text: """
  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
          :ref:`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):
      """
      Return the maximum of an array or maximum 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 maximum 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 maximum is computed. The default is to compute
          the maximum 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
          :ref:`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 `max` 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
      -------
      nanmax : 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
      --------
      nanmin :
          The minimum value of an array along a given axis, ignoring any NaNs.
      amax :
          The maximum value of an array along a given axis, propagating any NaNs.
      fmax :
          Element-wise maximum of two arrays, ignoring any NaNs.
      maximum :
          Element-wise maximum of two arrays, propagating any NaNs.
      isnan :
          Shows which elements are Not a Number (NaN).
      isfinite:
          Shows which elements are neither NaN nor infinity.
  
      amin, fmin, minimum
  
      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.max.
  
      Examples
      --------
      >>> a = np.array([[1, 2], [3, np.nan]])
      >>> np.nanmax(a)
      3.0
      >>> np.nanmax(a, axis=0)
      array([3.,  2.])
      >>> np.nanmax(a, axis=1)
      array([2.,  3.])
  
      When positive infinity and negative infinity are present:
  
      >>> np.nanmax([1, 2, np.nan, np.NINF])
      2.0
      >>> np.nanmax([1, 2, np.nan, np.inf])
      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 fmax correctly (gh-8975)
          res = np.fmax.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.amax(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 _nanargmin_dispatcher(a, axis=None):
      return (a,)
  
  
  @array_function_dispatch(_nanargmin_dispatcher)
  def nanargmin(a, axis=None):
      """
      Return the indices of the minimum values in the specified axis ignoring
      NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results
      cannot be trusted if a slice contains only NaNs and Infs.
  
      Parameters
      ----------
      a : array_like
          Input data.
      axis : int, optional
          Axis along which to operate.  By default flattened input is used.
  
      Returns
      -------
      index_array : ndarray
          An array of indices or a single index value.
  
      See Also
      --------
      argmin, nanargmax
  
      Examples
      --------
      >>> a = np.array([[np.nan, 4], [2, 3]])
      >>> np.argmin(a)
      0
      >>> np.nanargmin(a)
      2
      >>> np.nanargmin(a, axis=0)
      array([1, 1])
      >>> np.nanargmin(a, axis=1)
      array([1, 0])
  
      """
      a, mask = _replace_nan(a, np.inf)
      res = np.argmin(a, axis=axis)
      if mask is not None:
          mask = np.all(mask, axis=axis)
          if np.any(mask):
              raise ValueError("All-NaN slice encountered")
      return res
  
  
  def _nanargmax_dispatcher(a, axis=None):
      return (a,)
  
  
  @array_function_dispatch(_nanargmax_dispatcher)
  def nanargmax(a, axis=None):
      """
      Return the indices of the maximum values in the specified axis ignoring
      NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the
      results cannot be trusted if a slice contains only NaNs and -Infs.
  
  
      Parameters
      ----------
      a : array_like
          Input data.
      axis : int, optional
          Axis along which to operate.  By default flattened input is used.
  
      Returns
      -------
      index_array : ndarray
          An array of indices or a single index value.
  
      See Also
      --------
      argmax, nanargmin
  
      Examples
      --------
      >>> a = np.array([[np.nan, 4], [2, 3]])
      >>> np.argmax(a)
      0
      >>> np.nanargmax(a)
      1
      >>> np.nanargmax(a, axis=0)
      array([1, 0])
      >>> np.nanargmax(a, axis=1)
      array([1, 1])
  
      """
      a, mask = _replace_nan(a, -np.inf)
      res = np.argmax(a, axis=axis)
      if mask is not None:
          mask = np.all(mask, axis=axis)
          if np.any(mask):
              raise ValueError("All-NaN slice encountered")
      return res
  
  
  def _nansum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None):
      return (a, out)
  
  
  @array_function_dispatch(_nansum_dispatcher)
  def nansum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
      """
      Return the sum of array elements over a given axis treating Not a
      Numbers (NaNs) as zero.
  
      In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or
      empty. In later versions zero is returned.
  
      Parameters
      ----------
      a : array_like
          Array containing numbers whose sum 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 sum is computed. The default is to compute the
          sum of the flattened array.
      dtype : data-type, optional
          The type of the returned array and of the accumulator in which the
          elements are summed.  By default, the dtype of `a` is used.  An
          exception is when `a` has an integer type with less precision than
          the platform (u)intp. In that case, the default will be either
          (u)int32 or (u)int64 depending on whether the platform is 32 or 64
          bits. For inexact inputs, dtype must be inexact.
  
          .. versionadded:: 1.8.0
      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
          :ref:`ufuncs-output-type` for more details. The casting of NaN to integer
          can yield unexpected results.
  
          .. 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 `mean` or `sum` methods
          of sub-classes of `ndarray`.  If the sub-classes methods
          does not implement `keepdims` any exceptions will be raised.
  
