Exercises

Here are a selection of exercises covering various aspects of the course material. Their aim is to make you think about how to solve a problem using code. These are not assessed, but you are encouraged to try these out, because practice is the best way to learn how to code!

In several cases there are already exist functions, e.g., in NumPy, for performing some of these exercise problems. While generally you should use existing functions from well maintained libraries (they will be very well tested and robust), here (unless asked to use an appropriate library) the aim is for you to think about how you would code up the function yourself.

Python basics

Exercise 1

Part 1

Open a Python/IPython terminal and declare two variables as floating point numbers. Add the two variables and store the output as a new variable. Print out the new variable value to the screen.

Solution

$ ipython

>>> x = 1.2774392  # variable containing a floating point number
>>> y = -3.4374323  # another variable containing a floating point number
>>> z = x + y  # add the two variables and store result in z
>>> print(z)  # print the result z to the screen

Part 2

Print out the resulting variable to 3 decimal places.

Solution

Several options exist, e.g.,

>>> print("{0:.3f}".format(z))

or

>>> print(f"{z:.3f}")

or

>>> print("%.3f" % z)

Part 3

Perform the same task, but this time write the code in a text file saved with the .py extension. Run the code in VS Code and also from the command line.

Exercise 2

Question

In a Python/IPython terminal, or in a script, import an appropriate library to calculate the sine of a list of angles that are given in degrees.

Solution

A method using the math library is:

import math

# make a list of angles (assumed to be in degrees)
angles = [0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180]

sines = []
# loop over angles
for angle in angles:
    rad = math.radians(angle)  # convert angle to radians
    # rad = angle * math.pi / 180  # an alternative
    sines.append(math.sin(rad))  # calculate sine an append to list

A different method using the NumPy library is:

import numpy as np

rads = np.deg2rad(angles)  # convert angles to radians
sines = np.sin(rads)

Exercise 3

Part 1

Given a list of numbers, without using the built-in max() method, find the maximum value in the list. Try two different ways of looping through the list values.

Solution

Two different options are:

x = [-2, 3, 6, -5, 7, 8, 12, -9]

maximum = x[0]  # use first value as initial comparitor
for v in x[1:]:
    if v > maximum:
        maximum = v  # update comparitor

or (using the range() and len() functions):

maximum = x[0]
for i in range(1, len(x)):
    if x[i] > maximum:
        maximum = x[i]

Part 2

Given two equal length lists of numbers, create a new list containing the sum of the pairs of values from those lists. Try two different methods of doing this.

Solution

Two different options are:

x = [-2, 3, 6, -5, 7, 8, 12, -9]
y = [0, 12, -5, 2, 8, -8, 11, 2]

z = []
for i in range(len(x)):
    z.append(x[i] + y[i])

or (using the zip() function):

z = []
for vx, vy in zip(x, y):
    z.append(vx + vy)

Part 3

Given two equal length lists of numbers, add the numbers from the first list onto the values in the second list (do not create a new list).

Solution

Using the enumerate() function you can do:

x = [-2, 3, 6, -5, 7, 8, 12, -9]
y = [0, 12, -5, 2, 8, -8, 11, 2]

for i, v in enumerate(x):
    y[i] += v

Exercise 4

Part 1

Use list comprehension to generate a list containing the square roots of all integers between 1 and 50.

Solution

import math

sqroots = [math.sqrt(x) for x in range(1, 51)]

Part 2

Now use list comprehension to generate the square roots of only even numbers.

Solution

import math

sqroots = [math.sqrt(x) for x in range(1, 51) if x % 2 == 0]

Exercise 5

Question

Given a dictionary containing the following information

personaldata = {
    "firstname": "Sammy",
    "lastname": "Scissors",
    "housenumber": 2,
    "streetname": "Long Lane",
    "city": "Lancaster",
    "postcode": "LA1 8TF"
}

construct a single format string that will allow the address to be output in the form:

Sammy Scissors
2 Long Lane
Lancaster
LA1 8TF

Solution

A possible solution is

addressstring = (
    "{firstname} {lastname}\n"
    "{housenumber} {streetname}\n"
    "{city}\n"
    "{postcode}\n"
)

print(addressstring.format(**personaldata))

Exercise 6

Part 1

Create an \(3 \times 4\) (3 rows, 4 columns) array using a list of lists, where each value in the array is initialised to be 1.

Solution

The best way is to use list comprehension, e.g.,:

x = [[1 for _ in range(4)] for _ in range(3)]

Part 2

Set the corner values of the array to be zero.

Solution

x[0][0] = 0
x[-1][0] = 0
x[0][-1] = 0
x[-1][-1] = 0

Exercise 7

Part 1

Create a 2D \(3 \times 3\) matrix of numbers (using lists). Loop over the rows in the matrix and print out the sum of each row.

Solution

x = [[0.1, 0.5, 1.2], [-2.3, 4.5, 0.3], [5.7, -0.3, 1.4]]

# loop over each row
for row in x:
    print(sum(row))

Part 2

Now loop over the columns and print out the products of each column.

Solution

# loop over each column
for i in range(len(x)):
    # column has to be explicitly extracted
    column = [row[i] for row in x]

    product = 1.0
    for cv in column:
        product *= cv

    print(product)

Note that this is easier with NumPy arrays, for which the rows and column can be transposed, e.g.:

import numpy as np

y = np.array(x)

for row in y:
    print(np.sum(row))

for col in y.T:  # transpose of y
    print(np.prod(col))

Exercise 8

Part 1

Given the following dictionary:

charge = {
    "electron": -1,
    "positron": 1,
    "proton": 1,
    "neutron": 0,
    "up": 2/3,
    "down": -1/3
}

get a list of the dictionary keys and a list of the dictionary values.

Solution

The lists of keys and values can be extracted with:

keys = list(charge.keys())  # need to explicitly convert iterator to list
values = list(charge.values())

Part 2

Add a new particle and its charge to the dictionary.

Solution

charge["strange"] = -1/3

Part 2

Find the number of positively charged particles in the dictionary and get a list of their names.

Solution

One option is:

npos = 0  # counter for positive particles
positive = []  # list of positive particles
for particle, c in charge.items():
    if c > 0:
        npos += 1
        positive.append(particle)

Another method, using list comprehension, is:

positive = [c for c in charge.values() if c > 0]
npos = len(positive)

Exercise 9

Part 1

Create a dictionary with three keys "a", "b" and "c", where each key value is an empty list.

Solution

data = {"a": [], "b": [], "c": []}
# alternative
# data = dict(a=[], b=[], c=[])

Part 2

Add another key, "d", into the dictionary that is also an empty list.

Solution

data["d"] = []

Part 3

For each string in the list:

alpha = ["aadb", "bbcd", "aaaa", "bccc", "dddd", "cbcb", "daca"]

append the numbers of each letter to the appropriate list in the dictionary.

