frequencies.py

from datetime import timedelta
from pandas.compat import long, zip
from pandas import compat
import re
import warnings

import numpy as np

from pandas.core.dtypes.generic import ABCSeries
from pandas.core.dtypes.common import (
    is_period_arraylike,
    is_timedelta64_dtype,
    is_datetime64_dtype)

import pandas.core.algorithms as algos
from pandas.core.algorithms import unique
from pandas.tseries.offsets import DateOffset
from pandas.util._decorators import cache_readonly, deprecate_kwarg
import pandas.tseries.offsets as offsets

from pandas._libs import lib, tslib
from pandas._libs.tslib import Timedelta
from pandas._libs.tslibs.frequencies import get_freq_code, _base_and_stride
from pytz import AmbiguousTimeError


class FreqGroup(object):
    FR_ANN = 1000
    FR_QTR = 2000
    FR_MTH = 3000
    FR_WK = 4000
    FR_BUS = 5000
    FR_DAY = 6000
    FR_HR = 7000
    FR_MIN = 8000
    FR_SEC = 9000
    FR_MS = 10000
    FR_US = 11000
    FR_NS = 12000


RESO_NS = 0
RESO_US = 1
RESO_MS = 2
RESO_SEC = 3
RESO_MIN = 4
RESO_HR = 5
RESO_DAY = 6


class Resolution(object):

    RESO_US = RESO_US
    RESO_MS = RESO_MS
    RESO_SEC = RESO_SEC
    RESO_MIN = RESO_MIN
    RESO_HR = RESO_HR
    RESO_DAY = RESO_DAY

    _reso_str_map = {
        RESO_NS: 'nanosecond',
        RESO_US: 'microsecond',
        RESO_MS: 'millisecond',
        RESO_SEC: 'second',
        RESO_MIN: 'minute',
        RESO_HR: 'hour',
        RESO_DAY: 'day'
    }

    # factor to multiply a value by to convert it to the next finer grained
    # resolution
    _reso_mult_map = {
        RESO_NS: None,
        RESO_US: 1000,
        RESO_MS: 1000,
        RESO_SEC: 1000,
        RESO_MIN: 60,
        RESO_HR: 60,
        RESO_DAY: 24
    }

    _reso_str_bump_map = {
        'D': 'H',
        'H': 'T',
        'T': 'S',
        'S': 'L',
        'L': 'U',
        'U': 'N',
        'N': None
    }

    _str_reso_map = dict([(v, k) for k, v in compat.iteritems(_reso_str_map)])

    _reso_freq_map = {
        'year': 'A',
        'quarter': 'Q',
        'month': 'M',
        'day': 'D',
        'hour': 'H',
        'minute': 'T',
        'second': 'S',
        'millisecond': 'L',
        'microsecond': 'U',
        'nanosecond': 'N'}

    _freq_reso_map = dict([(v, k)
                           for k, v in compat.iteritems(_reso_freq_map)])

    @classmethod
    def get_str(cls, reso):
        """
        Return resolution str against resolution code.

        Example
        -------
        >>> Resolution.get_str(Resolution.RESO_SEC)
        'second'
        """
        return cls._reso_str_map.get(reso, 'day')

    @classmethod
    def get_reso(cls, resostr):
        """
        Return resolution str against resolution code.

        Example
        -------
        >>> Resolution.get_reso('second')
        2

        >>> Resolution.get_reso('second') == Resolution.RESO_SEC
        True
        """
        return cls._str_reso_map.get(resostr, cls.RESO_DAY)

    @classmethod
    def get_freq_group(cls, resostr):
        """
        Return frequency str against resolution str.

        Example
        -------
        >>> f.Resolution.get_freq_group('day')
        4000
        """
        return get_freq_group(cls.get_freq(resostr))

    @classmethod
    def get_freq(cls, resostr):
        """
        Return frequency str against resolution str.

        Example
        -------
        >>> f.Resolution.get_freq('day')
        'D'
        """
        return cls._reso_freq_map[resostr]

    @classmethod
    def get_str_from_freq(cls, freq):
        """
        Return resolution str against frequency str.

        Example
        -------
        >>> Resolution.get_str_from_freq('H')
        'hour'
        """
        return cls._freq_reso_map.get(freq, 'day')

    @classmethod
    def get_reso_from_freq(cls, freq):
        """
        Return resolution code against frequency str.