          .. versionadded:: 1.8.0
  
      Returns
      -------
      nansum : ndarray.
          A new array holding the result is returned unless `out` is
          specified, in which it is returned. The result has the same
          size as `a`, and the same shape as `a` if `axis` is not None
          or `a` is a 1-d array.
  
      See Also
      --------
      numpy.sum : Sum across array propagating NaNs.
      isnan : Show which elements are NaN.
      isfinite : Show which elements are not NaN or +/-inf.
  
      Notes
      -----
      If both positive and negative infinity are present, the sum will be Not
      A Number (NaN).
  
      Examples
      --------
      >>> np.nansum(1)
      1
      >>> np.nansum([1])
      1
      >>> np.nansum([1, np.nan])
      1.0
      >>> a = np.array([[1, 1], [1, np.nan]])
      >>> np.nansum(a)
      3.0
      >>> np.nansum(a, axis=0)
      array([2.,  1.])
      >>> np.nansum([1, np.nan, np.inf])
      inf
      >>> np.nansum([1, np.nan, np.NINF])
      -inf
      >>> from numpy.testing import suppress_warnings
      >>> with suppress_warnings() as sup:
      ...     sup.filter(RuntimeWarning)
      ...     np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present
      nan
  
      """
      a, mask = _replace_nan(a, 0)
      return np.sum(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
  
  
  def _nanprod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None):
      return (a, out)
  
  
  @array_function_dispatch(_nanprod_dispatcher)
  def nanprod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
      """
      Return the product of array elements over a given axis treating Not a
      Numbers (NaNs) as ones.
  
      One is returned for slices that are all-NaN or empty.
  
      .. versionadded:: 1.10.0
  
      Parameters
      ----------
      a : array_like
          Array containing numbers whose product 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 product is computed. The default is to compute
          the product of the flattened array.
      dtype : data-type, optional
          The type of the returned array and of the accumulator in which the
          elements are summed.  By default, the dtype of `a` is used.  An
          exception is when `a` has an integer type with less precision than
          the platform (u)intp. In that case, the default will be either
          (u)int32 or (u)int64 depending on whether the platform is 32 or 64
          bits. For inexact inputs, dtype must be inexact.
      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
          :ref:`ufuncs-output-type` for more details. The casting of NaN to integer
          can yield unexpected results.
      keepdims : bool, optional
          If 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 `arr`.
  
      Returns
      -------
      nanprod : ndarray
          A new array holding the result is returned unless `out` is
          specified, in which case it is returned.
  
      See Also
      --------
      numpy.prod : Product across array propagating NaNs.
      isnan : Show which elements are NaN.
  
      Examples
      --------
      >>> np.nanprod(1)
      1
      >>> np.nanprod([1])
      1
      >>> np.nanprod([1, np.nan])
      1.0
      >>> a = np.array([[1, 2], [3, np.nan]])
      >>> np.nanprod(a)
      6.0
      >>> np.nanprod(a, axis=0)
      array([3., 2.])
  
      """
      a, mask = _replace_nan(a, 1)
      return np.prod(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
  
  
  def _nancumsum_dispatcher(a, axis=None, dtype=None, out=None):
      return (a, out)
  
  
  @array_function_dispatch(_nancumsum_dispatcher)
  def nancumsum(a, axis=None, dtype=None, out=None):
      """
      Return the cumulative sum of array elements over a given axis treating Not a
      Numbers (NaNs) as zero.  The cumulative sum does not change when NaNs are
      encountered and leading NaNs are replaced by zeros.
  
      Zeros are returned for slices that are all-NaN or empty.
  
      .. versionadded:: 1.12.0
  
      Parameters
      ----------
      a : array_like
          Input array.
      axis : int, optional
          Axis along which the cumulative sum is computed. The default
          (None) is to compute the cumsum over the flattened array.
      dtype : dtype, optional
          Type of the returned array and of the accumulator in which the
          elements are summed.  If `dtype` is not specified, it defaults
          to the dtype of `a`, unless `a` has an integer dtype with a
          precision less than that of the default platform integer.  In
          that case, the default platform integer is used.
      out : ndarray, optional
          Alternative output array in which to place the result. It must
          have the same shape and buffer length as the expected output
          but the type will be cast if necessary. See :ref:`ufuncs-output-type` for
          more details.
  
      Returns
      -------
      nancumsum : ndarray.
          A new array holding the result is returned unless `out` is
          specified, in which it is returned. The result has the same
          size as `a`, and the same shape as `a` if `axis` is not None
          or `a` is a 1-d array.
  
      See Also
      --------
      numpy.cumsum : Cumulative sum across array propagating NaNs.
      isnan : Show which elements are NaN.
  
      Examples
      --------
      >>> np.nancumsum(1)
      array([1])
      >>> np.nancumsum([1])
      array([1])
      >>> np.nancumsum([1, np.nan])
      array([1.,  1.])
      >>> a = np.array([[1, 2], [3, np.nan]])
      >>> np.nancumsum(a)
      array([1.,  3.,  6.,  6.])
      >>> np.nancumsum(a, axis=0)
      array([[1.,  2.],
             [4.,  2.]])
      >>> np.nancumsum(a, axis=1)
      array([[1.,  3.],
             [3.,  3.]])
  
