tile.py

"""
Quantilization functions and related stuff
"""
from functools import partial

import numpy as np

from pandas._libs.lib import infer_dtype

from pandas.core.dtypes.common import (
    _NS_DTYPE, ensure_int64, is_categorical_dtype, is_datetime64_dtype,
    is_datetime64tz_dtype, is_datetime_or_timedelta_dtype, is_integer,
    is_scalar, is_timedelta64_dtype)
from pandas.core.dtypes.missing import isna

from pandas import (
    Categorical, Index, Interval, IntervalIndex, Series, Timedelta, Timestamp,
    to_datetime, to_timedelta)
import pandas.core.algorithms as algos
import pandas.core.nanops as nanops


def cut(x, bins, right=True, labels=None, retbins=False, precision=3,
        include_lowest=False, duplicates='raise'):
    """
    Bin values into discrete intervals.

    Use `cut` when you need to segment and sort data values into bins. This
    function is also useful for going from a continuous variable to a
    categorical variable. For example, `cut` could convert ages to groups of
    age ranges. Supports binning into an equal number of bins, or a
    pre-specified array of bins.

    Parameters
    ----------
    x : array-like
        The input array to be binned. Must be 1-dimensional.
    bins : int, sequence of scalars, or IntervalIndex
        The criteria to bin by.

        * int : Defines the number of equal-width bins in the range of `x`. The
          range of `x` is extended by .1% on each side to include the minimum
          and maximum values of `x`.
        * sequence of scalars : Defines the bin edges allowing for non-uniform
          width. No extension of the range of `x` is done.
        * IntervalIndex : Defines the exact bins to be used. Note that
          IntervalIndex for `bins` must be non-overlapping.

    right : bool, default True
        Indicates whether `bins` includes the rightmost edge or not. If
        ``right == True`` (the default), then the `bins` ``[1, 2, 3, 4]``
        indicate (1,2], (2,3], (3,4]. This argument is ignored when
        `bins` is an IntervalIndex.
    labels : array or bool, optional
        Specifies the labels for the returned bins. Must be the same length as
        the resulting bins. If False, returns only integer indicators of the
        bins. This affects the type of the output container (see below).
        This argument is ignored when `bins` is an IntervalIndex.
    retbins : bool, default False
        Whether to return the bins or not. Useful when bins is provided
        as a scalar.
    precision : int, default 3
        The precision at which to store and display the bins labels.
    include_lowest : bool, default False
        Whether the first interval should be left-inclusive or not.
    duplicates : {default 'raise', 'drop'}, optional
        If bin edges are not unique, raise ValueError or drop non-uniques.

        .. versionadded:: 0.23.0

    Returns
    -------
    out : Categorical, Series, or ndarray
        An array-like object representing the respective bin for each value
        of `x`. The type depends on the value of `labels`.

        * True (default) : returns a Series for Series `x` or a
          Categorical for all other inputs. The values stored within
          are Interval dtype.

        * sequence of scalars : returns a Series for Series `x` or a
          Categorical for all other inputs. The values stored within
          are whatever the type in the sequence is.

        * False : returns an ndarray of integers.

    bins : numpy.ndarray or IntervalIndex.
        The computed or specified bins. Only returned when `retbins=True`.
        For scalar or sequence `bins`, this is an ndarray with the computed
        bins. If set `duplicates=drop`, `bins` will drop non-unique bin. For
        an IntervalIndex `bins`, this is equal to `bins`.

    See Also
    --------
    qcut : Discretize variable into equal-sized buckets based on rank
        or based on sample quantiles.
    Categorical : Array type for storing data that come from a
        fixed set of values.
    Series : One-dimensional array with axis labels (including time series).
    IntervalIndex : Immutable Index implementing an ordered, sliceable set.

    Notes
    -----
    Any NA values will be NA in the result. Out of bounds values will be NA in
    the resulting Series or Categorical object.

