=min_periods).max()


# ---------------------------------------------

def rolling_weighted_mean(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    try:
        return series.ewm(span=window, min_periods=min_periods).mean()
    except Exception as e:  # noqa: F841
        return pd.ewma(series, span=window, min_periods=min_periods)


# ---------------------------------------------

def hull_moving_average(series, window=200, min_periods=None):
    min_periods = window if min_periods is None else min_periods
    ma = (2 * rolling_weighted_mean(series, window / 2, min_periods)) - \
        rolling_weighted_mean(series, window, min_periods)
    return rolling_weighted_mean(ma, np.sqrt(window), min_periods)


# ---------------------------------------------

def sma(series, window=200, min_periods=None):
    return rolling_mean(series, window=window, min_periods=min_periods)


# ---------------------------------------------

def wma(series, window=200, min_periods=None):
    return rolling_weighted_mean(series, window=window, min_periods=min_periods)


# ---------------------------------------------

def hma(series, window=200, min_periods=None):
    return hull_moving_average(series, window=window, min_periods=min_periods)


# ---------------------------------------------

def vwap(bars):
    """
    calculate vwap of entire time series
    (input can be pandas series or numpy array)
    bars are usually mid [ (h+l)/2 ] or typical [ (h+l+c)/3 ]
    """
    typical = ((bars['high'] + bars['low'] + bars['close']) / 3).values
    volume = bars['volume'].values

    return pd.Series(index=bars.index,
                     data=np.cumsum(volume * typical) / np.cumsum(volume))


# ---------------------------------------------

def rolling_vwap(bars, window=200, min_periods=None):
    """
    calculate vwap using moving window
    (input can be pandas series or numpy array)
    bars are usually mid [ (h+l)/2 ] or typical [ (h+l+c)/3 ]
    """
    min_periods = window if min_periods is None else min_periods

    typical = ((bars['high'] + bars['low'] + bars['close']) / 3)
    volume = bars['volume']

    left = (volume * typical).rolling(window=window,
                                      min_periods=min_periods).sum()
    right = volume.rolling(window=window, min_periods=min_periods).sum()

    return pd.Series(index=bars.index, data=(left / right)
                     ).replace([np.inf, -np.inf], float('NaN')).ffill()


# ---------------------------------------------

def rsi(series, window=14):
    """
    compute the n period relative strength indicator
    """

    # 100-(100/relative_strength)
    deltas = np.diff(series)
    seed = deltas[:window + 1]

    # default values
    ups = seed[seed > 0].sum() / window
    downs = -seed[seed < 0].sum() / window
    rsival = np.zeros_like(series)
    rsival[:window] = 100. - 100. / (1. + ups / downs)

    # period values
    for i in range(window, len(series)):
        delta = deltas[i - 1]
        if delta > 0:
            upval = delta
            downval = 0
        else:
            upval = 0
            downval = -delta

        ups = (ups * (window - 1) + upval) / window
        downs = (downs * (window - 1.) + downval) / window
        rsival[i] = 100. - 100. / (1. + ups / downs)

    # return rsival
    return pd.Series(index=series.index, data=rsival)


# ---------------------------------------------

def macd(series, fast=3, slow=10, smooth=16):
    """
    compute the MACD (Moving Average Convergence/Divergence)
    using a fast and slow exponential moving avg'
    return value is emaslow, emafast, macd which are len(x) arrays
    """
    macd_line = rolling_weighted_mean(series, window=fast) - \
        rolling_weighted_mean(series, window=slow)
    signal = rolling_weighted_mean(macd_line, window=smooth)
    histogram = macd_line - signal
    # return macd_line, signal, histogram
    return pd.DataFrame(index=series.index, data={
        'macd': macd_line.values,
        'signal': signal.values,
        'histogram': histogram.values
    })