      """
      a, mask = _replace_nan(a, 0)
      return np.cumsum(a, axis=axis, dtype=dtype, out=out)
  
  
  def _nancumprod_dispatcher(a, axis=None, dtype=None, out=None):
      return (a, out)
  
  
  @array_function_dispatch(_nancumprod_dispatcher)
  def nancumprod(a, axis=None, dtype=None, out=None):
      """
      Return the cumulative product of array elements over a given axis treating Not a
      Numbers (NaNs) as one.  The cumulative product does not change when NaNs are
      encountered and leading NaNs are replaced by ones.
  
      Ones are returned for slices that are all-NaN or empty.
  
      .. versionadded:: 1.12.0
  
      Parameters
      ----------
      a : array_like
          Input array.
      axis : int, optional
          Axis along which the cumulative product is computed.  By default
          the input is flattened.
      dtype : dtype, optional
          Type of the returned array, as well as of the accumulator in which
          the elements are multiplied.  If *dtype* is not specified, it
          defaults to the dtype of `a`, unless `a` has an integer dtype with
          a precision less than that of the default platform integer.  In
          that case, the default platform integer is used instead.
      out : ndarray, optional
          Alternative output array in which to place the result. It must
          have the same shape and buffer length as the expected output
          but the type of the resulting values will be cast if necessary.
  
      Returns
      -------
      nancumprod : ndarray
          A new array holding the result is returned unless `out` is
          specified, in which case it is returned.
  
      See Also
      --------
      numpy.cumprod : Cumulative product across array propagating NaNs.
      isnan : Show which elements are NaN.
  
      Examples
      --------
      >>> np.nancumprod(1)
      array([1])
      >>> np.nancumprod([1])
      array([1])
      >>> np.nancumprod([1, np.nan])
      array([1.,  1.])
      >>> a = np.array([[1, 2], [3, np.nan]])
      >>> np.nancumprod(a)
      array([1.,  2.,  6.,  6.])
      >>> np.nancumprod(a, axis=0)
      array([[1.,  2.],
             [3.,  2.]])
      >>> np.nancumprod(a, axis=1)
      array([[1.,  2.],
             [3.,  3.]])
  
      """
      a, mask = _replace_nan(a, 1)
      return np.cumprod(a, axis=axis, dtype=dtype, out=out)
  
  
  def _nanmean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None):
      return (a, out)
  
  
  @array_function_dispatch(_nanmean_dispatcher)
  def nanmean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
      """
      Compute the arithmetic mean along the specified axis, ignoring NaNs.
  
      Returns the average of the array elements.  The average is taken over
      the flattened array by default, otherwise over the specified axis.
      `float64` intermediate and return values are used for integer inputs.
  
      For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.
  
      .. versionadded:: 1.8.0
  
      Parameters
      ----------
      a : array_like
          Array containing numbers whose mean 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 means are computed. The default is to compute
          the mean of the flattened array.
      dtype : data-type, optional
          Type to use in computing the mean.  For integer inputs, the default
          is `float64`; for inexact inputs, it is the same as the input
          dtype.
      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
          :ref:`ufuncs-output-type` for more details.
      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 `mean` or `sum` methods
          of sub-classes of `ndarray`.  If the sub-classes methods
          does not implement `keepdims` any exceptions will be raised.
  
      Returns
      -------
      m : ndarray, see dtype parameter above
          If `out=None`, returns a new array containing the mean values,
          otherwise a reference to the output array is returned. Nan is
          returned for slices that contain only NaNs.
  
      See Also
      --------
      average : Weighted average
      mean : Arithmetic mean taken while not ignoring NaNs
      var, nanvar
  
      Notes
      -----
      The arithmetic mean is the sum of the non-NaN elements along the axis
      divided by the number of non-NaN elements.
  
      Note that for floating-point input, the mean is computed using the same
      precision the input has.  Depending on the input data, this can cause
      the results to be inaccurate, especially for `float32`.  Specifying a
      higher-precision accumulator using the `dtype` keyword can alleviate
      this issue.
  
