#
# Import numpy as `np`, and set the display precision to two decimal places
#
import numpy as np
np.set_printoptions(precision=2)

#
# We generate three ndarrays to represent sales number of three products in four different seasons
#
np.random.seed(0)
sales = np.random.uniform(-20, 20, size=(4,3))
products = np.array(['apple', 'orange', 'banana'])
seasons = np.array(['spring', 'summer', 'fall', 'winter'])

#
# The products
#
products

array(['apple', 'orange', 'banana'], dtype='<U6')

#
# The seasons
#
seasons

array(['spring', 'summer', 'fall', 'winter'], dtype='<U6')

#
# The sales as a (4,3) ndarray
sales

array([[ 1.95,  8.61,  4.11],
       [ 1.8 , -3.05,  5.84],
       [-2.5 , 15.67, 18.55],
       [-4.66, 11.67,  1.16]])

#
# We can also pack the seasons and products into a single
# (4,3) ndarray of strings.
#
info = np.array(
    ["%s-%s"%(s,p) for s in seasons for p in products]
).reshape(4,-1)
info

array([['spring-apple', 'spring-orange', 'spring-banana'],
       ['summer-apple', 'summer-orange', 'summer-banana'],
       ['fall-apple', 'fall-orange', 'fall-banana'],
       ['winter-apple', 'winter-orange', 'winter-banana']], dtype='<U13')

Boolean Arrays¶

Boolean operations allows us to construct boolean ndarrays from numerical ndarrays using element-wise logical relational operators.

#
# sales that are negative
#
sales < 0

array([[False, False, False],
       [False,  True, False],
       [ True, False, False],
       [ True, False, False]])

Logical operators can combine multiple boolean ndarrays to express complex conditions.

#
# sales that are between 0 and 2.0
#
np.logical_and(sales >= 0, sales < 2.0)

array([[ True, False, False],
       [ True, False, False],
       [False, False, False],
       [False, False,  True]])

It's possible to find the indexes of all the true elements in a boolean ndarray. The result is given as indexes along each dimension.

X,Y = np.where(...)

X is the row entries, and Y is the column entries.

#
# the ndarray indices for negative sales
#
np.where(sales < 0)

(array([1, 2, 3]), array([1, 0, 0]))

Boolean Indexing¶

We can make use of boolean arrays as indexes to extract the elements of a ndarray based on the corresponding boolean values.

#
# We can retrieve the actual sales figures for the negative sales
#
sales[sales < 0]

array([-3.05, -2.5 , -4.66])

#
# We can retrieve the info of the negative sales
#
info[sales < 0]

array(['summer-orange', 'fall-apple', 'winter-apple'], dtype='<U13')

I,J = np.where(sales < 0)
print(list(zip(I,J)))

[(1, 1), (2, 0), (3, 0)]

seasons[I]

array(['summer', 'fall', 'winter'], dtype='<U6')

products[J]

array(['orange', 'apple', 'apple'], dtype='<U6')

L = (sales < 0)
I, J = np.where(L)
for (season, product, loss) in zip(seasons[I], products[J], sales[L]):
    print("We lost %.2f selling %s in %s" % (loss, product, season))

We lost -3.05 selling orange in summer
We lost -2.50 selling apple in fall
We lost -4.66 selling apple in winter

Index

Creating and Indexing with Boolean NDArrays

Boolean Indexing

Boolean Arrays¶

Boolean Indexing¶