# ---------------------------------------------

def bollinger_bands(series, window=20, stds=2):
    ma = rolling_mean(series, window=window, min_periods=1)
    std = rolling_std(series, window=window, min_periods=1)
    upper = ma + std * stds
    lower = ma - std * stds

    return pd.DataFrame(index=series.index, data={
        'upper': upper,
        'mid': ma,
        'lower': lower
    })


# ---------------------------------------------

def weighted_bollinger_bands(series, window=20, stds=2):
    ema = rolling_weighted_mean(series, window=window)
    std = rolling_std(series, window=window)
    upper = ema + std * stds
    lower = ema - std * stds

    return pd.DataFrame(index=series.index, data={
        'upper': upper.values,
        'mid': ema.values,
        'lower': lower.values
    })


# ---------------------------------------------

def returns(series):
    try:
        res = (series / series.shift(1) -
               1).replace([np.inf, -np.inf], float('NaN'))
    except Exception as e:  # noqa: F841
        res = nans(len(series))

    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def log_returns(series):
    try:
        res = np.log(series / series.shift(1)
                     ).replace([np.inf, -np.inf], float('NaN'))
    except Exception as e:  # noqa: F841
        res = nans(len(series))

    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def implied_volatility(series, window=252):
    try:
        logret = np.log(series / series.shift(1)
                        ).replace([np.inf, -np.inf], float('NaN'))
        res = numpy_rolling_std(logret, window) * np.sqrt(window)
    except Exception as e:  # noqa: F841
        res = nans(len(series))

    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def keltner_channel(bars, window=14, atrs=2):
    typical_mean = rolling_mean(typical_price(bars), window)
    atrval = atr(bars, window) * atrs

    upper = typical_mean + atrval
    lower = typical_mean - atrval

    return pd.DataFrame(index=bars.index, data={
        'upper': upper.values,
        'mid': typical_mean.values,
        'lower': lower.values
    })


# ---------------------------------------------

def roc(series, window=14):
    """
    compute rate of change
    """
    res = (series - series.shift(window)) / series.shift(window)
    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def cci(series, window=14):
    """
    compute commodity channel index
    """
    price = typical_price(series)
    typical_mean = rolling_mean(price, window)
    res = (price - typical_mean) / (.015 * np.std(typical_mean))
    return pd.Series(index=series.index, data=res)


# ---------------------------------------------

def stoch(df, window=14, d=3, k=3, fast=False):
    """
    compute the n period relative strength indicator
    http://excelta.blogspot.co.il/2013/09/stochastic-oscillator-technical.html
    """

    my_df = pd.DataFrame(index=df.index)

    my_df['rolling_max'] = df['high'].rolling(window).max()
    my_df['rolling_min'] = df['low'].rolling(window).min()

    my_df['fast_k'] = (
        100 * (df['close'] - my_df['rolling_min']) /
        (my_df['rolling_max'] - my_df['rolling_min'])
    )
    my_df['fast_d'] = my_df['fast_k'].rolling(d).mean()

    if fast:
        return my_df.loc[:, ['fast_k', 'fast_d']]

    my_df['slow_k'] = my_df['fast_k'].rolling(k).mean()
    my_df['slow_d'] = my_df['slow_k'].rolling(d).mean()

    return my_df.loc[:, ['slow_k', 'slow_d']]

# ---------------------------------------------


def zlma(series, window=20, min_periods=None, kind="ema"):
    """
    John Ehlers' Zero lag (exponential) moving average
    https://en.wikipedia.org/wiki/Zero_lag_exponential_moving_average
    """
    min_periods = window if min_periods is None else min_periods

    lag = (window - 1) // 2
    series = 2 * series - series.shift(lag)
    if kind in ['ewm', 'ema']:
        return wma(series, lag, min_periods)
    elif kind == "hma":
        return hma(series, lag, min_periods)
    return sma(series, lag, min_periods)


def zlema(series, window, min_periods=None):
    return zlma(series, window, min_periods, kind="ema")


def zlsma(series, window, min_periods=None):
    return zlma(series, window, min_periods, kind="sma")


def zlhma(series, window, min_periods=None):
    return zlma(series, window, min_periods, kind="hma")

