Which Direction Are We Adding?

Build the table one row at a time

The outer list contains two items, each of which is itself a list. The first lookup chooses Tuesday's list. The second lookup chooses the middle greenhouse within that list. NumPy accepts these equally long rows as a rectangular numerical array.

import numpy as np

days = [
    [10, 20, 30],
    [14, 22, 36],
]
print(days[1])
print(days[1][1])

temperatures = np.array(days, dtype=float)
print(temperatures.tolist())

[14, 22, 36]
22
[[10.0, 20.0, 30.0], [14.0, 22.0, 36.0]]

The double square brackets in the final output preserve the rows: this is a list containing lists. A Python nested list could have unequal row lengths, but those rows would not form the regular numerical table we need here.

Read the shape as a tuple of axis lengths

A tuple is an ordered collection whose entries cannot be replaced after it is created. Python commonly writes tuples with parentheses. NumPy reports an array's shape as a tuple: one length for each axis, in axis order.

The ndim attribute counts axes. The size attribute counts all entries. These describe different things, so let's print each one separately.

import numpy as np

temperatures = np.array([
    [10, 20, 30],
    [14, 22, 36],
])
shape = temperatures.shape

print(shape)
print(shape[0])
print(shape[1])
print(temperatures.ndim)
print(temperatures.size)

(2, 3)
2
3
2
6

There are two day rows, three greenhouse columns, two axes, and six temperatures. The shape tuple records the lengths; it contains none of the temperatures. We can index that tuple to read a length, but we cannot replace one of its entries as we could with a list.

Ask for one reading, one day, or one greenhouse

In a two-dimensional array, the comma inside square brackets separates the row selection from the column selection. A colon by itself means all positions along that axis. So we can choose one row and one column, all columns of a row, or all rows of a column.

import numpy as np

temperatures = np.array([
    [10, 20, 30],
    [14, 22, 36],
])

print(temperatures[1, 1])
print(temperatures[0, :].tolist())
print(temperatures[:, 1].tolist())

22
[10, 20, 30]
[20, 22]

The first result is Tuesday's middle greenhouse reading. The second is all of Monday. The third follows the middle greenhouse across both days. Selecting one row or one column this way leaves a one-dimensional array.

Keep one answer per greenhouse

The mean method calculates an average. Its axis argument says which direction to combine. The result's shape is a one-entry tuple. The trailing comma is how Python distinguishes a one-entry tuple from parentheses around a single number.

import numpy as np

temperatures = np.array([
    [10, 20, 30],
    [14, 22, 36],
])
per_greenhouse = temperatures.mean(axis=0)

print(per_greenhouse.tolist())
print(per_greenhouse.shape)

[12.0, 21.0, 33.0]
(3,)

The result has one axis of length three. It is not a table with three rows and an unspecified number of columns. It has no second axis.

Compare a daily summary with a single overall value

Providing axis one gives a result for each day. Leaving out axis asks mean to combine every entry into one scalar. That single number no longer keeps either day or greenhouse separate.

import numpy as np

temperatures = np.array([
    [10, 20, 30],
    [14, 22, 36],
])
per_day = temperatures.mean(axis=1)

print(per_day.tolist())
print(per_day.shape)
print(temperatures.mean())

[20.0, 24.0]
(2,)
22.0

The list has two daily means. The final number averages all six readings. Before writing a reduction, say what one answer should represent and how many answers you need.

A view shares readings; a copy keeps its own

We select Monday's row twice. One selection remains a view. For the other, we call copy to give it its own numerical storage. Then we change the first entry of each selection.

import numpy as np

temperatures = np.array([
    [10, 20, 30],
    [14, 22, 36],
])
monday_view = temperatures[0, :]
monday_copy = temperatures[0, :].copy()

monday_view[0] = 11
monday_copy[0] = 99

print(temperatures[0, :].tolist())
print(monday_copy.tolist())

[11, 20, 30]
[99, 20, 30]

Changing the view changed Monday in the original table. Changing the copy did not. The workshop will summarise the readings, and the challenges will calculate both kinds of mean without modifying their inputs.