        Example
        -------
        >>> Resolution.get_reso_from_freq('H')
        4

        >>> Resolution.get_reso_from_freq('H') == Resolution.RESO_HR
        True
        """
        return cls.get_reso(cls.get_str_from_freq(freq))

    @classmethod
    def get_stride_from_decimal(cls, value, freq):
        """
        Convert freq with decimal stride into a higher freq with integer stride

        Parameters
        ----------
        value : integer or float
        freq : string
            Frequency string

        Raises
        ------
        ValueError
            If the float cannot be converted to an integer at any resolution.

        Example
        -------
        >>> Resolution.get_stride_from_decimal(1.5, 'T')
        (90, 'S')

        >>> Resolution.get_stride_from_decimal(1.04, 'H')
        (3744, 'S')

        >>> Resolution.get_stride_from_decimal(1, 'D')
        (1, 'D')
        """

        if np.isclose(value % 1, 0):
            return int(value), freq
        else:
            start_reso = cls.get_reso_from_freq(freq)
            if start_reso == 0:
                raise ValueError(
                    "Could not convert to integer offset at any resolution"
                )

            next_value = cls._reso_mult_map[start_reso] * value
            next_name = cls._reso_str_bump_map[freq]
            return cls.get_stride_from_decimal(next_value, next_name)


def get_to_timestamp_base(base):
    """
    Return frequency code group used for base of to_timestamp against
    frequency code.

    Example
    -------
    # Return day freq code against longer freq than day
    >>> get_to_timestamp_base(get_freq_code('D')[0])
    6000
    >>> get_to_timestamp_base(get_freq_code('W')[0])
    6000
    >>> get_to_timestamp_base(get_freq_code('M')[0])
    6000

    # Return second freq code against hour between second
    >>> get_to_timestamp_base(get_freq_code('H')[0])
    9000
    >>> get_to_timestamp_base(get_freq_code('S')[0])
    9000
    """
    if base < FreqGroup.FR_BUS:
        return FreqGroup.FR_DAY
    if FreqGroup.FR_HR <= base <= FreqGroup.FR_SEC:
        return FreqGroup.FR_SEC
    return base


def get_freq_group(freq):
    """
    Return frequency code group of given frequency str or offset.

    Example
    -------
    >>> get_freq_group('W-MON')
    4000

    >>> get_freq_group('W-FRI')
    4000
    """
    if isinstance(freq, offsets.DateOffset):
        freq = freq.rule_code

    if isinstance(freq, compat.string_types):
        base, mult = get_freq_code(freq)
        freq = base
    elif isinstance(freq, int):
        pass
    else:
        raise ValueError('input must be str, offset or int')
    return (freq // 1000) * 1000


def get_freq(freq):
    """
    Return frequency code of given frequency str.
    If input is not string, return input as it is.

    Example
    -------
    >>> get_freq('A')
    1000

    >>> get_freq('3A')
    1000
    """
    if isinstance(freq, compat.string_types):
        base, mult = get_freq_code(freq)
        freq = base
    return freq


def _get_freq_str(base, mult=1):
    code = _reverse_period_code_map.get(base)
    if mult == 1:
        return code
    return str(mult) + code


# ---------------------------------------------------------------------
# Offset names ("time rules") and related functions


from pandas.tseries.offsets import (Nano, Micro, Milli, Second,  # noqa
                                    Minute, Hour,
                                    Day, BDay, CDay, Week, MonthBegin,
                                    MonthEnd, BMonthBegin, BMonthEnd,
                                    QuarterBegin, QuarterEnd, BQuarterBegin,
                                    BQuarterEnd, YearBegin, YearEnd,
                                    BYearBegin, BYearEnd, prefix_mapping)
try:
    cday = CDay()
except NotImplementedError:
    cday = None

