repo_description: matplotlib: plotting with Python
repo_topics: data-science data-visualization gtk matplotlib plotting python qt tk wx
code: """
  Matplotlib provides sophisticated date plotting capabilities, standing on the
  shoulders of python :mod:`datetime` and the add-on module dateutil_.
  
  By default, Matplotlib uses the units machinery described in
  `~matplotlib.units` to convert `datetime.datetime`, and `numpy.datetime64`
  objects when plotted on an x- or y-axis. The user does not
  need to do anything for dates to be formatted, but dates often have strict
  formatting needs, so this module provides many tick locators and formatters.
  A basic example using `numpy.datetime64` is::
  
      import numpy as np
  
      times = np.arange(np.datetime64('2001-01-02'),
                        np.datetime64('2002-02-03'), np.timedelta64(75, 'm'))
      y = np.random.randn(len(times))
  
      fig, ax = plt.subplots()
      ax.plot(times, y)
  
  .. seealso::
  
      - :doc:`/gallery/text_labels_and_annotations/date`
      - :doc:`/gallery/ticks/date_concise_formatter`
      - :doc:`/gallery/ticks/date_demo_convert`
  
  .. _date-format:
  
  Matplotlib date format
  ----------------------
  
  Matplotlib represents dates using floating point numbers specifying the number
  of days since a default epoch of 1970-01-01 UTC; for example,
  1970-01-01, 06:00 is the floating point number 0.25. The formatters and
  locators require the use of `datetime.datetime` objects, so only dates between
  year 0001 and 9999 can be represented.  Microsecond precision
  is achievable for (approximately) 70 years on either side of the epoch, and
  20 microseconds for the rest of the allowable range of dates (year 0001 to
  9999). The epoch can be changed at import time via `.dates.set_epoch` or
  :rc:`date.epoch` to other dates if necessary; see
  :doc:`/gallery/ticks/date_precision_and_epochs` for a discussion.
  
  .. note::
  
     Before Matplotlib 3.3, the epoch was 0000-12-31 which lost modern
     microsecond precision and also made the default axis limit of 0 an invalid
     datetime.  In 3.3 the epoch was changed as above.  To convert old
     ordinal floats to the new epoch, users can do::
  
       new_ordinal = old_ordinal + mdates.date2num(np.datetime64('0000-12-31'))
  
  
  There are a number of helper functions to convert between :mod:`datetime`
  objects and Matplotlib dates:
  
  .. currentmodule:: matplotlib.dates
  
  .. autosummary::
     :nosignatures:
  
     datestr2num
     date2num
     num2date
     num2timedelta
     drange
     set_epoch
     get_epoch
  
  .. note::
  
     Like Python's `datetime.datetime`, Matplotlib uses the Gregorian calendar
     for all conversions between dates and floating point numbers. This practice
     is not universal, and calendar differences can cause confusing
     differences between what Python and Matplotlib give as the number of days
     since 0001-01-01 and what other software and databases yield.  For
     example, the US Naval Observatory uses a calendar that switches
     from Julian to Gregorian in October, 1582.  Hence, using their
     calculator, the number of days between 0001-01-01 and 2006-04-01 is
     732403, whereas using the Gregorian calendar via the datetime
     module we find::
  
       In [1]: date(2006, 4, 1).toordinal() - date(1, 1, 1).toordinal()
       Out[1]: 732401
  
  All the Matplotlib date converters, locators and formatters are timezone aware.
  If no explicit timezone is provided, :rc:`timezone` is assumed, provided as a
  string.  If you want to use a different timezone, pass the *tz* keyword
  argument of `num2date` to any date tick locators or formatters you create. This
  can be either a `datetime.tzinfo` instance or a string with the timezone name
  that can be parsed by `~dateutil.tz.gettz`.
  
  A wide range of specific and general purpose date tick locators and
  formatters are provided in this module.  See
  :mod:`matplotlib.ticker` for general information on tick locators
  and formatters.  These are described below.
  
  The dateutil_ module provides additional code to handle date ticking, making it
  easy to place ticks on any kinds of dates.  See examples below.
  
  .. _dateutil: https://dateutil.readthedocs.io
  
  .. _date-locators:
  
  Date tick locators
  ------------------
  
  Most of the date tick locators can locate single or multiple ticks. For example::
  
      # import constants for the days of the week
      from matplotlib.dates import MO, TU, WE, TH, FR, SA, SU
  
      # tick on Mondays every week
      loc = WeekdayLocator(byweekday=MO, tz=tz)
  
      # tick on Mondays and Saturdays
      loc = WeekdayLocator(byweekday=(MO, SA))
  
  In addition, most of the constructors take an interval argument::
  
      # tick on Mondays every second week
      loc = WeekdayLocator(byweekday=MO, interval=2)
  
  The rrule locator allows completely general date ticking::
  
      # tick every 5th easter
      rule = rrulewrapper(YEARLY, byeaster=1, interval=5)
      loc = RRuleLocator(rule)
  
  The available date tick locators are:
  
  * `MicrosecondLocator`: Locate microseconds.
  
  * `SecondLocator`: Locate seconds.
  
  * `MinuteLocator`: Locate minutes.
  
  * `HourLocator`: Locate hours.
  
  * `DayLocator`: Locate specified days of the month.
  
  * `WeekdayLocator`: Locate days of the week, e.g., MO, TU.
  
  * `MonthLocator`: Locate months, e.g., 7 for July.
  
  * `YearLocator`: Locate years that are multiples of base.
  
  * `RRuleLocator`: Locate using a `rrulewrapper`.
    `rrulewrapper` is a simple wrapper around dateutil_'s `dateutil.rrule`
    which allow almost arbitrary date tick specifications.
    See :doc:`rrule example </gallery/ticks/date_demo_rrule>`.
  
  * `AutoDateLocator`: On autoscale, this class picks the best `DateLocator`
    (e.g., `RRuleLocator`) to set the view limits and the tick locations.  If
    called with ``interval_multiples=True`` it will make ticks line up with
    sensible multiples of the tick intervals.  For example, if the interval is
    4 hours, it will pick hours 0, 4, 8, etc. as ticks.  This behaviour is not
    guaranteed by default.
  
  .. _date-formatters:
  
  Date formatters
  ---------------
  
  The available date formatters are:
  
  * `AutoDateFormatter`: attempts to figure out the best format to use.  This is
    most useful when used with the `AutoDateLocator`.
  
  * `ConciseDateFormatter`: also attempts to figure out the best format to use,
    and to make the format as compact as possible while still having complete
    date information.  This is most useful when used with the `AutoDateLocator`.
  
  * `DateFormatter`: use `~datetime.datetime.strftime` format strings.
  """
  
  import datetime
  import functools
  import logging
  import re
  
  from dateutil.rrule import (rrule, MO, TU, WE, TH, FR, SA, SU, YEARLY,
                              MONTHLY, WEEKLY, DAILY, HOURLY, MINUTELY,
                              SECONDLY)
  from dateutil.relativedelta import relativedelta
  import dateutil.parser
  import dateutil.tz
  import numpy as np
  
  import matplotlib as mpl
  from matplotlib import _api, cbook, ticker, units
  
  __all__ = ('datestr2num', 'date2num', 'num2date', 'num2timedelta', 'drange',
             'set_epoch', 'get_epoch', 'DateFormatter', 'ConciseDateFormatter',
             'AutoDateFormatter', 'DateLocator', 'RRuleLocator',
             'AutoDateLocator', 'YearLocator', 'MonthLocator', 'WeekdayLocator',
             'DayLocator', 'HourLocator', 'MinuteLocator',
             'SecondLocator', 'MicrosecondLocator',
             'rrule', 'MO', 'TU', 'WE', 'TH', 'FR', 'SA', 'SU',
             'YEARLY', 'MONTHLY', 'WEEKLY', 'DAILY',
             'HOURLY', 'MINUTELY', 'SECONDLY', 'MICROSECONDLY', 'relativedelta',
             'DateConverter', 'ConciseDateConverter', 'rrulewrapper')
  
  
  _log = logging.getLogger(__name__)
  UTC = datetime.timezone.utc
  
  
  def _get_tzinfo(tz=None):
      """
      Generate `~datetime.tzinfo` from a string or return `~datetime.tzinfo`.
      If None, retrieve the preferred timezone from the rcParams dictionary.
      """
      tz = mpl._val_or_rc(tz, 'timezone')
      if tz == 'UTC':
          return UTC
      if isinstance(tz, str):
          tzinfo = dateutil.tz.gettz(tz)
          if tzinfo is None:
              raise ValueError(f"{tz} is not a valid timezone as parsed by"
                               " dateutil.tz.gettz.")
          return tzinfo
      if isinstance(tz, datetime.tzinfo):
          return tz
      raise TypeError(f"tz must be string or tzinfo subclass, not {tz!r}.")
  
