One index: one item
closes[1]It gives 187.2 · one number, not a list
The number in the brackets is a position, counted from 0. You get the item itself, not a list.
Before you look at a result, say out loud which boxes you expect to turn gold. Then check. Every picture and every result on this page was produced by running the code.
Slicing a list
Five closing prices, one per day:
closes = [190.5, 187.2, 193.8, 185.1, 191.4]A slice cuts between the boxes
closes[1:4]It gives [187.2, 193.8, 185.1] · a list of 3
Think of start and stop as cuts BETWEEN the boxes. You keep what lies between the cuts: boxes 1, 2 and 3. Box 4 is not included.
Leave out start: from the beginning
closes[:2]It gives [190.5, 187.2] · a list of 2
No start means: cut at the very left. [:2] is the first two items. Length = stop − start = 2.
Negative numbers count from the end
closes[-2:]It gives [185.1, 191.4] · a list of 2
−1 is the last box, −2 the one before it. [-2:] is the last two items, however long the list is.
A step: every second item
closes[::2]It gives [190.5, 193.8, 191.4] · a list of 3
start:stop:step. With no start and no stop the slice covers the whole list; step 2 takes every second box. The small numbers show the order.
Step −1: backwards
closes[::-1]It gives [191.4, 185.1, 193.8, 187.2, 190.5] · a list of 5
A negative step walks from the right to the left. [::-1] is the whole list, reversed. Look at the small numbers: the last box comes first.
One item or a list of one?
closes[1]It gives 187.2 · one number, not a list
closes[1:2]It gives [187.2] · a list of 1
An index gives the item. A slice ALWAYS gives a list, even a list of one. That difference comes back in numpy as a difference in shape.
Slicing a 2-D array
The price grid from the lecture: one row per position, one column per day. In prices[rows, columns], each side of the comma is sliced on its own.
prices = np.array([[185.0, 188.2, 190.5], # AAPL
[104.1, 103.0, 102.3], # NESN
[505.0, 509.9, 512.0]]) # VOOA row: one number, then nothing
prices[1]It gives [104.1, 103.0, 102.3] · shape (3,)
One number in the brackets picks a row: NESN. The row has 3 prices, so the shape is (3,): one dimension.
A column: : for every row
prices[:, -1]It gives [190.5, 102.3, 512.0] · shape (3,)
: before the comma means every row. −1 after it is the last day. You get the last price of each position, again shape (3,).
Two numbers: one cell
prices[1, 2]It gives 102.3 · shape ()
Row 1, column 2. Two single numbers remove both dimensions: one number, shape ().
Two slices: a block
prices[:2, 1:]It gives [[188.2, 190.5], [103.0, 102.3]] · shape (2, 2)
Rows up to 2 (AAPL, NESN), columns from 1 on (days 1 and 2). Slices keep their dimension, so the result is still a table: (2, 2).
A list of columns
prices[:, [0, 2]]It gives [[185.0, 190.5], [104.1, 102.3], [505.0, 512.0]] · shape (3, 2)
A LIST in a position picks exactly those columns, here the first and the last day. All rows, two columns: (3, 2).
A row as a slice keeps the table shape
prices[1:2]It gives [[104.1, 103.0, 102.3]] · shape (1, 3)
Same cells as prices[1], but a slice keeps the dimension: a table with one row, shape (1, 3), not (3,).
The rule to count shapes
Count what is in the brackets. Every single number removes a dimension. Every slice (with :) or list keeps one. prices[1] → (3,) · prices[1:2] → (1, 3) · prices[1, 2] → () · prices[:2, 1:] → (2, 2). When numpy surprises you, print .shape first.
Two shifted slices: daily returns
Each day divided by the day before. The two slices have the same shape, so numpy divides cell by cell.
prices[:, 1:] # days 1, 2prices[:, :-1] # days 0, 1returns = prices[:, 1:] / prices[:, :-1] - 1It gives [[0.0173, 0.0122], [-0.0106, -0.0068], [0.0097, 0.0041]] (rounded to 4) · shape (3, 2)
Three days give two returns per position, so the shape is (3, 2).