#: cache of previously seen offsets
_offset_map = {}

_offset_to_period_map = {
    'WEEKDAY': 'D',
    'EOM': 'M',
    'BM': 'M',
    'BQS': 'Q',
    'QS': 'Q',
    'BQ': 'Q',
    'BA': 'A',
    'AS': 'A',
    'BAS': 'A',
    'MS': 'M',
    'D': 'D',
    'C': 'C',
    'B': 'B',
    'T': 'T',
    'S': 'S',
    'L': 'L',
    'U': 'U',
    'N': 'N',
    'H': 'H',
    'Q': 'Q',
    'A': 'A',
    'W': 'W',
    'M': 'M',
    'Y': 'A',
    'BY': 'A',
    'YS': 'A',
    'BYS': 'A',
}

need_suffix = ['QS', 'BQ', 'BQS', 'YS', 'AS', 'BY', 'BA', 'BYS', 'BAS']
for __prefix in need_suffix:
    for _m in tslib._MONTHS:
        _alias = '{prefix}-{month}'.format(prefix=__prefix, month=_m)
        _offset_to_period_map[_alias] = _offset_to_period_map[__prefix]
for __prefix in ['A', 'Q']:
    for _m in tslib._MONTHS:
        _alias = '{prefix}-{month}'.format(prefix=__prefix, month=_m)
        _offset_to_period_map[_alias] = _alias

_days = ['MON', 'TUE', 'WED', 'THU', 'FRI', 'SAT', 'SUN']
for _d in _days:
    _alias = 'W-{day}'.format(day=_d)
    _offset_to_period_map[_alias] = _alias


def get_period_alias(offset_str):
    """ alias to closest period strings BQ->Q etc"""
    return _offset_to_period_map.get(offset_str, None)


_lite_rule_alias = {
    'W': 'W-SUN',
    'Q': 'Q-DEC',

    'A': 'A-DEC',  # YearEnd(month=12),
    'Y': 'A-DEC',
    'AS': 'AS-JAN',  # YearBegin(month=1),
    'YS': 'AS-JAN',
    'BA': 'BA-DEC',  # BYearEnd(month=12),
    'BY': 'BA-DEC',
    'BAS': 'BAS-JAN',  # BYearBegin(month=1),
    'BYS': 'BAS-JAN',

    'Min': 'T',
    'min': 'T',
    'ms': 'L',
    'us': 'U',
    'ns': 'N'
}


_name_to_offset_map = {'days': Day(1),
                       'hours': Hour(1),
                       'minutes': Minute(1),
                       'seconds': Second(1),
                       'milliseconds': Milli(1),
                       'microseconds': Micro(1),
                       'nanoseconds': Nano(1)}


_INVALID_FREQ_ERROR = "Invalid frequency: {0}"


@deprecate_kwarg(old_arg_name='freqstr', new_arg_name='freq')
def to_offset(freq):
    """
    Return DateOffset object from string or tuple representation
    or datetime.timedelta object

    Parameters
    ----------
    freq : str, tuple, datetime.timedelta, DateOffset or None

    Returns
    -------
    delta : DateOffset
        None if freq is None

    Raises
    ------
    ValueError
        If freq is an invalid frequency

    See Also
    --------
    pandas.DateOffset

    Examples
    --------
    >>> to_offset('5min')
    <5 * Minutes>

    >>> to_offset('1D1H')
    <25 * Hours>

    >>> to_offset(('W', 2))
    <2 * Weeks: weekday=6>

    >>> to_offset((2, 'B'))
    <2 * BusinessDays>

    >>> to_offset(datetime.timedelta(days=1))
    <Day>

    >>> to_offset(Hour())
    <Hour>
    """
    if freq is None:
        return None

    if isinstance(freq, DateOffset):
        return freq

    if isinstance(freq, tuple):
        name = freq[0]
        stride = freq[1]
        if isinstance(stride, compat.string_types):
            name, stride = stride, name
        name, _ = _base_and_stride(name)
        delta = get_offset(name) * stride

    elif isinstance(freq, timedelta):
        delta = None
        freq = Timedelta(freq)
        try:
            for name in freq.components._fields:
                offset = _name_to_offset_map[name]
                stride = getattr(freq.components, name)
                if stride != 0:
                    offset = stride * offset
                    if delta is None:
                        delta = offset
                    else:
                        delta = delta + offset
        except Exception:
            raise ValueError(_INVALID_FREQ_ERROR.format(freq))

