MATLAB Legends and Scientific Computation: The Application of Legends in Scientific Computation and Modeling, Enhancing Model Visualization

# 1. Introduction to MATLAB Legends

A legend in MATLAB is a graphical element used to explain the meaning of different lines, bars, or markers in a plot. It assists users in understanding the data within a graph by displaying a box next to the graph containing samples of each line, bar, or marker along with their corresponding labels.

Legends play a crucial role in scientific computing as they allow users to quickly identify and differentiate between different datasets within a graph. They are particularly useful for scientific visualization, data analysis, and modeling and simulation tasks.

# 2. The Application of Legends in Scientific Computing

## 2.1 Legends in Scientific Visualization

Legends are essential in scientific visualization as they provide explanations for the meanings of different elements in a graph. With the use of legends, the audience can easily recognize data points, curves, and regions, thus understanding the implications of the data.

MATLAB offers various options for creating and customizing legends. Legends can be manually created using the `legend` function, or they can be automatically generated using the `legend` dialog box.

### 2.1.1 Manually Creating Legends

% Create a graph with three curves
figure;
plot(x1, y1, 'r-', 'LineWidth', 2);
hold on;
plot(x2, y2, 'g--', 'LineWidth', 2);
plot(x3, y3, 'b:', 'LineWidth', 2);

% Manually create a legend using the legend function
legend('Curve 1', 'Curve 2', 'Curve 3');

### 2.1.2 Automatically Generating Legends

% Create a graph with three curves
figure;
plot(x1, y1, 'r-', 'LineWidth', 2, 'DisplayName', 'Curve 1');
hold on;
plot(x2, y2, 'g--', 'LineWidth', 2, 'DisplayName', 'Curve 2');
plot(x3, y3, 'b:', 'LineWidth', 2, 'DisplayName', 'Curve 3');

% Automatically generate a legend using the legend dialog box
legend('show');

## 2.2 Legends in Data Analysis

Legends are also useful in data analysis as they help in identifying and comparing different datasets. For instance, in bar charts or line graphs, legends can show the meaning of each bar or line, facilitating data comparison.

### 2.2.1 Creating Legends for Data Analysis

% Create a bar chart with three bars
figure;
bar(x, [y1, y2, y3]);

% Create a legend using the legend function
legend('Dataset 1', 'Dataset 2', 'Dataset 3');

### 2.2.2 Using Legends for Data Comparison

% Create a line chart with three curves
figure;
plot(x, y1, 'r-', 'LineWidth', 2);
hold on;
plot(x, y2, 'g--', 'LineWidth', 2);
plot(x, y3, 'b:', 'LineWidth', 2);

% Create a legend using the legend function
legend('Curve 1', 'Curve 2', 'Curve 3');

% Use the legend to compare different curves
disp('Average value of Curve 1:');
disp(mean(y1));

disp('Average value of Curve 2:');
disp(mean(y2));

disp('Average value of Curve 3:');
disp(mean(y3));

## 2.3 Legends in Modeling and Simulation

In modeling and simulation, legends can help visualize the output of complex models. For example, in finite element analysis, legends can display the distribution of stress or strain across different regions.

### 2.3.1 Creating Legends for Modeling and Simulation

% Create a finite element model
model = createpde();

% Add geometry and boundary conditions
geometryFromEdges(model, [0 0; 1 0; 1 1; 0 1]);
applyBoundaryCondition(model, 'dirichlet', 'Edge', 1, 'u', 0);
applyBoundaryCondition(model, 'dirichlet', 'Edge', 2, 'u', 1);

% Solve the model
solvepde(model);

% Visualize the results and create a legend
figure;
pdeplot(model, 'XYData', 'stress');
title('Stress Distribution');
colorbar;

# 3.1 Legends in Physical Modeling

In physical modeling, legends are used to represent the relationships between different physical quantities or variables within a model. For instance, in a fluid dynamics model, a legend can represent the relationship between the fluid's velocity, pressure, and temperature.

#### Legend Design

Legend design in physical modeling should consider the following factors:

- **Variable Types:** Variables in a legend can be scalars (e.g., temperature),