Bottleneck provides the following functions:
reduce  nansum, nanmean, nanstd, nanvar, nanmin, nanmax, median, nanmedian, ss, nanargmin, nanargmax, anynan, allnan 
nonreduce  replace 
nonreduce with axis  rankdata, nanrankdata, partsort, argpartsort, 
moving window  move_sum, move_mean, move_std, move_min, move_max 
moving window without min_count  move_median 
Functions the reduce the input array along the specified axis.
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 64bit operating systems, 32bit input is NOT upcast to 64bit accumulator and return values.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

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
Mean of array elements along given axis ignoring NaNs.
float64 intermediate and return values are used for integer inputs.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

See also
Notes
No error is raised on overflow. (The sum is computed and then the result is divided by the number of nonNaN 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
Standard deviation along the specified axis, ignoring NaNs.
float64 intermediate and return values are used for integer inputs.
Instead of a faster onepass algorithm, a more stable twopass algorithm is used.
An example of a onepass algorithm:
>>> np.sqrt((arr*arr).mean()  arr.mean()**2)
An example of a twopass algorithm:
>>> np.sqrt(((arr  arr.mean())**2).mean())
Note in the twopass algorithm the mean must be found (first pass) before the squared deviation (second pass) can be found.
Parameters:  arr : array_like
axis : {int, None}, optional
ddof : int, optional


Returns:  y : ndarray

See also
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
Variance along the specified axis, ignoring NaNs.
float64 intermediate and return values are used for integer inputs.
Instead of a faster onepass algorithm, a more stable twopass algorithm is used.
An example of a onepass algorithm:
>>> (arr*arr).mean()  arr.mean()**2
An example of a twopass algorithm:
>>> ((arr  arr.mean())**2).mean()
Note in the twopass algorithm the mean must be found (first pass) before the squared deviation (second pass) can be found.
Parameters:  arr : array_like
axis : {int, None}, optional
ddof : int, optional


Returns:  y : ndarray

See also
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])
nan
Minimum values along specified axis, ignoring NaNs.
When allNaN slices are encountered, NaN is returned for that slice.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

See also
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.])
Maximum values along specified axis, ignoring NaNs.
When allNaN slices are encountered, NaN is returned for that slice.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

See also
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.])
Median of array elements along given axis.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

See also
Notes
This function returns the same output as NumPy’s median except when the input contains NaN.
Examples
>>> a = np.array([[10, 7, 4], [3, 2, 1]])
>>> a
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.])
Median of array elements along given axis ignoring NaNs.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

See also
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. ])
Sum of the square of each element along the specified axis.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

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.])
Indices of the minimum values along an axis, ignoring NaNs.
For allNaN slices ValueError is raised. Unlike NumPy, the results can be trusted if a slice contains only NaNs and Infs.
Parameters:  a : array_like
axis : {int, None}, optional


Returns:  index_array : ndarray

See also
Examples
>>> a = np.array([[np.nan, 4], [2, 3]])
>>> bn.nanargmin(a)
2
>>> a.flat[1]
2.0
>>> bn.nanargmax(a, axis=0)
array([1, 1])
>>> bn.nanargmax(a, axis=1)
array([1, 0])
Indices of the maximum values along an axis, ignoring NaNs.
For allNaN slices ValueError is raised. Unlike NumPy, the results can be trusted if a slice contains only NaNs and Infs.
Parameters:  a : array_like
axis : {int, None}, optional


Returns:  index_array : ndarray

See also
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])
Test whether any array element along a given axis is NaN.
Returns the same output as np.isnan(arr).any(axis)
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : bool or ndarray

See also
Examples
>>> bn.anynan(1)
False
>>> bn.anynan(np.nan)
True
>>> bn.anynan([1, np.nan])
True
>>> a = np.array([[1, 4], [1, np.nan]])
>>> bn.anynan(a)
True
>>> bn.anynan(a, axis=0)
array([False, True], dtype=bool)
Test whether all array elements along a given axis are NaN.
Returns the same output as np.isnan(arr).all(axis)
Note that allnan([]) is True to match np.isnan([]).all() and all([])
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : bool or ndarray