    else:
        delta = None
        stride_sign = None
        try:
            splitted = re.split(opattern, freq)
            if splitted[-1] != '' and not splitted[-1].isspace():
                # the last element must be blank
                raise ValueError('last element must be blank')
            for sep, stride, name in zip(splitted[0::4], splitted[1::4],
                                         splitted[2::4]):
                if sep != '' and not sep.isspace():
                    raise ValueError('separator must be spaces')
                prefix = _lite_rule_alias.get(name) or name
                if stride_sign is None:
                    stride_sign = -1 if stride.startswith('-') else 1
                if not stride:
                    stride = 1
                if prefix in Resolution._reso_str_bump_map.keys():
                    stride, name = Resolution.get_stride_from_decimal(
                        float(stride), prefix
                    )
                stride = int(stride)
                offset = get_offset(name)
                offset = offset * int(np.fabs(stride) * stride_sign)
                if delta is None:
                    delta = offset
                else:
                    delta = delta + offset
        except Exception:
            raise ValueError(_INVALID_FREQ_ERROR.format(freq))

    if delta is None:
        raise ValueError(_INVALID_FREQ_ERROR.format(freq))

    return delta


# hack to handle WOM-1MON
opattern = re.compile(
    r'([\-]?\d*|[\-]?\d*\.\d*)\s*([A-Za-z]+([\-][\dA-Za-z\-]+)?)'
)


def get_base_alias(freqstr):
    """
    Returns the base frequency alias, e.g., '5D' -> 'D'
    """
    return _base_and_stride(freqstr)[0]


_dont_uppercase = set(('MS', 'ms'))


def get_offset(name):
    """
    Return DateOffset object associated with rule name

    Examples
    --------
    get_offset('EOM') --> BMonthEnd(1)
    """
    if name not in _dont_uppercase:
        name = name.upper()
        name = _lite_rule_alias.get(name, name)
        name = _lite_rule_alias.get(name.lower(), name)
    else:
        name = _lite_rule_alias.get(name, name)

    if name not in _offset_map:
        try:
            split = name.split('-')
            klass = prefix_mapping[split[0]]
            # handles case where there's no suffix (and will TypeError if too
            # many '-')
            offset = klass._from_name(*split[1:])
        except (ValueError, TypeError, KeyError):
            # bad prefix or suffix
            raise ValueError(_INVALID_FREQ_ERROR.format(name))
        # cache
        _offset_map[name] = offset
    # do not return cache because it's mutable
    return _offset_map[name].copy()


getOffset = get_offset


def get_standard_freq(freq):
    """
    Return the standardized frequency string
    """

    msg = ("get_standard_freq is deprecated. Use to_offset(freq).rule_code "
           "instead.")
    warnings.warn(msg, FutureWarning, stacklevel=2)
    return to_offset(freq).rule_code


# ---------------------------------------------------------------------
# Period codes

# period frequency constants corresponding to scikits timeseries
# originals
_period_code_map = {
    # Annual freqs with various fiscal year ends.
    # eg, 2005 for A-FEB runs Mar 1, 2004 to Feb 28, 2005
    "A-DEC": 1000,  # Annual - December year end
    "A-JAN": 1001,  # Annual - January year end
    "A-FEB": 1002,  # Annual - February year end
    "A-MAR": 1003,  # Annual - March year end
    "A-APR": 1004,  # Annual - April year end
    "A-MAY": 1005,  # Annual - May year end
    "A-JUN": 1006,  # Annual - June year end
    "A-JUL": 1007,  # Annual - July year end
    "A-AUG": 1008,  # Annual - August year end
    "A-SEP": 1009,  # Annual - September year end
    "A-OCT": 1010,  # Annual - October year end
    "A-NOV": 1011,  # Annual - November year end

    # Quarterly frequencies with various fiscal year ends.
    # eg, Q42005 for Q-OCT runs Aug 1, 2005 to Oct 31, 2005
    "Q-DEC": 2000,    # Quarterly - December year end
    "Q-JAN": 2001,    # Quarterly - January year end
    "Q-FEB": 2002,    # Quarterly - February year end
    "Q-MAR": 2003,    # Quarterly - March year end
    "Q-APR": 2004,    # Quarterly - April year end
    "Q-MAY": 2005,    # Quarterly - May year end
    "Q-JUN": 2006,    # Quarterly - June year end
    "Q-JUL": 2007,    # Quarterly - July year end
    "Q-AUG": 2008,    # Quarterly - August year end
    "Q-SEP": 2009,    # Quarterly - September year end
    "Q-OCT": 2010,    # Quarterly - October year end
    "Q-NOV": 2011,    # Quarterly - November year end

