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ss(a, axis=None)

Sum of the square of each element along the specified axis.

Parameters
----------
a : array_like
    Array whose sum of squares is desired. If `a` is not an array, a
    conversion is attempted.
axis : {int, None}, optional
    Axis along which the sum of squares is computed. The default
    (axis=None) is to sum the squares of the flattened array.

Returns
-------
y : ndarray
    The sum of a**2 along the given axis.

Examples
--------
>>> a = np.array([1., 2., 5.])
>>> bn.ss(a)
30.0

And calculating along an axis:

>>> b = np.array([[1., 2., 5.], [2., 5., 6.]])
>>> bn.ss(b, axis=1)
array([ 30., 65.])

Bottleneck functions that reduce the input array along a specified axis.nanmin(a, axis=None)

Minimum values along specified axis, ignoring NaNs.

When all-NaN slices are encountered, NaN is returned for that slice.

Parameters
----------
a : array_like
    Input array. If `a` is not an array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the minimum is computed. The default (axis=None) is
    to compute the minimum of the flattened array.

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. The
    same dtype as `a` is returned.

See also
--------
bottleneck.nanmax: Maximum along specified axis, ignoring NaNs.
bottleneck.nanargmin: Indices of minimum values along axis, ignoring NaNs.

Examples
--------
>>> bn.nanmin(1)
1
>>> bn.nanmin([1])
1
>>> bn.nanmin([1, np.nan])
1.0
>>> a = np.array([[1, 4], [1, np.nan]])
>>> bn.nanmin(a)
1.0
>>> bn.nanmin(a, axis=0)
array([ 1.,  4.])

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nanmedian(a, axis=None)

Median of array elements along given axis ignoring NaNs.

Parameters
----------
a : array_like
    Input array. If `a` is not an array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the median is computed. The default (axis=None) is to
    compute the median of the flattened array.

Returns
-------
y : ndarray
    An array with the same shape as `a`, except that the specified axis
    has been removed. If `a` is a 0d array, or if axis is None, a scalar
    is returned. `float64` return values are used for integer inputs.

See also
--------
bottleneck.median: Median along specified axis.

Examples
--------
>>> a = np.array([[np.nan, 7, 4], [3, 2, 1]])
>>> a
array([[ nan,   7.,   4.],
       [  3.,   2.,   1.]])
>>> bn.nanmedian(a)
3.0
>> bn.nanmedian(a, axis=0)
array([ 3. ,  4.5,  2.5])
>> bn.nanmedian(a, axis=1)
array([ 5.5,  2. ])

nanstd(a, axis=None, ddof=0)

Standard deviation along the specified axis, ignoring NaNs.

`float64` intermediate and return values are used for integer inputs.

Instead of a faster one-pass algorithm, a more stable two-pass algorithm
is used.

An example of a one-pass algorithm:

    >>> np.sqrt((a*a).mean() - a.mean()**2)

An example of a two-pass algorithm:

    >>> np.sqrt(((a - a.mean())**2).mean())

Note in the two-pass algorithm the mean must be found (first pass) before
the squared deviation (second pass) can be found.

Parameters
----------
a : array_like
    Input array. If `a` is not an array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the standard deviation is computed. The default
    (axis=None) is to compute the standard deviation of the flattened
    array.
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.

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.
    `float64` intermediate and return values are used for integer inputs.
    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
--------
bottleneck.nanvar: Variance along specified axis ignoring NaNs

Notes
-----
If positive or negative infinity are present the result is Not A Number
(NaN).

Examples
--------
>>> bn.nanstd(1)
0.0
>>> bn.nanstd([1])
0.0
>>> bn.nanstd([1, np.nan])
0.0
>>> a = np.array([[1, 4], [1, np.nan]])
>>> bn.nanstd(a)
1.4142135623730951
>>> bn.nanstd(a, axis=0)
array([ 0.,  0.])

When positive infinity or negative infinity are present NaN is returned:

>>> bn.nanstd([1, np.nan, np.inf])
nan

nanmean(a, axis=None)

Mean of array elements along given axis ignoring NaNs.

`float64` intermediate and return values are used for integer inputs.

Parameters
----------
a : array_like
    Array containing numbers whose mean is desired. If `a` is not an
    array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the means are computed. The default (axis=None) is to
    compute the mean of the flattened array.

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.
    `float64` intermediate and return values are used for integer inputs.

See also
--------
bottleneck.nanmedian: Median along specified axis, ignoring NaNs.

Notes
-----
No error is raised on overflow. (The sum is computed and then the result
is divided by the number of non-NaN elements.)

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).

Examples
--------
>>> bn.nanmean(1)
1.0
>>> bn.nanmean([1])
1.0
>>> bn.nanmean([1, np.nan])
1.0
>>> a = np.array([[1, 4], [1, np.nan]])
>>> bn.nanmean(a)
2.0
>>> bn.nanmean(a, axis=0)
array([ 1.,  4.])

When positive infinity and negative infinity are present:

>>> bn.nanmean([1, np.nan, np.inf])
inf
>>> bn.nanmean([1, np.nan, np.NINF])
-inf
>>> bn.nanmean([1, np.nan, np.inf, np.NINF])
nan

nanmax(a, axis=None)

Maximum values along specified axis, ignoring NaNs.

