Reshape and Transpose

A flat sequence can contain all the values we need without showing what a row or column means. NumPy can regroup those entries with reshape. When data has the right groups but reversed axes, transpose can exchange the axes instead. These operations may produce the same shape while making different claims about the data.

Regroup Flat Values with Reshape

Start with six readings in observation order. Every two consecutive values belong to one observation:

[[18.5 20. ]
 [21.5 22. ]
 [19.  24. ]]
(3, 2)

reshape(3, 2) regroups the six entries as three observations by two sensors. It does not sort or calculate new readings. The entry count is preserved:

6 entries = 3 × 2 entries

A requested shape whose sizes do not multiply to six cannot hold exactly these values, so NumPy raises an error rather than dropping or inventing entries.

Infer One Axis Length

When one axis length is known, -1 asks NumPy to infer the other:

(3, 2)

Three observation rows must share six entries, so NumPy infers two sensor positions per row. Use at most one -1 in a reshape: two unknown lengths would not state enough information to choose one result.

Inference checks arithmetic, not meaning. NumPy can also form shape (2, 3), but it cannot know whether 2 means sensors, observations, or something else. The program's data contract must supply those axis names.

table = values.reshape(4, -1)

Exchange Two Axes with Transpose

Suppose a source gives one row per sensor and one column per observation:

(2, 3)

The values are already grouped by sensor. To represent observations as rows and sensors as columns, exchange the two axes:

[[18.5 20. ]
 [21.5 22. ]
 [19.  24. ]]
(3, 2)

For a two-dimensional array, .T turns row positions into column positions and column positions into row positions. The entry at [sensor, observation] becomes the entry at [observation, sensor]. The same six values remain.

Reshape and transpose are not interchangeable:

Shape alone cannot prove that either result has the intended meaning. A transpose repairs the reversed table only because the source contract says its axes are (sensors, observations). If the source rows meant unrelated groups, the same operation would preserve the numbers but make a false claim about them.

readings = reversed_axes.T