    "M": 3000,        # Monthly

    "W-SUN": 4000,    # Weekly - Sunday end of week
    "W-MON": 4001,    # Weekly - Monday end of week
    "W-TUE": 4002,    # Weekly - Tuesday end of week
    "W-WED": 4003,    # Weekly - Wednesday end of week
    "W-THU": 4004,    # Weekly - Thursday end of week
    "W-FRI": 4005,    # Weekly - Friday end of week
    "W-SAT": 4006,    # Weekly - Saturday end of week

    "B": 5000,        # Business days
    "D": 6000,        # Daily
    "H": 7000,        # Hourly
    "T": 8000,        # Minutely
    "S": 9000,        # Secondly
    "L": 10000,       # Millisecondly
    "U": 11000,       # Microsecondly
    "N": 12000,       # Nanosecondly
}

_reverse_period_code_map = {}
for _k, _v in compat.iteritems(_period_code_map):
    _reverse_period_code_map[_v] = _k

# Yearly aliases
year_aliases = {}

for k, v in compat.iteritems(_period_code_map):
    if k.startswith("A-"):
        alias = "Y" + k[1:]
        year_aliases[alias] = v

_period_code_map.update(**year_aliases)
del year_aliases

_period_code_map.update({
    "Q": 2000,  # Quarterly - December year end (default quarterly)
    "A": 1000,  # Annual
    "W": 4000,  # Weekly
    "C": 5000,  # Custom Business Day
})


def _period_str_to_code(freqstr):
    freqstr = _lite_rule_alias.get(freqstr, freqstr)

    if freqstr not in _dont_uppercase:
        lower = freqstr.lower()
        freqstr = _lite_rule_alias.get(lower, freqstr)

    if freqstr not in _dont_uppercase:
        freqstr = freqstr.upper()
    try:
        return _period_code_map[freqstr]
    except KeyError:
        raise ValueError(_INVALID_FREQ_ERROR.format(freqstr))


def infer_freq(index, warn=True):
    """
    Infer the most likely frequency given the input index. If the frequency is
    uncertain, a warning will be printed.

    Parameters
    ----------
    index : DatetimeIndex or TimedeltaIndex
      if passed a Series will use the values of the series (NOT THE INDEX)
    warn : boolean, default True

    Returns
    -------
    freq : string or None
        None if no discernible frequency
        TypeError if the index is not datetime-like
        ValueError if there are less than three values.
    """
    import pandas as pd

    if isinstance(index, ABCSeries):
        values = index._values
        if not (is_datetime64_dtype(values) or
                is_timedelta64_dtype(values) or
                values.dtype == object):
            raise TypeError("cannot infer freq from a non-convertible dtype "
                            "on a Series of {dtype}".format(dtype=index.dtype))
        index = values

    if is_period_arraylike(index):
        raise TypeError("PeriodIndex given. Check the `freq` attribute "
                        "instead of using infer_freq.")
    elif isinstance(index, pd.TimedeltaIndex):
        inferer = _TimedeltaFrequencyInferer(index, warn=warn)
        return inferer.get_freq()

    if isinstance(index, pd.Index) and not isinstance(index, pd.DatetimeIndex):
        if isinstance(index, (pd.Int64Index, pd.Float64Index)):
            raise TypeError("cannot infer freq from a non-convertible index "
                            "type {type}".format(type=type(index)))
        index = index.values

    if not isinstance(index, pd.DatetimeIndex):
        try:
            index = pd.DatetimeIndex(index)
        except AmbiguousTimeError:
            index = pd.DatetimeIndex(index.asi8)

    inferer = _FrequencyInferer(index, warn=warn)
    return inferer.get_freq()


_ONE_MICRO = long(1000)
_ONE_MILLI = _ONE_MICRO * 1000
_ONE_SECOND = _ONE_MILLI * 1000
_ONE_MINUTE = 60 * _ONE_SECOND
_ONE_HOUR = 60 * _ONE_MINUTE
_ONE_DAY = 24 * _ONE_HOUR


class _FrequencyInferer(object):
    """
    Not sure if I can avoid the state machine here
    """

    def __init__(self, index, warn=True):
        self.index = index
        self.values = np.asarray(index).view('i8')

