NTNUs Python-on-exam

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Keywords

Keyword Description Code example
False, True Data values from the data type Boolean False == (1 > 2), True == (2 > 1)
and, or, not Logical operators:
• (x and y) → both x and y must be True
• (x or y) → either x or y must be True
• (not x) → x must be false		 x, y = True, False
(x or y) == True # True
(x and y) == False # True
(not y) == True # True
break Ends loop prematurely while(True):
break # no infinite loop
print("hello world")
continue Finishes current loop iteration while(True):
continue
print("43") # dead code
class Defines a new class → a real-world concept (object-oriented programming) class Beer:
def __init__(self): self.content = 1.0
def drink(self): self.content = 0.0
becks = Beer()
becks.drink()
def Defines a new function or method. First parameter (“self”) refers to the instance (implicit on calls). (included in class example)
if, elif, else Conditional execution: checks branches in order until one is True x = int(input("your value: "))
if x > 3: print("Big")
elif x == 3: print("Medium")
else: print("Small")
for, while Loop declarations for i in [0,1,2]: print(i)
j = 0
while j < 3:
print(j)
j = j + 1
in Checks whether element is in sequence 42 in [2, 39, 42] # True
is Checks whether both elements reference the same object y = x = 3
x is y # True
[3] is [3] # False
None Empty value constant def f(): x = 2
f() is None # True
lambda Anonymous function (lambda x: x + 3)(3) # returns 6
return Terminates function execution and optionally returns a value def incrementor(x): return x + 1
incrementor(4) # returns 5

Basic Data Types

Type Description Example
Boolean Truth values: True or False.

Boolean operators (in order of priority):
• not x
• x and y
• x or y

Values considered False: None, 0, 0.0, '', [], {}, set()		 1. Boolean Operations
x, y = True, False
print(x and not y) → True
print(not x and y or x) → True

2. Falsey conditions:
if None or 0 or 0.0 or '' or [] or {} or set():
print("Dead code") # Not reached
Integer, Float Integers have no decimals; floats have decimal precision.
Integer division // returns floor value.		 3. Arithmetic Operations
x, y = 3, 2
x + y → 5
x - y → 1
x * y → 6
x / y → 1.5
x // y → 1
x % y → 1
-x → -3
abs(-x) → 3
int(3.9) → 3
float(3) → 3.0
x ** y → 9
String Strings are sequences of characters. Created using:
1) single quotes 'Yes'
2) double quotes "Yes"
3) triple quotes """Yes"""
4) str(...)
5) concatenation "Ma" + "hatma"		 4. Indexing and Slicing
s = "The youngest pope was 11 years old"
s[0] → 'T'
s[1:3] → 'he'
s[-3:-1] → 'ol'
s[-3:] → 'old'
x = s.split()
x[-3] + " " + x[-1] + " " + x[2] + "s" → '11 old popes'

5. String Methods:
y = " This is lazy\t\n "
y.strip() → 'This is lazy'
"DrDre".lower() → 'drdre'
"attention".upper() → 'ATTENTION'
"smartphone".startswith("smart") → True
"smartphone".endswith("phone") → True
"another".find("other") → 2
"cheat".replace("ch","m") → 'meat'
','.join(["F","B","I"]) → 'F,B,I'
len("Rumpelstiltskin") → 15
"ear" in "earth" → True