    Examples
    --------
    Discretize into three equal-sized bins.

    >>> pd.cut(np.array([1, 7, 5, 4, 6, 3]), 3)
    ... # doctest: +ELLIPSIS
    [(0.994, 3.0], (5.0, 7.0], (3.0, 5.0], (3.0, 5.0], (5.0, 7.0], ...
    Categories (3, interval[float64]): [(0.994, 3.0] < (3.0, 5.0] ...

    >>> pd.cut(np.array([1, 7, 5, 4, 6, 3]), 3, retbins=True)
    ... # doctest: +ELLIPSIS
    ([(0.994, 3.0], (5.0, 7.0], (3.0, 5.0], (3.0, 5.0], (5.0, 7.0], ...
    Categories (3, interval[float64]): [(0.994, 3.0] < (3.0, 5.0] ...
    array([0.994, 3.   , 5.   , 7.   ]))

    Discovers the same bins, but assign them specific labels. Notice that
    the returned Categorical's categories are `labels` and is ordered.

    >>> pd.cut(np.array([1, 7, 5, 4, 6, 3]),
    ...        3, labels=["bad", "medium", "good"])
    [bad, good, medium, medium, good, bad]
    Categories (3, object): [bad < medium < good]

    ``labels=False`` implies you just want the bins back.

    >>> pd.cut([0, 1, 1, 2], bins=4, labels=False)
    array([0, 1, 1, 3])

    Passing a Series as an input returns a Series with categorical dtype:

    >>> s = pd.Series(np.array([2, 4, 6, 8, 10]),
    ...               index=['a', 'b', 'c', 'd', 'e'])
    >>> pd.cut(s, 3)
    ... # doctest: +ELLIPSIS
    a    (1.992, 4.667]
    b    (1.992, 4.667]
    c    (4.667, 7.333]
    d     (7.333, 10.0]
    e     (7.333, 10.0]
    dtype: category
    Categories (3, interval[float64]): [(1.992, 4.667] < (4.667, ...

    Passing a Series as an input returns a Series with mapping value.
    It is used to map numerically to intervals based on bins.

    >>> s = pd.Series(np.array([2, 4, 6, 8, 10]),
    ...               index=['a', 'b', 'c', 'd', 'e'])
    >>> pd.cut(s, [0, 2, 4, 6, 8, 10], labels=False, retbins=True, right=False)
    ... # doctest: +ELLIPSIS
    (a    0.0
     b    1.0
     c    2.0
     d    3.0
     e    4.0
     dtype: float64, array([0, 2, 4, 6, 8]))

    Use `drop` optional when bins is not unique

    >>> pd.cut(s, [0, 2, 4, 6, 10, 10], labels=False, retbins=True,
    ...        right=False, duplicates='drop')
    ... # doctest: +ELLIPSIS
    (a    0.0
     b    1.0
     c    2.0
     d    3.0
     e    3.0
     dtype: float64, array([0, 2, 4, 6, 8]))

    Passing an IntervalIndex for `bins` results in those categories exactly.
    Notice that values not covered by the IntervalIndex are set to NaN. 0
    is to the left of the first bin (which is closed on the right), and 1.5
    falls between two bins.

    >>> bins = pd.IntervalIndex.from_tuples([(0, 1), (2, 3), (4, 5)])
    >>> pd.cut([0, 0.5, 1.5, 2.5, 4.5], bins)
    [NaN, (0, 1], NaN, (2, 3], (4, 5]]
    Categories (3, interval[int64]): [(0, 1] < (2, 3] < (4, 5]]
    """
    # NOTE: this binning code is changed a bit from histogram for var(x) == 0

    # for handling the cut for datetime and timedelta objects
    x_is_series, series_index, name, x = _preprocess_for_cut(x)
    x, dtype = _coerce_to_type(x)

    if not np.iterable(bins):
        if is_scalar(bins) and bins < 1:
            raise ValueError("`bins` should be a positive integer.")