  
  # Time-related constants.
  EPOCH_OFFSET = float(datetime.datetime(1970, 1, 1).toordinal())
  # EPOCH_OFFSET is not used by matplotlib
  MICROSECONDLY = SECONDLY + 1
  HOURS_PER_DAY = 24.
  MIN_PER_HOUR = 60.
  SEC_PER_MIN = 60.
  MONTHS_PER_YEAR = 12.
  
  DAYS_PER_WEEK = 7.
  DAYS_PER_MONTH = 30.
  DAYS_PER_YEAR = 365.0
  
  MINUTES_PER_DAY = MIN_PER_HOUR * HOURS_PER_DAY
  
  SEC_PER_HOUR = SEC_PER_MIN * MIN_PER_HOUR
  SEC_PER_DAY = SEC_PER_HOUR * HOURS_PER_DAY
  SEC_PER_WEEK = SEC_PER_DAY * DAYS_PER_WEEK
  
  MUSECONDS_PER_DAY = 1e6 * SEC_PER_DAY
  
  MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY, SUNDAY = (
      MO, TU, WE, TH, FR, SA, SU)
  WEEKDAYS = (MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY, SUNDAY)
  
  # default epoch: passed to np.datetime64...
  _epoch = None
  
  
  def _reset_epoch_test_example():
      """
      Reset the Matplotlib date epoch so it can be set again.
  
      Only for use in tests and examples.
      """
      global _epoch
      _epoch = None
  
  
  def set_epoch(epoch):
      """
      Set the epoch (origin for dates) for datetime calculations.
  
      The default epoch is :rc:`date.epoch`.
  
      If microsecond accuracy is desired, the date being plotted needs to be
      within approximately 70 years of the epoch. Matplotlib internally
      represents dates as days since the epoch, so floating point dynamic
      range needs to be within a factor of 2^52.
  
      `~.dates.set_epoch` must be called before any dates are converted
      (i.e. near the import section) or a RuntimeError will be raised.
  
      See also :doc:`/gallery/ticks/date_precision_and_epochs`.
  
      Parameters
      ----------
      epoch : str
          valid UTC date parsable by `numpy.datetime64` (do not include
          timezone).
  
      """
      global _epoch
      if _epoch is not None:
          raise RuntimeError('set_epoch must be called before dates plotted.')
      _epoch = epoch
  
  
  def get_epoch():
      """
      Get the epoch used by `.dates`.
  
      Returns
      -------
      epoch : str
          String for the epoch (parsable by `numpy.datetime64`).
      """
      global _epoch
  
      _epoch = mpl._val_or_rc(_epoch, 'date.epoch')
      return _epoch
  
  
  def _dt64_to_ordinalf(d):
      """
      Convert a `numpy.ndarray` of np.datetime64 to
      Gregorian date as UTC float relative to the epoch (see `.get_epoch`).
      Roundoff is float64 precision.  Practically: microseconds for dates
      between 290301 BC, 294241 AD, milliseconds for larger dates
      (see `numpy.datetime64`).
      """
  
      # the "extra" ensures that we at least allow the dynamic range out to
      # seconds.  That should get out to +/-2e11 years.
      dseconds = d.astype('datetime64[s]')
      extra = (d - dseconds).astype('timedelta64[ns]')
      t0 = np.datetime64(get_epoch(), 's')
      dt = (dseconds - t0).astype(np.float64)
      dt += extra.astype(np.float64) / 1.0e9
      dt = dt / SEC_PER_DAY
  
      NaT_int = np.datetime64('NaT').astype(np.int64)
      d_int = d.astype(np.int64)
      dt[d_int == NaT_int] = np.nan
      return dt
  
  
  def _from_ordinalf(x, tz=None):
      """
      Convert Gregorian float of the date, preserving hours, minutes,
      seconds and microseconds.  Return value is a `.datetime`.
  
      The input date *x* is a float in ordinal days at UTC, and the output will
      be the specified `.datetime` object corresponding to that time in
      timezone *tz*, or if *tz* is ``None``, in the timezone specified in
      :rc:`timezone`.
      """
  
      tz = _get_tzinfo(tz)
  
      dt = (np.datetime64(get_epoch()) +
            np.timedelta64(int(np.round(x * MUSECONDS_PER_DAY)), 'us'))
      if dt < np.datetime64('0001-01-01') or dt >= np.datetime64('10000-01-01'):
          raise ValueError(f'Date ordinal {x} converts to {dt} (using '
                           f'epoch {get_epoch()}), but Matplotlib dates must be '
                            'between year 0001 and 9999.')
      # convert from datetime64 to datetime:
      dt = dt.tolist()
  
      # datetime64 is always UTC:
      dt = dt.replace(tzinfo=dateutil.tz.gettz('UTC'))
      # but maybe we are working in a different timezone so move.
      dt = dt.astimezone(tz)
      # fix round off errors
      if np.abs(x) > 70 * 365:
          # if x is big, round off to nearest twenty microseconds.
          # This avoids floating point roundoff error
          ms = round(dt.microsecond / 20) * 20
          if ms == 1000000:
              dt = dt.replace(microsecond=0) + datetime.timedelta(seconds=1)
          else:
              dt = dt.replace(microsecond=ms)
  
      return dt
  
  
  # a version of _from_ordinalf that can operate on numpy arrays
  _from_ordinalf_np_vectorized = np.vectorize(_from_ordinalf, otypes="O")
  # a version of dateutil.parser.parse that can operate on numpy arrays
  _dateutil_parser_parse_np_vectorized = np.vectorize(dateutil.parser.parse)
  
  
  def datestr2num(d, default=None):
      """
      Convert a date string to a datenum using `dateutil.parser.parse`.
  
      Parameters
      ----------
      d : str or sequence of str
          The dates to convert.
  
      default : datetime.datetime, optional
          The default date to use when fields are missing in *d*.
      """
      if isinstance(d, str):
          dt = dateutil.parser.parse(d, default=default)
          return date2num(dt)
      else:
          if default is not None:
              d = [date2num(dateutil.parser.parse(s, default=default))
                   for s in d]
              return np.asarray(d)
          d = np.asarray(d)
          if not d.size:
              return d
          return date2num(_dateutil_parser_parse_np_vectorized(d))
  
  
  def date2num(d):
      """
      Convert datetime objects to Matplotlib dates.
  
      Parameters
      ----------
      d : `datetime.datetime` or `numpy.datetime64` or sequences of these
  
      Returns
      -------
      float or sequence of floats
          Number of days since the epoch.  See `.get_epoch` for the
          epoch, which can be changed by :rc:`date.epoch` or `.set_epoch`.  If
          the epoch is "1970-01-01T00:00:00" (default) then noon Jan 1 1970
          ("1970-01-01T12:00:00") returns 0.5.
  
