Ask Each Row a Question

A greenhouse report includes comfortable temperatures and readings that need attention. We want to see only the readings at or above 25 degrees, while keeping the original collection available.

We can ask the same question of every entry. The answers form another array, containing true or false at each position. This array of decisions is called a mask.

Choose an example, then change a value. Follow the calculation below to see which result changes and why. These are small teaching examples; the construction later asks you to choose the operations yourself.

Botie needs to know which greenhouses have readings at or above the alert temperature. We could inspect each reading ourselves, but a program needs an explicit decision rule. A comparison asks a question about a value and returns a Boolean: either True or False.

Applying the comparison to an array produces another array with a Boolean at each position. This array of decisions is called a mask. Its entries answer whether to keep a reading; they are not temperatures.

20 ≥ 25 → false
27 ≥ 25 → true
25 ≥ 25 → true
18 ≥ 25 → false

Our boundary counts. A strictly greater-than comparison would omit the reading exactly at the threshold.

import numpy as np

print(27 >= 25)
readings = np.array([20, 27, 25, 18])
mask = readings >= 25

print(mask.tolist())
print(mask.dtype)
print(mask.shape)

True
[False, True, True, False]
bool
(4,)

We now have two aligned collections: the temperatures and the decisions. Putting the Boolean mask inside the readings' square brackets tells NumPy to keep the positions marked True. For this one-dimensional selection, the mask must have one decision per reading.

A Boolean mask and an array of integer indices are different structures for making a selection. The Boolean array asks yes or no at each position. The integer array names the positions to retrieve, in the order requested.

The workshop displays decisions as zero and one. In NumPy we must actually use Boolean values for a mask. A numerical array containing zeros and ones would instead be interpreted as positions.

import numpy as np

readings = np.array([20, 27, 25, 18])
mask = np.array([False, True, True, False])
positions = np.array([0, 1, 1, 0])

print(readings[mask].tolist())
print(readings[positions].tolist())

[27, 25]
[20, 27, 27, 20]

After selecting the readings, we can count them or calculate their average. Both the total and the count must come from the selected group. The original report's count would give us the wrong denominator.

Selected total = 27 + 25 = 52
Selected count = 2
Selected mean = 52 / 2 = 26

An empty selection still has a count of zero, but it has no mean. There are no temperatures to average, so a displayed zero would wrongly suggest an observed temperature.

import numpy as np

readings = np.array([20, 27, 25, 18])
selected = readings[readings >= 25]

print(selected.tolist())
print(selected.size)
print(f"{selected.mean():.1f}")

[27, 25]
2
26.0

import numpy as np

readings = np.array([19, 21])
selected = readings[readings >= 25]

print(selected.tolist())
print(selected.shape)
if selected.size == 0:
    print("No readings met the alert rule.")
else:
    print(selected.mean())

[]
(0,)
No readings met the alert rule.

The mean of readings above the limit does not describe the whole report without qualification. We deliberately chose warmer readings. That is useful for inspecting alerts, but someone reading the result needs to know which observations contributed.

Another Python structure, the set, keeps distinct items. It is useful when we care whether a value occurred, but it discards repeated occurrences and does not give us positions to index like a list. That would lose information if we used it to store repeated measurements.

Let's distinguish asking which temperatures occurred from asking how many readings triggered an alert.

alert_readings = [27, 27, 25]
distinct_temperatures = set(alert_readings)

print(len(alert_readings))
print(sorted(distinct_temperatures))
print(len(distinct_temperatures))
print(27 in distinct_temperatures)

3
[25, 27]
2
True