Solution

# loop over the list
for a in alpha:
    # loop over each letter in the dictionary
    for letter in data:
        # count number of letters in each string
        numlet = a.count(letter)

        # append to list in dictionary
        data[letter].append(numlet)

Exercise 10

Question

Suppose you have a set of files containing the results of multiple consecutive experiments/simulations. To distinguish the files each file name is suffixed by an integer with preceding zeros, such the number is always 3 digits long (assuming no more than 1000 files exist), e.g.,:

experimental_results_000.txt
experimental_results_001.txt
...
experimental_results_258.txt
experimental_results_259.txt

Assuming you know how many files you have and the file name format, how might you loop over all the files to read them in?

Solution

A possible solution is:

N = 260  # total number of files

basename = "experimental_results_{0:03d}.txt"

# loop over files and read in results
results = []
for i in range(N):
    thisfile = basename.format(i)

    # read in the results in some form
    with open(thisfile, "r") as fp:
        results.append(fp.read())

Python functions

Exercise 11

Question

In a Python file, write a function that asks the user to input a date in the format "YYYY-MM-DD" and then prints out the day of the week (see the Python datetime library). In another Python script, or Python/IPython terminal, import the function that you have written and run it.

Solution

Create a Python (called, say, weekday.py) file containing:

from datetime import datetime

def getweekday():
    # ask user for input
    datestr = input("Input a date in the format YYYY-MM-DD: ")

    # split string into parts
    year, month, day = datestr.split("-")

    # convert into datetime object
    d = datetime(int(year), int(month), int(day))

    # get the day of the week
    weekday = d.strftime("%A")

    # output day of the week
    print(f"The date {datestr} was on a {weekday}")

You may want to add a check that the date in is the correct format. This function could then be used with:

$ ipython

>>> from weekday import getweekday
>>> getweekday()  # run the function

Exercise 12

Part 1

Write a function that takes in a list of numbers as an argument and returns their mean.

Answer

An example of how to do this is:

def mean(values):
    s = 0.0  # variable to hold sum of values
    for value in values:
        s += value

    # return the mean
    return s / len(values)

You could add some checking that values is indeed a list. You could also use the built-in Python sum() function rather than using the for loop.

Part 2

Write a function that takes in a list of numbers as an argument and returns their standard deviation. Can the function from Part 1 be re-used?

Solution

An example of how to do this is:

def std(values):
    # get the mean of the values (re-use the previous function)
    mu = mean(values)

    # get the variance (re-use mean function again)
    var = mean([(x - mu)**2 for x in values])

    # return the standard deviation
    return var ** 0.5

Part 3

Write a function that takes in list of numbers as an argument and returns the median.

Solution

An example of how to do this is:

def median(values):
    # use the built-in sorted function to sort the values in ascending order
    sortvals = sorted(values)

    # get the halfway index
    half = int(len(values) / 2)

    # check if values contains an odd or even number of values
    if len(values) % 2 == 0:
        # an even number, so return average of middle two numbers
        return (values[half - 1] + values[half]) / 2
    else:
        # an odd number, so return middle number
        return values[half]

Exercise 13

Question

Write a function that:

• takes in a list of strings as an argument,
• finds the unique strings,
• counts the number of occurrences of each of those unique strings in the list
• returns those number counts in a dictionary keyed by the unique string values.

E.g.,

>>> animals = ['cat', 'dog', 'dog', 'dog', 'cat', 'horse']
>>> counts = count_occurrences(animals)
>>> print(counts)
{'cat': 2, 'dog': 3, 'horse': 1}

Solution

A way of doing this is:

def count_occurrences(values):
    # get unique strings by converting to a set
    unique = set(values)

    # create empty dictionary for counts
    counts = {}

    # loop over unique strings and count occurrences
    for word in unique:
        count = 0
        for w in values:
            if w == word:
                count += 1

        # short method (use count method of a list)
        #counts[word] = values.count(word)

    return counts

Exercise 14

Part 1

Write a function that takes in a list as an argument and returns a new list containing the square of every \(n\)th index (starting at the 0 index), where \(n\) is another argument to the function with a default value of 2.

E.g.,

>>> values = [2, 3, 4, 5, 6, 7, 8, 9, 10]
>>> sq = square_index(values)
>>> print(sq)
[4, 16, 36, 64, 100]

Solution

A way of doing this is:

def square_index(values, step=2):
    squ = []

    # loop over list in steps of "step"
    for i in range(0, len(values), step):
        squ.append(values[i] ** 2)

    return squ

    # short method (using slice notation instead)
    #return [x ** 2 for x in values[::step]]

You may want to include checks that values is a list and that step is an integer.

Part 1

Alter the function so that it takes in another argument, reverse, which defaults to False, but if True makes the function return the list in reverse order.

Solution

A way of doing this is:

def square_index(values, step=2, reverse=False):
    squ = []

    # get indices to return
    if reverse:
        idxs = range(len(values), 0, -step)
    else:
        idxs = range(0, len(values), step)

    # loop over list in steps of "step"
    for i in idxs:
        squ.append(values[i] ** 2)

    return squ

The slice() function could also be used rather than the range() function.

Exercise 15

Part 1

Given a square 2D matrix, e.g.,:

M = [[1.5, 2.1, 3.6, 4.1], [-0.2, 6.1, 7.2, -5.0], [3.4, 10.1, 1.7, 12.9], [-13.0, 1.3, -2.4, 0.8]]

write a function that takes in the matrix as an argument and returns its diagonal elements as a list.

Solution

def diag(M):
    """
    Return the diagonal elements of a square 2D matrix.

    Parameters
    ----------
    M: matrix
        A square 2D matrix

    Returns
    -------
    list:
        A list of the diagonal elements of the matrix.
    """

    de = []

    # loop over length of matrix
    for i in range(len(M)):
        de.append(M[i][i])

    return de

You may want to include tests that the matrix is two-dimensional and square.

Part 2

Write a function to calculate the determinant of the matrix.

Hint: The built-in Python itertools module can calculate permutations. You will also need to calculate the signature (or parity) of the permutation.

Solution

from itertools import permutations

def sgn(permutation):
    """
    Get the signature, or parity of a permutation (based on
    https://gist.github.com/lycantropos/217710b0afc40b3031762274275c204a)
    of numbers between 0 and N, where N is the length of the permutation
    list.

    Parameters
    ----------
    permutation: list
        A permutation of the numbers from 0 to len(list)

    Returns
    -------
    int:
        A 1 for an even permutation, -1 for an odd permutation.
    """

    if len(permutation) == 1:
        return 1

    transitions_count = 0
    for idx, element in enumerate(permutation):
        for next_element in permutation[idx + 1:]:
            if element > next_element:
                transitions_count += 1

    return 1 if not (transitions_count % 2) else -1

def det(M):
    """
    Calculate the determinant of a square 2D matrix.