      Notes
      -----
      The Gregorian calendar is assumed; this is not universal practice.
      For details see the module docstring.
      """
      # Unpack in case of e.g. Pandas or xarray object
      d = cbook._unpack_to_numpy(d)
  
      # make an iterable, but save state to unpack later:
      iterable = np.iterable(d)
      if not iterable:
          d = [d]
  
      masked = np.ma.is_masked(d)
      mask = np.ma.getmask(d)
      d = np.asarray(d)
  
      # convert to datetime64 arrays, if not already:
      if not np.issubdtype(d.dtype, np.datetime64):
          # datetime arrays
          if not d.size:
              # deals with an empty array...
              return d
          tzi = getattr(d[0], 'tzinfo', None)
          if tzi is not None:
              # make datetime naive:
              d = [dt.astimezone(UTC).replace(tzinfo=None) for dt in d]
              d = np.asarray(d)
          d = d.astype('datetime64[us]')
  
      d = np.ma.masked_array(d, mask=mask) if masked else d
      d = _dt64_to_ordinalf(d)
  
      return d if iterable else d[0]
  
  
  def num2date(x, tz=None):
      """
      Convert Matplotlib dates to `~datetime.datetime` objects.
  
      Parameters
      ----------
      x : float or sequence of floats
          Number of days (fraction part represents hours, minutes, seconds)
          since the epoch.  See `.get_epoch` for the
          epoch, which can be changed by :rc:`date.epoch` or `.set_epoch`.
      tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
          Timezone of *x*. If a string, *tz* is passed to `dateutil.tz`.
  
      Returns
      -------
      `~datetime.datetime` or sequence of `~datetime.datetime`
          Dates are returned in timezone *tz*.
  
          If *x* is a sequence, a sequence of `~datetime.datetime` objects will
          be returned.
  
      Notes
      -----
      The Gregorian calendar is assumed; this is not universal practice.
      For details, see the module docstring.
      """
      tz = _get_tzinfo(tz)
      return _from_ordinalf_np_vectorized(x, tz).tolist()
  
  
  _ordinalf_to_timedelta_np_vectorized = np.vectorize(
      lambda x: datetime.timedelta(days=x), otypes="O")
  
  
  def num2timedelta(x):
      """
      Convert number of days to a `~datetime.timedelta` object.
  
      If *x* is a sequence, a sequence of `~datetime.timedelta` objects will
      be returned.
  
      Parameters
      ----------
      x : float, sequence of floats
          Number of days. The fraction part represents hours, minutes, seconds.
  
      Returns
      -------
      `datetime.timedelta` or list[`datetime.timedelta`]
      """
      return _ordinalf_to_timedelta_np_vectorized(x).tolist()
  
  
  def drange(dstart, dend, delta):
      """
      Return a sequence of equally spaced Matplotlib dates.
  
      The dates start at *dstart* and reach up to, but not including *dend*.
      They are spaced by *delta*.
  
      Parameters
      ----------
      dstart, dend : `~datetime.datetime`
          The date limits.
      delta : `datetime.timedelta`
          Spacing of the dates.
  
      Returns
      -------
      `numpy.array`
          A list floats representing Matplotlib dates.
  
      """
      f1 = date2num(dstart)
      f2 = date2num(dend)
      step = delta.total_seconds() / SEC_PER_DAY
  
      # calculate the difference between dend and dstart in times of delta
      num = int(np.ceil((f2 - f1) / step))
  
      # calculate end of the interval which will be generated
      dinterval_end = dstart + num * delta
  
      # ensure, that a half open interval will be generated [dstart, dend)
      if dinterval_end >= dend:
          # if the endpoint is greater than or equal to dend,
          # just subtract one delta
          dinterval_end -= delta
          num -= 1
  
      f2 = date2num(dinterval_end)  # new float-endpoint
      return np.linspace(f1, f2, num + 1)
  
  
  def _wrap_in_tex(text):
      p = r'([a-zA-Z]+)'
      ret_text = re.sub(p, r'}$\1$\\mathdefault{', text)
  
      # Braces ensure symbols are not spaced like binary operators.
      ret_text = ret_text.replace('-', '{-}').replace(':', '{:}')
      # To not concatenate space between numbers.
      ret_text = ret_text.replace(' ', r'\;')
      ret_text = '$\\mathdefault{' + ret_text + '}$'
      ret_text = ret_text.replace('$\\mathdefault{}$', '')
      return ret_text
  
  
  ## date tick locators and formatters ###
  
  
  class DateFormatter(ticker.Formatter):
      """
      Format a tick (in days since the epoch) with a
      `~datetime.datetime.strftime` format string.
      """
  
      def __init__(self, fmt, tz=None, *, usetex=None):
          """
          Parameters
          ----------
          fmt : str
              `~datetime.datetime.strftime` format string
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          usetex : bool, default: :rc:`text.usetex`
              To enable/disable the use of TeX's math mode for rendering the
              results of the formatter.
          """
          self.tz = _get_tzinfo(tz)
          self.fmt = fmt
          self._usetex = mpl._val_or_rc(usetex, 'text.usetex')
  
      def __call__(self, x, pos=0):
          result = num2date(x, self.tz).strftime(self.fmt)
          return _wrap_in_tex(result) if self._usetex else result
  
      def set_tzinfo(self, tz):
          self.tz = _get_tzinfo(tz)
  
  
  class ConciseDateFormatter(ticker.Formatter):
      """
      A `.Formatter` which attempts to figure out the best format to use for the
      date, and to make it as compact as possible, but still be complete. This is
      most useful when used with the `AutoDateLocator`::
  
      >>> locator = AutoDateLocator()
      >>> formatter = ConciseDateFormatter(locator)
  
      Parameters
      ----------
      locator : `.ticker.Locator`
          Locator that this axis is using.
  
      tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
          Ticks timezone, passed to `.dates.num2date`.
  
      formats : list of 6 strings, optional
          Format strings for 6 levels of tick labelling: mostly years,
          months, days, hours, minutes, and seconds.  Strings use
          the same format codes as `~datetime.datetime.strftime`.  Default is
          ``['%Y', '%b', '%d', '%H:%M', '%H:%M', '%S.%f']``
  
      zero_formats : list of 6 strings, optional
          Format strings for tick labels that are "zeros" for a given tick
          level.  For instance, if most ticks are months, ticks around 1 Jan 2005
          will be labeled "Dec", "2005", "Feb".  The default is
          ``['', '%Y', '%b', '%b-%d', '%H:%M', '%H:%M']``
  
      offset_formats : list of 6 strings, optional
          Format strings for the 6 levels that is applied to the "offset"
          string found on the right side of an x-axis, or top of a y-axis.
          Combined with the tick labels this should completely specify the
          date.  The default is::
  
              ['', '%Y', '%Y-%b', '%Y-%b-%d', '%Y-%b-%d', '%Y-%b-%d %H:%M']
  
      show_offset : bool, default: True
          Whether to show the offset or not.
  
      usetex : bool, default: :rc:`text.usetex`
          To enable/disable the use of TeX's math mode for rendering the results
          of the formatter.
  
      Examples
      --------
      See :doc:`/gallery/ticks/date_concise_formatter`
  
      .. plot::
  
          import datetime
          import matplotlib.dates as mdates
  
          base = datetime.datetime(2005, 2, 1)
          dates = np.array([base + datetime.timedelta(hours=(2 * i))
                            for i in range(732)])
          N = len(dates)
          np.random.seed(19680801)
          y = np.cumsum(np.random.randn(N))
  
          fig, ax = plt.subplots(constrained_layout=True)
          locator = mdates.AutoDateLocator()
          formatter = mdates.ConciseDateFormatter(locator)
          ax.xaxis.set_major_locator(locator)
          ax.xaxis.set_major_formatter(formatter)
  
          ax.plot(dates, y)
          ax.set_title('Concise Date Formatter')
  