# ---------------------------------------------


def zscore(bars, window=20, stds=1, col='close'):
    """ get zscore of price """
    std = numpy_rolling_std(bars[col], window)
    mean = numpy_rolling_mean(bars[col], window)
    return (bars[col] - mean) / (std * stds)

# ---------------------------------------------


def pvt(bars):
    """ Price Volume Trend """
    trend = ((bars['close'] - bars['close'].shift(1)) /
             bars['close'].shift(1)) * bars['volume']
    return trend.cumsum()


def chopiness(bars, window=14):
    atrsum = true_range(bars).rolling(window).sum()
    highs = bars['high'].rolling(window).max()
    lows = bars['low'].rolling(window).min()
    return 100 * np.log10(atrsum / (highs - lows)) / np.log10(window)


# =============================================


PandasObject.session = session
PandasObject.atr = atr
PandasObject.bollinger_bands = bollinger_bands
PandasObject.cci = cci
PandasObject.crossed = crossed
PandasObject.crossed_above = crossed_above
PandasObject.crossed_below = crossed_below
PandasObject.heikinashi = heikinashi
PandasObject.hull_moving_average = hull_moving_average
PandasObject.ibs = ibs
PandasObject.implied_volatility = implied_volatility
PandasObject.keltner_channel = keltner_channel
PandasObject.log_returns = log_returns
PandasObject.macd = macd
PandasObject.returns = returns
PandasObject.roc = roc
PandasObject.rolling_max = rolling_max
PandasObject.rolling_min = rolling_min
PandasObject.rolling_mean = rolling_mean
PandasObject.rolling_std = rolling_std
PandasObject.rsi = rsi
PandasObject.stoch = stoch
PandasObject.zscore = zscore
PandasObject.pvt = pvt
PandasObject.chopiness = chopiness
PandasObject.tdi = tdi
PandasObject.true_range = true_range
PandasObject.mid_price = mid_price
PandasObject.typical_price = typical_price
PandasObject.vwap = vwap
PandasObject.rolling_vwap = rolling_vwap
PandasObject.weighted_bollinger_bands = weighted_bollinger_bands
PandasObject.rolling_weighted_mean = rolling_weighted_mean

PandasObject.sma = sma
PandasObject.wma = wma
PandasObject.ema = wma
PandasObject.hma = hma

PandasObject.zlsma = zlsma
PandasObject.zlwma = zlema
PandasObject.zlema = zlema
PandasObject.zlhma = zlhma
PandasObject.zlma = zlma

freqtrade/vendor/qtpylib/indicators.py
diff --git a/freqtrade/vendor/qtpylib/indicators.py b/freqtrade/vendor/qtpylib/indicators.py
index bef1403969c..e5a4048622c 100644
--- a/freqtrade/vendor/qtpylib/indicators.py
+++ b/freqtrade/vendor/qtpylib/indicators.py
@@ -222,7 +222,7 @@ def crossed(series1, series2, direction=None):
     if isinstance(series1, np.ndarray):
         series1 = pd.Series(series1)
 
-    if isinstance(series2, (float, int, np.ndarray)):
+    if isinstance(series2, (float, int, np.ndarray, np.integer, np.floating)):
         series2 = pd.Series(index=series1.index, data=series2)
 