Complex data types

Category Description Example
List A container type storing a sequence of elements. Lists are mutable. l = [1, 2, 2]
len(l) → 3
Adding elements Add elements with: (i) append, (ii) insert, (iii) list concatenation. append is fastest. [1, 2, 2].append(4) → [1, 2, 2, 4]
[1, 2, 4].insert(2, 2) → [1, 2, 2, 4]
[1, 2, 2] + [4] → [1, 2, 2, 4]
Removal Removing an element can be slow. [1, 2, 2, 4].remove(1) → [2, 2, 4]
Reversing Reverses the list elements. [1, 2, 3].reverse() → [3, 2, 1]
Sorting Sorts a list. Complexity is linearithmic. [2, 4, 2].sort() → [2, 2, 4]
Indexing Finds first occurrence of element; may be slow. [2, 2, 4].index(2) → 0
[2, 2, 4].index(2, 1) → 1
Stack Lists can act as stacks using append() and pop(). stack = [3]
stack.append(42) → [3, 42]
stack.pop() → 42
stack.pop() → 3
Set Unordered collection of unique elements. basket = {'apple','eggs','banana','orange'}
same = set(['apple','eggs','banana','orange'])
Dictionary Stores key–value pairs. calories = {'apple':52, 'banana':89, 'choco':546}
Read & write elements Access items using keys; use keys() and values() for iteration. calories['apple'] < calories['choco'] → True
calories['cappu'] = 74
'apple' in calories.keys() → True
52 in calories.values() → True
Dictionary looping Use items() to loop through key–value pairs. for k,v in calories.items():
print(k) if v > 500 else None
→ prints "chocolate"
Membership operator in checks element existence. Set containment is faster than list containment. basket = {'apple','eggs','banana','orange'}
'eggs' in basket → True
'mushroom' in basket → False
List & Set comprehension Concise way to build lists or sets with for and optional if. List comprehension:
l = [('Hi ' + x) for x in ['Alice','Bob','Pete']]→ ['Hi Alice','Hi Bob','Hi Pete']
l2 = [x*y for x in range(3) for y in range(3) if x>y]→ [0, 0, 2]
Set comprehension:
squares = {x**2 for x in [0,2,4] if x < 4} → {0, 4}

Functions and tricks

Function / Trick Description Example Result
map(func, iter) Applies a function to all elements of an iterable list(map(lambda x: x[0], ['red','green','blue'])) ['r', 'g', 'b']
map(func, i1, …, ik) Applies function to each tuple of elements from k iterables list(map(lambda x, y: str(x) + ' ' + y + 's', [0,2,2], ['apple','orange','banana'])) ['0 apples','2 oranges','2 bananas']
string.join(iter) Joins elements with a separator string ' marries '.join(['Alice','Bob']) 'Alice marries Bob'
filter(func, iter) Keeps elements for which function returns True list(filter(lambda x: True if x>17 else False, [1,15,17,18])) [18]
string.strip() Removes leading and trailing whitespace " \n \t 42 \t ".strip() 42
sorted(iter) Sorts iterable in ascending order sorted([8,3,2,42,5]) [2,3,5,8,42]
sorted(iter, key=…) Sorts iterable using a key function sorted([8,3,2,42,5], key=lambda x: 0 if x==42 else x) [42,2,3,5,8]
help(func) Shows documentation for a function help(str.upper) '...to uppercase...'
zip(i1, i2, …) Groups i-th elements from each iterator list(zip(['Alice','Anna'], ['Bob','Jon','Frank'])) [('Alice','Bob'), ('Anna','Jon')]
Unzip Unzips zipped iterables list(zip(*[('Alice','Bob'),('Anna','Jon')])) [('Alice','Anna'), ('Bob','Jon')]
enumerate(iter) Assigns index numbers to elements list(enumerate(['Alice','Bob','Jon'])) [(0,'Alice'),(1,'Bob'),(2,'Jon')]
**python -m http.server Starts a simple file-sharing server on port <P> Run in terminal PC files accessible in browser
import antigravity Opens “xkcd” comic about Python import antigravity Opens browser comic
import this Shows the Zen of Python import this Prints Zen of Python text
Swap variables Pythonic variable swap a, b = 'Jane','Alice'; a, b = b, a a='Alice', b='Jane'
Unpacking args Use * for sequences and ** for dicts as function arguments def f(x,y,z): return x+y*z
f(*[1,3,4])
f(**{'z':4,'x':1,'y':3})		 13
13
Extended unpacking Assign multiple values with unpacking a, *b = [1,2,3,4,5] a=1, b=[2,3,4,5]
Merge dictionaries Combine dictionaries with unpacking x={'Alice':18}
y={'Bob':27,'Ann':22}
z={**x,**y}		 {'Alice':18,'Bob':27,'Ann':22}

