# Source code for dask.array.percentile

    from __future__ import annotations

    import warnings
    from collections.abc import Iterator
    from functools import wraps
    from numbers import Number

    import numpy as np
    from tlz import merge

    from dask.array.core import Array
    from dask.base import tokenize
    from dask.highlevelgraph import HighLevelGraph
    from dask.utils import derived_from

    @wraps(np.percentile)
    def _percentile(a, q, method="linear"):
        n = len(a)
        if not len(a):
            return None, n
        if isinstance(q, Iterator):
            q = list(q)
        if a.dtype.name == "category":
            result = np.percentile(a.cat.codes, q, method=method)
            import pandas as pd

            return pd.Categorical.from_codes(result, a.dtype.categories, a.dtype.ordered), n
        if type(a.dtype).__name__ == "DatetimeTZDtype":
            import pandas as pd

            if isinstance(a, (pd.Series, pd.Index)):
                a = a.values

        if np.issubdtype(a.dtype, np.datetime64):
            values = a
            if type(a).__name__ in ("Series", "Index"):
                a2 = values.astype("i8")
            else:
                a2 = values.view("i8")
            result = np.percentile(a2, q, method=method).astype(values.dtype)
            if q[0] == 0:
                # https://github.com/dask/dask/issues/6864
                result[0] = min(result[0], values.min())
            return result, n
        if not np.issubdtype(a.dtype, np.number):
            method = "nearest"
        return np.percentile(a, q, method=method), n

    def _tdigest_chunk(a):
        from crick import TDigest

        t = TDigest()
        t.update(a)

        return t

    def _percentiles_from_tdigest(qs, digests):
        from crick import TDigest

        t = TDigest()
        t.merge(*digests)

        return np.array(t.quantile(qs / 100.0))

    def percentile(a, q, method="linear", internal_method="default", **kwargs):
        """Approximate percentile of 1-D array

        Parameters
        ----------
        a : Array
        q : array_like of float
            Percentile or sequence of percentiles to compute, which must be between
            0 and 100 inclusive.
        method : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}, optional
            The interpolation method to use when the desired percentile lies
            between two data points ``i < j``. Only valid for ``internal_method='dask'``.

            - 'linear': ``i + (j - i) * fraction``, where ``fraction``
              is the fractional part of the index surrounded by ``i``
              and ``j``.
            - 'lower': ``i``.
            - 'higher': ``j``.
            - 'nearest': ``i`` or ``j``, whichever is nearest.
            - 'midpoint': ``(i + j) / 2``.

            .. versionchanged:: 2022.1.0
                This argument was previously called "interpolation"

        internal_method : {'default', 'dask', 'tdigest'}, optional
            What internal method to use. By default will use dask's internal custom
            algorithm (``'dask'``).  If set to ``'tdigest'`` will use tdigest for
            floats and ints and fallback to the ``'dask'`` otherwise.

            .. versionchanged:: 2022.1.0
                This argument was previously called “method”.

        interpolation : str, optional
            Deprecated name for the method keyword argument.

            .. deprecated:: 2022.1.0

        See Also
        --------
        numpy.percentile : Numpy's equivalent Percentile function
        """
        from dask.array.dispatch import percentile_lookup as _percentile
        from dask.array.reductions import quantile
        from dask.array.utils import array_safe, meta_from_array

        if a.ndim > 1:
            q = np.true_divide(q, a.dtype.type(100) if a.dtype.kind == "f" else 100)

            return quantile(a, q, method=method, **kwargs)

        allowed_internal_methods = ["default", "dask", "tdigest"]

        if method in allowed_internal_methods:
            warnings.warn(
                "The `method=` argument was renamed to `internal_method=`",
                FutureWarning,
            )
            internal_method = method

        if "interpolation" in kwargs:
            warnings.warn(
                "The `interpolation=` argument to percentile was renamed to " "`method= ` ",
                FutureWarning,
            )
            method = kwargs.pop("interpolation")

        if kwargs:
            raise TypeError(
                f"percentile() got an unexpected keyword argument {kwargs.keys()}"
            )

        if not a.ndim == 1:
            raise NotImplementedError("Percentiles only implemented for 1-d arrays")
        if isinstance(q, Number):
            q = [q]
        q = array_safe(q, like=meta_from_array(a))
        token = tokenize(a, q, method)

        dtype = a.dtype
        if np.issubdtype(dtype, np.integer):
            dtype = (array_safe([], dtype=dtype, like=meta_from_array(a)) / 0.5).dtype
        meta = meta_from_array(a, dtype=dtype)

        if internal_method not in allowed_internal_methods:
            raise ValueError(
                f"`internal_method=` must be one of {allowed_internal_methods}"
            )