    Parameters
    ----------
    M: matrix
        A square 2D matrix

    Returns
    -------
    float:
        The determinant value.
    """

    # length of matrix
    n = len(M)

    D = 0.0  # variable to sum up determinant

    # get permutations (use Leibniz formula)
    for perm in permutations(range(n)):
        subD = 1.0
        for i in range(n):
            subD *= M[i][perm[i]]

        # get signature of permutation
        D += sgn(perm) * subD

    return D

Exercise 16

Part 1

Write a function to "bin" a list of numbers, i.e., count how many of the numbers are in each of a set of intervals over the full range (e.g., the bin sizes in a histogram). The function arguments should be the list of numbers, the number of bins (defaulting to 10), and the lower and upper bin edges (if not given by the user these should default to use the smallest and largest number in the input list, respectively).

Try doing this without using NumPy!

Solution

def binned(samples, nbins=10, low=None, high=None):
    """
    Count the number of values within a set of bins.

    Parameters
    ----------
    samples: list
        A list of numbers which will be "binned"
    nbins: int
        The number of bins into which to split the range of numbers
    low: float
        The edge of the lowest bin (defaults to the smallest value in `samples`)
    high: float
        The edge of the highest bin (defaults to the largest values in `samples`)

    Returns
    -------
    tuple
        A tuple containing two lists: the bin edges and the number counts in each
        bin
    """

    # get the bin ranges
    if low is None:
        low = min(samples)

    if high is None:
        high = max(samples)

    # step size between bins
    binstep = (high - low) / nbins

    # lists to contain bin edges and number counts
    binedges = [low]
    bincounts = []

    # loop over bins
    for i in range(nbins):
        # set upper edge of bin
        binedges.append(binedges[-1] + binstep)

        # count number of samples in bin
        bincount = 0
        for sample in samples:
            if binedges[i] <= sample < binedges[i+1]:
                bincount += 1

            # add in amy samples that equal max value in the final bin
            if i == (nbins - 1) and sample == max:
                bincount += 1

        bincounts.append(bincount)

    return binedges, bincounts

Part 2

Edit the function to take another argument, norm, which if True normalises the bin counts so that the area under the histogram \(A = \sum_i^{N_{\rm bins}} n_i \Delta x\) adds up to 1.

Solution

def binned(samples, nbins=10, low=None, high=None, norm=False):
    """
    Count the number of values within a set of bins.

    Parameters
    ----------
    samples: list
        A list of numbers which will be "binned"
    nbins: int
        The number of bins into which to split the range of numbers
    low: float
        The edge of the lowest bin (defaults to the smallest value in `samples`)
    high: float
        The edge of the highest bin (defaults to the largest values in `samples`)
    norm: bool
        If True normalise the bin counts (default is False)

    Returns
    -------
    tuple
        A tuple containing two lists: the bin edges and the number counts in each
        bin
    """

    # get the bin ranges
    if low is None:
        low = min(samples)

    if high is None:
        high = max(samples)

    # step size between bins
    binstep = (high - low) / nbins

    # lists to contain bin edges and number counts
    binedges = [low]
    bincounts = []

    # total number of samples
    nsamples = len(samples)

    # loop over bins
    for i in range(nbins):
        # set upper edge of bin
        binedges.append(binedges[-1] + binstep)

        # count number of samples in bin
        bincount = 0
        for sample in samples:
            if binedges[i] <= sample < binedges[i+1]:
                bincount += 1

            # add in amy samples that equal max value in the final bin
            if i == (nbins - 1) and sample == max:
                bincount += 1

        if norm:
            # normalise the bin counts
            bincount = (bincount / nsamples) / binstep

        bincounts.append(bincount)

    return binedges, bincounts

Exercise 17

Part 1

Write a function that returns a boxcar function of the form:

\[ f(x) = \left\{\begin{array}{rl} C, & \text{if } a \leq x \leq b \\ 0, & \text{otherwise}, \end{array}\right. \]

where the arguments should be a list containing \(x\) values at which to evaluate the function, the limits \(a\) and \(b\) at which the boxcar starts and stops, and the amplitude \(C\). The following defaults (to give a standard rectangular function) should be set: \(a = -1/2\), \(b=1/2\), and \(C = 1\).

Solution

A potential way of doing this is:

def boxcar(x, a=-0.5, b=0.5, C=1):
    vals = []

    # loop over x-values
    for xs in x:
        if a <= xs <= b:
            # add box
            vals.append(C)
        else:
            # add zeros
            vals.append(0.0)

    return vals

You may want to include checks that x is a list, that a is less than b, and that C is positive. An alternative way using NumPy array operations would be:

import numpy as np

def boxcar(x, a=-0.5, b=0.5, C=1):
    # initialise the array filled with zeros and the same length as x
    vals = np.zeros_like(x)

    # get indices of x-array with the [a, b] range
    idx = np.argwhere((x > a) & (x < b))

    # fill in vals with C
    vals[idx] = C

    return vals

Part 2

Write a function to that returns a triangular function of the form:

\[ f(x) = \left\{\begin{array}{rl} C - \left|\frac{ {\rm d}y}{ {\rm d}x}(x - x_0)\right|, & \text{if } a \leq x \leq b \\ 0, & \text{otherwise}, \end{array}\right. \]

where \(x_0\) is the midpoint of the triangle and \({\rm d}y/{\rm d}x\) is the gradient of the sides of the triangle. The arguments should be a list containing \(x\) values at which to evaluate the function, the limits \(a\) and \(b\) at which the triangle starts and stops, and the peak triangle amplitude \(C\). The following defaults (to give a standard normalised triangular function) should be set: \(a = -1\), \(b=1\), and \(C = 1\).

Solution

A potential way to do this is:

def tri(x, a=-1, b=1, C=1):
    vals = []

    # get half-width of the triangle's base
    halfwidth = (b - a) / 2

    # mid-point of triangle
    mid = a + halfwidth

    # gradient of triangle sides dy/dx
    grad = C / halfwidth

    # loop over x-values
    for xs in x:
        if a < xs < b:
            vals.append(C - abs(grad * (xs - mid)))
        else:
            vals.append(0.0)

    return vals

You may want to include checks that x is a list, that a is less than b, and that C is positive. An alternative way using NumPy array operations would be:

import numpy as np

def tri(x, a=-1, b=1, C=1):
    # initialise the array filled with zeros and the same length as x
    vals = np.zeros_like(x)

    # get half-width of the triangle's base
    halfwidth = (b - a) / 2

    # mid-point of triangle
    mid = a + halfwidth

    # gradient of triangle sides dy/dx
    grad = C / halfwidth

    # get indices of x-array with the [a, b] range
    idx = np.argwhere((x > a) & (x < b))

    # fill in indices with a triangle
    vals[idx] = C - np.abs(grad * (x[idx] - mid))

    return vals

Part 3

Create a plot showing both a boxcar function and a triangle function evaluated over some range of \(x\)-values. The two functions should be plotted in different colours and there should be a legend giving the function names.