     if direction is None or direction == "above":
diff --git a/tests/test_indicators.py b/tests/test_indicators.py
new file mode 100644
index 00000000000..2f9bdc0f95d
--- /dev/null
+++ b/tests/test_indicators.py
@@ -0,0 +1,18 @@
+import freqtrade.vendor.qtpylib.indicators as qtpylib
+import numpy as np
+import pandas as pd
+
+
+def test_crossed_numpy_types():
+    """
+    This test is only present since this method currently diverges from the qtpylib implementation.
+    And we must ensure to not break this again once we update from the original source.
+    """
+    series = pd.Series([56, 97, 19, 76, 65, 25, 87, 91, 79, 79])
+    expected_result = pd.Series([False, True, False, True, False, False, True, False, False, False])
+
+    assert qtpylib.crossed_above(series, 60).equals(expected_result)
+    assert qtpylib.crossed_above(series, 60.0).equals(expected_result)
+    assert qtpylib.crossed_above(series, np.int32(60)).equals(expected_result)
+    assert qtpylib.crossed_above(series, np.int64(60)).equals(expected_result)
+    assert qtpylib.crossed_above(series, np.float64(60.0)).equals(expected_result)
diff --git a/tests/test_talib.py b/tests/test_talib.py
index 2c7f73eb172..4effc129b12 100644
--- a/tests/test_talib.py
+++ b/tests/test_talib.py
@@ -1,5 +1,3 @@
-
-
 import talib.abstract as ta
 import pandas as pd
 

cross_above problem with shift
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## Describe your environment

  * Operating system: Ubuntu 
  * Python Version: Python 3.8.2 (`python -V`)
  * CCXT version: ccxt==1.33.52 (`pip freeze | grep ccxt`)
  * Freqtrade Version: freqtrade develop-21f4aba4 (`freqtrade -V` or `docker-compose run --rm freqtrade -V` for Freqtrade running in docker)
  
## Your question

Hello, 
I am having a problem with the cross_above function in qtpylib. I am trying to optimize one strategy but as soon as I run it I receive the following exception:

Traceback (most recent call last):
  File "/home/trademad/freqtrade/.env/lib/python3.8/site-packages/joblib/externals/loky/process_executor.py", line 431, in _process_worker
    r = call_item()
  File "/home/trademad/freqtrade/.env/lib/python3.8/site-packages/joblib/externals/loky/process_executor.py", line 285, in __call__
    return self.fn(*self.args, **self.kwargs)
  File "/home/trademad/freqtrade/.env/lib/python3.8/site-packages/joblib/_parallel_backends.py", line 595, in __call__
    return self.func(*args, **kwargs)
  File "/home/trademad/freqtrade/.env/lib/python3.8/site-packages/joblib/parallel.py", line 252, in __call__
    return [func(*args, **kwargs)
  File "/home/trademad/freqtrade/.env/lib/python3.8/site-packages/joblib/parallel.py", line 252, in <listcomp>
    return [func(*args, **kwargs)
  File "/home/trademad/freqtrade/.env/lib/python3.8/site-packages/joblib/externals/loky/cloudpickle_wrapper.py", line 38, in __call__
    return self._obj(*args, **kwargs)
  File "/home/trademad/freqtrade/freqtrade/optimize/hyperopt.py", line 532, in generate_optimizer
    backtesting_results = self.backtesting.backtest(
  File "/home/trademad/freqtrade/freqtrade/optimize/backtesting.py", line 312, in backtest
    data: Dict = self._get_ohlcv_as_lists(processed)
  File "/home/trademad/freqtrade/freqtrade/optimize/backtesting.py", line 164, in _get_ohlcv_as_lists
    self.strategy.advise_buy(pair_data, {'pair': pair}), {'pair': pair})[headers].copy()
  File "/home/trademad/freqtrade/user_data/hyperopts/bbrsi_opt_v01.py", line 61, in populate_buy_trend
    conditions.append(qtpylib.crossed_above(dataframe['rsi'], params['rsi-value']))
  File "/home/trademad/freqtrade/freqtrade/vendor/qtpylib/indicators.py", line 243, in crossed_above
    return crossed(series1, series2, "above")
  File "/home/trademad/freqtrade/freqtrade/vendor/qtpylib/indicators.py", line 230, in crossed
    series1.shift(1) <= series2.shift(1)))
AttributeError: 'numpy.int64' object has no attribute 'shift'

Could it be a problem with pandas in the latest version?
thanks

*Ask the question you have not been able to find an answer in our [Documentation](https://www.freqtrade.io/en/latest/)*