        # This moves the values, which are implicitly in UTC, to the
        # the timezone so they are in local time
        if hasattr(index, 'tz'):
            if index.tz is not None:
                self.values = tslib.tz_convert(self.values, 'UTC', index.tz)

        self.warn = warn

        if len(index) < 3:
            raise ValueError('Need at least 3 dates to infer frequency')

        self.is_monotonic = (self.index.is_monotonic_increasing or
                             self.index.is_monotonic_decreasing)

    @cache_readonly
    def deltas(self):
        return tslib.unique_deltas(self.values)

    @cache_readonly
    def deltas_asi8(self):
        return tslib.unique_deltas(self.index.asi8)

    @cache_readonly
    def is_unique(self):
        return len(self.deltas) == 1

    @cache_readonly
    def is_unique_asi8(self):
        return len(self.deltas_asi8) == 1

    def get_freq(self):
        if not self.is_monotonic or not self.index.is_unique:
            return None

        delta = self.deltas[0]
        if _is_multiple(delta, _ONE_DAY):
            return self._infer_daily_rule()
        else:
            # Business hourly, maybe. 17: one day / 65: one weekend
            if self.hour_deltas in ([1, 17], [1, 65], [1, 17, 65]):
                return 'BH'
            # Possibly intraday frequency.  Here we use the
            # original .asi8 values as the modified values
            # will not work around DST transitions.  See #8772
            elif not self.is_unique_asi8:
                return None
            delta = self.deltas_asi8[0]
            if _is_multiple(delta, _ONE_HOUR):
                # Hours
                return _maybe_add_count('H', delta / _ONE_HOUR)
            elif _is_multiple(delta, _ONE_MINUTE):
                # Minutes
                return _maybe_add_count('T', delta / _ONE_MINUTE)
            elif _is_multiple(delta, _ONE_SECOND):
                # Seconds
                return _maybe_add_count('S', delta / _ONE_SECOND)
            elif _is_multiple(delta, _ONE_MILLI):
                # Milliseconds
                return _maybe_add_count('L', delta / _ONE_MILLI)
            elif _is_multiple(delta, _ONE_MICRO):
                # Microseconds
                return _maybe_add_count('U', delta / _ONE_MICRO)
            else:
                # Nanoseconds
                return _maybe_add_count('N', delta)

    @cache_readonly
    def day_deltas(self):
        return [x / _ONE_DAY for x in self.deltas]

    @cache_readonly
    def hour_deltas(self):
        return [x / _ONE_HOUR for x in self.deltas]

    @cache_readonly
    def fields(self):
        return tslib.build_field_sarray(self.values)

    @cache_readonly
    def rep_stamp(self):
        return lib.Timestamp(self.values[0])

    def month_position_check(self):
        # TODO: cythonize this, very slow
        calendar_end = True
        business_end = True
        calendar_start = True
        business_start = True

        years = self.fields['Y']
        months = self.fields['M']
        days = self.fields['D']
        weekdays = self.index.dayofweek

        from calendar import monthrange
        for y, m, d, wd in zip(years, months, days, weekdays):

            if calendar_start:
                calendar_start &= d == 1
            if business_start:
                business_start &= d == 1 or (d <= 3 and wd == 0)

            if calendar_end or business_end:
                _, daysinmonth = monthrange(y, m)
                cal = d == daysinmonth
                if calendar_end:
                    calendar_end &= cal
                if business_end:
                    business_end &= cal or (daysinmonth - d < 3 and wd == 4)
            elif not calendar_start and not business_start:
                break

        if calendar_end:
            return 'ce'
        elif business_end:
            return 'be'
        elif calendar_start:
            return 'cs'
        elif business_start:
            return 'bs'
        else:
            return None

    @cache_readonly
    def mdiffs(self):
        nmonths = self.fields['Y'] * 12 + self.fields['M']
        return tslib.unique_deltas(nmonths.astype('i8'))

