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Challenge 1 (Answers):

%auto
import numpy as np
%default_mode python

a = np.arange(4); a.shape
(4,) 
a = np.arange(24).reshape(2,3,4)
a.shape
(2, 3, 4) 
np.arange(1).reshape(1,1,1,1).ndim
4 
np.array(['fred']).dtype
dtype('S4') 
np.array([]).itemsize
8

** Challenge 2 (Answers): **

np.linspace(0, 1, 10)
array([ 0. , 0.11111111, 0.22222222, 0.33333333, 0.44444444, 0.55555556, 0.66666667, 0.77777778, 0.88888889, 1. ]) 
v = np.linspace(0,1,1000000)
%timeit np.sin(v)
%timeit np.array([np.sin(x) for x in v])
%timeit np.array([math.sin(x) for x in v])
25 loops, best of 3: 18.1 ms per loop 5 loops, best of 3: 1.15 s per loop 5 loops, best of 3: 213 ms per loop 
1/.018
.213/.018
55.55555555555556 11.833333333333334 
# Yep, works fine on any dimensional array.
np.sin(np.array([[1,2],[3,4]]))
array([[ 0.84147098, 0.90929743], [ 0.14112001, -0.7568025 ]])

Challenge 5 (Answers):

%timeit np.arange(1000000).sum()
125 loops, best of 3: 1.71 ms per loop 
%timeit  sum(range(1000000))
25 loops, best of 3: 32.6 ms per loop 
32.6/1.71
19.06432748538012 
a = np.arange(1000000)
a.std()
%timeit a.std()
288675.13459466852 125 loops, best of 3: 4.63 ms per loop 
import pandas
df = pandas.DataFrame(np.arange(1000000))
df.std()
%timeit df.std()
0 288675.278932 dtype: float64 5 loops, best of 3: 57.5 ms per loop 
v = stats.TimeSeries(range(1000000))
v.standard_deviation()
%timeit v.standard_deviation()
288675.27893349814 125 loops, best of 3: 4.97 ms per loop

Challenge 1 (Answers):

%auto
import numpy as np
%default_mode python

a = np.arange(4); a.shape
(4,) 
a = np.arange(24).reshape(2,3,4)
a.shape
(2, 3, 4) 
np.arange(1).reshape(1,1,1,1).ndim
4 
np.array(['fred']).dtype
dtype('S4') 
np.array([]).itemsize
8

** Challenge 2 (Answers): **

np.linspace(0, 1, 10)
array([ 0. , 0.11111111, 0.22222222, 0.33333333, 0.44444444, 0.55555556, 0.66666667, 0.77777778, 0.88888889, 1. ]) 
v = np.linspace(0,1,1000000)
%timeit np.sin(v)
%timeit np.array([np.sin(x) for x in v])
%timeit np.array([math.sin(x) for x in v])
25 loops, best of 3: 18.1 ms per loop 5 loops, best of 3: 1.15 s per loop 5 loops, best of 3: 213 ms per loop 
1/.018
.213/.018
55.55555555555556 11.833333333333334 
# Yep, works fine on any dimensional array.
np.sin(np.array([[1,2],[3,4]]))
array([[ 0.84147098, 0.90929743], [ 0.14112001, -0.7568025 ]])

Challenge 5 (Answers):

%timeit np.arange(1000000).sum()
125 loops, best of 3: 1.71 ms per loop 
%timeit  sum(range(1000000))
25 loops, best of 3: 32.6 ms per loop 
32.6/1.71
19.06432748538012 
a = np.arange(1000000)
a.std()
%timeit a.std()
288675.13459466852 125 loops, best of 3: 4.63 ms per loop 
import pandas
df = pandas.DataFrame(np.arange(1000000))
df.std()
%timeit df.std()
0 288675.278932 dtype: float64 5 loops, best of 3: 57.5 ms per loop 
v = stats.TimeSeries(range(1000000))
v.standard_deviation()
%timeit v.standard_deviation()
288675.27893349814 125 loops, best of 3: 4.97 ms per loop