        try:  # for array-like
            sz = x.size
        except AttributeError:
            x = np.asarray(x)
            sz = x.size

        if sz == 0:
            raise ValueError('Cannot cut empty array')

        rng = (nanops.nanmin(x), nanops.nanmax(x))
        mn, mx = [mi + 0.0 for mi in rng]

        if np.isinf(mn) or np.isinf(mx):
            # GH 24314
            raise ValueError('cannot specify integer `bins` when input data '
                             'contains infinity')
        elif mn == mx:  # adjust end points before binning
            mn -= .001 * abs(mn) if mn != 0 else .001
            mx += .001 * abs(mx) if mx != 0 else .001
            bins = np.linspace(mn, mx, bins + 1, endpoint=True)
        else:  # adjust end points after binning
            bins = np.linspace(mn, mx, bins + 1, endpoint=True)
            adj = (mx - mn) * 0.001  # 0.1% of the range
            if right:
                bins[0] -= adj
            else:
                bins[-1] += adj

    elif isinstance(bins, IntervalIndex):
        if bins.is_overlapping:
            raise ValueError('Overlapping IntervalIndex is not accepted.')

    else:
        if is_datetime64tz_dtype(bins):
            bins = np.asarray(bins, dtype=_NS_DTYPE)
        else:
            bins = np.asarray(bins)
        bins = _convert_bin_to_numeric_type(bins, dtype)

        # GH 26045: cast to float64 to avoid an overflow
        if (np.diff(bins.astype('float64')) < 0).any():
            raise ValueError('bins must increase monotonically.')

    fac, bins = _bins_to_cuts(x, bins, right=right, labels=labels,
                              precision=precision,
                              include_lowest=include_lowest,
                              dtype=dtype,
                              duplicates=duplicates)

    return _postprocess_for_cut(fac, bins, retbins, x_is_series,
                                series_index, name, dtype)


def qcut(x, q, labels=None, retbins=False, precision=3, duplicates='raise'):
    """
    Quantile-based discretization function. Discretize variable into
    equal-sized buckets based on rank or based on sample quantiles. For example
    1000 values for 10 quantiles would produce a Categorical object indicating
    quantile membership for each data point.

    Parameters
    ----------
    x : 1d ndarray or Series
    q : integer or array of quantiles
        Number of quantiles. 10 for deciles, 4 for quartiles, etc. Alternately
        array of quantiles, e.g. [0, .25, .5, .75, 1.] for quartiles
    labels : array or boolean, default None
        Used as labels for the resulting bins. Must be of the same length as
        the resulting bins. If False, return only integer indicators of the
        bins.
    retbins : bool, optional
        Whether to return the (bins, labels) or not. Can be useful if bins
        is given as a scalar.
    precision : int, optional
        The precision at which to store and display the bins labels
    duplicates : {default 'raise', 'drop'}, optional
        If bin edges are not unique, raise ValueError or drop non-uniques.

        .. versionadded:: 0.20.0

    Returns
    -------
    out : Categorical or Series or array of integers if labels is False
        The return type (Categorical or Series) depends on the input: a Series
        of type category if input is a Series else Categorical. Bins are
        represented as categories when categorical data is returned.
    bins : ndarray of floats
        Returned only if `retbins` is True.

    Notes
    -----
    Out of bounds values will be NA in the resulting Categorical object

    Examples
    --------
    >>> pd.qcut(range(5), 4)
    ... # doctest: +ELLIPSIS
    [(-0.001, 1.0], (-0.001, 1.0], (1.0, 2.0], (2.0, 3.0], (3.0, 4.0]]
    Categories (4, interval[float64]): [(-0.001, 1.0] < (1.0, 2.0] ...

