Array Operations
To get revenue for each of the eight sales with plain lists, you would write a loop that multiplies copies by price one pair at a time. With NumPy you write copies * price and it is done, for eight values or eight million. Thinking in whole arrays instead of loops is the first real habit of data analysis.
The rule
Operators work element by element; a single number stretches to fit.
copies = np.array([3, 5, 2, 4, 1, 6, 2, 3])
price = np.array([250, 400, 400, 250, 250, 120, 120, 400])
revenue = copies * price
# [ 750 2000 800 1000 250 720 240 1200]Two arrays of the same shape are combined position by position: first with first, second with second. This is called vectorised arithmetic, and it runs in fast compiled code rather than a Python loop.
When one side is a single number, NumPy broadcasts it: the number is reused against every element.
price * 1.18 # add 18% tax to every price
copies + 1 # [4 6 3 5 2 7 3 4]
copies > 3 # [False True False True False True False False]Comparisons are element-wise too, giving an array of booleans you will soon use for filtering.
Aggregations collapse an array to a summary:
revenue.sum() # 6960
copies.mean() # 3.25
copies.max() # 6
copies.argmax() # 5, the position of the largest valueOn a 2-D array, axis chooses the direction. With grid = copies.reshape(2, 4):
grid.sum(axis=0) # [ 4 11 4 7] one total per column
grid.sum(axis=1) # [14 12] one total per rowThe shortcut
For axis, remember "the axis you name is the one that disappears." A (2, 4) array summed along axis 0 loses its 2 and becomes shape (4,). Summed along axis 1 it loses its 4 and becomes (2,).
Write the shape
gridhas shape(2, 4): 2 rows, 4 columns.
The trap is shape mismatch: adding an array of length 8 to one of length 3 raises an error, because there is no sensible way to pair them up.
Drills
Answer fast — trust the rule.
What is np.array([1, 2, 3]) * 10?
What is np.array([2, 4]) + np.array([10, 20])?
copies is [3 5 2 4 1 6 2 3]. What does (copies > 3).sum() return?
An array has shape (12, 5). What shape does .mean(axis=0) return?
Remember
- Operators work element by element; a single number stretches to fit.
- The axis you name is the one that disappears.
- Arrays of different, incompatible shapes cannot be combined.