        # Allow using t-digest if method is allowed and dtype is of floating or integer type
        if (
            internal_method == "tdigest"
            and method == "linear"
            and (np.issubdtype(dtype, np.floating) or np.issubdtype(dtype, np.integer))
        ):
            from dask.utils import import_required

            import_required(
                "crick", "crick is a required dependency for using the t-digest method."
            )

            name = "percentile_tdigest_chunk-" + token
            dsk = {
                (name, i): (_tdigest_chunk, key) for i, key in enumerate(a.__dask_keys__())
            }

            name2 = "percentile_tdigest-" + token

            dsk2 = {(name2, 0): (_percentiles_from_tdigest, q, sorted(dsk))}

        # Otherwise use the custom percentile algorithm
        else:
            # Add 0 and 100 during calculation for more robust behavior (hopefully)
            calc_q = np.pad(q, 1, mode="constant")
            calc_q[-1] = 100
            name = "percentile_chunk-" + token
            dsk = {
                (name, i): (_percentile, key, calc_q, method)
                for i, key in enumerate(a.__dask_keys__())
            }

            name2 = "percentile-" + token
            dsk2 = {
                (name2, 0): (
                    merge_percentiles,
                    q,
                    [calc_q] * len(a.chunks[0]),
                    sorted(dsk),
                    method,
                )
            }

        dsk = merge(dsk, dsk2)
        graph = HighLevelGraph.from_collections(name2, dsk, dependencies=[a])
        return Array(graph, name2, chunks=((len(q),),), meta=meta)

    def merge_percentiles(finalq, qs, vals, method="lower", Ns=None, raise_on_nan=True):
        """Combine several percentile calculations of different data.

        Parameters
        ----------

        finalq : numpy.array
            Percentiles to compute (must use same scale as ``qs``).
        qs : sequence of :class:`numpy.array`s
            Percentiles calculated on different sets of data.
        vals : sequence of :class:`numpy.array`s
            Resulting values associated with percentiles ``qs``.
        Ns : sequence of integers
            The number of data elements associated with each data set.
        method : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
            Specify the interpolation method to use to calculate final
            percentiles.  For more information, see :func:`numpy.percentile`.

        Examples
        --------

        >>> finalq = [10, 20, 30, 40, 50, 60, 70, 80]
        >>> qs = [[20, 40, 60, 80], [20, 40, 60, 80]]
        >>> vals = [np.array([1, 2, 3, 4]), np.array([10, 11, 12, 13])]
        >>> Ns = [100, 100]  # Both original arrays had 100 elements

        >>> merge_percentiles(finalq, qs, vals, Ns=Ns)
        array([ 1,  2,  3,  4, 10, 11, 12, 13])
        """
        from dask.array.utils import array_safe

        if isinstance(finalq, Iterator):
            finalq = list(finalq)
        finalq = array_safe(finalq, like=finalq)
        qs = list(map(list, qs))
        vals = list(vals)
        if Ns is None:
            vals, Ns = zip(*vals)
        Ns = list(Ns)

        L = list(zip(*[(q, val, N) for q, val, N in zip(qs, vals, Ns) if N]))
        if not L:
            if raise_on_nan:
                raise ValueError("No non-trivial arrays found")
            return np.full(len(qs[0]) - 2, np.nan)
        qs, vals, Ns = L

        # TODO: Perform this check above in percentile once dtype checking is easy
        #       Here we silently change meaning
        if vals[0].dtype.name == "category":
            result = merge_percentiles(
                finalq, qs, [v.codes for v in vals], method, Ns, raise_on_nan
            )
            import pandas as pd

            return pd.Categorical.from_codes(result, vals[0].categories, vals[0].ordered)
        if not np.issubdtype(vals[0].dtype, np.number):
            method = "nearest"

        if len(vals) != len(qs) or len(Ns) != len(qs):
            raise ValueError("qs, vals, and Ns parameters must be the same length")

        # transform qs and Ns into number of observations between percentiles
        counts = []
        for q, N in zip(qs, Ns):
            count = np.empty_like(finalq, shape=len(q))
            count[1:] = np.diff(array_safe(q, like=q[0]))
            count[0] = q[0]
            count *= N
            counts.append(count)

        # Sort by calculated percentile values, then number of observations.
        combined_vals = np.concatenate(vals)
        combined_counts = array_safe(np.concatenate(counts), like=combined_vals)
        sort_order = np.argsort(combined_vals)
        combined_vals = np.take(combined_vals, sort_order)
        combined_counts = np.take(combined_counts, sort_order)

        # percentile-like, but scaled by total number of observations
        combined_q = np.cumsum(combined_counts)

        # rescale finalq percentiles to match combined_q
        finalq = array_safe(finalq, like=combined_vals)
        desired_q = finalq * sum(Ns)

        # the behavior of different interpolation methods should be
        # investigated further.
        if method == "linear":
            rv = np.interp(desired_q, combined_q, combined_vals)
        else:
            left = np.searchsorted(combined_q, desired_q, side="left")
            right = np.searchsorted(combined_q, desired_q, side="right") - 1
            np.minimum(left, len(combined_vals) - 1, left)  # don't exceed max index
            lower = np.minimum(left, right)
            upper = np.maximum(left, right)
            if method == "lower":
                rv = combined_vals[lower]
            elif method == "higher":
                rv = combined_vals[upper]
            elif method == "midpoint":
                rv = 0.5 * (combined_vals[lower] + combined_vals[upper])
            elif method == "nearest":
                lower_residual = np.abs(combined_q[lower] - desired_q)
                upper_residual = np.abs(combined_q[upper] - desired_q)
                mask = lower_residual > upper_residual
                index = lower  # alias; we no longer need lower
                index[mask] = upper[mask]
                rv = combined_vals[index]
            else:
                raise ValueError(
                    "interpolation method can only be 'linear', 'lower', "
                    "'higher', 'midpoint', or 'nearest'"
                )
        return rv

    @derived_from(np)
    def nanpercentile(a, q, **kwargs):
        from dask.array.reductions import nanquantile

        q = np.true_divide(q, a.dtype.type(100) if a.dtype.kind == "f" else 100)

        return nanquantile(a, q, **kwargs)