Bottleneck provides the following functions:
NumPy/SciPy  median, nanmedian, rankdata, ss, nansum, nanmin, nanmax, nanmean, nanstd, nanargmin, nanargmax 
Functions  nanrankdata, nanvar, partsort, argpartsort, replace, nn, anynan, allnan 
Moving window  move_sum, move_nansum, move_mean, move_nanmean, move_median, move_std, move_nanstd, move_min, move_nanmin, move_max, move_nanmax 
Fast replacements for NumPy and SciPy functions.
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. ])
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.]])
Sum of the square of each element along specified axis.
Parameters :  arr : array_like
axis : {int, None}, optional


Returns :  y : ndarray

See also
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.])
Sum of array elements along given axis ignoring NaNs.
When the input has an integer type with less precision than the default platform integer, the default platform integer is used for the 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
Minimum values along specified axis, ignoring NaNs.
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.
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.])
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
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])
Miscellaneous functions.
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.]])
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:
>>> 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.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
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])
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.])
Distance of nearest neighbor (and its index) along specified axis.
The Euclidian distance between arr0 and its nearest neighbor in arr is returned along with the index of the nearest neighbor in arr.
The squared distance used to determine the nearest neighbor of arr0 is equivalent to np.sum((arr  arr0) ** 2), axis) where arr is 2d and arr0 is 1d and arr0 must be reshaped if axis is 1.
If all distances are NaN then the distance returned is NaN and the index is zero.
Parameters :  arr : array_like
arr0 : array_like
axis : int, optional


Returns :  dist : np.float64
idx : int

See also
Notes
A brute force algorithm is used to find the nearest neighbor.
Depending on the shapes of arr and arr0, SciPy’s cKDTree may be faster than bn.nn(). So benchmark if speed is important.
The relative speed also depends on how many times you will use the same array arr to find nearest neighbors with different arr0. That is because it takes time to set up SciPy’s cKDTree.
Examples
Create the input arrays:
>>> arr = np.array([[1, 2], [3, 4]])
>>> arr0 = np.array([2, 4])
Find nearest neighbor of arr0 in arr along axis 1:
>>> dist, idx = bn.nn(arr, arr0, axis=1)
>>> dist
1.0
>>> idx
1
Find nearest neighbor of arr0 in arr along axis 0:
>>> dist, idx = bn.nn(arr, arr0, axis=0)
>>> dist
0.0
>>> idx
1
Test whether any array element along a given axis is NaN.
Returns single boolean unless axis is not None.
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 single boolean unless axis is not None.
Note that allnan([]) is True to match np.isnan([]).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
Moving window functions with a 1d window.
Moving window sum along the specified axis.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, 4.0])
>>> bn.move_sum(arr, window=2)
array([ nan, 3., 5., 7.])
Moving window sum along the specified axis, ignoring NaNs.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, 4.0])
>>> bn.move_nansum(arr, window=2)
array([ nan, 3., 5., 7.])
Moving window mean along the specified axis.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, 4.0])
>>> bn.move_mean(arr, window=2)
array([ nan, 1.5, 2.5, 3.5])
Moving window mean along the specified axis, ignoring NaNs.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, 4.0])
>>> bn.move_nanmean(arr, window=2)
array([ nan, 1.5, 2.5, 3.5])
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.
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])
Moving window standard deviation along the specified axis.
Unlike bn.nanstd, which uses a more rubust twopass algorithm, move_std 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
axis : int, optional
ddof : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, 4.0])
>>> bn.move_std(arr, window=2)
array([ nan, 1.5, 2.5, 3.5])
Moving window standard deviation along the specified axis, 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
axis : int, optional
ddof : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 3.0, 4.0])
>>> bn.move_nanstd(arr, window=2)
array([ nan, 1.5, 2.5, 3.5])
Moving window minimum along the specified axis.
float64 output is returned for all input data types.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 4.0, 3.0])
>>> bn.move_min(arr, window=2)
array([ nan, 1., 2., 3.])
Moving window minimum along the specified axis, ignoring NaNs.
float64 output is returned for all input data types.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 4.0, 3.0])
>>> bn.move_nanmin(arr, window=2)
array([ nan, 2., 4., 4.])
Moving window maximum along the specified axis.
float64 output is returned for all input data types.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 4.0, 3.0])
>>> bn.move_max(arr, window=2)
array([ nan, 2., 4., 4.])
Moving window maximum along the specified axis, ignoring NaNs.
float64 output is returned for all input data types.
Parameters :  arr : ndarray
window : int
axis : int, optional


Returns :  y : ndarray

Examples
>>> arr = np.array([1.0, 2.0, 4.0, 3.0])
>>> bn.move_nanmax(arr, window=2)
array([ nan, 2., 4., 4.])