"""
Functions that ignore NaN.

Functions
---------

- `nanmin` -- minimum non-NaN value
- `nanmax` -- maximum non-NaN value
- `nanargmin` -- index of minimum non-NaN value
- `nanargmax` -- index of maximum non-NaN value
- `nansum` -- sum of non-NaN values
- `nanprod` -- product of non-NaN values
- `nancumsum` -- cumulative sum of non-NaN values
- `nancumprod` -- cumulative product of non-NaN values
- `nanmean` -- mean of non-NaN values
- `nanvar` -- variance of non-NaN values
- `nanstd` -- standard deviation of non-NaN values
- `nanmedian` -- median of non-NaN values
- `nanquantile` -- qth quantile of non-NaN values
- `nanpercentile` -- qth percentile of non-NaN values

"""
import functools
import warnings
import numpy as np
from numpy.lib import function_base
from numpy.core import overrides


array_function_dispatch = functools.partial(
    overrides.array_function_dispatch, module='numpy')


__all__ = [
    'nansum', 'nanmax', 'nanmin', 'nanargmax', 'nanargmin', 'nanmean',
    'nanmedian', 'nanpercentile', 'nanvar', 'nanstd', 'nanprod',
    'nancumsum', 'nancumprod', 'nanquantile'
    ]


def _nan_mask(a, out=None):
    """
    Parameters
    ----------
    a : array-like
        Input array with at least 1 dimension.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output and will prevent the allocation of a new array.

    Returns
    -------
    y : bool ndarray or True
        A bool array where ``np.nan`` positions are marked with ``False``
        and other positions are marked with ``True``. If the type of ``a``
        is such that it can't possibly contain ``np.nan``, returns ``True``.
    """
    # we assume that a is an array for this private function

    if a.dtype.kind not in 'fc':
        return True

    y = np.isnan(a, out=out)
    y = np.invert(y, out=y)
    return y

def _replace_nan(a, val):
    """
    If `a` is of inexact type, make a copy of `a`, replace NaNs with
    the `val` value, and return the copy together with a boolean mask
    marking the locations where NaNs were present. If `a` is not of
    inexact type, do nothing and return `a` together with a mask of None.

    Note that scalars will end up as array scalars, which is important
    for using the result as the value of the out argument in some
    operations.

    Parameters
    ----------
    a : array-like
        Input array.
    val : float
        NaN values are set to val before doing the operation.

    Returns
    -------
    y : ndarray
        If `a` is of inexact type, return a copy of `a` with the NaNs
        replaced by the fill value, otherwise return `a`.
    mask: {bool, None}
        If `a` is of inexact type, return a boolean mask marking locations of
        NaNs, otherwise return None.

    """
    a = np.asanyarray(a)

    if a.dtype == np.object_:
        # object arrays do not support `isnan` (gh-9009), so make a guess
        mask = np.not_equal(a, a, dtype=bool)
    elif issubclass(a.dtype.type, np.inexact):
        mask = np.isnan(a)
    else:
        mask = None

    if mask is not None:
        a = np.array(a, subok=True, copy=True)
        np.copyto(a, val, where=mask)

    return a, mask


def _copyto(a, val, mask):
    """
    Replace values in `a` with NaN where `mask` is True.  This differs from
    copyto in that it will deal with the case where `a` is a numpy scalar.

    Parameters
    ----------
    a : ndarray or numpy scalar
        Array or numpy scalar some of whose values are to be replaced
        by val.
    val : numpy scalar
        Value used a replacement.
    mask : ndarray, scalar
        Boolean array. Where True the corresponding element of `a` is
        replaced by `val`. Broadcasts.

    Returns
    -------
    res : ndarray, scalar
        Array with elements replaced or scalar `val`.

    """
    if isinstance(a, np.ndarray):
        np.copyto(a, val, where=mask, casting='unsafe')
    else:
        a = a.dtype.type(val)
    return a


def _remove_nan_1d(arr1d, overwrite_input=False):
    """
    Equivalent to arr1d[~arr1d.isnan()], but in a different order

    Presumably faster as it incurs fewer copies

    Parameters
    ----------
    arr1d : ndarray
        Array to remove nans from
    overwrite_input : bool
        True if `arr1d` can be modified in place

    Returns
    -------
    res : ndarray
        Array with nan elements removed
    overwrite_input : bool
        True if `res` can be modified in place, given the constraint on the
        input
    """

    c = np.isnan(arr1d)
    s = np.nonzero(c)[0]
    if s.size == arr1d.size:
        warnings.warn("All-NaN slice encountered", RuntimeWarning,
                      stacklevel=5)
        return arr1d[:0], True
    elif s.size == 0:
        return arr1d, overwrite_input
    else:
        if not overwrite_input:
            arr1d = arr1d.copy()
        # select non-nans at end of array
        enonan = arr1d[-s.size:][~c[-s.size:]]
        # fill nans in beginning of array with non-nans of end
        arr1d[s[:enonan.size]] = enonan

        return arr1d[:-s.size], True


def _divide_by_count(a, b, out=None):
    """
    Compute a/b ignoring invalid results. If `a` is an array the division
    is done in place. If `a` is a scalar, then its type is preserved in the
    output. If out is None, then then a is used instead so that the
    division is in place. Note that this is only called with `a` an inexact
    type.