      Examples
      --------
      >>> a = np.array([[1, np.nan], [3, 4]])
      >>> np.nanmean(a)
      2.6666666666666665
      >>> np.nanmean(a, axis=0)
      array([2.,  4.])
      >>> np.nanmean(a, axis=1)
      array([1.,  3.5]) # may vary
  
      """
      arr, mask = _replace_nan(a, 0)
      if mask is None:
          return np.mean(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
  
      if dtype is not None:
          dtype = np.dtype(dtype)
      if dtype is not None and not issubclass(dtype.type, np.inexact):
          raise TypeError("If a is inexact, then dtype must be inexact")
      if out is not None and not issubclass(out.dtype.type, np.inexact):
          raise TypeError("If a is inexact, then out must be inexact")
  
      cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=keepdims)
      tot = np.sum(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
      avg = _divide_by_count(tot, cnt, out=out)
  
      isbad = (cnt == 0)
      if isbad.any():
          warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=3)
          # NaN is the only possible bad value, so no further
          # action is needed to handle bad results.
      return avg
  
  
  def _nanmedian1d(arr1d, overwrite_input=False):
      """
      Private function for rank 1 arrays. Compute the median ignoring NaNs.
      See nanmedian for parameter usage
      """
      arr1d_parsed, overwrite_input = _remove_nan_1d(
          arr1d, overwrite_input=overwrite_input,
      )
  
      if arr1d_parsed.size == 0:
          # Ensure that a nan-esque scalar of the appropiate type (and unit)
          # is returned for `timedelta64` and `complexfloating`
          return arr1d[-1]
  
      return np.median(arr1d_parsed, overwrite_input=overwrite_input)
  
  
  def _nanmedian(a, axis=None, out=None, overwrite_input=False):
      """
      Private function that doesn't support extended axis or keepdims.
      These methods are extended to this function using _ureduce
      See nanmedian for parameter usage
  
      """
      if axis is None or a.ndim == 1:
          part = a.ravel()
          if out is None:
              return _nanmedian1d(part, overwrite_input)
          else:
              out[...] = _nanmedian1d(part, overwrite_input)
              return out
      else:
          # for small medians use sort + indexing which is still faster than
          # apply_along_axis
          # benchmarked with shuffled (50, 50, x) containing a few NaN
          if a.shape[axis] < 600:
              return _nanmedian_small(a, axis, out, overwrite_input)
          result = np.apply_along_axis(_nanmedian1d, axis, a, overwrite_input)
          if out is not None:
              out[...] = result
          return result
  
  
  def _nanmedian_small(a, axis=None, out=None, overwrite_input=False):
      """
      sort + indexing median, faster for small medians along multiple
      dimensions due to the high overhead of apply_along_axis
  
      see nanmedian for parameter usage
      """
      a = np.ma.masked_array(a, np.isnan(a))
      m = np.ma.median(a, axis=axis, overwrite_input=overwrite_input)
      for i in range(np.count_nonzero(m.mask.ravel())):
          warnings.warn("All-NaN slice encountered", RuntimeWarning,
                        stacklevel=4)
  
      fill_value = np.timedelta64("NaT") if m.dtype.kind == "m" else np.nan
      if out is not None:
          out[...] = m.filled(fill_value)
          return out
      return m.filled(fill_value)
  
  
  def _nanmedian_dispatcher(
          a, axis=None, out=None, overwrite_input=None, keepdims=None):
      return (a, out)
  
  
  @array_function_dispatch(_nanmedian_dispatcher)
  def nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=np._NoValue):
      """
      Compute the median along the specified axis, while ignoring NaNs.
  
      Returns the median of the array elements.
  
      .. versionadded:: 1.9.0
  
      Parameters
      ----------
      a : array_like
          Input array or object that can be converted to an array.
      axis : {int, sequence of int, None}, optional
          Axis or axes along which the medians are computed. The default
          is to compute the median along a flattened version of the array.
          A sequence of axes is supported since version 1.9.0.
      out : ndarray, optional
          Alternative output array in which to place the result. It must
          have the same shape and buffer length as the expected output,
          but the type (of the output) will be cast if necessary.
      overwrite_input : bool, optional
         If True, then allow use of memory of input array `a` for
         calculations. The input array will be modified by the call to
         `median`. This will save memory when you do not need to preserve
         the contents of the input array. Treat the input as undefined,
         but it will probably be fully or partially sorted. Default is
         False. If `overwrite_input` is ``True`` and `a` is not already an
         `ndarray`, an error will be raised.
      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 this is anything but the default value it will be passed
          through (in the special case of an empty array) to the
          `mean` function of the underlying array.  If the array is
          a sub-class and `mean` does not have the kwarg `keepdims` this
          will raise a RuntimeError.
  
      Returns
      -------
      median : ndarray
          A new array holding the result. If the input contains integers
          or floats smaller than ``float64``, then the output data-type is
          ``np.float64``.  Otherwise, the data-type of the output is the
          same as that of the input. If `out` is specified, that array is
          returned instead.
  
      See Also
      --------
      mean, median, percentile
  
      Notes
      -----
      Given a vector ``V`` of length ``N``, the median of ``V`` is the
      middle value of a sorted copy of ``V``, ``V_sorted`` - i.e.,
      ``V_sorted[(N-1)/2]``, when ``N`` is odd and the average of the two
      middle values of ``V_sorted`` when ``N`` is even.
  
