Data Fitting in MATLAB: A COVID-19 Dataset
MATLAB assignments often require data analysis and fitting, particularly when dealing with real-world datasets. In this blog, we will explore how you can effectively solve your curve fitting assignment that involve fitting data, using an example COVID-19 dataset to illustrate the steps and techniques. While this example focuses on a specific dataset, the principles and methods discussed can be applied to various data fitting tasks.
Understanding the Assignment Requirements
Data Structure and Loading
The first step in any MATLAB assignment is to understand the data structure and load it correctly. For instance, if you are given a .mat file containing structures with various fields, it is crucial to know how to handle such data.
Load the Data: Use the load function to import the data into your workspace.
load('COVID_data.mat');
Inspect the Data: Examine the loaded data to understand its structure. Use commands like whos to check the variables and fieldnames to explore the structure fields.
data = load('COVID_data.mat');
disp(fieldnames(data));
Setting Up Your Environment
To ensure a clean workspace and avoid conflicts with previous sessions, start your script with the following commands:
clear all; close all;
This command clears the workspace and closes all figure windows.
Steps to Tackle the Assignment
Loading and Inspecting Data
After loading the data, it is essential to inspect it to understand its structure and the information it contains. This step is crucial for extracting the relevant fields for further analysis.
1. Load and Inspect:
data = load('COVID_data.mat');
dates = data.COVID_data.dates;
infected = data.COVID_data.currently_infected;
new_cases = data.COVID_data.daily_new_cases;
new_deaths = data.COVID_data.daily_new_deaths;
2. Explore the Data: Use commands like plot and hist to visualize the data and gain insights into its distribution and trends.
Data Preparation
Extract the relevant fields from the structure for analysis. This step involves selecting the data points that will be used for fitting.
1. Extract Relevant Fields:
dates = data.COVID_data.dates;
infected = data.COVID_data.currently_infected;
new_cases = data.COVID_data.daily_new_cases;
new_deaths = data.COVID_data.daily_new_deaths;
Fitting Data
Data fitting involves using various functions to model the data and find the best fit. MATLAB offers several functions for this purpose, including polyfit, fit, and lsqcurvefit.
Polynomial Fitting
Polynomial fitting is a common technique for modeling data. The polyfit function fits a polynomial to the data, and polyval evaluates the polynomial at specified points.
1. Fit the Data:
p = polyfit(dates, infected, 3);
yfit = polyval(p, dates);
subplot(3,1,1);
plot(dates, infected, 'o', dates, yfit, '-');
title('Polynomial Fit of Currently Infected Cases');
Separate Peaks
If the assignment requires fitting data separately for different time periods, you can divide the data and fit each segment individually.
1. Fit Separate Peaks:
before_date = dates <= datenum('25-May-2020');
after_date = dates > datenum('25-May-2020');
p1 = polyfit(dates(before_date), infected(before_date), 3);
p2 = polyfit(dates(after_date), infected(after_date), 3);
Advanced Fitting Techniques
For more complex assignments, advanced fitting techniques using functions like fit and lsqcurvefit can be employed.
Using fit Function
The fit function offers more flexibility in fitting types, allowing you to choose from various fit types.
1. Advanced Fit:
f1 = fit(dates(before_date), infected(before_date), 'poly3');
f2 = fit(dates(after_date), infected(after_date), 'poly3');
subplot(3,1,2);
plot(f1, dates(before_date), infected(before_date));
hold on;
plot(f2, dates(after_date), infected(after_date));
title('Advanced Fit of Currently Infected Cases');
hold off;
Using lsqcurvefit Function
The lsqcurvefit function allows fitting custom equations to the data, providing greater flexibility and precision.
1. Custom Fit:
model = @(b,x) b(1) * exp(b(2) * x);
b0 = [1, 0.1];
[b, resnorm] = lsqcurvefit(model, b0, dates, infected);
yfit = model(b, dates);
subplot(3,1,3);
plot(dates, infected, 'o', dates, yfit, '-');
title('Custom Fit Using lsqcurvefit');
Best Practices
Maintaining clean, well-commented code and following best practices is essential for success in MATLAB assignments.
Code Commenting
Add meaningful comments to explain your code. Aim for at least 15-33% of your lines to be commented.
1. Example Commenting:
% Fit a polynomial to the currently infected data
p = polyfit(dates, infected, 3); % Polynomial coefficients
yfit = polyval(p, dates); % Fitted values
Code Formatting
Maintain proper indentation and minimize redundant code. Modularize your code using functions for clarity and reusability.
1. Example Modular Code:
function yfit = polynomialFit(x, y, degree)
p = polyfit(x, y, degree);
yfit = polyval(p, x);
end
Validation and Testing
Test your code with different datasets to ensure robustness. Handle exceptions and edge cases gracefully.
1. Example Validation:
% Test the function with a different dataset
yfit_test = polynomialFit(test_dates, test_infected, 3);
Turning in Your Work
To ensure your submission is correct and runs without errors, follow these guidelines:
- File Naming: Name your main script file correctly (e.g., YourName.m).
- Include All Necessary Files: Place all required files in a single ZIP or RAR file.
- Test Your Code: Run your code multiple times to ensure it executes without errors.
Example Submission
1. Main Script File:
clear all; close all;
% Load and process data
data = load('COVID_data.mat');
dates = data.COVID_data.dates;
infected = data.COVID_data.currently_infected;
% Fit and plot data
yfit = polynomialFit(dates, infected, 3);
plot(dates, infected, 'o', dates, yfit, '-');
title('Polynomial Fit of Currently Infected Cases');
1. ZIP or RAR File: Include all .m and .mlx files required to run your code.
Conclusion
By following the steps outlined in this blog, you can systematically approach and solve MATLAB assignments involving data fitting. Focus on understanding the data, using appropriate fitting techniques, and maintaining clean, well-commented code. These principles will not only help you with this assignment but also prepare you for similar tasks in the future.
MATLAB assignments can be challenging, but with the right approach and techniques, you can successfully analyze and fit data, providing valuable insights and solutions. Happy coding!