      """
  
      def __init__(self, locator, tz=None, formats=None, offset_formats=None,
                   zero_formats=None, show_offset=True, *, usetex=None):
          """
          Autoformat the date labels.  The default format is used to form an
          initial string, and then redundant elements are removed.
          """
          self._locator = locator
          self._tz = tz
          self.defaultfmt = '%Y'
          # there are 6 levels with each level getting a specific format
          # 0: mostly years,  1: months,  2: days,
          # 3: hours, 4: minutes, 5: seconds
          if formats:
              if len(formats) != 6:
                  raise ValueError('formats argument must be a list of '
                                   '6 format strings (or None)')
              self.formats = formats
          else:
              self.formats = ['%Y',  # ticks are mostly years
                              '%b',          # ticks are mostly months
                              '%d',          # ticks are mostly days
                              '%H:%M',       # hrs
                              '%H:%M',       # min
                              '%S.%f',       # secs
                              ]
          # fmt for zeros ticks at this level.  These are
          # ticks that should be labeled w/ info the level above.
          # like 1 Jan can just be labelled "Jan".  02:02:00 can
          # just be labeled 02:02.
          if zero_formats:
              if len(zero_formats) != 6:
                  raise ValueError('zero_formats argument must be a list of '
                                   '6 format strings (or None)')
              self.zero_formats = zero_formats
          elif formats:
              # use the users formats for the zero tick formats
              self.zero_formats = [''] + self.formats[:-1]
          else:
              # make the defaults a bit nicer:
              self.zero_formats = [''] + self.formats[:-1]
              self.zero_formats[3] = '%b-%d'
  
          if offset_formats:
              if len(offset_formats) != 6:
                  raise ValueError('offset_formats argument must be a list of '
                                   '6 format strings (or None)')
              self.offset_formats = offset_formats
          else:
              self.offset_formats = ['',
                                     '%Y',
                                     '%Y-%b',
                                     '%Y-%b-%d',
                                     '%Y-%b-%d',
                                     '%Y-%b-%d %H:%M']
          self.offset_string = ''
          self.show_offset = show_offset
          self._usetex = mpl._val_or_rc(usetex, 'text.usetex')
  
      def __call__(self, x, pos=None):
          formatter = DateFormatter(self.defaultfmt, self._tz,
                                    usetex=self._usetex)
          return formatter(x, pos=pos)
  
      def format_ticks(self, values):
          tickdatetime = [num2date(value, tz=self._tz) for value in values]
          tickdate = np.array([tdt.timetuple()[:6] for tdt in tickdatetime])
  
          # basic algorithm:
          # 1) only display a part of the date if it changes over the ticks.
          # 2) don't display the smaller part of the date if:
          #    it is always the same or if it is the start of the
          #    year, month, day etc.
          # fmt for most ticks at this level
          fmts = self.formats
          # format beginnings of days, months, years, etc.
          zerofmts = self.zero_formats
          # offset fmt are for the offset in the upper left of the
          # or lower right of the axis.
          offsetfmts = self.offset_formats
          show_offset = self.show_offset
  
          # determine the level we will label at:
          # mostly 0: years,  1: months,  2: days,
          # 3: hours, 4: minutes, 5: seconds, 6: microseconds
          for level in range(5, -1, -1):
              unique = np.unique(tickdate[:, level])
              if len(unique) > 1:
                  # if 1 is included in unique, the year is shown in ticks
                  if level < 2 and np.any(unique == 1):
                      show_offset = False
                  break
              elif level == 0:
                  # all tickdate are the same, so only micros might be different
                  # set to the most precise (6: microseconds doesn't exist...)
                  level = 5
  
          # level is the basic level we will label at.
          # now loop through and decide the actual ticklabels
          zerovals = [0, 1, 1, 0, 0, 0, 0]
          labels = [''] * len(tickdate)
          for nn in range(len(tickdate)):
              if level < 5:
                  if tickdate[nn][level] == zerovals[level]:
                      fmt = zerofmts[level]
                  else:
                      fmt = fmts[level]
              else:
                  # special handling for seconds + microseconds
                  if (tickdatetime[nn].second == tickdatetime[nn].microsecond
                          == 0):
                      fmt = zerofmts[level]
                  else:
                      fmt = fmts[level]
              labels[nn] = tickdatetime[nn].strftime(fmt)
  
          # special handling of seconds and microseconds:
          # strip extra zeros and decimal if possible.
          # this is complicated by two factors.  1) we have some level-4 strings
          # here (i.e. 03:00, '0.50000', '1.000') 2) we would like to have the
          # same number of decimals for each string (i.e. 0.5 and 1.0).
          if level >= 5:
              trailing_zeros = min(
                  (len(s) - len(s.rstrip('0')) for s in labels if '.' in s),
                  default=None)
              if trailing_zeros:
                  for nn in range(len(labels)):
                      if '.' in labels[nn]:
                          labels[nn] = labels[nn][:-trailing_zeros].rstrip('.')
  
          if show_offset:
              # set the offset string:
              if (self._locator.axis and
                      self._locator.axis.__name__ in ('xaxis', 'yaxis')
                      and self._locator.axis.get_inverted()):
                  self.offset_string = tickdatetime[0].strftime(offsetfmts[level])
              else:
                  self.offset_string = tickdatetime[-1].strftime(offsetfmts[level])
              if self._usetex:
                  self.offset_string = _wrap_in_tex(self.offset_string)
          else:
              self.offset_string = ''
  
          if self._usetex:
              return [_wrap_in_tex(l) for l in labels]
          else:
              return labels
  
      def get_offset(self):
          return self.offset_string
  
      def format_data_short(self, value):
          return num2date(value, tz=self._tz).strftime('%Y-%m-%d %H:%M:%S')
  
  
  class AutoDateFormatter(ticker.Formatter):
      """
      A `.Formatter` which attempts to figure out the best format to use.  This
      is most useful when used with the `AutoDateLocator`.
  
      `.AutoDateFormatter` has a ``.scale`` dictionary that maps tick scales (the
      interval in days between one major tick) to format strings; this dictionary
      defaults to ::
  
          self.scaled = {
              DAYS_PER_YEAR: rcParams['date.autoformatter.year'],
              DAYS_PER_MONTH: rcParams['date.autoformatter.month'],
              1: rcParams['date.autoformatter.day'],
              1 / HOURS_PER_DAY: rcParams['date.autoformatter.hour'],
              1 / MINUTES_PER_DAY: rcParams['date.autoformatter.minute'],
              1 / SEC_PER_DAY: rcParams['date.autoformatter.second'],
              1 / MUSECONDS_PER_DAY: rcParams['date.autoformatter.microsecond'],
          }
  
      The formatter uses the format string corresponding to the lowest key in
      the dictionary that is greater or equal to the current scale.  Dictionary
      entries can be customized::
  
          locator = AutoDateLocator()
          formatter = AutoDateFormatter(locator)
          formatter.scaled[1/(24*60)] = '%M:%S' # only show min and sec
  
      Custom callables can also be used instead of format strings.  The following
      example shows how to use a custom format function to strip trailing zeros
      from decimal seconds and adds the date to the first ticklabel::
  
          def my_format_function(x, pos=None):
              x = matplotlib.dates.num2date(x)
              if pos == 0:
                  fmt = '%D %H:%M:%S.%f'
              else:
                  fmt = '%H:%M:%S.%f'
              label = x.strftime(fmt)
              label = label.rstrip("0")
              label = label.rstrip(".")
              return label
  
          formatter.scaled[1/(24*60)] = my_format_function
      """
  
      # This can be improved by providing some user-level direction on
      # how to choose the best format (precedence, etc.).
  
      # Perhaps a 'struct' that has a field for each time-type where a
      # zero would indicate "don't show" and a number would indicate
      # "show" with some sort of priority.  Same priorities could mean
      # show all with the same priority.
  
      # Or more simply, perhaps just a format string for each
      # possibility...
  
      def __init__(self, locator, tz=None, defaultfmt='%Y-%m-%d', *,
                   usetex=None):
          """
          Autoformat the date labels.
  
          Parameters
          ----------
          locator : `.ticker.Locator`
              Locator that this axis is using.
  