      Examples
      --------
      >>> a = np.array([[10.0, 7, 4], [3, 2, 1]])
      >>> a[0, 1] = np.nan
      >>> a
      array([[10., nan,  4.],
             [ 3.,  2.,  1.]])
      >>> np.median(a)
      nan
      >>> np.nanmedian(a)
      3.0
      >>> np.nanmedian(a, axis=0)
      array([6.5, 2. , 2.5])
      >>> np.median(a, axis=1)
      array([nan,  2.])
      >>> b = a.copy()
      >>> np.nanmedian(b, axis=1, overwrite_input=True)
      array([7.,  2.])
      >>> assert not np.all(a==b)
      >>> b = a.copy()
      >>> np.nanmedian(b, axis=None, overwrite_input=True)
      3.0
      >>> assert not np.all(a==b)
  
      """
      a = np.asanyarray(a)
      # apply_along_axis in _nanmedian doesn't handle empty arrays well,
      # so deal them upfront
      if a.size == 0:
          return np.nanmean(a, axis, out=out, keepdims=keepdims)
  
      r, k = function_base._ureduce(a, func=_nanmedian, axis=axis, out=out,
                                    overwrite_input=overwrite_input)
      if keepdims and keepdims is not np._NoValue:
          return r.reshape(k)
      else:
          return r
  
  
  def _nanpercentile_dispatcher(a, q, axis=None, out=None, overwrite_input=None,
                                interpolation=None, keepdims=None):
      return (a, q, out)
  
  
  @array_function_dispatch(_nanpercentile_dispatcher)
  def nanpercentile(a, q, axis=None, out=None, overwrite_input=False,
                    interpolation='linear', keepdims=np._NoValue):
      """
      Compute the qth percentile of the data along the specified axis,
      while ignoring nan values.
  
      Returns the qth percentile(s) of the array elements.
  
      .. versionadded:: 1.9.0
  
      Parameters
      ----------
      a : array_like
          Input array or object that can be converted to an array, containing
          nan values to be ignored.
      q : array_like of float
          Percentile or sequence of percentiles to compute, which must be between
          0 and 100 inclusive.
      axis : {int, tuple of int, None}, optional
          Axis or axes along which the percentiles are computed. The
          default is to compute the percentile(s) along a flattened
          version of the array.
      out : ndarray, optional
          Alternative output array in which to place the result. It must
          have the same shape and buffer length as the expected output,
          but the type (of the output) will be cast if necessary.
      overwrite_input : bool, optional
          If True, then allow the input array `a` to be modified by intermediate
          calculations, to save memory. In this case, the contents of the input
          `a` after this function completes is undefined.
      interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
          This optional parameter specifies the interpolation method to
          use when the desired percentile lies between two data points
          ``i < j``:
  
          * '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``.
      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 array `a`.
  
          If this is anything but the default value it will be passed
          through (in the special case of an empty array) to the
          `mean` function of the underlying array.  If the array is
          a sub-class and `mean` does not have the kwarg `keepdims` this
          will raise a RuntimeError.
  
      Returns
      -------
      percentile : scalar or ndarray
          If `q` is a single percentile and `axis=None`, then the result
          is a scalar. If multiple percentiles are given, first axis of
          the result corresponds to the percentiles. The other axes are
          the axes that remain after the reduction of `a`. If the input
          contains integers or floats smaller than ``float64``, the output
          data-type is ``float64``. Otherwise, the output data-type is the
          same as that of the input. If `out` is specified, that array is
          returned instead.
  
      See Also
      --------
      nanmean
      nanmedian : equivalent to ``nanpercentile(..., 50)``
      percentile, median, mean
      nanquantile : equivalent to nanpercentile, but with q in the range [0, 1].
  
      Notes
      -----
      Given a vector ``V`` of length ``N``, the ``q``-th percentile of
      ``V`` is the value ``q/100`` of the way from the minimum to the
      maximum in a sorted copy of ``V``. The values and distances of
      the two nearest neighbors as well as the `interpolation` parameter
      will determine the percentile if the normalized ranking does not
      match the location of ``q`` exactly. This function is the same as
      the median if ``q=50``, the same as the minimum if ``q=0`` and the
      same as the maximum if ``q=100``.
  
      Examples
      --------
      >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
      >>> a[0][1] = np.nan
      >>> a
      array([[10.,  nan,   4.],
            [ 3.,   2.,   1.]])
      >>> np.percentile(a, 50)
      nan
      >>> np.nanpercentile(a, 50)
      3.0
      >>> np.nanpercentile(a, 50, axis=0)
      array([6.5, 2. , 2.5])
      >>> np.nanpercentile(a, 50, axis=1, keepdims=True)
      array([[7.],
             [2.]])
      >>> m = np.nanpercentile(a, 50, axis=0)
      >>> out = np.zeros_like(m)
      >>> np.nanpercentile(a, 50, axis=0, out=out)
      array([6.5, 2. , 2.5])
      >>> m
      array([6.5,  2. ,  2.5])
  
      >>> b = a.copy()
      >>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)
      array([7., 2.])
      >>> assert not np.all(a==b)
  