    @cache_readonly
    def ydiffs(self):
        return tslib.unique_deltas(self.fields['Y'].astype('i8'))

    def _infer_daily_rule(self):
        annual_rule = self._get_annual_rule()
        if annual_rule:
            nyears = self.ydiffs[0]
            month = _month_aliases[self.rep_stamp.month]
            alias = '{prefix}-{month}'.format(prefix=annual_rule, month=month)
            return _maybe_add_count(alias, nyears)

        quarterly_rule = self._get_quarterly_rule()
        if quarterly_rule:
            nquarters = self.mdiffs[0] / 3
            mod_dict = {0: 12, 2: 11, 1: 10}
            month = _month_aliases[mod_dict[self.rep_stamp.month % 3]]
            alias = '{prefix}-{month}'.format(prefix=quarterly_rule,
                                              month=month)
            return _maybe_add_count(alias, nquarters)

        monthly_rule = self._get_monthly_rule()
        if monthly_rule:
            return _maybe_add_count(monthly_rule, self.mdiffs[0])

        if self.is_unique:
            days = self.deltas[0] / _ONE_DAY
            if days % 7 == 0:
                # Weekly
                day = _weekday_rule_aliases[self.rep_stamp.weekday()]
                return _maybe_add_count('W-{day}'.format(day=day), days / 7)
            else:
                return _maybe_add_count('D', days)

        if self._is_business_daily():
            return 'B'

        wom_rule = self._get_wom_rule()
        if wom_rule:
            return wom_rule

    def _get_annual_rule(self):
        if len(self.ydiffs) > 1:
            return None

        if len(algos.unique(self.fields['M'])) > 1:
            return None

        pos_check = self.month_position_check()
        return {'cs': 'AS', 'bs': 'BAS',
                'ce': 'A', 'be': 'BA'}.get(pos_check)

    def _get_quarterly_rule(self):
        if len(self.mdiffs) > 1:
            return None

        if not self.mdiffs[0] % 3 == 0:
            return None

        pos_check = self.month_position_check()
        return {'cs': 'QS', 'bs': 'BQS',
                'ce': 'Q', 'be': 'BQ'}.get(pos_check)

    def _get_monthly_rule(self):
        if len(self.mdiffs) > 1:
            return None
        pos_check = self.month_position_check()
        return {'cs': 'MS', 'bs': 'BMS',
                'ce': 'M', 'be': 'BM'}.get(pos_check)

    def _is_business_daily(self):
        # quick check: cannot be business daily
        if self.day_deltas != [1, 3]:
            return False

        # probably business daily, but need to confirm
        first_weekday = self.index[0].weekday()
        shifts = np.diff(self.index.asi8)
        shifts = np.floor_divide(shifts, _ONE_DAY)
        weekdays = np.mod(first_weekday + np.cumsum(shifts), 7)
        return np.all(((weekdays == 0) & (shifts == 3)) |
                      ((weekdays > 0) & (weekdays <= 4) & (shifts == 1)))

    def _get_wom_rule(self):
        #         wdiffs = unique(np.diff(self.index.week))
        # We also need -47, -49, -48 to catch index spanning year boundary
        #     if not lib.ismember(wdiffs, set([4, 5, -47, -49, -48])).all():
        #         return None

        weekdays = unique(self.index.weekday)
        if len(weekdays) > 1:
            return None

        week_of_months = unique((self.index.day - 1) // 7)
        # Only attempt to infer up to WOM-4. See #9425
        week_of_months = week_of_months[week_of_months < 4]
        if len(week_of_months) == 0 or len(week_of_months) > 1:
            return None

        # get which week
        week = week_of_months[0] + 1
        wd = _weekday_rule_aliases[weekdays[0]]

        return 'WOM-{week}{weekday}'.format(week=week, weekday=wd)


class _TimedeltaFrequencyInferer(_FrequencyInferer):

    def _infer_daily_rule(self):
        if self.is_unique:
            days = self.deltas[0] / _ONE_DAY
            if days % 7 == 0:
                # Weekly
                wd = _weekday_rule_aliases[self.rep_stamp.weekday()]
                alias = 'W-{weekday}'.format(weekday=wd)
                return _maybe_add_count(alias, days / 7)
            else:
                return _maybe_add_count('D', days)


def _maybe_add_count(base, count):
    if count != 1:
        return '{count}{base}'.format(count=int(count), base=base)
    else:
        return base


def _maybe_coerce_freq(code):
    """ we might need to coerce a code to a rule_code
    and uppercase it

    Parameters
    ----------
    source : string
        Frequency converting from

    Returns
    -------
    string code
    """

    assert code is not None
    if isinstance(code, offsets.DateOffset):
        code = code.rule_code
    return code.upper()


def is_subperiod(source, target):
    """
    Returns True if downsampling is possible between source and target
    frequencies

    Parameters
    ----------
    source : string
        Frequency converting from
    target : string
        Frequency converting to

