MAINT: Refactor nanfunctions.

nanmax, nanmin
--------------
Add out and keepdims keywords.

nanargmin, nanargmax
--------------------
A NanWarning is raised if an all NaN slice detected. For all such
slices np.iingo(np.intp).min is returned as the index value.

nansum
------
The keywords dtype, out, and keepdims are added.

A FutureWarning is raised, as in the future the mean of an empty
slice after NaN replacement will be 0 instead of the current NaN.

nanmean, nanvar, nanstd
-----------------------
For all, if the input array is of inexact type then the dtype and out
parameters must be of inexact type if specified.  That insures that NaNs
can be returned when appropriate.

The nanmean function detects empty slices after NaN replacement and
raises a NanWarning. NaN is returned as the value for all such slices.

The nanmean and nanstd functions detect degrees of freedom <= 0 after
NaN replacement and raise a NanWarning. NaN is returned as the value for
all such slices.

1 files changed, 468 insertions, 333 deletions

diff --git a/numpy/lib/nanfunctions.py b/numpy/lib/nanfunctions.py
index f0e635791..12f4a8376 100644
--- a/numpy/lib/nanfunctions.py
+++ b/numpy/lib/nanfunctions.py
@@ -1,215 +1,147 @@
-"""Functions that ignore nan.
+"""
+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
+- `nanmean` -- mean of non-NaN values
+- `nanvar` -- variance of non-NaN values
+- `nanstd` -- standard deviation of non-NaN values
+
+Classes
+-------
+- `NanWarning` -- Warning raised by nanfunctions
 
 """
 from __future__ import division, absolute_import, print_function
 
+import warnings
 import numpy as np
 
 __all__ = [
     'nansum', 'nanmax', 'nanmin', 'nanargmax', 'nanargmin', 'nanmean',
-    'nanvar', 'nanstd'
+    'nanvar', 'nanstd', 'NanWarning'
     ]
 
-
-def _nanmean(a, axis=None, dtype=None, out=None, keepdims=False):
-    # Using array() instead of asanyarray() because the former always
-    # makes a copy, which is important due to the copyto() action later
-    arr = np.array(a, subok=True)
-    mask = np.isnan(arr)
-
-    # Cast bool, unsigned int, and int to float64
-    if np.dtype is None and issubclass(arr.dtype.type, (np.integer, np.bool_)):
-        ret = np.add.reduce(arr, axis=axis, dtype='f8',
-                            out=out, keepdims=keepdims)
-    else:
-        np.copyto(arr, 0.0, where=mask)
-        ret = np.add.reduce(arr, axis=axis, dtype=dtype,
-                            out=out, keepdims=keepdims)
-    rcount = (~mask).sum(axis=axis)
-    if isinstance(ret, np.ndarray):
-        ret = np.true_divide(ret, rcount, out=ret, casting='unsafe',
-                             subok=False)
-    else:
-        ret = ret / rcount
-    return ret
-
-
-def _nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
-    # Using array() instead of asanyarray() because the former always
-    # makes a copy, which is important due to the copyto() action later
-    arr = np.array(a, subok=True)
-    mask = np.isnan(arr)
-
-    # First compute the mean, saving 'rcount' for reuse later
-    if dtype is None and issubclass(arr.dtype.type, (np.integer, np.bool_)):
-        arrmean = np.add.reduce(arr, axis=axis, dtype='f8', keepdims=True)
-    else:
-        np.copyto(arr, 0.0, where=mask)
-        arrmean = np.add.reduce(arr, axis=axis, dtype=dtype, keepdims=True)
-    rcount = (~mask).sum(axis=axis, keepdims=True)
-    if isinstance(arrmean, np.ndarray):
-        arrmean = np.true_divide(arrmean, rcount,
-                            out=arrmean, casting='unsafe', subok=False)
-    else:
-        arrmean = arrmean / rcount
-
-    # arr - arrmean
-    x = arr - arrmean
-    np.copyto(x, 0.0, where=mask)
-
-    # (arr - arrmean) ** 2
-    if issubclass(arr.dtype.type, np.complex_):
-        x = np.multiply(x, np.conjugate(x), out=x).real
-    else:
-        x = np.multiply(x, x, out=x)
-
-    # add.reduce((arr - arrmean) ** 2, axis)
-    ret = np.add.reduce(x, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
-
-    # add.reduce((arr - arrmean) ** 2, axis) / (n - ddof)
-    if not keepdims and isinstance(rcount, np.ndarray):
-        rcount = rcount.squeeze(axis=axis)
-    rcount -= ddof
-    if isinstance(ret, np.ndarray):
-        ret = np.true_divide(ret, rcount, out=ret, casting='unsafe', subok=False)
-    else:
-        ret = ret / rcount
-
-    return ret
+class NanWarning(RuntimeWarning): pass
 