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
  
          defaultfmt : str
              The default format to use if none of the values in ``self.scaled``
              are greater than the unit returned by ``locator._get_unit()``.
  
          usetex : bool, default: :rc:`text.usetex`
              To enable/disable the use of TeX's math mode for rendering the
              results of the formatter. If any entries in ``self.scaled`` are set
              as functions, then it is up to the customized function to enable or
              disable TeX's math mode itself.
          """
          self._locator = locator
          self._tz = tz
          self.defaultfmt = defaultfmt
          self._formatter = DateFormatter(self.defaultfmt, tz)
          rcParams = mpl.rcParams
          self._usetex = mpl._val_or_rc(usetex, 'text.usetex')
          self.scaled = {
              DAYS_PER_YEAR: rcParams['date.autoformatter.year'],
              DAYS_PER_MONTH: rcParams['date.autoformatter.month'],
              1: rcParams['date.autoformatter.day'],
              1 / HOURS_PER_DAY: rcParams['date.autoformatter.hour'],
              1 / MINUTES_PER_DAY: rcParams['date.autoformatter.minute'],
              1 / SEC_PER_DAY: rcParams['date.autoformatter.second'],
              1 / MUSECONDS_PER_DAY: rcParams['date.autoformatter.microsecond']
          }
  
      def _set_locator(self, locator):
          self._locator = locator
  
      def __call__(self, x, pos=None):
          try:
              locator_unit_scale = float(self._locator._get_unit())
          except AttributeError:
              locator_unit_scale = 1
          # Pick the first scale which is greater than the locator unit.
          fmt = next((fmt for scale, fmt in sorted(self.scaled.items())
                      if scale >= locator_unit_scale),
                     self.defaultfmt)
  
          if isinstance(fmt, str):
              self._formatter = DateFormatter(fmt, self._tz, usetex=self._usetex)
              result = self._formatter(x, pos)
          elif callable(fmt):
              result = fmt(x, pos)
          else:
              raise TypeError(f'Unexpected type passed to {self!r}.')
  
          return result
  
  
  class rrulewrapper:
      """
      A simple wrapper around a `dateutil.rrule` allowing flexible
      date tick specifications.
      """
      def __init__(self, freq, tzinfo=None, **kwargs):
          """
          Parameters
          ----------
          freq : {YEARLY, MONTHLY, WEEKLY, DAILY, HOURLY, MINUTELY, SECONDLY}
              Tick frequency. These constants are defined in `dateutil.rrule`,
              but they are accessible from `matplotlib.dates` as well.
          tzinfo : `datetime.tzinfo`, optional
              Time zone information. The default is None.
          **kwargs
              Additional keyword arguments are passed to the `dateutil.rrule`.
          """
          kwargs['freq'] = freq
          self._base_tzinfo = tzinfo
  
          self._update_rrule(**kwargs)
  
      def set(self, **kwargs):
          """Set parameters for an existing wrapper."""
          self._construct.update(kwargs)
  
          self._update_rrule(**self._construct)
  
      def _update_rrule(self, **kwargs):
          tzinfo = self._base_tzinfo
  
          # rrule does not play nicely with timezones - especially pytz time
          # zones, it's best to use naive zones and attach timezones once the
          # datetimes are returned
          if 'dtstart' in kwargs:
              dtstart = kwargs['dtstart']
              if dtstart.tzinfo is not None:
                  if tzinfo is None:
                      tzinfo = dtstart.tzinfo
                  else:
                      dtstart = dtstart.astimezone(tzinfo)
  
                  kwargs['dtstart'] = dtstart.replace(tzinfo=None)
  
          if 'until' in kwargs:
              until = kwargs['until']
              if until.tzinfo is not None:
                  if tzinfo is not None:
                      until = until.astimezone(tzinfo)
                  else:
                      raise ValueError('until cannot be aware if dtstart '
                                       'is naive and tzinfo is None')
  
                  kwargs['until'] = until.replace(tzinfo=None)
  
          self._construct = kwargs.copy()
          self._tzinfo = tzinfo
          self._rrule = rrule(**self._construct)
  
      def _attach_tzinfo(self, dt, tzinfo):
          # pytz zones are attached by "localizing" the datetime
          if hasattr(tzinfo, 'localize'):
              return tzinfo.localize(dt, is_dst=True)
  
          return dt.replace(tzinfo=tzinfo)
  
      def _aware_return_wrapper(self, f, returns_list=False):
          """Decorator function that allows rrule methods to handle tzinfo."""
          # This is only necessary if we're actually attaching a tzinfo
          if self._tzinfo is None:
              return f
  
          # All datetime arguments must be naive. If they are not naive, they are
          # converted to the _tzinfo zone before dropping the zone.
          def normalize_arg(arg):
              if isinstance(arg, datetime.datetime) and arg.tzinfo is not None:
                  if arg.tzinfo is not self._tzinfo:
                      arg = arg.astimezone(self._tzinfo)
  
                  return arg.replace(tzinfo=None)
  
              return arg
  
          def normalize_args(args, kwargs):
              args = tuple(normalize_arg(arg) for arg in args)
              kwargs = {kw: normalize_arg(arg) for kw, arg in kwargs.items()}
  
              return args, kwargs
  
          # There are two kinds of functions we care about - ones that return
          # dates and ones that return lists of dates.
          if not returns_list:
              def inner_func(*args, **kwargs):
                  args, kwargs = normalize_args(args, kwargs)
                  dt = f(*args, **kwargs)
                  return self._attach_tzinfo(dt, self._tzinfo)
          else:
              def inner_func(*args, **kwargs):
                  args, kwargs = normalize_args(args, kwargs)
                  dts = f(*args, **kwargs)
                  return [self._attach_tzinfo(dt, self._tzinfo) for dt in dts]
  
          return functools.wraps(f)(inner_func)
  
      def __getattr__(self, name):
          if name in self.__dict__:
              return self.__dict__[name]
  
          f = getattr(self._rrule, name)
  
          if name in {'after', 'before'}:
              return self._aware_return_wrapper(f)
          elif name in {'xafter', 'xbefore', 'between'}:
              return self._aware_return_wrapper(f, returns_list=True)
          else:
              return f
  
      def __setstate__(self, state):
          self.__dict__.update(state)
  
  
  class DateLocator(ticker.Locator):
      """
      Determines the tick locations when plotting dates.
  
      This class is subclassed by other Locators and
      is not meant to be used on its own.
      """
      hms0d = {'byhour': 0, 'byminute': 0, 'bysecond': 0}
  
      def __init__(self, tz=None):
          """
          Parameters
          ----------
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          self.tz = _get_tzinfo(tz)
  
      def set_tzinfo(self, tz):
          """
          Set timezone info.
  
          Parameters
          ----------
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          self.tz = _get_tzinfo(tz)
  
      def datalim_to_dt(self):
          """Convert axis data interval to datetime objects."""
          dmin, dmax = self.axis.get_data_interval()
          if dmin > dmax:
              dmin, dmax = dmax, dmin
  
          return num2date(dmin, self.tz), num2date(dmax, self.tz)
  
      def viewlim_to_dt(self):
          """Convert the view interval to datetime objects."""
          vmin, vmax = self.axis.get_view_interval()
          if vmin > vmax:
              vmin, vmax = vmax, vmin
          return num2date(vmin, self.tz), num2date(vmax, self.tz)
  
      def _get_unit(self):
          """
          Return how many days a unit of the locator is; used for
          intelligent autoscaling.
          """
          return 1
  
      def _get_interval(self):
          """
          Return the number of units for each tick.
          """
          return 1
  
      def nonsingular(self, vmin, vmax):
          """
          Given the proposed upper and lower extent, adjust the range
          if it is too close to being singular (i.e. a range of ~0).
          """
          if not np.isfinite(vmin) or not np.isfinite(vmax):
              # Except if there is no data, then use 1970 as default.
              return (date2num(datetime.date(1970, 1, 1)),
                      date2num(datetime.date(1970, 1, 2)))
          if vmax < vmin:
              vmin, vmax = vmax, vmin
          unit = self._get_unit()
          interval = self._get_interval()
          if abs(vmax - vmin) < 1e-6:
              vmin -= 2 * unit * interval
              vmax += 2 * unit * interval
          return vmin, vmax
  
  
  class RRuleLocator(DateLocator):
      # use the dateutil rrule instance
  
      def __init__(self, o, tz=None):
          super().__init__(tz)
          self.rule = o
  
      def __call__(self):
          # if no data have been set, this will tank with a ValueError
          try:
              dmin, dmax = self.viewlim_to_dt()
          except ValueError:
              return []
  
          return self.tick_values(dmin, dmax)
  
      def tick_values(self, vmin, vmax):
          start, stop = self._create_rrule(vmin, vmax)
          dates = self.rule.between(start, stop, True)
          if len(dates) == 0:
              return date2num([vmin, vmax])
          return self.raise_if_exceeds(date2num(dates))
  
      def _create_rrule(self, vmin, vmax):
          # set appropriate rrule dtstart and until and return
          # start and end
          delta = relativedelta(vmax, vmin)
  
