Put the Same Readings Into the Right Arrangement

Botie's logger sends six readings in order: all three greenhouses on Monday, then all three on Tuesday. The message has no row breaks. We need to restore the table before asking for a daily or greenhouse summary.

Reshaping changes how existing entries are grouped. Transposing exchanges axes. Joining combines separate collections. These operations can produce similar-looking shapes while assigning very different meanings to their positions.

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.

The default reshape order reads the original entries in row order and puts them into the requested row order. It cannot create or discard entries. The product of the new dimensions must match the number of existing entries.

One dimension may be minus one, meaning infer this length from the remaining dimensions and the number of entries. It does not mean a missing observation.

import numpy as np

flat = np.array([10,20,30,14,22,36])
days = flat.reshape(2, 3)
print(days.tolist())
print(flat.reshape(-1, 3).shape)
print(days.ravel().tolist())

[[10, 20, 30], [14, 22, 36]]
(2, 3)
[10, 20, 30, 14, 22, 36]

Regrouping the sequence into three pairs is not the same as following each greenhouse across days. A transpose exchanges the roles of rows and columns while keeping each value attached to its original coordinates.

The T attribute is a convenient transpose for a matrix. On arrays with more axes, name the intended axis order explicitly rather than assuming that reversing all axes is what the task needs.

import numpy as np

days = np.array([[10,20,30],[14,22,36]])
print(days.reshape(3, 2).tolist())
print(days.T.tolist())

[[10, 20], [30, 14], [22, 36]]
[[10, 14], [20, 22], [30, 36]]

concatenate extends an existing axis. stack creates a new axis to keep its inputs separate. Suppose we have two daily vectors. Concatenating them makes a longer vector; stacking them makes a table of days.

When joining tables, all dimensions other than the concatenation axis must match. When stacking, the input shapes must match because each becomes a slice along the new axis.

import numpy as np

monday = np.array([10,20,30])
tuesday = np.array([14,22,36])
print(np.concatenate([monday, tuesday]).shape)
days = np.stack([monday, tuesday], axis=0)
print(days.tolist())
wednesday = np.array([[16,24,38]])
print(np.concatenate([days, wednesday], axis=0).tolist())

(6,)
[[10, 20, 30], [14, 22, 36]]
[[10, 20, 30], [14, 22, 36], [16, 24, 38]]

A model often receives a table with observations in rows and features in columns. column_stack turns equally long vectors into feature columns. A batch adds another meaning: a group of observations processed together.

When there are three or more axes, write down what each one means before manipulating the shape. Equal lengths do not make two axes interchangeable.

import numpy as np

temperature = np.array([12., 18., 24.])
humidity = np.array([50., 60., 70.])
features = np.column_stack([temperature, humidity])
batch = np.expand_dims(features, axis=0)
print(features.tolist())
print(batch.shape)
print(np.squeeze(batch, axis=0).shape)

[[12.0, 50.0], [18.0, 60.0], [24.0, 70.0]]
(1, 3, 2)
(3, 2)