 
-def _nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
-    ret = _nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
-                  keepdims=keepdims)
-
-    if isinstance(ret, np.ndarray):
-        ret = np.sqrt(ret, out=ret)
-    else:
-        ret = np.sqrt(ret)
-
-    return ret
-
-
-def _nanop(op, fill, a, axis=None):
+def _replace_nan(a, val):
     """
-    General operation on arrays with not-a-number values.
+    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.
 
     Parameters
     ----------
-    op : callable
-        Operation to perform.
-    fill : float
-        NaN values are set to fill before doing the operation.
     a : array-like
         Input array.
-    axis : {int, None}, optional
-        Axis along which the operation is computed.
-        By default the input is flattened.
+    val : float
+        NaN values are set to val before doing the operation.
 
     Returns
     -------
-    y : {ndarray, scalar}
-        Processed data.
+    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.
 
     """
-    y = np.array(a, subok=True)
-
-    # We only need to take care of NaN's in floating point arrays
-    dt = y.dtype
-    if np.issubdtype(dt, np.integer) or np.issubdtype(dt, np.bool_):
-        return op(y, axis=axis)
+    is_new = not isinstance(a, np.ndarray)
+    if is_new:
+        a = np.array(a)
+    if not issubclass(a.dtype.type, np.inexact):
+        return a, None
+    if not is_new:
+        # need copy
+        a = np.array(a, subok=True)
 
     mask = np.isnan(a)
-    # y[mask] = fill
-    # We can't use fancy indexing here as it'll mess w/ MaskedArrays
-    # Instead, let's fill the array directly...
-    np.copyto(y, fill, where=mask)
-    res = op(y, axis=axis)
-    mask_all_along_axis = mask.all(axis=axis)
-
-    # Along some axes, only nan's were encountered.  As such, any values
-    # calculated along that axis should be set to nan.
-    if mask_all_along_axis.any():
-        if np.isscalar(res):
-            res = np.nan
-        else:
-            res[mask_all_along_axis] = np.nan
+    np.copyto(a, val, where=mask)
+    return a, mask
 
-    return res
 
-
-def nansum(a, axis=None):
+def _copyto(a, val, mask):
     """
-    Return the sum of array elements over a given axis treating
-    Not a Numbers (NaNs) as zero.
+    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 : array_like
-        Array containing numbers whose sum is desired. If `a` is not an
-        array, a conversion is attempted.
-    axis : int, optional
-        Axis along which the sum is computed. The default is to compute
-        the sum of the flattened array.
+    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
     -------
-    y : 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, a scalar is returned with
-        the same dtype as `a`.
-
-    See Also
-    --------
-    numpy.sum : Sum across array including Not a Numbers.
-    isnan : Shows which elements are Not a Number (NaN).
-    isfinite: Shows which elements are not: Not a Number, positive and
-             negative infinity
+    res : ndarray, scalar
+        Array with elements replaced or scalar `val`.
 
-    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.
-    If positive or negative infinity are present the result is positive or
-    negative infinity. But if both positive and negative infinity are present,
-    the result is Not A Number (NaN).
-
-    Arithmetic is modular when using integer types (all elements of `a` must
-    be finite i.e. no elements that are NaNs, positive infinity and negative
-    infinity because NaNs are floating point types), and no error is raised
-    on overflow.
+    """
+    if isinstance(a, np.ndarray):
+        np.copyto(a, val, where=mask, casting='unsafe')
+    else:
+        a = a.dtype.type(val)
+    return a
 
 
-    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.])
+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.
 