      """
      a = np.asanyarray(a)
      q = np.true_divide(q, 100.0)  # handles the asarray for us too
      if not function_base._quantile_is_valid(q):
          raise ValueError("Percentiles must be in the range [0, 100]")
      return _nanquantile_unchecked(
          a, q, axis, out, overwrite_input, interpolation, keepdims)
  
  
  def _nanquantile_dispatcher(a, q, axis=None, out=None, overwrite_input=None,
                              interpolation=None, keepdims=None):
      return (a, q, out)
  
  
  @array_function_dispatch(_nanquantile_dispatcher)
  def nanquantile(a, q, axis=None, out=None, overwrite_input=False,
                  interpolation='linear', keepdims=np._NoValue):
      """
      Compute the qth quantile of the data along the specified axis,
      while ignoring nan values.
      Returns the qth quantile(s) of the array elements.
  
      .. versionadded:: 1.15.0
  
      Parameters
      ----------
      a : array_like
          Input array or object that can be converted to an array, containing
          nan values to be ignored
      q : array_like of float
          Quantile or sequence of quantiles to compute, which must be between
          0 and 1 inclusive.
      axis : {int, tuple of int, None}, optional
          Axis or axes along which the quantiles are computed. The
          default is to compute the quantile(s) along a flattened
          version of the array.
      out : ndarray, optional
          Alternative output array in which to place the result. It must
          have the same shape and buffer length as the expected output,
          but the type (of the output) will be cast if necessary.
      overwrite_input : bool, optional
          If True, then allow the input array `a` to be modified by intermediate
          calculations, to save memory. In this case, the contents of the input
          `a` after this function completes is undefined.
      interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
          This optional parameter specifies the interpolation method to
          use when the desired quantile lies between two data points
          ``i < j``:
  
          * 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``.
  
      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 array `a`.
  
          If this is anything but the default value it will be passed
          through (in the special case of an empty array) to the
          `mean` function of the underlying array.  If the array is
          a sub-class and `mean` does not have the kwarg `keepdims` this
          will raise a RuntimeError.
  
      Returns
      -------
      quantile : scalar or ndarray
          If `q` is a single percentile and `axis=None`, then the result
          is a scalar. If multiple quantiles are given, first axis of
          the result corresponds to the quantiles. The other axes are
          the axes that remain after the reduction of `a`. If the input
          contains integers or floats smaller than ``float64``, the output
          data-type is ``float64``. Otherwise, the output data-type is the
          same as that of the input. If `out` is specified, that array is
          returned instead.
  
      See Also
      --------
      quantile
      nanmean, nanmedian
      nanmedian : equivalent to ``nanquantile(..., 0.5)``
      nanpercentile : same as nanquantile, but with q in the range [0, 100].
  
      Examples
      --------
      >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
      >>> a[0][1] = np.nan
      >>> a
      array([[10.,  nan,   4.],
            [ 3.,   2.,   1.]])
      >>> np.quantile(a, 0.5)
      nan
      >>> np.nanquantile(a, 0.5)
      3.0
      >>> np.nanquantile(a, 0.5, axis=0)
      array([6.5, 2. , 2.5])
      >>> np.nanquantile(a, 0.5, axis=1, keepdims=True)
      array([[7.],
             [2.]])
      >>> m = np.nanquantile(a, 0.5, axis=0)
      >>> out = np.zeros_like(m)
      >>> np.nanquantile(a, 0.5, axis=0, out=out)
      array([6.5, 2. , 2.5])
      >>> m
      array([6.5,  2. ,  2.5])
      >>> b = a.copy()
      >>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)
      array([7., 2.])
      >>> assert not np.all(a==b)
      """
      a = np.asanyarray(a)
      q = np.asanyarray(q)
      if not function_base._quantile_is_valid(q):
          raise ValueError("Quantiles must be in the range [0, 1]")
      return _nanquantile_unchecked(
          a, q, axis, out, overwrite_input, interpolation, keepdims)
  
  
  def _nanquantile_unchecked(a, q, axis=None, out=None, overwrite_input=False,
                             interpolation='linear', keepdims=np._NoValue):
      """Assumes that q is in [0, 1], and is an ndarray"""
      # apply_along_axis in _nanpercentile doesn't handle empty arrays well,
      # so deal them upfront
      if a.size == 0:
          return np.nanmean(a, axis, out=out, keepdims=keepdims)
  
      r, k = function_base._ureduce(
          a, func=_nanquantile_ureduce_func, q=q, axis=axis, out=out,
          overwrite_input=overwrite_input, interpolation=interpolation
      )
      if keepdims and keepdims is not np._NoValue:
          return r.reshape(q.shape + k)
      else:
          return r
  
