21 Jul 2025

Python Conditionals, Loops, and Iteration

python control-structures conditionals loops iteration

Control structures decide which statements run and how often they run. Python uses indentation, rather than braces, to mark every conditional and loop body.

Conditional statements

Comparisons produce the Boolean values True or False:

x < y
x <= y
x == y
x != y
x >= y
x > y

The assignment operator = stores a value; the comparison operator == tests equality. Conditions can be combined with and, or, and not.

An if statement selects one branch:

energy = -2.0

if energy < 0.0:
    print("bound state")
else:
    print("unbound state")

Several mutually exclusive cases use elif:

x = -0.25

if x > 0.0:
    print("positive")
elif x < 0.0:
    print("negative")
else:
    print("zero")

Python tests from top to bottom and executes the first true branch.

For loops

A for loop processes a known sequence. range(start, stop, step) generates integers up to, but not including, stop:

for n in range(1, 6):
    print(n, n**2)

The output contains $n=1,2,3,4,5$. A loop can also process stored readings directly:

readings = [1.2, 1.4, 1.3, 1.5]
total = 0.0

for value in readings:
    total = total + value

mean = total / len(readings)
print(mean)

After $k$ loop passes, total equals the sum of the first $k$ readings. This invariant explains why the final value is the complete sum.

While loops and numerical convergence

A while loop repeats while its condition is true. It is natural when the required number of iterations is not known in advance.

For the fixed-point equation $x=\cos x$,

import math

x_old = 0.5
tolerance = 1.0e-8
change = float("inf")

while change > tolerance:
    x_new = math.cos(x_old)
    change = abs(x_new - x_old)
    x_old = x_new

print(f"root = {x_old:.10f}")

The loop body computes a new approximation, measures the change, and updates the stored point. Omitting the update would make the condition remain true indefinitely.

When a numerical method also has an equation residual, both tests can appear in the condition:

while change > x_tolerance or residual > f_tolerance:
    # compute the next approximation
    ...

The loop stops only when the change and residual are both within tolerance. A mathematical convergence condition must still be checked; a loop merely executes the chosen iteration.