-    When positive infinity and negative infinity are present
+    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.
 
-    >>> np.nansum([1, np.nan, np.inf])
-    inf
-    >>> np.nansum([1, np.nan, np.NINF])
-    -inf
-    >>> np.nansum([1, np.nan, np.inf, np.NINF])
-    nan
+    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.
 
     """
-    return _nanop(np.sum, 0, a, axis)
+    with np.errstate(invalid='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(a, axis=None):
+def nanmin(a, axis=None, out=None, keepdims=False):
     """
-    Return the minimum of an array or minimum along an axis, ignoring any NaNs.
+    Return the minimum of an array or minimum along an axis, ignoring any
+    NaNs.
 
     Parameters
     ----------
@@ -219,6 +151,19 @@ def nanmin(a, axis=None):
     axis : int, optional
         Axis 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 `doc.ufuncs` for 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`.
+
+        .. versionadded:: 1.8.0
 
     Returns
     -------
@@ -271,50 +216,10 @@ def nanmin(a, axis=None):
     -inf
 
     """
-    a = np.asanyarray(a)
-    if axis is not None:
-        return np.fmin.reduce(a, axis)
-    else:
-        return np.fmin.reduce(a.flat)
-
-
-def nanargmin(a, axis=None):
-    """
-    Return indices of the minimum values over an axis, ignoring NaNs.
-
-    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])
-
-    """
-    return _nanop(np.argmin, np.inf, a, axis)
+    return np.fmin.reduce(a, axis=axis, out=out, keepdims=keepdims)
 
 
-def nanmax(a, axis=None):
+def nanmax(a, axis=None, out=None, keepdims=False):
     """
     Return the maximum of an array or maximum along an axis, ignoring any NaNs.
 
@@ -326,6 +231,19 @@ def nanmax(a, axis=None):
     axis : int, optional
         Axis 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 `doc.ufuncs` for 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`.
+
+        .. versionadded:: 1.8.0
 
     Returns
     -------
@@ -378,16 +296,61 @@ def nanmax(a, axis=None):
     inf
 
     """
-    a = np.asanyarray(a)
-    if axis is not None:
-        return np.fmax.reduce(a, axis)
-    else:
-        return np.fmax.reduce(a.flat)
+    return np.fmax.reduce(a, axis=axis, out=out, keepdims=keepdims)
+
+
+def nanargmin(a, axis=None):
+    """
+    Return indices of the minimum values over an axis, ignoring NaNs.  For
+    all NaN slices the minimum value of the np.intp type is returned and a
+    `NanWarning` is raised.
+
+    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)
+    if mask is None:
+        return np.argmin(a, axis)
+    # May later want to do something special for all nan slices.
+    mask = mask.all(axis=axis)
+    ind = np.argmin(a, axis)
+    if mask.any():
+        warnings.warn("All NaN axis detected.", NanWarning)
+        ind =_copyto(ind, np.iinfo(np.intp).min, mask)
+    return ind
 
 
 def nanargmax(a, axis=None):
     """
-    Return indices of the maximum values over an axis, ignoring NaNs.
+    Return indices of the maximum values over an axis, ignoring NaNs. For
+    all NaN slices the minimum value of the np.intp type is returned and
+    a `NanWarning` is raised.
 
     Parameters
     ----------
@@ -418,7 +381,116 @@ def nanargmax(a, axis=None):
     array([1, 1])
 
