vectorize complex slicing with pandas dataframe - datetime

Question

I'd like to be able to vectorize, for speed purposes, this piece of code. the purpose is to calculate a function, in this case a standard deviation, from a tuple of pair of dates that are cointained in two separate arrays.
import pandas as pd
import numpy as np
asd_1 = pd.Series(0.01 * np.random.randn(252), index=pd.date_range('2011-1-1', periods=252))
index_1 = pd.to_datetime(['2011-2-2', '2011-4-3', '2011-5-1',])
index_2 = pd.to_datetime(['2011-2-15', '2011-4-16', '2011-5-17',])
index_tot = list(zip(index_1,index_2))
aux_learning_std = pd.DataFrame([np.nanstd(asd_1.loc[i:j]) for i, j in index_tot], index=index_1)
the solution, that works, is performed through a loop but i'd rather be able to vectorize it through numpy/pandas, which is much faster. initially I though about using something like:
df_aux = pd.concat([asd_1 for _ in range(len(index_1))], axis=1)
results = df_aux.apply(lambda x: np.nanstd(x.loc[i,j]), axis = 0)
but here I fail to put together the vectors into one operation.
any and all advice is welcome.
p.s.: below there is an image for explanatory purposes

Answer 1

Vectorized standard deviation across ranges in an array
def get_ranges_arr(starts,ends):
# Taken from http://stackoverflow.com/a/37626057/3293881
counts = ends - starts
counts_csum = counts.cumsum()
id_arr = np.ones(counts_csum[-1],dtype=int)
id_arr[0] = starts[0]
id_arr[counts_csum[:-1]] = starts[1:] - ends[:-1] + 1
return id_arr.cumsum()
def ranged_std(arr,starts,ends):
# Get all indices and the IDs corresponding to same groups
idx = get_ranges_arr(starts,ends)
id_arr = np.repeat(np.arange(starts.size),ends-starts)
# Extract relevant data
slice_arr = arr[idx]
# Simulate standard deviation implementation for a number of groups
# using id_arr as the basis to perform various mathematical operations
# within each group. Since, std. deviation performs sum/mean reduction,
# we can simply use np.bincount for an efficient implementation.
# Std. deviation formula used :
#https://github.com/numpy/numpy/blob/v1.11.0/numpy/core/fromnumeric.py#L2939
grp_counts = np.bincount(id_arr)
mean_vals = np.bincount(id_arr,slice_arr)/grp_counts
abs_vals = np.abs(slice_arr - mean_vals[id_arr])**2
return np.sqrt(np.bincount(id_arr,abs_vals)/grp_counts)
Sample run (verify against a loopy version)
In [173]: arr = np.random.randint(0,9,(20))
In [174]: starts = np.array([2,6,11])
In [175]: ends = np.array([8,9,15])
In [176]: [np.std(arr[i:j]) for i,j in zip(starts,ends)]
Out[176]: [1.9720265943665387, 0.81649658092772603, 0.82915619758884995]
In [177]: ranged_std(arr,starts,ends)
Out[177]: array([ 1.97202659, 0.81649658, 0.8291562 ])
Runtime test
Case #1 : Very small number of ranges 3
In [21]: arr = np.random.randint(0,9,(20))
In [22]: starts = np.array([2,6,11])
In [23]: ends = np.array([8,9,15])
In [24]: %timeit [np.std(arr[i:j]) for i,j in zip(starts,ends)]
10000 loops, best of 3: 146 µs per loop
In [25]: %timeit ranged_std(arr,starts,ends)
10000 loops, best of 3: 45 µs per loop
Case #2 : Decent number of ranges 1000
In [32]: arr = np.random.randint(0,9,(1010))
In [33]: starts = np.random.randint(0,9,(1000))
In [34]: ends = starts + np.random.randint(0,9,(1000))
In [35]: %timeit [np.std(arr[i:j]) for i,j in zip(starts,ends)]
10 loops, best of 3: 47.5 ms per loop
In [36]: %timeit ranged_std(arr,starts,ends)
1000 loops, best of 3: 217 µs per loop
Case #3 : Large number of ranges 10000
In [60]: arr = np.random.randint(0,9,(1010))
In [61]: arr = np.random.randint(0,9,(10010))
In [62]: starts = np.random.randint(0,9,(10000))
In [63]: ends = starts + np.random.randint(0,9,(10000))
In [64]: %timeit [np.std(arr[i:j]) for i,j in zip(starts,ends)]
1 loops, best of 3: 474 ms per loop
In [65]: %timeit ranged_std(arr,starts,ends)
100 loops, best of 3: 2.17 ms per loop
Really amazing speedups of 200x+!
Using ranged_std to solve our case
# Get start, stop numeric indices as needed for getting ranges array later on
starts = asd_1.index.searchsorted(index_1)
ends = asd_1.index.searchsorted(index_2)
# Create final dataframe output using ranged_std func
df = pd.DataFrame(ranged_std(asd_1.values,starts,ends+1),index=index_1)
Sample run for verification -
In [17]: asd_1 = pd.Series(0.01 * np.random.randn(252), index=\
...: pd.date_range('2011-1-1', periods=252))
...:
...: index_1 = pd.to_datetime(['2011-2-2', '2011-4-3', '2011-5-1',])
...: index_2 = pd.to_datetime(['2011-2-15', '2011-4-16', '2011-5-17',])
...:
...: index_tot = list(zip(index_1,index_2))
...: aux_learning_std = pd.DataFrame([np.nanstd(asd_1.loc[i:j]) for i, j in \
...: index_tot], index=index_1)
...:
In [18]: starts = asd_1.index.searchsorted(index_1)
...: ends = asd_1.index.searchsorted(index_2)
...: df = pd.DataFrame(ranged_std(asd_1.values,starts,ends+1),index=index_1)
...:
In [19]: aux_learning_std
Out[19]:
0
2011-02-02 0.007244
2011-04-03 0.012862
2011-05-01 0.010155
In [20]: df
Out[20]:
0
2011-02-02 0.007244
2011-04-03 0.012862
2011-05-01 0.010155