Lecture VII - NumPy for Scientific Computing

Programming with Python

Dr. Tobias Vlćek

Kühne Logistics University Hamburg - Fall 2026

EP 7: Numbers Deck

The numbers deck is due

The investor wants a numbers deck. Two weeks of orders sit in the system, one row each: minutes, price, zone.

Tobi’s plan is a 40-tab spreadsheet, one tab per zone, copied by hand. He looks at the pile, then at his list-of-lists, and says the only true thing he’ll say all week:

“We need a bigger boat than a list.”

Today we get the bigger boat: NumPy, one object that holds a thousand numbers and does arithmetic on all of them at once.

Warm-up

Question 1

Three questions from Episode 6. Commit. Hands up before the reveal.

from math import ceil

# which line works?

a) ceil(3.2) b) math.ceil(3.2) c) both

Answer 1

from math import ceil

print(ceil(3.2))
print(math.ceil(3.2))

4

NameError: name 'math' is not defined

a) ceil(3.2): from math import ceil binds only the name ceil. The module math itself was never imported, so math.ceil has nothing to reach through.

Question 2

import random

random.seed(42)
print(random.randint(1, 20))
print(random.randint(1, 20))
print(random.randint(1, 20))

Tobi runs this exact script today and again tomorrow. Tomorrow’s numbers are…

a) different: random is random b) an error: seed 42 was already used c) the same three numbers

Answer 2

import random

random.seed(42)   # today
print(random.randint(1, 20), random.randint(1, 20), random.randint(1, 20))
random.seed(42)   # tomorrow: a fresh run starts from the seed again
print(random.randint(1, 20), random.randint(1, 20), random.randint(1, 20))

4 1 9
4 1 9

c) the same three numbers. Every run starts from seed 42, so the stream replays from the top. That is the entire job of a seed: reproducible randomness. (Two batches inside one run would differ: the stream continues; a fresh run rewinds it.)

Question 3

import statistics

statistics.median([9, 2, 5])

returns…

a) 2 b) 5 c) an error: the list is not sorted

Answer 3

import statistics

statistics.median([9, 2, 5])

5

b) 5: median sorts the values internally before picking the middle one. You never have to sort first; 5 is the middle of 2, 5, 9.

A thousand at once

From a list to an array

A NumPy array holds many numbers under one name, like a list, but built for math. You make one from a list, then ask it about itself:

import numpy as np

prices = np.array([12.0, 9.0, 15.0])
print(prices)
print(prices.shape)   # how many, in each dimension
print(prices.dtype)   # what kind of number
print(prices.size)    # how many in total

[12.  9. 15.]
(3,)
float64
3

np.array([...]) wraps a list; np is the nickname everyone uses. .shape is (3,), .dtype is float64, .size is 3. One dtype for the whole array: all elements share one type, part of what makes it fast.

One operation, every element

Here’s the bigger boat. The deck needs gross prices: 19% VAT on all three. With a list you loop; with an array you just multiply:

# the painful way: a loop, item by item
gross = []
for p in [12.0, 9.0, 15.0]:
    gross.append(p * 1.19)

import numpy as np

prices = np.array([12.0, 9.0, 15.0])
print(prices * 1.19)   # every element, one expression

[14.28 10.71 17.85]

One operation lands on all elements at once: [14.28 10.71 17.85]. No loop, no .append, and on a thousand orders it’s also far faster.

Your turn

Open the exercise

Scan the QR or type the link:

python.tobiasvlcek.com/notebooks/ex_07_a/

Any questions? Let me know!

Arrays from scratch

Two builders make evenly-spaced arrays without typing every number, handy for axes and ranges:

import numpy as np

print(np.arange(0, 10, 2))     # start, stop (excluded), step
print(np.linspace(0, 1, 5))    # start, stop (included), how many

[0 2 4 6 8]
[0.   0.25 0.5  0.75 1.  ]

arange walks by a step and stops before the end, just like range. linspace splits a span into a fixed count of points, endpoints included.