     """
-    return _nanop(np.argmax, -np.inf, a, axis)
+    a, mask = _replace_nan(a, -np.inf)
+    if mask is None:
+        return np.argmax(a, axis)
+    # May later want to do something special for all nan slices.
+    mask = mask.all(axis=axis)
+    ind = np.argmax(a, axis)
+    if mask.any():
+        warnings.warn("All NaN axis detected.", NanWarning)
+        ind = _copyto(ind, np.iinfo(np.intp).min, mask)
+    return ind
+
+
+def nansum(a, axis=None, dtype=None, out=None, keepdims=0):
+    """
+    Return the sum of array elements over a given axis treating
+    Not a Numbers (NaNs) as zero.
+
+    FutureWarning: In Numpy versions <= 1.8 Nan is returned for slices that
+    are all NaN or empty. In later versions zero will be returned.
+
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose sum is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : int, optional
+        Axis along which the sum is computed. The default is to compute
+        the sum of the flattened array.
+    dtype : data-type, optional
+        Type to use in computing the sum.  For integer inputs, the default
+        is the same as `int64`. For inexact inputs, it 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 `doc.ufuncs` for details. The casting of NaN to integer can
+        yield unexpected results.
+
+        .. versionadded:: 1.8.0
+    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`.
+
+        .. versionadded:: 1.8.0
+
+    Returns
+    -------
+    y : ndarray or numpy scalar
+
+    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
+    -----
+    Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic
+    (IEEE 754). This means that Not a Number is not equivalent to infinity.
+    If positive or negative infinity are present the result is positive or
+    negative infinity. But if both positive and negative infinity are present,
+    the result is Not A Number (NaN).
+
+    Arithmetic is modular when using integer types (all elements of `a` must
+    be finite i.e. no elements that are NaNs, positive infinity and negative
+    infinity because NaNs are floating point types), and no error is raised
+    on overflow.
+
+
+    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.])
+
+    When positive infinity and negative infinity are present
+
+    >>> np.nansum([1, np.nan, np.inf])
+    inf
+    >>> np.nansum([1, np.nan, np.NINF])
+    -inf
+    >>> np.nansum([1, np.nan, np.inf, np.NINF])
+    nan
+
+    """
+    a, mask = _replace_nan(a, 0)
+    # In version 1.9 uncomment the following line and delete the rest.
+    #return a.sum(axis, dtype, out, keepdims)
+    warnings.warn("In Numpy 1.9 the sum along empty slices will be zero.",
+            FutureWarning)
+
+    if mask is None:
+        return a.sum(axis, dtype, out, keepdims)
+    mask = mask.all(axis, keepdims=keepdims)
+    tot = np.add.reduce(a, axis, dtype, out, keepdims)
+    if mask.any():
+        tot = _copyto(tot, np.nan, mask)
+    return tot
 
 
 def nanmean(a, axis=None, dtype=None, out=None, keepdims=False):
@@ -429,6 +501,10 @@ def nanmean(a, axis=None, dtype=None, out=None, keepdims=False):
     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 `NanWarning` is raised.
+
+    .. versionadded:: 1.8.0
+
     Parameters
     ----------
     a : array_like
@@ -439,7 +515,7 @@ def nanmean(a, axis=None, dtype=None, out=None, keepdims=False):
         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 floating point inputs, it is the same as the
+        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
@@ -455,7 +531,8 @@ def nanmean(a, axis=None, dtype=None, out=None, keepdims=False):
     -------
     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.
+        otherwise a reference to the output array is returned. Nan is
+        returned for slices that contain only NaNs.
 
     See Also
     --------
@@ -465,8 +542,8 @@ def nanmean(a, axis=None, dtype=None, out=None, keepdims=False):
 
     Notes
     -----
-    The arithmetic mean is the sum of the non-nan elements along the axis
-    divided by the number of non-nan elements.
+    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
@@ -485,14 +562,161 @@ def nanmean(a, axis=None, dtype=None, out=None, keepdims=False):
     array([ 1.,  3.5])
 
     """
-    if not (type(a) is np.ndarray):
-        try:
-            mean = a.nanmean
-            return mean(axis=axis, dtype=dtype, out=out)
-        except AttributeError:
-            pass
+    arr, mask = _replace_nan(a, 0)
+    if mask is None:
+        return np.mean(arr, 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")
+
+    # The warning context speeds things up.
+    with warnings.catch_warnings():
+        warnings.simplefilter('ignore')
+        cnt = np.add.reduce(~mask, axis, dtype=np.intp, keepdims=keepdims)
+        tot = np.add.reduce(arr, 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", NanWarning)
+        # NaN is the only possible bad value, so no further
+        # action is needed to handle bad results.
+    return avg
 