Solution

A potential solution is:

from matplotlib import pyplot as plt
import numpy as np

# create a range of x-values
x = np.linspace(-5, 5, 1000)

# get boxcar function (choosing some input values)
b = boxcar(x, a=-4.5, b=-1.5, C=3.5)

# get triangle function (choosing some input values)
t = tri(x, a=-3.1, b=2.5, C=6.0)

# make the plot
plt.plot(x, b, color="r", label="boxcar")
plt.plot(x, t, color="b", linestyle="--", label="triangle")
plt.legend()  # add the legend based on the label values
plt.xlim([x[0], x[-1]])  # make x-axis limits stick to the x range
plt.show()

Reading/writing data

Exercise 18

Part 1

You have a file containing the student grades for 3 different exercises. The file consists of a header line (denoted by starting with a #), followed by lines containing four values separated by commas ("comma separated values", or CSV):

1. unique student ID
2. grade for exercise 1 (mark out of 20)
3. grade for exercise 2 (mark out of 30)
4. grade for exercise 3 (mark out of 40)

E.g.,:

# Student ID, Exercise 1 (20), Exercise 2 (30), Exercise 3 (40)
1234, 12, 23, 29
1235, 9, 28, 31
1236, 13, 8, 25

Read in the file and then calculate each student's total mark (as a percentage rounded to the nearest integer), where the three exercises are weighted at 25%, 25% and 50%, respectively. You can used a library such as NumPy to read in the data.

Solution

A possible way without using, e.g., NumPy

resfile = "results.csv"  # the results file

maxmarks = [20, 30, 40]  # maximum marks for each exercise
weights = [0.25, 0.25, 0.50]  # fractional weights for each exercise

# read in results
grades = {}
with open(resfile, "r") as fp:
    for line in fp.readlines():
        # ignore header lines starting with a #
        if line[0] != "#":
            # split the line on commas
            splitline = line.split(",")

            # get student ID (string trailing whitespace)
            studentid = splitline[0].strip()

            # get grades (converting to integers)
            grades[studentid] = [int(grade.strip()) for grade in splitline[1:]]

# calculate final weighted grades
finalgrades = {}
for studentid in grades:
    finalgrade = 0.0
    for i in range(len(maxmarks)):
        finalgrade += weights[i] * (grades[studentid][i] / maxmarks[i])

    finalgrades[studentid] = round(finalgrade * 100)  # convert to percentage

This can be more compact using NumPy's loadtxt() function or the more complete genfromtxt() function, e.g.,:

import numpy as np

resfile = "results.csv"  # the results file

maxmarks = [20, 30, 40]  # maximum marks for each exercise
weights = [0.25, 0.25, 0.50]  # fractional weights for each exercise

results = np.loadtxt(
    resfile,
    comments="#",  # ignore header (could also use skiprows=1)
    delimiter=",",  # comma separated values
)

# calculate final weighted grades
gradevalues = np.round(
    100 * sum(weights[i] * results[:,i+1] / maxmarks[i] for i in range(len(weights)))
)

for i in range(len(results)):
    studentid = str(results[i, 0])  # convert ID to string
    finalgrades[studentid] = gradevalues[i]

Another option would be to use the pandas read_csv() function.

Part 2

Write the results to a new CSV file with the total grade as a new fifth column.

Solution

There are again multiple ways of doing this. E.g., using the NumPy savetxt() function (assuming we have the results and finalgrades as above):

import numpy as np

# append final results onto the "results" array
results = np.hstack((results, [grade for grade in finalgrades.items()]))

outputfile = "final_results.csv"
header = "np.Student ID, Exercise 1 (20), Exercise 2 (30), Exercise 3 (40), Final grade (%)"

np.savetxt(outputfile, results, fmt="%d", delimiter=",", header=header)

Exercise 19

Part 1

Suppose you have the following class to hold some experimental data consisting of the electric field strength at a set of positions on a uniform grid:

import numpy as np

class ElectricField:
    def __init__(self, E, xpos, ypos, label="Efield"):
        """
        Store the measured electric field at a set of 2D coordinates.

        Parameters
        ----------
        E: array
            A 2D array of values of the electric field strength.
        xpos: array
            A 1D array of the x-positions of the measurements.
        ypos: array
            A 1D array of the y-positions of the measurements.
        label: str
            A label/name for the experiment. Default is "Efield"
        """

        # store copy of E-field as the E attribute
        self.E = np.array(E) 

        # store x and y positions
        self.x = np.array(xpos)
        self.y = np.array(ypos)

        # check E and grid positions are consistent
        if self.E.shape != (len(self.x), len(self.y)):
            raise ValueError("Shape of E is not consistent with grid points")

        self.label = label

Add a method to this class that saves the class itself as a pickle file (you can used the NumPy save() function with the allow_pickle=True option set). It should use the label attribute to construct the name of the save file (with appropriate extension added).

Also add a classmethod to read in a saved object.

Create an instance of the object and try saving it at reading it back in.

Part 2

Add a new method to the class that will return the electric field interpolated at any point within the grid. You may want to use the SciPy interp2d class. The method should raise an error if trying to interpolate outside the bounds of the \(x\)-\(y\) grid.

Try reading in a previously saved object and using this new method on that object.

Solution

An example of the class could be:

import numpy as np
from scipy.interpolate import interp2d


class ElectricField:
    """Store the measured electric field at a set of 2D coordinates.

    Parameters
    ----------
    E: array
        A 2D array of values of the electric field strength.
    xpos: array
        A 1D array of the x-positions of the measurements.
    ypos: array
        A 1D array of the y-positions of the measurements.
    label: str
        A label/name for the experiment. Default is "Efield"
    """


    def __init__(self, E, xpos, ypos, label="Efield"):
        # store copy of E-field as the E attribute
        self.E = np.array(E)

        # store x and y positions
        self.x = np.array(xpos)
        self.y = np.array(ypos)

        # check E and grid positions are consistent
        if self.E.shape != (len(self.x), len(self.y)):
            raise ValueError("Shape of E is not consistent with grid points")

        self.label = label

    def save(self, fname=None):
        """
        Save the class to a NumPy pickle file.

        Parameters
        ----------
        fname: str
            The output file name for storing the class. If not given the
            `label` attribute of the class will be used and ".npy" will be
            extension.
        """

        if fname is None:
            fname = self.label

        np.save(fname, self, allow_pickle=True)

    @classmethod
    def load(cls, fname):
        """
        Load a saved file containing an instance of this class. The file will
        be a NumPy pickle object with a ".npy" extension.

