# Boolean Masking In Numpy

We will learn how to apply comparison operators (

`<`

, `>`

, `<=`

, `>=`

, `==`

& `!-`

) on the NumPy array which returns a boolean array with `True`

for all elements who fulfill the comparison operator and `False`

for those who doesn’t.import numpy as np

# making an array of random integers from 0 to 1000

# array shape is (5,5)

rand = np.random.RandomState(42)

arr = rand.randint(1000, size=(5,5))

print(arr)

# which elements value is greater than 500

print(arr > 500)

# which elements value is less than 750

print(arr < 750)

[[102 435 860 270 106]

[ 71 700 20 614 121]

[466 214 330 458 87]

[372 99 871 663 130]

[661 308 769 343 491]]

[[False False True False False]

[False True False True False]

[False False False False False]

[False False True True False]

[ True False True False False]]

[[ True True False True True]

[ True True True True True]

[ True True True True True]

[ True True False True True]

[ True True False True True]]

There are equivalent ufunc for comparison operators as listed in the table below:

Operator | unfunc |
---|---|

> | np.less |

< | np.greater |

>= | np.greater_equal |

<= | np.less_equal |

== | np.equal |

!= | np.no_equal |

# which elements value is greater than 500

print(np.greater(arr, 500))

# which elements value is less than 750

print(np.less(arr, 750))

[[False False True False False]

[False True False True False]

[False False False False False]

[False False True True False]

[ True False True False False]]

[[ True True False True True]

[ True True True True True]

[ True True True True True]

[ True True False True True]

[ True True False True True]]

In this section, we will study some useful functions/methods to work with boolean arrays we have created by applying comparison operator on numpy array

You must be thinking that how to count total number of

`True`

elements that passes the condition. There is a useful function for doing exactly the same, `no.count_nonzero()`

# counting the number of elements in array whose value > 500

print(np.count_nonzero(arr > 500))

# counting the number of elements in array whose value < 750

print(np.count_nonzero(arr < 750))

7

22

We can also use

`np.sum`

to count the elements that passes the condition. One major benefit of using this function is that we can provide kwarg `axis`

and can do the summation along preferred index# total in an array

print(np.sum(arr < 750))

# along axis=0

print(np.sum(arr < 750, axis=0))

# along axis=1

print(np.sum(arr < 750, axis=1))

22

[5 5 2 5 5]

[4 5 5 4 4]

`np.any`

returns`True`

, if*any*element in the array makes the condition pass. Otherwise returns`False`

`np.all`

returns`True`

, if*all*elements in the array makes the condition pass. Otherwise returns`False`

- We can also provide optional kwarg
`axis`

to apply function along preferred axis

# np.any

print(np.any(arr>500))

# np.all

print(np.all(arr>10))

# np.all along axis=1

print(np.all(arr>100, axis=1))

True

True

[ True False False False True]

Until now, we only applied a single comparison operator on an array. However, we can use Pythons bitwise logic operators (

`&`

, `|`

, `^`

and `~`

) to apply more than one comparison operators.For example, let suppose, for our array

`arr`

, we are interested to count number of elements that are greater than 500 but less than 750:# using boolean operator '&'

np.count_nonzero((arr >500) & (arr < 750))

4

# using boolean operator '|' or

np.count_nonzero((arr < 500) | (arr >= 500))

25

# using ~ before a condition revert the condition

# calculate no of elememnts NOT greater than 100 AND

# should be greater than 50

arr[(~(arr >100) & (arr > 50))]

array([71, 87, 99])

There are

`ufunc`

equivalent for all these boolean operators:Boolean Operator | unfunc |
---|---|

& | np.bitwise_and |

| |

^ | np.bitwise_xor |

~ | np.bitwise_not |

What is the difference between the keyword

`and`

and `or`

and boolean operators `&`

and `|`

?Keywords`and`

and`or`

measure the`True`

or`False`

status of an entire object, while`&`

and`|`

refer to bits within each object

# using '&'

print(np.count_nonzero((arr >500) & (arr < 750)))

# using 'and'

try:

(arr >500) and (arr < 750)

except Exception as e:

print(e)

4

The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

In the above section, we applied single or multiple conditional operators, which returns a boolean array with

`True`

for element(s) that passes the condition(s) and `False`

for those element(s) that don’t pass the condition(s)In this section, we will apply this boolean array to return the actual values from the array. This process is called boolean masking

First example we covered in this section is by passing condition

`arr > 500`

to get the boolean array of elements passing `True`

and not passing `False`

this condition. Now, lets apply this condition under `[]`

to return the actual values from the array, `arr`

# return array of elements with value < 500

arr[arr < 500]

array([102, 435, 270, 106, 71, 20, 121, 466, 214, 330, 458, 87, 372,

99, 130, 308, 343, 491])

# we can also use the ufunc

arr[np.less(arr,500)]

array([102, 435, 270, 106, 71, 20, 121, 466, 214, 330, 458, 87, 372,

99, 130, 308, 343, 491])

# passing more than one conditions

# using boolean operator

arr[(arr >500) & (arr < 750)]

array([700, 614, 663, 661])

Last modified 6mo ago