See also
Examples
>>> bn.allnan(1)
False
>>> bn.allnan(np.nan)
True
>>> bn.allnan([1, np.nan])
False
>>> a = np.array([[1, np.nan], [1, np.nan]])
>>> bn.allnan(a)
False
>>> bn.allnan(a, axis=0)
array([False, True], dtype=bool)
An empty array returns True:
>>> bn.allnan([])
True
which is similar to:
>>> all([])
True
>>> np.isnan([]).all()
True
Functions that do not reduce the input array.
Replace (inplace) given scalar values of an array with new values.
The equivalent numpy function:
arr[arr==old] = new
Or in the case where old=np.nan:
arr[np.isnan(old)] = new
Parameters:  arr : numpy.ndarray
old : scalar
new : scalar


Returns:  None, the operation is inplace. : 
Examples
Replace zero with 3 (note that the input array is modified):
>>> a = np.array([1, 2, 0])
>>> bn.replace(a, 0, 3)
>>> a
array([1, 2, 3])
Replace np.nan with 0:
>>> a = np.array([1, 2, np.nan])
>>> bn.replace(a, np.nan, 0)
>>> a
array([ 1., 2., 0.])
Functions that do not reduce the input array but operate along a specified axis.
Ranks the data, dealing with ties appropriately.
Equal values are assigned a rank that is the average of the ranks that would have been otherwise assigned to all of the values within that set. Ranks begin at 1, not 0.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

See also
Examples
>>> bn.rankdata([0, 2, 2, 3])
array([ 1. , 2.5, 2.5, 4. ])
>>> bn.rankdata([[0, 2], [2, 3]])
array([ 1. , 2.5, 2.5, 4. ])
>>> bn.rankdata([[0, 2], [2, 3]], axis=0)
array([[ 1., 1.],
[ 2., 2.]])
>>> bn.rankdata([[0, 2], [2, 3]], axis=1)
array([[ 1., 2.],
[ 1., 2.]])
Ranks the data, dealing with ties and NaNs appropriately.
Equal values are assigned a rank that is the average of the ranks that would have been otherwise assigned to all of the values within that set. Ranks begin at 1, not 0.
NaNs in the input array are returned as NaNs.
Parameters:  arr : array_like
axis : {int, None}, optional


Returns:  y : ndarray

See also
Examples
>>> bn.nanrankdata([np.nan, 2, 2, 3])
array([ nan, 1.5, 1.5, 3. ])
>>> bn.nanrankdata([[np.nan, 2], [2, 3]])
array([ nan, 1.5, 1.5, 3. ])
>>> bn.nanrankdata([[np.nan, 2], [2, 3]], axis=0)
array([[ nan, 1.],
[ 1., 2.]])
>>> bn.nanrankdata([[np.nan, 2], [2, 3]], axis=1)
array([[ nan, 1.],
[ 1., 2.]])
Partial sorting of array elements along given axis.
A partially sorted array is one in which the n smallest values appear (in any order) in the first n elements. The remaining largest elements are also unordered. Due to the algorithm used (Wirth’s method), the nth smallest element is in its sorted position (at index n1).
Shuffling the input array may change the output. The only guarantee is that the first n elements will be the n smallest and the remaining element will appear in the remainder of the output.
This functions is not protected against NaN. Therefore, you may get unexpected results if the input contains NaN.
Parameters:  arr : array_like
n : int
axis : {int, None}, optional


Returns:  y : ndarray

See also
Notes
Unexpected results may occur if the input array contains NaN.
Examples
Create a numpy array:
>>> a = np.array([1, 0, 3, 4, 2])
Partially sort array so that the first 3 elements are the smallest 3 elements (note, as in this example, that the smallest 3 elements may not be sorted):
>>> bn.partsort(a, n=3)
array([1, 0, 2, 4, 3])
Now partially sort array so that the last 2 elements are the largest 2 elements:
>>> bn.partsort(a, n=a.shape[0]2)
array([1, 0, 2, 3, 4])
Return indices that would partially sort an array.
A partially sorted array is one in which the n smallest values appear (in any order) in the first n elements. The remaining largest elements are also unordered. Due to the algorithm used (Wirth’s method), the nth smallest element is in its sorted position (at index n1).
Shuffling the input array may change the output. The only guarantee is that the first n elements will be the n smallest and the remaining element will appear in the remainder of the output.
This functions is not protected against NaN. Therefore, you may get unexpected results if the input contains NaN.
Parameters:  arr : array_like
n : int
axis : {int, None}, optional


