Lecture 09

E21 Computer Engineering Fundamentals

Emad Masroor

September 29, 2026

Test 1 + Survey

Mid-semester survey

Installing numpy with Thonny Code Editor

numpy arrays

• numpy arrays are objects of type numpy.ndarray

• The numpy.array() function creates numpy.ndarray objects

>>> a = numpy.array([0.4, 6, -0.9])
>>> a
array([ 0.4,  6. , -0.9])
>>> type(a)
<class 'numpy.ndarray'>
>>> 

• Arrays in numpy are similar to lists.
  • They can be indexed
  • Their elements are mutable
  • They are iterable — can be used with for loops
• Arrays also have some differences compared to lists
  • Unlike lists, one array can have only one type of element
  • Appending is possible but discouraged — pre-allocate!

Importing the package

• After installing numpy for your version of Python, you need to import numpy in any code you write.

• A common approach is:

  import numpy as np
  a = np.array([1,2.5,3])

  This shortens numpy.<function name> to np.<function name> and has no other function.

• Other approaches that work:

  • Import using full name

    import numpy
    a = numpy.array([1,2.5,3])

  • Import specific functions only

    from numpy import array
    a = array([1,2.5,3])

numpy arrays are inherently n-dimensional

• In Python lists, we used the concept of a list of lists to encode two-dimensional information.

Native Python Approach

pattern3 = [["p", "p", "t", "g"],
            ["p", "p", "g", "t"],
            ["t", "g", "p", "p"],
            ["g", "t", "p", "p"]]
print(pattern3[1][2])

numpy Approach

p= np.array([["p", "p", "t", "g"],
            ["p", "p", "g", "t"],
            ["t", "g", "p", "p"],
            ["g", "t", "p", "p"]])
print(p[1,2])

• Looks similar, but now you should think matrix
• Access multi-dimensional arrays using the [row,column] syntax
• For example, p[1,2] will give the string"g"

numpy arrays support vectorized operations

• In regular Python, lists aren’t very useful for manipulating many numbers.
• By default, the mathematical/boolean operators work element by element.

Native Python Approach

>>> f1 = [[0.3, 0.5, 0.6],
          [0.2, -0.3, 0.7]]
>>> f1 + 100
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can only concatenate list ...

numpy Approach

>>> f = np.array([[0.3, 0.5, 0.6],
                  [0.2,-0.3, 0.7]])
>>> f + 100
array([[100.3, 100.5, 100.6],
       [100.2,  99.7, 100.7]])
>>> f ** 2
array([[0.09, 0.25, 0.36],
       [0.04, 0.09, 0.49]])
>>> f = np.array([[0.3, 0.5, 0.6],
                  [0.2,-0.3, 0.7]])
>>> g = np.array([[0.2, 0.5, -0.6],[0.2,-0.3,1.9]])
>>> f == g
array([[False,  True, False],
       [ True,  True, False]])

More about n-dimensional arrays

Numpy arrays have a property shape

>>> f = np.array([[0.3, 0.5, 0.6],
                  [0.2,-0.3, 0.7]])
>>> f.shape
(2, 3)
>>> np.shape(f)
(2, 3)

• The shape tells you how many rows and columns an array has.
• If there are more than two dimensions, there is no name for the third and higher ‘rows/columns’.

numpy and floating-point binary numbers

• By default, all numbers in numpy are 64-bit floating point binary numbers.

  >>> a = np.array([0.3])
  >>> type(a)
  <class 'numpy.ndarray'>
  >>> type(a[0])
  <class 'numpy.float64'>
  >>> 

• You can choose numbers with a different precision.

  a1 = np.float16(3.2)
  a2 = np.float32(4.2)
  a3 = np.float64(5.2)

One-dimensional arrays vs. Two-dimensional arrays

from numpy.random import random

A 5-element 1-dimensional array

>>> a = random(5)
>>> a
array([0.57549695, 
       0.81646336, 
       0.80189814, 
       0.11415026, 
       0.62458897])

A 5x1-element 2-dimensional array

>>> b = random((5,1))
>>> b
array([[0.32551251],
       [0.54539388],
       [0.97696562],
       [0.53288049],
       [0.13886612]])

Manipulating Data in numpy

Download the data file here and look at the official documentation here

Consists of 3 days of temperature data recorded at half-hour intervals.

1. Reformat the data in the form of an N rows, 2 column numpy array.
2. Save the data as csv files for the three days separately.

• array()
• zeros()
• reshape
• append
• flatten
• transpose
• savetxt
• loadtxt

Exploring floating-point numbers with numpy

Try out the following code and explain the behavior. Make sure you use immport numpy as np first.

z  = np.float16(128)
z1 = np.float16(0.2)
print(z + z1 + z1 + z1)

y  = np.float16(16)
y1 = np.float16(0.2)
print(y + y1 + y1 + y1)

v  = np.float32(1048576)
v1 = np.float32(0.2)
v2 = v + v1 + v1 + v1
print(f"{v2:9.2f}")