        Parameters
        ----------
        fname: str
            The name of the file to load

        Returns
        -------
        ElectricField
            An ElectricField object.
        """

        E = np.load(fname, allow_pickle=True)

        # NumPy load will load the data as a 0-D NumPy array, so extract the
        # ElectricField object
        E = E.item()

        # check it's the correct type
        if not isinstance(E, cls):
            raise TypeError("Loaded file does not contain an ElectricField")

        return E

    def field_strength(self, x, y):
        """
        Return the electric field strength at any point (interpolated if not
        on the original grid).

        Parameters
        ----------
        x: float
            The x-coordinate position
        y: float
            The y-coordinate position

        Returns
        -------
        float
            The electric field strength at the given point.
        """

        # create interpolator
        fieldinterp = interp2d(self.x, self.y, self.E, bounds_error=True)

        try:
            E = fieldinterp(x, y)[0]
        except ValueError:
            raise ValueError(f"x-y coordinates ({x}, {y}) are outside grid "
                             "bounds.")

        return E

Writing out the class, reading it back in, and using the field_strength() method could be done with (assuming the class is defined in a file called efield.py):

from efield import ElectricField

# get x-y positions
x = [-2, -1, 0, 1, 2]
y = [-2, -1, 0, 1, 2]

# "measure" E-field magnitude on the grid
measured = [
    [0.1, 0.2, 0.3, 0.2, 0.1],
    [0.15, 0.25, 0.35, 0.25, 0.15],
    [0.17, 0.29, 0.40, 0.31, 0.22],
    [0.18, 0.31, 0.46, 0.38, 0.30],
    [0.18, 0.32, 0.52, 0.51, 0.48]
]

# create class
E = ElectricField(measured, x, y, label="experiment1")

# save field
E.save()

# re-load experiment data
Edata = ElectricField.load("experiment1.npy")

# get field at given point
xp, yp = -1.5, 0.4
ef = Edata.field_strength(xp, yp)

print(f"Field strength at ({xp}, {yp}) is {ef}")

Exercise 20

Question

Write a script that plots the two-dimensional data in the file density.txt. Use the information contained in the file data_description.txt to define the axes of your plot (note that "clabel" refers to a label for a colour bar).

Solution

A potential solution is:

#!/usr/bin/env python3

import numpy as np
import matplotlib.pyplot as plt

# read density.txt and store data into a numpy two-dimensional array
data_file = 'density.txt'
density = np.loadtxt(data_file)

# read data_description.txt and store information in the proper variables
with open('data_description.txt',encoding='utf-8') as file:
    for line in file:
        idx = line.index("=")
        if "xmin" in line:
            xmin = float(line[idx+1:-1])
        elif "xmax" in line:
            xmax = float(line[idx+1:-1])
        elif "ymin" in line:
            ymin = float(line[idx+1:-1])
        elif "ymax" in line:
            ymax = float(line[idx+1:-1])
        elif "xlabel" in line:
            xlabel = line[idx+1:-1]
        elif "ylabel" in line:
            ylabel = line[idx+1:-1]
        elif "clabel" in line:
            clabel = line[idx+1:-1]

# create a pseudocolor plot
fig = plt.figure()

ax = fig.add_subplot(111)

c = ax.imshow(
    density,
    cmap='viridis',
    extent=[xmin, xmax, ymin, ymax],
    interpolation='antialiased',
    origin='lower'
)
ax.set_xlabel(xlabel, fontsize=20)
ax.set_ylabel(ylabel, fontsize=20)
ax.tick_params(labelsize=20)
cbar = fig.colorbar(c)
cbar.set_label(clabel, fontsize=20)
cbar.ax.tick_params(labelsize=20)

fig.tight_layout()

plt.show()

A different way of reading the data_description.txt file could be done with:

lims = {}
labels = {}
with open("data_description.txt", "r") as file:
    for line in file:
        key, value = line.split("=")

        # get limit and label values
        if value.strip().replace(".", "").isnumeric():
            lims[key.strip()] = float(value.strip())
        else:
            labels[key.strip()] = value.strip()

where the limits and labels are stored in dictionaries. Or, it could be read in using the TOML package.

Python classes

Exercise 21

Part 1

Create a class to hold data from an astronomical survey. It will store the name of each object and the object's magnitude. Upon initialisation the class should take in a single argument, which is a dictionary keyed to object names with their magnitudes as the values. By default it should be initialised with an empty dictionary if nothing is passed to it. It should raise an error if supplied with something other than a dictionary.

The class should have a method for adding in new objects, and methods for returning lists of the names and magnitudes of all objects in the survey, respectively.

Solution

A possible class is:

class AstroSurvey:
    def __init__(self, survey={}):
        # create an attribute that will store the survey - it is useful to use a dictionary
        self.survey = {}

        if not isinstance(survey, dict):
            raise TypeError("Input must be a dictionary")

        # add copy of all objects into the survey
        for key, value in survey.items():
            self.add_object(key, value)

    def add_object(self, name, magnitude):
        """
        Add a new object into the survey.

        Parameters
        ----------
        name: str
            The name of the object.
        magnitude: float
            The magnitude of the object.
        """

        if not isinstance(name, str):
            raise TypeError("The object name must be a string")

        if not isinstance(magnitude, (float, int)):
            raise TypeError("The object's magnitude must be a number")

        # add into survey attribute
        self.survey[name] = magnitude

    def object_names(self):
        """
        Return a list of object names.
        """

        return list(self.survey.keys())

    def object_magnitudes(self):
        """
        Return a list of object magnitudes.
        """

        return list(self.survey.values())

This could be used by doing, e.g.,:

# create an empty survey
survey = AstroSurvey()    

# add some objects (first few Messier objects)
survey.add_object("M1", 8.4)
survey.add_object("M2", 6.3)
survey.add_object("M3", 6.2)
survey.add_object("M4", 5.9)

You might note that this currently doesn't do much more than copying one dictionary into another, albeit with some additional type checking!

Part 2

Add a methods that return the name of the brightest and dimmest objects. Note that for magnitudes in astronomy the lower the number the brighter the object!

Solution

class AstroSurvey:
    def __init__(self, survey={}):
        # create an attribute that will store the survey - it is useful to use a dictionary
        self.survey = {}

        if not isinstance(survey, dict):
            raise TypeError("Input must be a dictionary")

        # add copy of all objects into the survey
        for key, value in survey.items():
            self.add_object(key, value)

    def add_object(self, name, magnitude):
        """
        Add a new object into the survey.