Returns:  y : ndarray

See also
Notes
Unexpected results may occur if the input array contains NaN.
Examples
Create a numpy array:
>>> a = np.array([1, 0, 3, 4, 2])
Find the indices that partially sort that array so that the first 3 elements are the smallest 3 elements:
>>> index = bn.argpartsort(a, n=3)
>>> index
array([0, 1, 4, 3, 2])
Let’s use the indices to partially sort the array (note, as in this example, that the smallest 3 elements may not be in order):
>>> a[index]
array([1, 0, 2, 4, 3])
Moving window functions (with a 1d window) that take min_count as an optional input.
Moving window sum along the specified axis, optionally ignoring NaNs.
Parameters:  arr : ndarray
window : int
min_count: {int, None}, optional :
axis : int, optional


Returns:  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, np.nan, 5.0])
>>> bn.move_sum(arr, window=2)
array([ nan, 3., 5., nan, nan])
>>> bn.move_sum(arr, window=2, min_count=1)
array([ 1., 3., 5., 3., 5.])
Moving window mean along the specified axis, optionally ignoring NaNs.
Parameters:  arr : ndarray
window : int
min_count: {int, None}, optional :
axis : int, optional


Returns:  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, np.nan, 5.0])
>>> bn.move_mean(arr, window=2)
array([ nan, 1.5, 2.5, nan, nan])
>>> bn.move_mean(arr, window=2, min_count=1)
array([ 1. , 1.5, 2.5, 3. , 5. ])
Moving window standard deviation along the specified axis, optionally ignoring NaNs.
Unlike bn.nanstd, which uses a more rubust twopass algorithm, move_nanstd uses a faster onepass algorithm.
An example of a onepass algorithm:
>>> np.sqrt((arr*arr).mean()  arr.mean()**2)
An example of a twopass algorithm:
>>> np.sqrt(((arr  arr.mean())**2).mean())
Note in the twopass algorithm the mean must be found (first pass) before the squared deviation (second pass) can be found.
Parameters:  arr : ndarray
window : int
min_count: {int, None}, optional :
axis : int, optional
ddof : int, optional


Returns:  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, np.nan, 5.0])
>>> bn.move_std(arr, window=2)
array([ nan, 0.5, 0.5, nan, nan])
>>> bn.move_std(arr, window=2, min_count=1)
array([ 0. , 0.5, 0.5, 0. , 0. ])
Moving window minimum along the specified axis, optionally ignoring NaNs.
float64 output is returned for all input data types.
Parameters:  arr : ndarray
window : int
min_count: {int, None}, optional :
axis : int, optional


Returns:  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, np.nan, 5.0])
>>> bn.move_min(arr, window=2)
array([ nan, 1., 2., nan, nan])
>>> bn.move_min(arr, window=2, min_count=1)
array([ 1., 1., 2., 3., 5.])
Moving window maximum along the specified axis, optionally ignoring NaNs.
float64 output is returned for all input data types.
Parameters:  arr : ndarray
window : int
min_count: {int, None}, optional :
axis : int, optional


Returns:  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, np.nan, 5.0])
>>> bn.move_max(arr, window=2)
array([ nan, 2., 3., nan, nan])
>>> bn.move_max(arr, window=2, min_count=1)
array([ 1., 2., 3., 3., 5.])
Moving window functions (with a 1d window) that do NOT take min_count as an optional input. In other works, NaNs in will results in NaNs in the output.
Moving window median along the specified axis.
This functions is not protected against NaN. Therefore, you may get unexpected results if the input contains NaN.
Parameters:  arr : ndarray
window : int
axis : int, optional


Returns:  y : ndarray

Notes
Unexpected results may occur if the input array contains NaN. This function does NOT take min_count as an input.
Examples
>>> arr = np.array([1.0, 2.0, 3.0, 4.0])
>>> bn.move_median(arr, window=2)
array([ nan, 1.5, 2.5, 3.5])