          # We need to cap at the endpoints of valid datetime
          try:
              start = vmin - delta
          except (ValueError, OverflowError):
              # cap
              start = datetime.datetime(1, 1, 1, 0, 0, 0,
                                        tzinfo=datetime.timezone.utc)
  
          try:
              stop = vmax + delta
          except (ValueError, OverflowError):
              # cap
              stop = datetime.datetime(9999, 12, 31, 23, 59, 59,
                                       tzinfo=datetime.timezone.utc)
  
          self.rule.set(dtstart=start, until=stop)
  
          return vmin, vmax
  
      def _get_unit(self):
          # docstring inherited
          freq = self.rule._rrule._freq
          return self.get_unit_generic(freq)
  
      @staticmethod
      def get_unit_generic(freq):
          if freq == YEARLY:
              return DAYS_PER_YEAR
          elif freq == MONTHLY:
              return DAYS_PER_MONTH
          elif freq == WEEKLY:
              return DAYS_PER_WEEK
          elif freq == DAILY:
              return 1.0
          elif freq == HOURLY:
              return 1.0 / HOURS_PER_DAY
          elif freq == MINUTELY:
              return 1.0 / MINUTES_PER_DAY
          elif freq == SECONDLY:
              return 1.0 / SEC_PER_DAY
          else:
              # error
              return -1  # or should this just return '1'?
  
      def _get_interval(self):
          return self.rule._rrule._interval
  
  
  class AutoDateLocator(DateLocator):
      """
      On autoscale, this class picks the best `DateLocator` to set the view
      limits and the tick locations.
  
      Attributes
      ----------
      intervald : dict
  
          Mapping of tick frequencies to multiples allowed for that ticking.
          The default is ::
  
              self.intervald = {
                  YEARLY  : [1, 2, 4, 5, 10, 20, 40, 50, 100, 200, 400, 500,
                             1000, 2000, 4000, 5000, 10000],
                  MONTHLY : [1, 2, 3, 4, 6],
                  DAILY   : [1, 2, 3, 7, 14, 21],
                  HOURLY  : [1, 2, 3, 4, 6, 12],
                  MINUTELY: [1, 5, 10, 15, 30],
                  SECONDLY: [1, 5, 10, 15, 30],
                  MICROSECONDLY: [1, 2, 5, 10, 20, 50, 100, 200, 500,
                                  1000, 2000, 5000, 10000, 20000, 50000,
                                  100000, 200000, 500000, 1000000],
              }
  
          where the keys are defined in `dateutil.rrule`.
  
          The interval is used to specify multiples that are appropriate for
          the frequency of ticking. For instance, every 7 days is sensible
          for daily ticks, but for minutes/seconds, 15 or 30 make sense.
  
          When customizing, you should only modify the values for the existing
          keys. You should not add or delete entries.
  
          Example for forcing ticks every 3 hours::
  
              locator = AutoDateLocator()
              locator.intervald[HOURLY] = [3]  # only show every 3 hours
      """
  
      def __init__(self, tz=None, minticks=5, maxticks=None,
                   interval_multiples=True):
          """
          Parameters
          ----------
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          minticks : int
              The minimum number of ticks desired; controls whether ticks occur
              yearly, monthly, etc.
          maxticks : int
              The maximum number of ticks desired; controls the interval between
              ticks (ticking every other, every 3, etc.).  For fine-grained
              control, this can be a dictionary mapping individual rrule
              frequency constants (YEARLY, MONTHLY, etc.) to their own maximum
              number of ticks.  This can be used to keep the number of ticks
              appropriate to the format chosen in `AutoDateFormatter`. Any
              frequency not specified in this dictionary is given a default
              value.
          interval_multiples : bool, default: True
              Whether ticks should be chosen to be multiple of the interval,
              locking them to 'nicer' locations.  For example, this will force
              the ticks to be at hours 0, 6, 12, 18 when hourly ticking is done
              at 6 hour intervals.
          """
          super().__init__(tz=tz)
          self._freq = YEARLY
          self._freqs = [YEARLY, MONTHLY, DAILY, HOURLY, MINUTELY,
                         SECONDLY, MICROSECONDLY]
          self.minticks = minticks
  
          self.maxticks = {YEARLY: 11, MONTHLY: 12, DAILY: 11, HOURLY: 12,
                           MINUTELY: 11, SECONDLY: 11, MICROSECONDLY: 8}
          if maxticks is not None:
              try:
                  self.maxticks.update(maxticks)
              except TypeError:
                  # Assume we were given an integer. Use this as the maximum
                  # number of ticks for every frequency and create a
                  # dictionary for this
                  self.maxticks = dict.fromkeys(self._freqs, maxticks)
          self.interval_multiples = interval_multiples
          self.intervald = {
              YEARLY:   [1, 2, 4, 5, 10, 20, 40, 50, 100, 200, 400, 500,
                         1000, 2000, 4000, 5000, 10000],
              MONTHLY:  [1, 2, 3, 4, 6],
              DAILY:    [1, 2, 3, 7, 14, 21],
              HOURLY:   [1, 2, 3, 4, 6, 12],
              MINUTELY: [1, 5, 10, 15, 30],
              SECONDLY: [1, 5, 10, 15, 30],
              MICROSECONDLY: [1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000,
                              5000, 10000, 20000, 50000, 100000, 200000, 500000,
                              1000000],
                              }
          if interval_multiples:
              # Swap "3" for "4" in the DAILY list; If we use 3 we get bad
              # tick loc for months w/ 31 days: 1, 4, ..., 28, 31, 1
              # If we use 4 then we get: 1, 5, ... 25, 29, 1
              self.intervald[DAILY] = [1, 2, 4, 7, 14]
  
          self._byranges = [None, range(1, 13), range(1, 32),
                            range(0, 24), range(0, 60), range(0, 60), None]
  
      def __call__(self):
          # docstring inherited
          dmin, dmax = self.viewlim_to_dt()
          locator = self.get_locator(dmin, dmax)
          return locator()
  
      def tick_values(self, vmin, vmax):
          return self.get_locator(vmin, vmax).tick_values(vmin, vmax)
  
      def nonsingular(self, vmin, vmax):
          # whatever is thrown at us, we can scale the unit.
          # But default nonsingular date plots at an ~4 year period.
          if not np.isfinite(vmin) or not np.isfinite(vmax):
              # Except if there is no data, then use 1970 as default.
              return (date2num(datetime.date(1970, 1, 1)),
                      date2num(datetime.date(1970, 1, 2)))
          if vmax < vmin:
              vmin, vmax = vmax, vmin
          if vmin == vmax:
              vmin = vmin - DAYS_PER_YEAR * 2
              vmax = vmax + DAYS_PER_YEAR * 2
          return vmin, vmax
  
      def _get_unit(self):
          if self._freq in [MICROSECONDLY]:
              return 1. / MUSECONDS_PER_DAY
          else:
              return RRuleLocator.get_unit_generic(self._freq)
  
      def get_locator(self, dmin, dmax):
          """Pick the best locator based on a distance."""
          delta = relativedelta(dmax, dmin)
          tdelta = dmax - dmin
  