NumPy

Name / Operation Description Example Output
a.shape Returns a tuple describing the dimensions of array a. a = np.array([[1,2],[1,1],[0,0]])
print(np.shape(a))		 (3, 2)
a.ndim Number of array dimensions (length of shape tuple). print(np.ndim(a)) 2
* (Hadamard product) Element-wise multiplication of two arrays with the same shape. a = np.array([[2,0],[0,2]])
b = np.array([[1,1],[1,1]])
print(a*b)		 [[2 0] [0 2]]
np.matmul(a, b), a @ b Matrix multiplication (dot product). print(np.matmul(a,b)) [[2 2] [2 2]]
np.arange(start, stop, step) Creates a 1D array with evenly spaced values. np.arange(0,10,2) [0 2 4 6 8]
np.linspace(start, stop, num) Creates a 1D array with num evenly spaced values between start and stop. np.linspace(0,10,3) [ 0. 5. 10.]
np.average(a) Computes average of all elements. a = np.array([[2,0],[0,2]])
np.average(a)		 1.0
slice assignment Replace part of an array by assigning to a slice. a = np.array([0,1,0,0,0])
a[::2] = 2		 [2 1 2 0 2]
np.var(a) Variance of values in array. a = np.array([2,6])
np.var(a)		 4.0
np.std(a) Standard deviation of values in array. np.std(a) 2.0
np.diff(a) Differences between consecutive elements. fibs = np.array([0,1,1,2,3,5])
np.diff(fibs, n=1)		 [1 0 1 1 2]
np.cumsum(a) Cumulative sum of array elements. np.cumsum(np.arange(5)) [0 1 3 6 10]
np.sort(a) Returns a sorted copy of the array. a = np.array([10,3,7,1,0])
np.sort(a)		 [0 1 3 7 10]
np.argsort(a) Returns indices that would sort the array. np.argsort(a) [4 3 1 2 0]
np.max(a) Maximum value in array. np.max(a) 10
np.argmax(a) Index of the maximum value. np.argmax(a) 0
np.nonzero(a) Indices of non-zero elements. np.nonzero(a) [0 1 2 3] (for example)

numpy/sympy

Oprettelse av numpy-matriser

Opprettelse av numerisk funksjon f = np.sin(x*y)

Integrasjon og derivasjon scipy

Integrasjon og derivasjon med sympy

Innsetting av verdier

Plotting med matplotlib

Det er en bug in matplotlib – alle lerretene er lenket sammen. To funksjoner cla() og cls() er en workaround. Noen eksempler er skjult bak kommentartegnet for å gjøre denne fanen lettere.

Plot av en graf til \(f(x)\)

Viser et 2D-array med skalardata som et bilde ved bruk av det spesifiserte «hot»-fargekartet. (Kopier til ditt vindu og ta bort kommentar-tegnet.)

Plot av en overflate i 3D. (Kopier til ditt vindu og ta bort kommentar-tegnet.)

Optimering

Unconstrained Minimization (2 Variables)

This example minimizes the two-variable function \(f(x,y)=(x-1)^{2}+(y-2.5)^{2}\), which has a minimum at \((x,y)=(1,2.5)\).

Constrained Optimization

This example demonstrates how to minimize the Rosenbrock function subject to a set of linear constraints. We aim to minimize the function \(f(x_{0},x_{1})=100(x_{1}-x_{0}^{2})^{2}+(1-x_{0})^{2}\), subject to the following constraints: \(x_{0}+2x_{1}\le 1\), \(2x_{0}+x_{1}=1\), \(0\le x_{0}\le 1\), \(-0.5\le x_{1}\le 2.0\).

Minimizing \(f(x)\) with a spherical constraint

This example minimizes the objective function \(f(x)=(x_{0}+x_{1})^{2}\) subject to the nonlinear equality constraint \(x_{0}^{2}+x_{1}^{2}=1\) (which defines a unit circle).

Linear least squares

We solve a linear least-squares problem with bounds on the variables. The goal is to minimize \(0.5*||Ax-b||^{2}\) subject to \(lb\le x\le ub\)

Linear programming

Problem: Minimize: \(f(x_{0},x_{1})=2x_{0}+3x_{1}\) Subject to: \(-x_{0}-x_{1}\le -4\), \(2x_{0}+x_{1}\le 6\), \(x_{0}\ge 0,x_{1}\ge 0\) (default bounds)