Predict: times two

Tobi multiplies a row of counts by two. What does this print?

print([1, 2, 3] * 2)

a) [1, 2, 3, 1, 2, 3] b) [2, 4, 6] c) an error

Predict. Pick a letter, then I reveal the answer.

Answer: repeat versus compute

import numpy as np

print([1, 2, 3] * 2)              # list → repeated
print(np.array([1, 2, 3]) * 2)    # array → doubled

[1, 2, 3, 1, 2, 3]
[2 4 6]

a) [1, 2, 3, 1, 2, 3]. That’s a plain list, and * 2 on a list repeats it. Wrap it in an array and the same * 2 does the math instead.

Lists repeat; arrays compute. That’s why we’re here.

Predict: plus

Tobi adds this week’s zone counts to last week’s. What does this print?

print([1, 2, 3] + [10, 20, 30])

a) [11, 22, 33], added pairwise b) an error: lists don’t add c) [1, 2, 3, 10, 20, 30]

Predict. Pick a letter, then I reveal the answer.

Answer: lists glue, arrays add

import numpy as np

print([1, 2, 3] + [10, 20, 30])                        # list → glued
print(np.array([1, 2, 3]) + np.array([10, 20, 30]))    # array → added

[1, 2, 3, 10, 20, 30]
[11 22 33]

c) [1, 2, 3, 10, 20, 30]. On lists, + glues them end to end, exactly like * 2 repeated. On arrays, + adds element by element, first with first, second with second.

Every operator follows the same rule: lists do list things, arrays do math.

Your turn

Open the exercise

Scan the QR or type the link:

python.tobiasvlcek.com/notebooks/ex_07_b/

Any questions? Let me know!

Ask the data

A comparison makes a mask

Compare an array to a number and you don’t get one True/False. You get a whole array of them, one per element. That’s a mask, and you can filter with it:

import numpy as np

times = np.array([25, 41, 18, 33])
print(times > 30)            # a True/False for every element
print(times[times > 30])     # keep only where the mask is True

[False  True False  True]
[41 33]

times > 30 is the mask; times[times > 30] reads the array through the mask and returns just the matching values. No loop, no if.

Counting without a loop

A mask answers two investor questions at once. .sum() counts the Trues (each counts as 1); .mean() gives the share that are True:

import numpy as np

times = np.array([25, 41, 18, 33, 52, 29, 44, 12])
late = times > 30
print(int(late.sum()))              # how many were late
print(float(times[late].mean()))    # average of just the late ones
print(float(late.mean()))           # the SHARE that were late

4
42.5
0.5

4 deliveries over 30 minutes, averaging 42.5, and late.mean() says half the run was late, one line each, straight into the deck. int(...) and float(...) turn NumPy’s numbers into plain Python numbers.

Predict: counting the Trues

What does calling .sum() on the mask give?

print((np.array([1, 5, 3]) > 2).sum())

a) True b) 2 c) [False, True, True]

Predict. Pick a letter, then I reveal the answer.

Answer: True counts as 1

import numpy as np

print(np.array([1, 5, 3]) > 2)            # [False  True  True]
print((np.array([1, 5, 3]) > 2).sum())    # Trues add up to 2

[False  True  True]
2

b) 2: .sum() adds the mask up, and each True is worth 1, each False 0. Two elements clear the bar, so the count is 2.

Summing a mask counts; averaging a mask shares. Same two tricks the lab asks for.

Predict: two conditions

The investor wants deliveries that took more than 20 and less than 40 minutes. Tobi writes what he’d write for two numbers:

times = np.array([25, 41, 18, 33])
print(times > 20 and times < 40)

a) an error: ambiguous truth value b) [ True False False True] c) True, both sides hold somewhere

Predict. Pick a letter, then I reveal the answer.

Answer: one and, four truths

import numpy as np

times = np.array([25, 41, 18, 33])
print(times > 20 and times < 40)

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

a) an error. and asks the left side “are you true?”, and a four-element mask has no single answer. Between two masks use &, and wrap each side in parentheses (& binds tighter than >):

print((times > 20) & (times < 40))    # element by element: & combines masks

[ True False False  True]

Your turn

Open the exercise

Scan the QR or type the link:

python.tobiasvlcek.com/notebooks/ex_07_c/

Any questions? Let me know!