        Parameters
        ----------
        name: str
            The name of the object.
        magnitude: float
            The magnitude of the object.
        """

        if not isinstance(name, str):
            raise TypeError("The object name must be a string")

        if not isinstance(magnitude, (float, int)):
            raise TypeError("The object's magnitude must be a number")

        # add into survey attribute
        self.survey[name] = magnitude

    def object_names(self):
        """
        Return a list of object names.
        """

        return list(self.survey.keys())

    def object_magnitudes(self):
        """
        Return a list of object magnitudes.
        """

        return list(self.survey.values())

    def brightest(self):
        """
        Return the name of the brightest object.
        """

        # get the index of the brightest object
        mag = min(self.object_magnitudes())
        idx = self.object_magnitudes().index(mag)

        return self.object_names()[idx]

    def dimmest(self):
        """
        Return the name of the dimmest object.
        """

        # get the index of the dimmest object
        mag = max(self.object_magnitudes())
        idx = self.object_magnitudes().index(mag)

        return self.object_names()[idx]

Using these with the previous example could be done with, e.g.,

brightest = survey.brightest()
print(f"The brightest object in the survey is {brightest}")

dimmest = survey.dimmest()
print(f"The dimmest object in the survey is {dimmest}")

Exercise 22

Question

Create a class that represents a black body. The class should contain class attributes that define the Stefan-Boltzmann constant and Wien's displacement constant. It should be initialised with a temperature (in Kelvin) and the body's radius including checks to make sure these are positive numbers.

It should include two methods that:

1. return the black body's bolometric luminosity,
2. return the wavelength at which the emission peaks (Wien's Law) in nanometres.

Solution

import numpy as np


class BlackBody:
    # Wien's displacement constant (m K)
    b = 2.897771955e-3

    # the Stefan-Boltzmann constant (W m^-2 K^-4) 
    sigma = 5.670374419e-8

    def __init__(self, T, radius):
        """
        A black-body.

        Parameters
        ----------
        T: float
            The temperature of the black body (K)
        radius: float
            The radius of the black body (m)
        """

        # check T is a number and greater than 0
        if not isinstance(T, (float, int)):
            raise TypeError("Temperature must be a number")

        if T <= 0:
            raise ValueError("Temperature must be a positive number")

        self.T = float(T)

        # check radius is a number and greater than 0
        if not isinstance(radius, (float, int)):
            raise TypeError("Radius must be a number")

        if radius <= 0:
            raise ValueError("Radius must be a positive number")

        self.radius = float(radius)

    def bolometric_luminosity(self):
        """
        Return the black body's bolometric luminosity using the Stefan-Boltzmann equation.
        """

        # objects surface area
        surfarea = 4 * np.pi * self.radius ** 2

        return self.sigma * surfarea * self.T ** 4

    def peak_wavelength(self):
        """
        Return the peak wavelength (in nanometres) of the black body's thermal
        radiation using Wien's Law.
        """

        return (self.b / self.T) * 1e9

Exercise 23

Part 1

Create a class to define Square objects. The class should be initialised using a tuple or list that contains four pairs (also tuples or lists) of \(x\) and \(y\) coordinates for the corners of the square, which should then be stored in th class. The class should contain a method to check that the input points define a valid square (i.e. all sides are the same length and all angles between sides are 90 degrees), which should be used during initialisation and an error raised if it fails the check.

Part 2

Add methods to the class that return the area and perimeter of the square.

Part 3

Add a method to the class that takes in a point, given by a tuple containing its \(x\) and \(y\) coordinates, and returns True if the point is within the square and False if not.

Part 4

Create a Square and then get a new Square based on the original, but rotated by 30 degrees about the first square's centre. Plot the two squares on the same figure.

Hint: you may have already written code, or a method, in the class that rotates a square.

Solution

A possible class is:

import numpy as np


class Square:
    """
    A class defining a Square object.

    Parameters
    ----------
    vertices: array
        A 4x2 array defining the x-y coordinates of the four corners of the
        square. The corner coordinates must be consecutive corners in
        either the clockwise or anticlockwise direction.
    """

    def __init__(self, vertices):
        # store copy of vertices as numpy array
        self.vertices = np.array(vertices)

        # check if valid square
        if not self.valid_square():
            raise ValueError("Input coordinates do not define a valid square")

        # get the centre of the square
        self.centre = (self.vertices[0] + self.vertices[2]) / 2.0

    def valid_square(self):
        """
        Check that vertices define a valid square: four vertices are given;
        each vertex has two points; all sides are the same length; all
        corners are 90 degrees.

        Returns
        -------
        bool
            False is not a valid square otherwise True
        """

        # check vertices contain four pairs of points
        if self.vertices.shape != (4, 2):
            return False

        # check side lengths
        distances = []
        for i in range(4):
            distance = self.side_length(self.vertices[i],
                                        self.vertices[(i + 1) % 4])
            distances.append(distance)

        if not np.allclose(distances, distances[0]):
            return False

        # check angles between sides
        angles = []
        for i in range(4):
            origin = self.vertices[i]
            prevv = self.vertices[(i + 4 - 1) % 4]
            nextv = self.vertices[(i + 1) % 4]
            vec1 = prevv - origin
            vec2 = nextv - origin

            angles.append(self.vertex_angle(vec1, vec2))

        if not np.allclose(angles, np.pi / 2.0):
            return False

        return True

    @staticmethod
    def side_length(x1, x2):
        """
        Get the distance between two coordinates.

        Parameters
        ----------
        x1: tuple
            A pair of x-y coorinates for a point
        x2: tuple
            A pair of x-y coorinates for a point

        Return
        ------
        float:
            The distance between points
        """

        return np.linalg.norm(x1 - x2)

    @staticmethod
    def vertex_angle(vec1, vec2):
        """
        Get the angle between two vectors.

        Parameters
        ----------
        vec1: 
            A vector (two coordinate points) defined from the origin
        vec2: tuple
            A vector (two coordinate points) defined from the origin

        Return
        ------
        float:
            The angle between the vectors
        """

        # dot product of two vectors
        dp = np.dot(vec1, vec2)

        # magnitude of vectors
        mag1 = np.linalg.norm(vec1)
        mag2 = np.linalg.norm(vec2)

        angle = np.arccos(dp / (mag1 * mag2))

        return angle

    def area(self):
        """
        Return the area of the square.
        """

        return self.side_length(self.vertices[0], self.vertices[1]) ** 2

    def perimeter(self):
        """
        Return the perimeter of the square.
        """

        return self.side_length(self.vertices[0], self.vertices[1]) * 4

    def in_square(self, point):
        """
        Check if a given point is in the square.

        Parameters
        ----------
        point: (list, tuple)
            A list consisting of the x, y coordinates of the point to test.