    >>> pd.qcut(range(5), 3, labels=["good", "medium", "bad"])
    ... # doctest: +SKIP
    [good, good, medium, bad, bad]
    Categories (3, object): [good < medium < bad]

    >>> pd.qcut(range(5), 4, labels=False)
    array([0, 0, 1, 2, 3])
    """
    x_is_series, series_index, name, x = _preprocess_for_cut(x)

    x, dtype = _coerce_to_type(x)

    if is_integer(q):
        quantiles = np.linspace(0, 1, q + 1)
    else:
        quantiles = q
    bins = algos.quantile(x, quantiles)
    fac, bins = _bins_to_cuts(x, bins, labels=labels,
                              precision=precision, include_lowest=True,
                              dtype=dtype, duplicates=duplicates)

    return _postprocess_for_cut(fac, bins, retbins, x_is_series,
                                series_index, name, dtype)


def _bins_to_cuts(x, bins, right=True, labels=None,
                  precision=3, include_lowest=False,
                  dtype=None, duplicates='raise'):

    if duplicates not in ['raise', 'drop']:
        raise ValueError("invalid value for 'duplicates' parameter, "
                         "valid options are: raise, drop")

    if isinstance(bins, IntervalIndex):
        # we have a fast-path here
        ids = bins.get_indexer(x)
        result = algos.take_nd(bins, ids)
        result = Categorical(result, categories=bins, ordered=True)
        return result, bins

    unique_bins = algos.unique(bins)
    if len(unique_bins) < len(bins) and len(bins) != 2:
        if duplicates == 'raise':
            raise ValueError("Bin edges must be unique: {bins!r}.\nYou "
                             "can drop duplicate edges by setting "
                             "the 'duplicates' kwarg".format(bins=bins))
        else:
            bins = unique_bins

    side = 'left' if right else 'right'
    ids = ensure_int64(bins.searchsorted(x, side=side))

    if include_lowest:
        ids[x == bins[0]] = 1

    na_mask = isna(x) | (ids == len(bins)) | (ids == 0)
    has_nas = na_mask.any()

    if labels is not False:
        if labels is None:
            labels = _format_labels(bins, precision, right=right,
                                    include_lowest=include_lowest,
                                    dtype=dtype)
        else:
            if len(labels) != len(bins) - 1:
                raise ValueError('Bin labels must be one fewer than '
                                 'the number of bin edges')
        if not is_categorical_dtype(labels):
            labels = Categorical(labels, categories=labels, ordered=True)

        np.putmask(ids, na_mask, 0)
        result = algos.take_nd(labels, ids - 1)

    else:
        result = ids - 1
        if has_nas:
            result = result.astype(np.float64)
            np.putmask(result, na_mask, np.nan)

    return result, bins


def _coerce_to_type(x):
    """
    if the passed data is of datetime/timedelta type,
    this method converts it to numeric so that cut method can
    handle it
    """
    dtype = None

    if is_datetime64tz_dtype(x):
        dtype = x.dtype
    elif is_datetime64_dtype(x):
        x = to_datetime(x)
        dtype = np.dtype('datetime64[ns]')
    elif is_timedelta64_dtype(x):
        x = to_timedelta(x)
        dtype = np.dtype('timedelta64[ns]')

    if dtype is not None:
        # GH 19768: force NaT to NaN during integer conversion
        x = np.where(x.notna(), x.view(np.int64), np.nan)

    return x, dtype


def _convert_bin_to_numeric_type(bins, dtype):
    """
    if the passed bin is of datetime/timedelta type,
    this method converts it to integer

    Parameters
    ----------
    bins : list-like of bins
    dtype : dtype of data

    Raises
    ------
    ValueError if bins are not of a compat dtype to dtype
    """
    bins_dtype = infer_dtype(bins, skipna=False)
    if is_timedelta64_dtype(dtype):
        if bins_dtype in ['timedelta', 'timedelta64']:
            bins = to_timedelta(bins).view(np.int64)
        else:
            raise ValueError("bins must be of timedelta64 dtype")
    elif is_datetime64_dtype(dtype) or is_datetime64tz_dtype(dtype):
        if bins_dtype in ['datetime', 'datetime64']:
            bins = to_datetime(bins).view(np.int64)
        else:
            raise ValueError("bins must be of datetime64 dtype")

    return bins


def _convert_bin_to_datelike_type(bins, dtype):
    """
    Convert bins to a DatetimeIndex or TimedeltaIndex if the orginal dtype is
    datelike