The days-by-zones grid

A grid of numbers

Real data isn’t one row. Stack rows and you get a 2D array: here three days (rows) across four zones (columns: Nord, Sued, Hafen, Altstadt):

import numpy as np

deliveries = np.array([[ 9, 14, 11,  6],
                       [15, 12,  8,  9],
                       [13, 20, 16, 11]])
print(deliveries.shape)      # (rows, columns) → (3, 4)
print(deliveries[0, 2])      # row 0, column 2

(3, 4)
11

.shape is now (3, 4): three days, four zones. One index picks the row, a second the column: deliveries[0, 2] is day 0, zone 2 (Hafen).

Predict: the shape

Tobi builds a grid with two more days. What does .shape say?

grid = np.array([[ 9, 14, 11,  6],
                 [15, 12,  8,  9],
                 [13, 20, 16, 11],
                 [10, 17, 12,  8],
                 [ 7, 11,  9,  5]])
print(grid.shape)

a) (20,) b) (5, 4) c) (4, 5)

Predict. Pick a letter, then I reveal the answer.

Answer: rows first, then columns

import numpy as np

grid = np.array([[ 9, 14, 11,  6],
                 [15, 12,  8,  9],
                 [13, 20, 16, 11],
                 [10, 17, 12,  8],
                 [ 7, 11,  9,  5]])
print(grid.shape)   # (rows, columns)
print(grid.size)    # rows × columns

(5, 4)
20

b) (5, 4). .shape is always (rows, columns): five inner lists make five rows, each with four numbers. (20,) would be one flat row of twenty; 20 is .size, the total count.

Same order as indexing: grid[row, column], rows first.

Which way to collapse?

To sum a grid you must say which way to collapse it. The axis tells NumPy which direction disappears:

          Nord  Sued  Hafen  Altstadt
   day0  [  9    14    11      6  ]
   day1  [ 15    12     8      9  ]
   day2  [ 13    20    16     11  ]

   axis=0 collapses DOWN the rows:
            ↓     ↓     ↓      ↓
           37    46    35     26      one number per column (zone)

   axis=1 collapses ACROSS the columns:
   day0 → 40   ·   day1 → 44   ·   day2 → 60      one number per row (day)

axis in code

The same grid, the same two collapses, one keyword each:

import numpy as np

deliveries = np.array([[ 9, 14, 11,  6],
                       [15, 12,  8,  9],
                       [13, 20, 16, 11]])
print(deliveries.sum(axis=0))   # DOWN the rows → per zone
print(deliveries.sum(axis=1))   # ACROSS the columns → per day

[37 46 35 26]
[40 44 60]

axis=0 collapses DOWN the rows, one number per column (zone): [37 46 35 26]. axis=1 collapses across, one per day: [40 44 60].

Your turn

Open the exercise

Scan the QR or type the link:

python.tobiasvlcek.com/notebooks/ex_07_d/

Any questions? Let me know!

Where does the max sit?

The per-zone totals answer “how many?”, but the investor asks “which zone?”. argmax tells you WHERE the maximum sits, as an index:

import numpy as np

deliveries = np.array([[ 9, 14, 11,  6],
                       [15, 12,  8,  9],
                       [13, 20, 16, 11]])
zone_totals = deliveries.sum(axis=0)   # [37 46 35 26]
print(int(zone_totals.argmax()))        # index of the biggest

1

max would give the value 46; argmax gives its position, 1. The busiest zone is Sued, sitting at index 1, not at the front. Position, not value: that’s the whole point of argmax.

Predict: which axis is which?

The investor wants four numbers, one per zone. Which call?

week = np.array([[ 9, 14, 11,  6],
                 [15, 12,  8,  9],
                 [13, 20, 16, 11]])

a) week.sum(axis=1) b) week.sum() c) week.sum(axis=0)

Predict. Pick a letter, then I reveal the answer.