  
  def _nanquantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False,
                                interpolation='linear'):
      """
      Private function that doesn't support extended axis or keepdims.
      These methods are extended to this function using _ureduce
      See nanpercentile for parameter usage
      """
      if axis is None or a.ndim == 1:
          part = a.ravel()
          result = _nanquantile_1d(part, q, overwrite_input, interpolation)
      else:
          result = np.apply_along_axis(_nanquantile_1d, axis, a, q,
                                       overwrite_input, interpolation)
          # apply_along_axis fills in collapsed axis with results.
          # Move that axis to the beginning to match percentile's
          # convention.
          if q.ndim != 0:
              result = np.moveaxis(result, axis, 0)
  
      if out is not None:
          out[...] = result
      return result
  
  
  def _nanquantile_1d(arr1d, q, overwrite_input=False, interpolation='linear'):
      """
      Private function for rank 1 arrays. Compute quantile ignoring NaNs.
      See nanpercentile for parameter usage
      """
      arr1d, overwrite_input = _remove_nan_1d(arr1d,
          overwrite_input=overwrite_input)
      if arr1d.size == 0:
          return np.full(q.shape, np.nan)[()]  # convert to scalar
  
      return function_base._quantile_unchecked(
          arr1d, q, overwrite_input=overwrite_input, interpolation=interpolation)
  
  
  def _nanvar_dispatcher(
          a, axis=None, dtype=None, out=None, ddof=None, keepdims=None):
      return (a, out)
  
  
  @array_function_dispatch(_nanvar_dispatcher)
  def nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue):
      """
      Compute the variance along the specified axis, while ignoring NaNs.
  
      Returns the variance of the array elements, a measure of the spread of
      a distribution.  The variance is computed for the flattened array by
      default, otherwise over the specified axis.
  
      For all-NaN slices or slices with zero degrees of freedom, NaN is
      returned and a `RuntimeWarning` is raised.
  
      .. versionadded:: 1.8.0
  
      Parameters
      ----------
      a : array_like
          Array containing numbers whose variance 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 variance is computed.  The default is to compute
          the variance of the flattened array.
      dtype : data-type, optional
          Type to use in computing the variance.  For arrays of integer type
          the default is `float64`; for arrays of float types it is the same as
          the array type.
      out : ndarray, optional
          Alternate output array in which to place the result.  It must have
          the same shape as the expected output, but the type is cast if
          necessary.
      ddof : int, optional
          "Delta Degrees of Freedom": the divisor used in the calculation is
          ``N - ddof``, where ``N`` represents the number of non-NaN
          elements. By default `ddof` is zero.
      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`.
  
  
      Returns
      -------
      variance : ndarray, see dtype parameter above
          If `out` is None, return a new array containing the variance,
          otherwise return a reference to the output array. If ddof is >= the
          number of non-NaN elements in a slice or the slice contains only
          NaNs, then the result for that slice is NaN.
  
      See Also
      --------
      std : Standard deviation
      mean : Average
      var : Variance while not ignoring NaNs
      nanstd, nanmean
      :ref:`ufuncs-output-type`
  
      Notes
      -----
      The variance is the average of the squared deviations from the mean,
      i.e.,  ``var = mean(abs(x - x.mean())**2)``.
  
      The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
      If, however, `ddof` is specified, the divisor ``N - ddof`` is used
      instead.  In standard statistical practice, ``ddof=1`` provides an
      unbiased estimator of the variance of a hypothetical infinite
      population.  ``ddof=0`` provides a maximum likelihood estimate of the
      variance for normally distributed variables.
  
      Note that for complex numbers, the absolute value is taken before
      squaring, so that the result is always real and nonnegative.
  
      For floating-point input, the variance is computed using the same
      precision the input has.  Depending on the input data, this can cause
      the results to be inaccurate, especially for `float32` (see example
      below).  Specifying a higher-accuracy accumulator using the ``dtype``
      keyword can alleviate this issue.
  
      For this function to work on sub-classes of ndarray, they must define
      `sum` with the kwarg `keepdims`
  
      Examples
      --------
      >>> a = np.array([[1, np.nan], [3, 4]])
      >>> np.nanvar(a)
      1.5555555555555554
      >>> np.nanvar(a, axis=0)
      array([1.,  0.])
      >>> np.nanvar(a, axis=1)
      array([0.,  0.25])  # may vary
  
      """
      arr, mask = _replace_nan(a, 0)
      if mask is None:
          return np.var(arr, axis=axis, dtype=dtype, out=out, ddof=ddof,
                        keepdims=keepdims)
  
      if dtype is not None:
          dtype = np.dtype(dtype)
      if dtype is not None and not issubclass(dtype.type, np.inexact):
          raise TypeError("If a is inexact, then dtype must be inexact")
      if out is not None and not issubclass(out.dtype.type, np.inexact):
          raise TypeError("If a is inexact, then out must be inexact")
  