          # take absolute difference
          if dmin > dmax:
              delta = -delta
              tdelta = -tdelta
          # The following uses a mix of calls to relativedelta and timedelta
          # methods because there is incomplete overlap in the functionality of
          # these similar functions, and it's best to avoid doing our own math
          # whenever possible.
          numYears = float(delta.years)
          numMonths = numYears * MONTHS_PER_YEAR + delta.months
          numDays = tdelta.days  # Avoids estimates of days/month, days/year.
          numHours = numDays * HOURS_PER_DAY + delta.hours
          numMinutes = numHours * MIN_PER_HOUR + delta.minutes
          numSeconds = np.floor(tdelta.total_seconds())
          numMicroseconds = np.floor(tdelta.total_seconds() * 1e6)
  
          nums = [numYears, numMonths, numDays, numHours, numMinutes,
                  numSeconds, numMicroseconds]
  
          use_rrule_locator = [True] * 6 + [False]
  
          # Default setting of bymonth, etc. to pass to rrule
          # [unused (for year), bymonth, bymonthday, byhour, byminute,
          #  bysecond, unused (for microseconds)]
          byranges = [None, 1, 1, 0, 0, 0, None]
  
          # Loop over all the frequencies and try to find one that gives at
          # least a minticks tick positions.  Once this is found, look for
          # an interval from a list specific to that frequency that gives no
          # more than maxticks tick positions. Also, set up some ranges
          # (bymonth, etc.) as appropriate to be passed to rrulewrapper.
          for i, (freq, num) in enumerate(zip(self._freqs, nums)):
              # If this particular frequency doesn't give enough ticks, continue
              if num < self.minticks:
                  # Since we're not using this particular frequency, set
                  # the corresponding by_ to None so the rrule can act as
                  # appropriate
                  byranges[i] = None
                  continue
  
              # Find the first available interval that doesn't give too many
              # ticks
              for interval in self.intervald[freq]:
                  if num <= interval * (self.maxticks[freq] - 1):
                      break
              else:
                  if not (self.interval_multiples and freq == DAILY):
                      _api.warn_external(
                          f"AutoDateLocator was unable to pick an appropriate "
                          f"interval for this date range. It may be necessary "
                          f"to add an interval value to the AutoDateLocator's "
                          f"intervald dictionary. Defaulting to {interval}.")
  
              # Set some parameters as appropriate
              self._freq = freq
  
              if self._byranges[i] and self.interval_multiples:
                  byranges[i] = self._byranges[i][::interval]
                  if i in (DAILY, WEEKLY):
                      if interval == 14:
                          # just make first and 15th.  Avoids 30th.
                          byranges[i] = [1, 15]
                      elif interval == 7:
                          byranges[i] = [1, 8, 15, 22]
  
                  interval = 1
              else:
                  byranges[i] = self._byranges[i]
              break
          else:
              interval = 1
  
          if (freq == YEARLY) and self.interval_multiples:
              locator = YearLocator(interval, tz=self.tz)
          elif use_rrule_locator[i]:
              _, bymonth, bymonthday, byhour, byminute, bysecond, _ = byranges
              rrule = rrulewrapper(self._freq, interval=interval,
                                   dtstart=dmin, until=dmax,
                                   bymonth=bymonth, bymonthday=bymonthday,
                                   byhour=byhour, byminute=byminute,
                                   bysecond=bysecond)
  
              locator = RRuleLocator(rrule, tz=self.tz)
          else:
              locator = MicrosecondLocator(interval, tz=self.tz)
              if date2num(dmin) > 70 * 365 and interval < 1000:
                  _api.warn_external(
                      'Plotting microsecond time intervals for dates far from '
                      f'the epoch (time origin: {get_epoch()}) is not well-'
                      'supported. See matplotlib.dates.set_epoch to change the '
                      'epoch.')
  
          locator.set_axis(self.axis)
          return locator
  
  
  class YearLocator(RRuleLocator):
      """
      Make ticks on a given day of each year that is a multiple of base.
  
      Examples::
  
        # Tick every year on Jan 1st
        locator = YearLocator()
  
        # Tick every 5 years on July 4th
        locator = YearLocator(5, month=7, day=4)
      """
      def __init__(self, base=1, month=1, day=1, tz=None):
          """
          Parameters
          ----------
          base : int, default: 1
              Mark ticks every *base* years.
          month : int, default: 1
              The month on which to place the ticks, starting from 1. Default is
              January.
          day : int, default: 1
              The day on which to place the ticks.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          rule = rrulewrapper(YEARLY, interval=base, bymonth=month,
                              bymonthday=day, **self.hms0d)
          super().__init__(rule, tz=tz)
          self.base = ticker._Edge_integer(base, 0)
  
      def _create_rrule(self, vmin, vmax):
          # 'start' needs to be a multiple of the interval to create ticks on
          # interval multiples when the tick frequency is YEARLY
          ymin = max(self.base.le(vmin.year) * self.base.step, 1)
          ymax = min(self.base.ge(vmax.year) * self.base.step, 9999)
  
          c = self.rule._construct
          replace = {'year': ymin,
                     'month': c.get('bymonth', 1),
                     'day': c.get('bymonthday', 1),
                     'hour': 0, 'minute': 0, 'second': 0}
  
          start = vmin.replace(**replace)
          stop = start.replace(year=ymax)
          self.rule.set(dtstart=start, until=stop)
  
          return start, stop
  
  
  class MonthLocator(RRuleLocator):
      """
      Make ticks on occurrences of each month, e.g., 1, 3, 12.
      """
      def __init__(self, bymonth=None, bymonthday=1, interval=1, tz=None):
          """
          Parameters
          ----------
          bymonth : int or list of int, default: all months
              Ticks will be placed on every month in *bymonth*. Default is
              ``range(1, 13)``, i.e. every month.
          bymonthday : int, default: 1
              The day on which to place the ticks.
          interval : int, default: 1
              The interval between each iteration. For example, if
              ``interval=2``, mark every second occurrence.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          if bymonth is None:
              bymonth = range(1, 13)
  
          rule = rrulewrapper(MONTHLY, bymonth=bymonth, bymonthday=bymonthday,
                              interval=interval, **self.hms0d)
          super().__init__(rule, tz=tz)
  
  
  class WeekdayLocator(RRuleLocator):
      """
      Make ticks on occurrences of each weekday.
      """
  
      def __init__(self, byweekday=1, interval=1, tz=None):
          """
          Parameters
          ----------
          byweekday : int, list of int, constant from :mod:`dateutil.rrule`, or \
              list of constants, default: 1 (Tuesday)
              Ticks will be placed on every weekday in *byweekday*. Default is
              every Tuesday.
  
              Elements of *byweekday* (if a sequence) must be either integers or
              MO, TU, WE, TH, FR, SA, SU, the constants from
              :mod:`dateutil.rrule`, which have been imported into the
              :mod:`matplotlib.dates` namespace.
          interval : int, default: 1
              The interval between each iteration. For example, if
              ``interval=2``, mark every second occurrence.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          rule = rrulewrapper(DAILY, byweekday=byweekday,
                              interval=interval, **self.hms0d)
          super().__init__(rule, tz=tz)
  
  
  class DayLocator(RRuleLocator):
      """
      Make ticks on occurrences of each day of the month.  For example,
      1, 15, 30.
      """
      def __init__(self, bymonthday=None, interval=1, tz=None):
          """
          Parameters
          ----------
          bymonthday : int or list of int, default: all days
              Ticks will be placed on every day in *bymonthday*. Default is
              ``bymonthday=range(1, 32)``, i.e., every day of the month.
          interval : int, default: 1
              The interval between each iteration. For example, if
              ``interval=2``, mark every second occurrence.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          if interval != int(interval) or interval < 1:
              raise ValueError("interval must be an integer greater than 0")
          if bymonthday is None:
              bymonthday = range(1, 32)
  
          rule = rrulewrapper(DAILY, bymonthday=bymonthday,
                              interval=interval, **self.hms0d)
          super().__init__(rule, tz=tz)
  
