Question

The program src/basic/lnsum.py produces, among other things, this output: $$ \begin{aligned} &\text { epsilon: } 1 e-04, \text { exact error: } 8.18 \mathrm{e}-04, \mathrm{n}=55 \\ &\text { epsilon: } 1 \mathrm{e}-06, \text { exact error: } 9.02 \mathrm{e}-06, \mathrm{n}=97 \\ &\text { epsilon: } 1 \mathrm{e}-08, \text { exact error: } 8.70 \mathrm{e}-08, \mathrm{n}=142 \\ &\text { epsilon: } 1 \mathrm{e}-10, \text { exact error: } 9.20 \mathrm{e}-10, \mathrm{n}=187 \\ &\text { epsilon: } 1 \mathrm{e}-12, \text { exact error: } 9.31 \mathrm{e}-12, \mathrm{n}=233 \end{aligned} $$ Redirect the output to a file. Write a Python program that reads the file and extracts the numbers corresponding to epsilon, exact error, and \(\mathrm{n}\). Store the numbers in three arrays and plot epsilon and the exact error versus \(\mathrm{n}\). Use a logarithmic scale on the \(y\) axis, which is enabled by the \(\log =\) ' \(\mathrm{y}\) ' keyword argument to the plot function. Name of program file: read_error.py.

Short answer

Redirect output to a file, extract values into arrays, and plot with log scale using matplotlib.

Step-by-step solution

Redirect Output to a File

To redirect the output of the `src/basic/lnsum.py` program to a file, use the command line with output redirection. For example, you can use the command `python src/basic/lnsum.py > output.txt` to save the output to a file named `output.txt`.

Read Data from File

Open the `output.txt` file in Python using the `open()` function. Read the contents of the file line by line using the `readlines()` method, which stores each line of the file as a separate element in a list.

Extract Values from the Data

Iterate through each line of the list and use string manipulation functions to extract the required values. You can use regular expressions with the `re` module to extract numerical values corresponding to epsilon, exact error, and n.

Store Values in Arrays

Initialize three empty lists or arrays for epsilon, exact error, and n. As you parse each line, append the corresponding extracted values to the respective lists.

Import Plotting Libraries

Ensure that you have installed Matplotlib in your Python environment. Import it using `import matplotlib.pyplot as plt` to use it for plotting.

Plot Values

Use Matplotlib to plot epsilon and exact error against n. Use `plt.plot(n, epsilon, label='Epsilon')` and `plt.plot(n, exact_error, label='Exact Error')`. Set the y-axis to a logarithmic scale with `plt.yscale('log')`.

Configure the Plot

Add labels for the axes using `plt.xlabel('n')` and `plt.ylabel('Values')`. Add a legend with `plt.legend()` to distinguish between epsilon and exact error.

Display the Plot

Use `plt.show()` to display the plot window. This will allow you to visually verify how epsilon and exact error vary with n, with the y-axis in logarithmic scale.

Key concepts

Data Extraction

Data extraction is a pivotal concept in Python programming, particularly when dealing with information stored in files. This process involves reading data from a given source—such as a file—and converting it into a usable format in your code.
For this exercise, after redirecting the output of the program to a file via the command line, we aim to read this file in Python. You can use the `open()` function to access the file's contents. Once the file is open, utilize the `readlines()` method to read it line-by-line; this method returns a list where each element is one line from the file.
Now, to extract the requisite numbers, you'll need to iterate over each line and seek out the specific patterns that represent our desired data points—epsilon, exact error, and n. String manipulation functions are key here, with regular expressions (via the `re` module) being particularly useful for identifying numerical values amidst text.

Matplotlib

Matplotlib is a widely used Python plotting library that offers a comprehensive set of features to create a variety of static, animated, and interactive visualizations.
In Python, before plotting the data, ensure Matplotlib is installed in your development environment using pip (`pip install matplotlib`). With the library installed, import it in your script using `import matplotlib.pyplot as plt`. This import allows you to access a range of plotting functions and customization options.
In this context, Matplotlib will be used to plot the extracted data, specifically epsilon and exact error in relation to n. You can represent the data using line plots by calling the `plot()` function. Labels and titles improve the plot's readability, and axes labels can be added using `xlabel()` and `ylabel()`. Additionally, `legend()` is needed to differentiate between the plotted lines.

File Handling

File handling is fundamental in programming for accessing and modifying files directly through code. In Python, file handling is both powerful and straightforward.
To redirect program output to a file, you can use shell command redirection: `python src/basic/lnsum.py > output.txt`. This command saves the console output directly to 'output.txt'.
Inside your Python script, files are opened with the `open()` function. Specify read ('r'), write ('w'), or append ('a') modes depending on your needs. For reading, `readlines()` captures all lines from the file into a list for processing. Be sure to close the file when done using `file.close()` or manage file opening with a `with` statement for automatic closure. This approach minimizes the risk of resource leaks and eases error handling.

Logarithmic Plotting

Logarithmic plotting involves using a logarithmic scale for the axes, which can be particularly beneficial when data spans several orders of magnitude. This method enhances data presentation and interpretation by displaying exponential relationships more clearly.
In Matplotlib, setting a logarithmic scale is straightforward. For the y-axis, use the `plt.yscale('log')` function after your plotting calls. This setting transforms the scaling of the y-axis into a logarithmic format. This transformation can be critical for understanding trends in data, such as small differences in epsilon or exact error against a backdrop of larger variations in n.
Logarithmic plots are especially useful when dealing with multiplicative factors or exponential growth patterns, as they can reveal patterns and relationships that may not be visible on a standard linear scale.