        Returns
        -------
        bool
            Give True if the point is in the square and False otherwise.
        """

        # rotate the square and the point, so they are aligned with the x-y axes
        vec1 = [1, 0]  # unit vector on x-axis
        vec2 = self.vertices[1] - self.vertices[0]  # a side of the square

        # angle between one of the squares sides and the x-axis
        angle = self.vertex_angle(vec1, vec2)

        # rotated square
        rotsquare = self.rotate_square(angle)

        # rotated test point about the centre
        rot = np.array(
            [[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]]
        )
        rotpoint = np.dot(rot, point - self.centre)

        # check point is within the square
        bottom = rotsquare.side("bottom")
        top = rotsquare.side("top")
        if rotpoint[1] < bottom[0][1] or rotpoint[1] > top[0][1]:
            # outside y-extent of square
            return False

        left = rotsquare.side("left")
        right = rotsquare.side("right")
        if rotpoint[0] < left[0][0] or rotpoint[0] > right[0][0]:
            # outside x-extent of square
            return False

        return True

    def rotate_square(self, angle):
        """
        Return a new Square object that is rotated by a given angle about the
        square's centre.

        Parameters
        ----------
        angle: float
            An angle in radian to rotate the square by.

        Returns
        -------
        Square
            A new Square object
        """

        # set rotation matrix
        rot = np.array(
            [[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]]
        )

        # store the rotation matrix
        self.rotation_matrix = rot

        # get the rotated vertices
        rotverts = np.array(
            [np.dot(rot, vertex - self.centre) for vertex in self.vertices]
        ) + self.centre

        return Square(rotverts)

    def side(self, which="bottom"):
        """
        Return the two vertices for the given side. If two sides are equivalent
        (e.g., are both as "low" as each other if given "bottom") then the
        first two be found is returned.

        Parameters
        ----------
        which: str
            A string with either "bottom", "top", "left" or "right" for the
            side to return.

        Returns
        -------
        tuple
            The two vertices defining the requested side.
        """

        if which[0].lower() == "l":
            # left side
            idx = np.argsort(self.vertices[:, 0])[0]
        elif which[0].lower() == "r":
            # right side
            idx = np.argsort(self.vertices[:, 0])[-1]
        elif which[0].lower() == "b":
            # bottom side
            idx = np.argsort(self.vertices[:, 1])[0]
        elif which[0].lower() == "t":
            # top side
            idx = np.argsort(self.vertices[:, 1])[-1]
        else:
            raise ValueError(f"Side '{which}' is not valid")

        idxs = [idx, (idx + 1) % 4]

        return self.vertices[idxs]

Given this class two squares can be plotted with:

import numpy as np
from matplotlib import pyplot as plt

# first square
s1 = Square([[4, 3], [4, 5], [6, 5], [6, 3]])

# rotated square
s2 = s1.rotate_square(np.deg2rad(30))

fig, ax = plt.subplots(figsize=(3.5,3.5),dpi=200)

# plot s1 in blue and s2 in red
for s, c in zip([s1, s2], ["b", "r"]):
    x = np.hstack((s.vertices[:, 0], s.vertices[0, 0]))
    y = np.hstack((s.vertices[:, 1], s.vertices[0, 1]))
    ax.plot(x, y, color=c)

# make axes have an equal aspect ratio
ax.set_aspect("equal")
fig.tight_layout()

plt.show()

A Rectangle patch could be used instead if you work out the bottom left corner and the required rotation angle.

Debugging

Exercise 24

Question

Fix this broken code:

import maths

deg hypotenuse(a=1.0, b)
    """
    A function to calculate and return the hypotenuse of a right angle
    triangle with opposite and adjacent sides with lengths a and b.
    """

    hyp = maths.sqrt(a ** 2 + b ** 2

    retrn hy

hp = hypotenus(a="3", b=4)

Solution

The problems are highlighted below

import maths  # "maths" is not a standard Python library

# several issues:
#  - typo in "def"
#  - no colon at the end of the line
#  - can't have a keyword argument before a positional argument
deg hypotenuse(a=1.0, b)
    """
    A function to calculate and return the hypotenuse of a right angle
    triangle with opposite and adjacent sides with lengths a and b.
    """

    hyp = maths.sqrt(a ** 2 + b ** 2  # closing bracket was missing, math library fixed

    retrn hy  # typo in "return" and returned variable name

# a couple of issues:
#  - typo in called function "hypotenuse"
#  - trying to pass a string when a number is required
hp = hypotenus(a="3", b=4)

A fixed version would be:

import math

def hypotenuse(a, b):
    """
    A function to calculate and return the hypotenuse of a right angle
    triangle with opposite and adjacent sides with lengths a and b.
    """

    hyp = math.sqrt(a ** 2 + b ** 2)

    return hyp

hp = hypotenuse(a=3, b=4)

Exercise 25

Question

Fix this broken code:

x = [1, 5, 1, 5 6, 2, 5, 7]

# sum the cube of each number
y = ""
for i = range(len(x) + 1)
    y += x[i] *** 3

Solution

The problems are highlighted below:

x = [1, 5, 1, 5 6, 2, 5, 7]  # missing comma between 5 and 6

# sum the cube of each number
y = ""  # should initialise as 0 not an empty string

# various issues:
#  - using "=" rather than in
#  - missing colon at end of for statement
#  - final index will be 1 too big for y
for i = range(len(x) + 1)
    y += x[i] *** 3  # should use "**" not "***"

A fixed version would be:

x = [1, 5, 1, 5, 6, 2, 5, 7]

# sum the cube of each number
y = 0.0
for i in range(len(x)):
    y += x[i] ** 3

Exercise 26

Question

Fix this broken code:

import numpy as npy

# create dictionary of numpy arrays
arrs = {
    "one": np.array([1, 2, 3])
    "two": np.array([4, 5, 6]),
    "three": np.array(7, 8, 9)
}

# concatenate the three arrays
full = np.concatenate(arrs["on"], arrs["two"], arr["three])

# get the shape of the array
shape = full.shape()

Solution

The problems are highlighted below:

import numpy as npy  # alias is not the same as used below

# create dictionary of numpy arrays
arrs = {
    "one": np.array([1, 2, 3])  # missing comma
    "two": np.array([4, 5, 6]),
    "three": np.array(7, 8, 9)  # missing square brackets
}

# concatenate the three arrays
# the errors are:
#  - "on" is not a valid key
#  - arr is not a known variable
#  - missing closing quotation mark on "three"
#  - concatenate requires a tuple
full = np.concatenate(arrs["on"], arrs["two"], arr["three])

# get the shape of the array
shape = full.shape()  # shape is a property not a method

A fixed version would be:

import numpy as np

# create dictionary of numpy arrays
arrs = {
    "one": np.array([1, 2, 3]),
    "two": np.array([4, 5, 6]),
    "three": np.array([7, 8, 9])
}

# concatenate the three arrays
full = np.concatenate((arrs["one"], arrs["two"], arrs["three"]))

# get the shape of the array
shape = full.shape

General problems

Exercise 27

Question

Estimate the value of \(\pi\) using a Monte Carlo method (i.e., through drawing random numbers).