    Returns
    -------
    is_subperiod : boolean
    """

    if target is None or source is None:
        return False
    source = _maybe_coerce_freq(source)
    target = _maybe_coerce_freq(target)

    if _is_annual(target):
        if _is_quarterly(source):
            return _quarter_months_conform(_get_rule_month(source),
                                           _get_rule_month(target))
        return source in ['D', 'C', 'B', 'M', 'H', 'T', 'S', 'L', 'U', 'N']
    elif _is_quarterly(target):
        return source in ['D', 'C', 'B', 'M', 'H', 'T', 'S', 'L', 'U', 'N']
    elif _is_monthly(target):
        return source in ['D', 'C', 'B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif _is_weekly(target):
        return source in [target, 'D', 'C', 'B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif target == 'B':
        return source in ['B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif target == 'C':
        return source in ['C', 'H', 'T', 'S', 'L', 'U', 'N']
    elif target == 'D':
        return source in ['D', 'H', 'T', 'S', 'L', 'U', 'N']
    elif target == 'H':
        return source in ['H', 'T', 'S', 'L', 'U', 'N']
    elif target == 'T':
        return source in ['T', 'S', 'L', 'U', 'N']
    elif target == 'S':
        return source in ['S', 'L', 'U', 'N']
    elif target == 'L':
        return source in ['L', 'U', 'N']
    elif target == 'U':
        return source in ['U', 'N']
    elif target == 'N':
        return source in ['N']


def is_superperiod(source, target):
    """
    Returns True if upsampling is possible between source and target
    frequencies

    Parameters
    ----------
    source : string
        Frequency converting from
    target : string
        Frequency converting to

    Returns
    -------
    is_superperiod : boolean
    """
    if target is None or source is None:
        return False
    source = _maybe_coerce_freq(source)
    target = _maybe_coerce_freq(target)

    if _is_annual(source):
        if _is_annual(target):
            return _get_rule_month(source) == _get_rule_month(target)

        if _is_quarterly(target):
            smonth = _get_rule_month(source)
            tmonth = _get_rule_month(target)
            return _quarter_months_conform(smonth, tmonth)
        return target in ['D', 'C', 'B', 'M', 'H', 'T', 'S', 'L', 'U', 'N']
    elif _is_quarterly(source):
        return target in ['D', 'C', 'B', 'M', 'H', 'T', 'S', 'L', 'U', 'N']
    elif _is_monthly(source):
        return target in ['D', 'C', 'B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif _is_weekly(source):
        return target in [source, 'D', 'C', 'B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif source == 'B':
        return target in ['D', 'C', 'B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif source == 'C':
        return target in ['D', 'C', 'B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif source == 'D':
        return target in ['D', 'C', 'B', 'H', 'T', 'S', 'L', 'U', 'N']
    elif source == 'H':
        return target in ['H', 'T', 'S', 'L', 'U', 'N']
    elif source == 'T':
        return target in ['T', 'S', 'L', 'U', 'N']
    elif source == 'S':
        return target in ['S', 'L', 'U', 'N']
    elif source == 'L':
        return target in ['L', 'U', 'N']
    elif source == 'U':
        return target in ['U', 'N']
    elif source == 'N':
        return target in ['N']


_get_rule_month = tslib._get_rule_month


def _is_annual(rule):
    rule = rule.upper()
    return rule == 'A' or rule.startswith('A-')


def _quarter_months_conform(source, target):
    snum = _month_numbers[source]
    tnum = _month_numbers[target]
    return snum % 3 == tnum % 3


def _is_quarterly(rule):
    rule = rule.upper()
    return rule == 'Q' or rule.startswith('Q-') or rule.startswith('BQ')


def _is_monthly(rule):
    rule = rule.upper()
    return rule == 'M' or rule == 'BM'


def _is_weekly(rule):
    rule = rule.upper()
    return rule == 'W' or rule.startswith('W-')


DAYS = ['MON', 'TUE', 'WED', 'THU', 'FRI', 'SAT', 'SUN']

MONTHS = tslib._MONTHS
_month_numbers = tslib._MONTH_NUMBERS
_month_aliases = tslib._MONTH_ALIASES
_weekday_rule_aliases = dict((k, v) for k, v in enumerate(DAYS))


def _is_multiple(us, mult):
    return us % mult == 0