-    return _nanmean(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
+
+def nanvar(a, axis=None, dtype=None, out=None, ddof=0,
+           keepdims=False):
+    """
+    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 NaN is returned and a `NanWarning` 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, optional
+        Axis 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 `float32`; 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 `arr`.
+
+    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
+    numpy.doc.ufuncs : Section "Output arguments"
+
+    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.
+
+    Examples
+    --------
+    >>> a = np.array([[1, np.nan], [3, 4]])
+    >>> np.var(a)
+    1.5555555555555554
+    >>> np.nanvar(a, axis=0)
+    array([ 1.,  0.])
+    >>> np.nanvar(a, axis=1)
+    array([ 0.,  0.25])
+
+    """
+    arr, mask = _replace_nan(a, 0)
+    if mask is None:
+        return np.var(arr, 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")
+
+    with warnings.catch_warnings():
+        warnings.simplefilter('ignore')
+
+        # Compute mean
+        cnt = np.add.reduce(~mask, axis, dtype=np.intp, keepdims=True)
+        tot = np.add.reduce(arr, axis, dtype=dtype, keepdims=True)
+        avg = np.divide(tot, cnt, out=tot)
+
+        # Compute squared deviation from mean.
+        x = arr - avg
+        np.copyto(x, 0, where=mask)
+        if issubclass(arr.dtype.type, np.complexfloating):
+            sqr = np.multiply(x, x.conj(), out=x).real
+        else:
+            sqr = np.multiply(x, x, out=x)
+
+        # adjust cnt.
+        if not keepdims:
+            cnt = cnt.squeeze(axis)
+        cnt -= ddof
+
+        # Compute variance.
+        var = np.add.reduce(sqr, axis, dtype=dtype, out=out, keepdims=keepdims)
+        var = _divide_by_count(var, cnt)
+
+    isbad = (cnt <= 0)
+    if isbad.any():
+        warnings.warn("Degrees of freedom <= 0 for slice.", NanWarning)
+        # 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(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
@@ -504,6 +728,10 @@ def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
     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 NaN is returned and a `NanWarning` is raised.
+
+    .. versionadded:: 1.8.0
+
     Parameters
     ----------
     a : array_like
@@ -521,8 +749,8 @@ def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
         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 elements.
-        By default `ddof` is zero.
+        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,
@@ -531,8 +759,10 @@ def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
     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 `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
     --------
@@ -575,104 +805,9 @@ def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False):
     array([ 0.,  0.5])
 
     """
-
-    if not (type(a) is np.ndarray):
-        try:
-            nanstd = a.nanstd
-            return nanstd(axis=axis, dtype=dtype, out=out, ddof=ddof)
-        except AttributeError:
-            pass
-
-    return _nanstd(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
-                   keepdims=keepdims)
-
-
-def nanvar(a, axis=None, dtype=None, out=None, ddof=0,
-           keepdims=False):
-    """
-    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.
-
-    Parameters
-    ----------
-    a : array_like
-        Array containing numbers whose variance is desired.  If `a` is not an
-        array, a conversion is attempted.
-    axis : int, optional
-        Axis 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 `float32`; 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 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 `arr`.
-
-    Returns
-    -------
-    variance : ndarray, see dtype parameter above
-        If ``out=None``, returns a new array containing the variance;
-        otherwise, a reference to the output array is returned.
-
-    See Also
-    --------
-    std : Standard deviation
-    mean : Average
-    var : Variance while not ignoring NaNs
-    nanstd, nanmean
-    numpy.doc.ufuncs : Section "Output arguments"
-
-    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.
-
-    Examples
-    --------
-    >>> a = np.array([[1, np.nan], [3, 4]])
-    >>> np.var(a)
-    1.5555555555555554
-    >>> np.nanvar(a, axis=0)
-    array([ 1.,  0.])
-    >>> np.nanvar(a, axis=1)
-    array([ 0.,  0.25])
-
-    """
-    if not (type(a) is np.ndarray):
-        try:
-            nanvar = a.nanvar
-            return nanvar(axis=axis, dtype=dtype, out=out, ddof=ddof)
-        except AttributeError:
-            pass
-
-    return _nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
-                            keepdims=keepdims)
+    var = nanvar(a, axis, dtype, out, ddof, keepdims)
+    if isinstance(var, np.ndarray):
+        std = np.sqrt(var, out=var)
+    else:
+        std = var.dtype.type(np.sqrt(var))
+    return std