Answer: days collapse, zones stay

import numpy as np

week = np.array([[ 9, 14, 11,  6],
                 [15, 12,  8,  9],
                 [13, 20, 16, 11]])
print(week.sum(axis=0))

[37 46 35 26]

c) week.sum(axis=0). Four zones means four numbers, so the days must disappear: axis=0 collapses DOWN the rows, one number per column (zone).

a) would give three numbers (one per day); b) would give one number: the grand total, 144.

Your turn

Open the exercise

Scan the QR or type the link:

python.tobiasvlcek.com/notebooks/ex_07_e/

Any questions? Let me know!

Wrap-up

Three things to remember

1. One array, one operation. np.array([...]) holds many numbers; arithmetic hits every element at once. No loop. Ask it .shape, .dtype, .size to know what you’re holding.
2. A comparison makes a mask. arr > 30 is a True/False array: arr[mask] filters, .sum() counts the Trues, .mean() gives their share.
3. In 2D, pick an axis. axis=0 collapses DOWN the rows (one number per column), axis=1 across the columns (one per row); argmax tells you where the maximum sits.

Next episode

Next episode starts with Checkpoint 4: 40 minutes, AI allowed, everything from Episodes 6-7. Then the investor opens a data room, and Tobi lets an AI write his pandas: the arrays get column names, and eighty orders become a table you can query.

Leaving the Browser

From a browser tab to your machine

For seven sessions everything ran in a browser tab. From Session VIII the labs run on your own laptop, with three free tools:

• uv installs Python and runs your scripts
• Zed is the editor you write code in
• Mistral Vibe is the AI agent inside Zed

We install all three now, together. Today’s lab starts for you once your setup passes the check.

Step 1: uv and your course folder

Follow the uv guide from the top through Adding packages, one command at a time. It does three things:

• installs uv and Python
• creates the folder python-labs, where every lab from Session VIII lives
• adds the two packages those labs need: pandas and matplotlib

Type each command once. A second uv init builds a second python-labs inside the first, and uv then refuses to work in either.

Step 2: Zed and Mistral Vibe

Follow AI inside Zed on the AI Tools page, steps 1 to 5:

1. Install Zed from zed.dev and open it once
2. In a terminal: uv tool install mistral-vibe
3. Run vibe and sign in with your Mistral account from last session
4. In Zed’s command palette (Cmd/Ctrl+Shift+P): zed: acp registry, then install Mistral Vibe
5. File → Open Folder and pick python-labs

vibe not found? Run uv tool update-shell, then close and reopen the terminal.

The check before the lab

In Zed, with python-labs open, open the terminal (Ctrl+`, or terminal panel: toggle in the command palette) and run:

uv run python -c "import pandas, matplotlib; print('ready')"

• The terminal prints ready
• In the agent panel (the sparkle icon, bottom right), pick Mistral Vibe and ask: What does main.py do? It answers

Show me both, then open the lab.

Stuck? Raise your hand early. No laptop that runs Zed, or only an iPad? Tell me. You start the Blank template at github.com/codespaces (a Linux computer in a browser tab), do Step 1 in its terminal, and show me ready there.

To the Lab

After the check: the lab

• Head to the lab notebook: Episode 7: The Numbers Deck
• You’ll count and average the critical deliveries with masks, fix two of Tobi’s numbers, and find the winning zone in the days-by-zones grid
• AI is allowed, so try the course chatbot or your Mistral account
• It still runs in your browser; unfinished parts are homework before Checkpoint 4

Download your .py before you leave. Closing the tab without downloading loses your work. Next session, bring this laptop: from Episode 8 the labs run in Zed.

Literature

Books to start with

• Downey, A. B. (2024). Think Python: How to think like a computer scientist (Third edition). O’Reilly. Link to free online version
• Elter, S. (2021). Schrödinger programmiert Python: Das etwas andere Fachbuch (1. Auflage). Rheinwerk Verlag.

NumPy has excellent free docs: the NumPy absolute beginner’s guide covers everything in this session and a little more.

For more, see the literature list of this course.