    Parameters
    ----------
    a : {ndarray, numpy scalar}
        Numerator. Expected to be of inexact type but not checked.
    b : {ndarray, numpy scalar}
        Denominator.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary.

    Returns
    -------
    ret : {ndarray, numpy scalar}
        The return value is a/b. If `a` was an ndarray the division is done
        in place. If `a` is a numpy scalar, the division preserves its type.

    """
    with np.errstate(invalid='ignore', divide='ignore'):
        if isinstance(a, np.ndarray):
            if out is None:
                return np.divide(a, b, out=a, casting='unsafe')
            else:
                return np.divide(a, b, out=out, casting='unsafe')
        else:
            if out is None:
                return a.dtype.type(a / b)
            else:
                # This is questionable, but currently a numpy scalar can
                # be output to a zero dimensional array.
                return np.divide(a, b, out=out, casting='unsafe')


def _nanmin_dispatcher(a, axis=None, out=None, keepdims=None):
    return (a, out)


@array_function_dispatch(_nanmin_dispatcher)
def nanmin(a, axis=None, out=None, keepdims=np._NoValue):
    """
    Return minimum of an array or minimum along an axis, ignoring any NaNs.
    When all-NaN slices are encountered a ``RuntimeWarning`` is raised and
    Nan is returned for that slice.

    Parameters
    ----------
    a : array_like
        Array containing numbers whose minimum is desired. If `a` is not an
        array, a conversion is attempted.
    axis : {int, tuple of int, None}, optional
        Axis or axes along which the minimum is computed. The default is to compute
        the minimum of the flattened array.
    out : ndarray, optional
        Alternate output array in which to place the result.  The default
        is ``None``; if provided, it must have the same shape as the
        expected output, but the type will be cast if necessary. See
        `ufuncs-output-type` for more details.

        .. versionadded:: 1.8.0
    keepdims : bool, optional
        If this is set to True, the axes which are reduced are left
        in the result as dimensions with size one. With this option,
        the result will broadcast correctly against the original `a`.

        If the value is anything but the default, then
        `keepdims` will be passed through to the `min` method
        of sub-classes of `ndarray`.  If the sub-classes methods
        does not implement `keepdims` any exceptions will be raised.

        .. versionadded:: 1.8.0

    Returns
    -------
    nanmin : ndarray
        An array with the same shape as `a`, with the specified axis
        removed.  If `a` is a 0-d array, or if axis is None, an ndarray
        scalar is returned.  The same dtype as `a` is returned.

    See Also
    --------
    nanmax :
        The maximum value of an array along a given axis, ignoring any NaNs.
    amin :
        The minimum value of an array along a given axis, propagating any NaNs.
    fmin :
        Element-wise minimum of two arrays, ignoring any NaNs.
    minimum :
        Element-wise minimum of two arrays, propagating any NaNs.
    isnan :
        Shows which elements are Not a Number (NaN).
    isfinite:
        Shows which elements are neither NaN nor infinity.

    amax, fmax, maximum

    Notes
    -----
    NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.
    Positive infinity is treated as a very large number and negative
    infinity is treated as a very small (i.e. negative) number.

    If the input has a integer type the function is equivalent to np.min.

    Examples
    --------
    >>> a = np.array([[1, 2], [3, np.nan]])
    >>> np.nanmin(a)
    1.0
    >>> np.nanmin(a, axis=0)
    array([1.,  2.])
    >>> np.nanmin(a, axis=1)
    array([1.,  3.])

    When positive infinity and negative infinity are present:

    >>> np.nanmin([1, 2, np.nan, np.inf])
    1.0
    >>> np.nanmin([1, 2, np.nan, np.NINF])
    -inf

    """
    kwargs = {}
    if keepdims is not np._NoValue:
        kwargs['keepdims'] = keepdims
    if type(a) is np.ndarray and a.dtype != np.object_:
        # Fast, but not safe for subclasses of ndarray, or object arrays,
        # which do not implement isnan (gh-9009), or fmin correctly (gh-8975)
        res = np.fmin.reduce(a, axis=axis, out=out, **kwargs)
        if np.isnan(res).any():
            warnings.warn("All-NaN slice encountered", RuntimeWarning,
                          stacklevel=3)
    else:
        # Slow, but safe for subclasses of ndarray
        a, mask = _replace_nan(a, +np.inf)
        res = np.amin(a, axis=axis, out=out, **kwargs)
        if mask is None:
            return res

        # Check for all-NaN axis
        mask = np.all(mask, axis=axis, **kwargs)
        if np.any(mask):
            res = _copyto(res, np.nan, mask)
            warnings.warn("All-NaN axis encountered", RuntimeWarning,
                          stacklevel=3)
    return res


def _nanmax_dispatcher(a, axis=None, out=None, keepdims=None):
    return (a, out)


@array_function_dispatch(_nanmax_dispatcher)
def nanmax(a, axis=None, out=None, keepdims=np._NoValue):
    """