    Parameters
    ----------
    bins : list-like of bins
    dtype : dtype of data

    Returns
    -------
    bins : Array-like of bins, DatetimeIndex or TimedeltaIndex if dtype is
           datelike
    """
    if is_datetime64tz_dtype(dtype):
        bins = to_datetime(bins.astype(np.int64),
                           utc=True).tz_convert(dtype.tz)
    elif is_datetime_or_timedelta_dtype(dtype):
        bins = Index(bins.astype(np.int64), dtype=dtype)
    return bins


def _format_labels(bins, precision, right=True,
                   include_lowest=False, dtype=None):
    """ based on the dtype, return our labels """

    closed = 'right' if right else 'left'

    if is_datetime64tz_dtype(dtype):
        formatter = partial(Timestamp, tz=dtype.tz)
        adjust = lambda x: x - Timedelta('1ns')
    elif is_datetime64_dtype(dtype):
        formatter = Timestamp
        adjust = lambda x: x - Timedelta('1ns')
    elif is_timedelta64_dtype(dtype):
        formatter = Timedelta
        adjust = lambda x: x - Timedelta('1ns')
    else:
        precision = _infer_precision(precision, bins)
        formatter = lambda x: _round_frac(x, precision)
        adjust = lambda x: x - 10 ** (-precision)

    breaks = [formatter(b) for b in bins]
    labels = IntervalIndex.from_breaks(breaks, closed=closed)

    if right and include_lowest:
        # we will adjust the left hand side by precision to
        # account that we are all right closed
        #
        # We cannot access labels[0].left because that
        # calls Interval(left, right, closed='right')
        # and before adjusting we may have left == right
        # so it will raise.
        v = adjust(labels.left[0])

        i = IntervalIndex([Interval(v, labels.right[0], closed='right')])
        labels = i.append(labels[1:])

    return labels


def _preprocess_for_cut(x):
    """
    handles preprocessing for cut where we convert passed
    input to array, strip the index information and store it
    separately
    """
    x_is_series = isinstance(x, Series)
    series_index = None
    name = None

    if x_is_series:
        series_index = x.index
        name = x.name

    # Check that the passed array is a Pandas or Numpy object
    # We don't want to strip away a Pandas data-type here (e.g. datetimetz)
    ndim = getattr(x, 'ndim', None)
    if ndim is None:
        x = np.asarray(x)
    if x.ndim != 1:
        raise ValueError("Input array must be 1 dimensional")

    return x_is_series, series_index, name, x


def _postprocess_for_cut(fac, bins, retbins, x_is_series,
                         series_index, name, dtype):
    """
    handles post processing for the cut method where
    we combine the index information if the originally passed
    datatype was a series
    """
    if x_is_series:
        fac = Series(fac, index=series_index, name=name)

    if not retbins:
        return fac

    bins = _convert_bin_to_datelike_type(bins, dtype)

    return fac, bins


def _round_frac(x, precision):
    """
    Round the fractional part of the given number
    """
    if not np.isfinite(x) or x == 0:
        return x
    else:
        frac, whole = np.modf(x)
        if whole == 0:
            digits = -int(np.floor(np.log10(abs(frac)))) - 1 + precision
        else:
            digits = precision
        return np.around(x, digits)


def _infer_precision(base_precision, bins):
    """Infer an appropriate precision for _round_frac
    """
    for precision in range(base_precision, 20):
        levels = [_round_frac(b, precision) for b in bins]
        if algos.unique(levels).size == bins.size:
            return precision
    return base_precision  # default