  
  class HourLocator(RRuleLocator):
      """
      Make ticks on occurrences of each hour.
      """
      def __init__(self, byhour=None, interval=1, tz=None):
          """
          Parameters
          ----------
          byhour : int or list of int, default: all hours
              Ticks will be placed on every hour in *byhour*. Default is
              ``byhour=range(24)``, i.e., every hour.
          interval : int, default: 1
              The interval between each iteration. For example, if
              ``interval=2``, mark every second occurrence.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          if byhour is None:
              byhour = range(24)
  
          rule = rrulewrapper(HOURLY, byhour=byhour, interval=interval,
                              byminute=0, bysecond=0)
          super().__init__(rule, tz=tz)
  
  
  class MinuteLocator(RRuleLocator):
      """
      Make ticks on occurrences of each minute.
      """
      def __init__(self, byminute=None, interval=1, tz=None):
          """
          Parameters
          ----------
          byminute : int or list of int, default: all minutes
              Ticks will be placed on every minute in *byminute*. Default is
              ``byminute=range(60)``, i.e., every minute.
          interval : int, default: 1
              The interval between each iteration. For example, if
              ``interval=2``, mark every second occurrence.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          if byminute is None:
              byminute = range(60)
  
          rule = rrulewrapper(MINUTELY, byminute=byminute, interval=interval,
                              bysecond=0)
          super().__init__(rule, tz=tz)
  
  
  class SecondLocator(RRuleLocator):
      """
      Make ticks on occurrences of each second.
      """
      def __init__(self, bysecond=None, interval=1, tz=None):
          """
          Parameters
          ----------
          bysecond : int or list of int, default: all seconds
              Ticks will be placed on every second in *bysecond*. Default is
              ``bysecond = range(60)``, i.e., every second.
          interval : int, default: 1
              The interval between each iteration. For example, if
              ``interval=2``, mark every second occurrence.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          if bysecond is None:
              bysecond = range(60)
  
          rule = rrulewrapper(SECONDLY, bysecond=bysecond, interval=interval)
          super().__init__(rule, tz=tz)
  
  
  class MicrosecondLocator(DateLocator):
      """
      Make ticks on regular intervals of one or more microsecond(s).
  
      .. note::
  
          By default, Matplotlib uses a floating point representation of time in
          days since the epoch, so plotting data with
          microsecond time resolution does not work well for
          dates that are far (about 70 years) from the epoch (check with
          `~.dates.get_epoch`).
  
          If you want sub-microsecond resolution time plots, it is strongly
          recommended to use floating point seconds, not datetime-like
          time representation.
  
          If you really must use datetime.datetime() or similar and still
          need microsecond precision, change the time origin via
          `.dates.set_epoch` to something closer to the dates being plotted.
          See :doc:`/gallery/ticks/date_precision_and_epochs`.
  
      """
      def __init__(self, interval=1, tz=None):
          """
          Parameters
          ----------
          interval : int, default: 1
              The interval between each iteration. For example, if
              ``interval=2``, mark every second occurrence.
          tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
              Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
          """
          super().__init__(tz=tz)
          self._interval = interval
          self._wrapped_locator = ticker.MultipleLocator(interval)
  
      def set_axis(self, axis):
          self._wrapped_locator.set_axis(axis)
          return super().set_axis(axis)
  
      def __call__(self):
          # if no data have been set, this will tank with a ValueError
          try:
              dmin, dmax = self.viewlim_to_dt()
          except ValueError:
              return []
  
          return self.tick_values(dmin, dmax)
  
      def tick_values(self, vmin, vmax):
          nmin, nmax = date2num((vmin, vmax))
          t0 = np.floor(nmin)
          nmax = nmax - t0
          nmin = nmin - t0
          nmin *= MUSECONDS_PER_DAY
          nmax *= MUSECONDS_PER_DAY
  
          ticks = self._wrapped_locator.tick_values(nmin, nmax)
  
          ticks = ticks / MUSECONDS_PER_DAY + t0
          return ticks
  
      def _get_unit(self):
          # docstring inherited
          return 1. / MUSECONDS_PER_DAY
  
      def _get_interval(self):
          # docstring inherited
          return self._interval
  
  
  class DateConverter(units.ConversionInterface):
      """
      Converter for `datetime.date` and `datetime.datetime` data, or for
      date/time data represented as it would be converted by `date2num`.
  
      The 'unit' tag for such data is None or a `~datetime.tzinfo` instance.
      """
  
      def __init__(self, *, interval_multiples=True):
          self._interval_multiples = interval_multiples
          super().__init__()
  
      def axisinfo(self, unit, axis):
          """
          Return the `~matplotlib.units.AxisInfo` for *unit*.
  
          *unit* is a `~datetime.tzinfo` instance or None.
          The *axis* argument is required but not used.
          """
          tz = unit
  
          majloc = AutoDateLocator(tz=tz,
                                   interval_multiples=self._interval_multiples)
          majfmt = AutoDateFormatter(majloc, tz=tz)
          datemin = datetime.date(1970, 1, 1)
          datemax = datetime.date(1970, 1, 2)
  
          return units.AxisInfo(majloc=majloc, majfmt=majfmt, label='',
                                default_limits=(datemin, datemax))
  
      @staticmethod
      def convert(value, unit, axis):
          """
          If *value* is not already a number or sequence of numbers, convert it
          with `date2num`.
  
          The *unit* and *axis* arguments are not used.
          """
          return date2num(value)
  
      @staticmethod
      def default_units(x, axis):
          """
          Return the `~datetime.tzinfo` instance of *x* or of its first element,
          or None
          """
          if isinstance(x, np.ndarray):
              x = x.ravel()
  
          try:
              x = cbook._safe_first_finite(x)
          except (TypeError, StopIteration):
              pass
  
          try:
              return x.tzinfo
          except AttributeError:
              pass
          return None
  
  
  class ConciseDateConverter(DateConverter):
      # docstring inherited
  
      def __init__(self, formats=None, zero_formats=None, offset_formats=None,
                   show_offset=True, *, interval_multiples=True):
          self._formats = formats
          self._zero_formats = zero_formats
          self._offset_formats = offset_formats
          self._show_offset = show_offset
          self._interval_multiples = interval_multiples
          super().__init__()
  
      def axisinfo(self, unit, axis):
          # docstring inherited
          tz = unit
          majloc = AutoDateLocator(tz=tz,
                                   interval_multiples=self._interval_multiples)
          majfmt = ConciseDateFormatter(majloc, tz=tz, formats=self._formats,
                                        zero_formats=self._zero_formats,
                                        offset_formats=self._offset_formats,
                                        show_offset=self._show_offset)
          datemin = datetime.date(1970, 1, 1)
          datemax = datetime.date(1970, 1, 2)
          return units.AxisInfo(majloc=majloc, majfmt=majfmt, label='',
                                default_limits=(datemin, datemax))
  
  
  class _SwitchableDateConverter:
      """
      Helper converter-like object that generates and dispatches to
      temporary ConciseDateConverter or DateConverter instances based on
      :rc:`date.converter` and :rc:`date.interval_multiples`.
      """
  
      @staticmethod
      def _get_converter():
          converter_cls = {
              "concise": ConciseDateConverter, "auto": DateConverter}[
                  mpl.rcParams["date.converter"]]
          interval_multiples = mpl.rcParams["date.interval_multiples"]
          return converter_cls(interval_multiples=interval_multiples)
  
      def axisinfo(self, *args, **kwargs):
          return self._get_converter().axisinfo(*args, **kwargs)
  
      def default_units(self, *args, **kwargs):
          return self._get_converter().default_units(*args, **kwargs)
  
      def convert(self, *args, **kwargs):
          return self._get_converter().convert(*args, **kwargs)
  
  
  units.registry[np.datetime64] = \
      units.registry[datetime.date] = \
      units.registry[datetime.datetime] = \
      _SwitchableDateConverter()
  