When all-NaN slices are encountered, NaN is returned for that slice.

Parameters
----------
a : array_like
    Input array. If `a` is not an array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the maximum is computed. The default (axis=None) is
    to compute the maximum of the flattened array.

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. The
    same dtype as `a` is returned.

See also
--------
bottleneck.nanmin: Minimum along specified axis, ignoring NaNs.
bottleneck.nanargmax: Indices of maximum values along axis, ignoring NaNs.

Examples
--------
>>> bn.nanmax(1)
1
>>> bn.nanmax([1])
1
>>> bn.nanmax([1, np.nan])
1.0
>>> a = np.array([[1, 4], [1, np.nan]])
>>> bn.nanmax(a)
4.0
>>> bn.nanmax(a, axis=0)
array([ 1.,  4.])

nanargmax(a, axis=None)

Indices of the maximum values along an axis, ignoring NaNs.

For all-NaN slices ``ValueError`` is raised. Unlike NumPy, the results
can be trusted if a slice contains only NaNs and Infs.

Parameters
----------
a : array_like
    Input array. If `a` is not an array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which to operate. By default (axis=None) flattened input
    is used.

See also
--------
bottleneck.nanargmin: Indices of the minimum values along an axis.
bottleneck.nanmax: Maximum values along specified axis, ignoring NaNs.

Returns
-------
index_array : ndarray
    An array of indices or a single index value.

Examples
--------
>>> a = np.array([[np.nan, 4], [2, 3]])
>>> bn.nanargmax(a)
1
>>> a.flat[1]
4.0
>>> bn.nanargmax(a, axis=0)
array([1, 0])
>>> bn.nanargmax(a, axis=1)
array([1, 1])

median(a, axis=None)

Median of array elements along given axis.

Parameters
----------
a : array_like
    Input array. If `a` is not an array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the median is computed. The default (axis=None) is to
    compute the median of the flattened array.

Returns
-------
y : ndarray
    An array with the same shape as `a`, except that the specified axis
    has been removed. If `a` is a 0d array, or if axis is None, a scalar
    is returned. `float64` return values are used for integer inputs. NaN
    is returned for a slice that contains one or more NaNs.

See also
--------
bottleneck.nanmedian: Median along specified axis ignoring NaNs.

Examples
--------
>>> a = np.array([[10, 7, 4], [3, 2, 1]])
>>> bn.median(a)
    3.5
>>> bn.median(a, axis=0)
    array([ 6.5,  4.5,  2.5])
>>> bn.median(a, axis=1)
    array([ 7.,  2.])

nansum(a, axis=None)

Sum of array elements along given axis treating NaNs as zero.

The data type (dtype) of the output is the same as the input. On 64-bit
operating systems, 32-bit input is NOT upcast to 64-bit accumulator and
return values.

Parameters
----------
a : array_like
    Array containing numbers whose sum is desired. If `a` is not an
    array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the sum is computed. The default (axis=None) is to
    compute the sum of the flattened array.

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.

Notes
-----
No error is raised on overflow.

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).

Examples
--------
>>> bn.nansum(1)
1
>>> bn.nansum([1])
1
>>> bn.nansum([1, np.nan])
1.0
>>> a = np.array([[1, 1], [1, np.nan]])
>>> bn.nansum(a)
3.0
>>> bn.nansum(a, axis=0)
array([ 2.,  1.])

When positive infinity and negative infinity are present:

>>> bn.nansum([1, np.nan, np.inf])
inf
>>> bn.nansum([1, np.nan, np.NINF])
-inf
>>> bn.nansum([1, np.nan, np.inf, np.NINF])
nan

nanvar(a, axis=None, ddof=0)

Variance along the specified axis, ignoring NaNs.

`float64` intermediate and return values are used for integer inputs.

Instead of a faster one-pass algorithm, a more stable two-pass algorithm
is used.

An example of a one-pass algorithm:

    >>> (a*a).mean() - a.mean()**2

An example of a two-pass algorithm:

    >>> ((a - a.mean())**2).mean()

Note in the two-pass algorithm the mean must be found (first pass) before
the squared deviation (second pass) can be found.

Parameters
----------
a : array_like
    Input array. If `a` is not an array, a conversion is attempted.
axis : {int, None}, optional
    Axis along which the variance is computed. The default (axis=None) is
    to compute the variance of the flattened array.
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.

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. `float64` intermediate and return values are used for
    integer inputs. 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
--------
bottleneck.nanstd: Standard deviation along specified axis ignoring NaNs.

Notes
-----
If positive or negative infinity are present the result is Not A Number
(NaN).

Examples
--------
>>> bn.nanvar(1)
0.0
>>> bn.nanvar([1])
0.0
>>> bn.nanvar([1, np.nan])
0.0
>>> a = np.array([[1, 4], [1, np.nan]])
>>> bn.nanvar(a)
2.0
>>> bn.nanvar(a, axis=0)
array([ 0.,  0.])

When positive infinity or negative infinity are present NaN is returned:

>>> bn.nanvar([1, np.nan, np.inf])