      # Compute mean
      if type(arr) is np.matrix:
          _keepdims = np._NoValue
      else:
          _keepdims = True
      # we need to special case matrix for reverse compatibility
      # in order for this to work, these sums need to be called with
      # keepdims=True, however matrix now raises an error in this case, but
      # the reason that it drops the keepdims kwarg is to force keepdims=True
      # so this used to work by serendipity.
      cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=_keepdims)
      avg = np.sum(arr, axis=axis, dtype=dtype, keepdims=_keepdims)
      avg = _divide_by_count(avg, cnt)
  
      # Compute squared deviation from mean.
      np.subtract(arr, avg, out=arr, casting='unsafe')
      arr = _copyto(arr, 0, mask)
      if issubclass(arr.dtype.type, np.complexfloating):
          sqr = np.multiply(arr, arr.conj(), out=arr).real
      else:
          sqr = np.multiply(arr, arr, out=arr)
  
      # Compute variance.
      var = np.sum(sqr, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
      if var.ndim < cnt.ndim:
          # Subclasses of ndarray may ignore keepdims, so check here.
          cnt = cnt.squeeze(axis)
      dof = cnt - ddof
      var = _divide_by_count(var, dof)
  
      isbad = (dof <= 0)
      if np.any(isbad):
          warnings.warn("Degrees of freedom <= 0 for slice.", RuntimeWarning,
                        stacklevel=3)
          # NaN, inf, or negative numbers are all possible bad
          # values, so explicitly replace them with NaN.
          var = _copyto(var, np.nan, isbad)
      return var
  
  
  def _nanstd_dispatcher(
          a, axis=None, dtype=None, out=None, ddof=None, keepdims=None):
      return (a, out)
  
  
  @array_function_dispatch(_nanstd_dispatcher)
  def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue):
      """
      Compute the standard deviation along the specified axis, while
      ignoring NaNs.
  
      Returns the standard deviation, a measure of the spread of a
      distribution, of the non-NaN array elements. The standard deviation is
      computed for the flattened array by default, otherwise over the
      specified axis.
  
      For all-NaN slices or slices with zero degrees of freedom, NaN is
      returned and a `RuntimeWarning` is raised.
  
      .. versionadded:: 1.8.0
  
      Parameters
      ----------
      a : array_like
          Calculate the standard deviation of the non-NaN values.
      axis : {int, tuple of int, None}, optional
          Axis or axes along which the standard deviation is computed. The default is
          to compute the standard deviation of the flattened array.
      dtype : dtype, optional
          Type to use in computing the standard deviation. For arrays of
          integer type the default is float64, for arrays of float types it
          is the same as the array type.
      out : ndarray, optional
          Alternative output array in which to place the result. It must have
          the same shape as the expected output but the type (of the
          calculated values) will be cast if necessary.
      ddof : int, optional
          Means Delta Degrees of Freedom.  The divisor used in calculations
          is ``N - ddof``, where ``N`` represents the number of non-NaN
          elements.  By default `ddof` is zero.
  
      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 this value is anything but the default it is passed through
          as-is to the relevant functions of the sub-classes.  If these
          functions do not have a `keepdims` kwarg, a RuntimeError will
          be raised.
  
      Returns
      -------
      standard_deviation : ndarray, see dtype parameter above.
          If `out` is None, return a new array containing the standard
          deviation, otherwise return a reference to the output array. If
          ddof is >= the number of non-NaN elements in a slice or the slice
          contains only NaNs, then the result for that slice is NaN.
  
      See Also
      --------
      var, mean, std
      nanvar, nanmean
      :ref:`ufuncs-output-type`
  
      Notes
      -----
      The standard deviation is the square root of the average of the squared
      deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``.
  
      The average squared deviation is normally calculated as
      ``x.sum() / N``, where ``N = len(x)``.  If, however, `ddof` is
      specified, the divisor ``N - ddof`` is used instead. In standard
      statistical practice, ``ddof=1`` provides an unbiased estimator of the
      variance of the infinite population. ``ddof=0`` provides a maximum
      likelihood estimate of the variance for normally distributed variables.
      The standard deviation computed in this function is the square root of
      the estimated variance, so even with ``ddof=1``, it will not be an
      unbiased estimate of the standard deviation per se.
  
      Note that, for complex numbers, `std` takes the absolute value before
      squaring, so that the result is always real and nonnegative.
  
      For floating-point input, the *std* is computed using the same
      precision the input has. Depending on the input data, this can cause
      the results to be inaccurate, especially for float32 (see example
      below).  Specifying a higher-accuracy accumulator using the `dtype`
      keyword can alleviate this issue.
  
      Examples
      --------
      >>> a = np.array([[1, np.nan], [3, 4]])
      >>> np.nanstd(a)
      1.247219128924647
      >>> np.nanstd(a, axis=0)
      array([1., 0.])
      >>> np.nanstd(a, axis=1)
      array([0.,  0.5]) # may vary
  
      """
      var = nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
                   keepdims=keepdims)
      if isinstance(var, np.ndarray):
          std = np.sqrt(var, out=var)
      else:
          std = var.dtype.type(np.sqrt(var))
      return std
  