Solution

A potential solution, based on the ratio of the area of a square with sides 2 units long (\(A_s = 2 \times 2 = 4\)) to a circle with radius of 1 unit (\(A_c = \pi r^2 = \pi\)), being \((A_s / A_c) = 4/\pi\), is:

# import numpy for random number generation
import numpy as np

# create random number generator
rstate = np.random.default_rng()

# set the number of samples to draw for estimation
nsamples = 10000

# draw nsamples samples in x and y uniformly from the square between -1 and +1
samples = rstate.uniform(-1, 1, (nsamples, 2))

# get "magnitude" of each point sqrt(x^2 + y^2)
radius = np.sqrt(samples[:, 0] ** 2 + samples[:, 1] ** 2)
# radius = np.linalg.norm(samples, axis=1)  # another option

# work out how many samples are within the unit circle (i.e., radius < 1)
numincirc = np.sum(radius < 1)

# get estimate of pi
estpi = 4 * (numincirc / nsamples)

print(estpi)

Exercise 28

Question

Write a function that implements the bisection method to find the root of a continuous function in a provided interval. Test your function by solving the equation \(\exp(-x)(x^2+5x+2) + 1 = 0\) between -1 and 0.

Solution

A potential solution is:

#!/usr/bin/env python3

import math
import textwrap as tw


def test_function(x):
    """Function whose roots we seek."""
    return math.e**(-x) * (x*(x + 5) + 2.0) + 1.0


def bisection(fun, xrange, toll = 1e-12, niter = 1000):
    """
    A function that implements the bisection method to find the root of a
    function in a given interval.

    Parameters:
    -----------
    fun: callable
        the function to be solved

    xrange: list
        list containing the interval where the 0 of the function lies

    toll: float
        tolerance between two iterations, defaults to 1e-12

    niter: integer
        maximum number of iterations, defaults to 1000

    Returns:
    --------
    c: float
       root of the given equation with toll precision

    fc: float
       value of the given function at c (approximately 0.0)

    n: integer
       number of iterations done to reach the given solution

    """
    a = xrange[0]
    fa = fun(a)

    b = xrange[1]
    fb = fun(b)

    if fa * fb >= 0.0:
        raise ValueError("The provided function does not contain zeros in the "
                         "given interval")

    eps = 10000.0
    n = 0
    c_old = a
    fc = fa

    while eps > toll and n <= niter and fc != 0.0:

        c = (a + b) / 2
        fc = fun(c)
        if fa * fc < 0.0:
            b = c
            fb = fc
        elif fb * fc < 0.0:
            a = c
            fa = fc
        else:
            raise ValueError("Oh oh, you missed the zero")

        eps = abs(c - c_old)
        c_old = c
        n += 1

    if n == niter:
        print(f"niter, n = {n}")
        raise ValueError("Maximum number of iterations reached")

    return c, fc, n


xrange = [-1.0, 0.0]
sol, fsol, niter = bisection(test_function, xrange)

print(tw.fill(f"The root of your function is approximately x = {sol}, where "
              f"the function value is {fsol}.  This solution has been reached "
              f"after {niter} bisection iterations."))

Advanced exercises

These exercises are very much just for fun if you fancy something a bit more challenging!

Exercise 29

Question

Write a class that implements a noughts-and-crosses game.

Solution

A potential solution is:

#!/usr/bin/env python3

"""
A class to create a tic-tac-toe game. The class can either be imported and run
in a Python terminal, or the script can be run from the command line.
"""

import sys
import numpy as np


class TicTacToe:
    """
    A tic-tac-toe game. After creating the object, the game can be played
    by calling it, e.g.

    >>> game = TicTacToe()
    >>> game()
    """

    def __init__(self):
        player1 = input("Input the name of the first player: ")
        player2 = input("Input the name of the second player: ")
        self.players = [player1, player2]

        try:
            self.gridsize = int(input("Set the grid size (integer): "))
        except ValueError:
            raise ValueError("Grid size must be an integer")

        # initialise grid as empty single space strings
        self.grid = np.full((self.gridsize, self.gridsize), " ")
        self.linecount = 3  # number of lines to rewind by

    def __call__(self):
        # start game
        self.drawgrid()

        self.currentplayer = False  # boolean to flip between players
        while not self.checkstate():
            # get player one's turn
            self.getturn()

            # check if game has been completed
            if self.checkstate():
                break

            # get player two's turn
            self.getturn()

        self.showwinner()

    play = __call__

    def drawgrid(self):
        """
        Draw the current state of the grid.
        """

        # rewind to overwrite previous grid (see, e.g.,
        # https://stackoverflow.com/a/59147732/1862861)
        for _ in range(self.linecount):
            sys.stdout.write("\x1b[1A\x1b[2K")

        print()
        for i, row in enumerate(self.grid):
            rowstr = "|".join([f" {x} " for x in row])
            print(rowstr)
            if i < self.gridsize - 1:
                print("-" * (self.gridsize * 3 + (self.gridsize - 1)))
        print()

        self.linecount = 2 * self.gridsize + 1

    def getturn(self):
        """
        Ask player for input coordinates and re-draw grid.
        """

        counters = ["✕", "○"]
        playeridx = int(self.currentplayer)

        # make sure coordinates are valid
        while 1:
            coords = input(
                f"{self.players[playeridx]}: Input the grid coordinates 'x y'"
                f" (between 1 and {self.gridsize}) for your move: "
            )
            self.linecount += 1

            x, y = [int(coord.strip()) for coord in coords.split()]

            # check grid coordinates are valid
            if not (1 <= x <= self.gridsize) or not (1 <= y <= self.gridsize):
                print("x and y coordinates must be between 1 and "
                      f"{self.gridsize}")
                self.linecount += 1
                continue

            # check grid cooridate has not already been used
            if self.grid[self.gridsize - y][x - 1] != " ":
                print("That grid point has already be used. Try again.")
                self.linecount += 1
                continue

            break

        # fill in grid
        self.grid[self.gridsize - y][x - 1] = counters[playeridx]

        # draw the grid
        self.drawgrid()

        # flip player
        self.currentplayer = not self.currentplayer

    def checkstate(self):
        """
        Check whether anyone has won.
        """

        # check if any rows are completed
        complete = False
        for row in (
            [np.diag(self.grid), np.diag(np.fliplr(self.grid))]
            + list(self.grid)
            + list(np.transpose(self.grid))
        ):
            # ignore "empty" rows
            if not np.all(row == " "):
                # check if all values in row are the same
                if np.all(row == row[0]):
                    complete = True
                    break

        return complete

    def showwinner(self):
        """
        Show the winner.
        """

        playeridx = int(not self.currentplayer)
        print(f"The winner is {self.players[playeridx]}!")


# run the game if calling the code directly
if __name__ == "__main__":
    game = TicTacToe()
    game()