Vector & Matrix Calculator 🚀

🖥️ Overview

This project is a C++ library that implements data types for vectors and matrices, offering a comprehensive set of mathematical operations commonly used in various applications.

Usage

1. Click on the Option button in the UI.
2. Select Load Data to load a text file containing vectors and/or matrices.
3. Input the desired operation in the Command column.
4. Press the Execute button to perform the operation.

Data Format

The input text file can contain two data types: vectors and matrices. Each row in the text file represents a vector or a matrix in the following format:

Vector

To represent a vector, use the following format:

• {dimension}: The dimension of the vector (number of elements).
• {value1} {value2} ... {valueN}: The values of the vector's elements.

// V {dimention} {value}
V 3 1 2 3

$$ v=\begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} $$

Matrix

To represent a matrix, use the following format:

• {rows}: The number of rows in the matrix.
• {cols}: The number of columns in the matrix.
• {value1} {value2} ... {valueN}: The values of the matrix elements in row-major order.

// M {rows} {cols} {value}
M 3 2 0 1 2 3 4 5 // row=3, col=2

$$ m= \begin{bmatrix} 0 & 1 \\ 2 & 3 \\ 4 & 5 \\ \end{bmatrix} $$

📄 Vector Library

➕ Operators

This section introduces vector operator functions that perform element-wise operations on vectors. If one of the input vectors is 1D, the operation will be a scalar operation.

Operator	Description	Input	Output
+	Element-wise addition of vectors.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^n$
-	Element-wise subtraction of vectors.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^n$
*	Element-wise product of vectors.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^n$

🔧 Functions

The following functionalities have been implemented in the vector functions:

Function	Description	Input	Output
dot(a, b)	Compute the dot product of two vectors.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^1$
norm(a)	Calculate the norm (magnitude) of a vector.	$\vec{a} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^1$
normal(a)	Normalize a vector to a unit vector.	$\vec{a} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^n$
cross(a, b)	Compute the cross product of two 3D vectors.	$\vec{a}, \vec{b} \in \mathbb{R}^3$	$\vec{v} \in \mathbb{R}^3$
com(a, b)	Find the component of vector a along vector b.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^1$
proj(a, b)	Compute the projection of vector a onto vector b.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^n$
area(a, b)	Calculate the area of the triangle formed by vectors a and b.	$\vec{a}, \vec{b} \in \mathbb{R}^n, n\in{2,3}$	$\vec{v} \in \mathbb{R}^1$
angle(a, b)	Determine the angle (in radians) between two vectors.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	$\vec{v} \in \mathbb{R}^1$
pn(a, b)	Compute the normal vector of the plane formed by two 3D vectors.	$\vec{a}, \vec{b} \in \mathbb{R}^3$	$\vec{v} \in \mathbb{R}^3$
ob(a, b, c ...)	Use Gram-Schmidt process to find orthonormal basis from multiple vectors.	$\vec{a}, \vec{b}, \vec{c}, \ldots \in \mathbb{R}^n$	String Vector array (not for operation)

Judgement Functions 🔧 This section includes functions to assess the relationship between two vectors.

Function	Description	Input	Output
isparallel(a, b)	Checks if vectors a and b are parallel.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	String: Yes or No
isorthogonal(a, b)	Checks if vectors a and b are orthogonal.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	String: Yes or No
isli(a, b)	Checks if vectors a and b are linearly independent.	$\vec{a}, \vec{b} \in \mathbb{R}^n$	String: Yes or No

📄 Matrix Library

➕ Operators

If one of the matrices has a size of 1x1, the library will perform a scalar product, which is a special operation that treats the matrix as a scalar value.

Operator	Description	Input	Output
+	Element-wise addition.	$\mathbf{A} \in \mathbb{R}^{m \times n}$, $\mathbf{B} \in \mathbb{R}^{m \times n}$	$\mathbf{C} \in \mathbb{R}^{m \times n}$
-	Element-wise subtraction.	$\mathbf{A} \in \mathbb{R}^{m \times n}$, $\mathbf{B} \in \mathbb{R}^{m \times n}$	$\mathbf{C} \in \mathbb{R}^{m \times n}$
*	Element-wise product.	$\mathbf{A} \in \mathbb{R}^{m \times n}$, $\mathbf{B} \in \mathbb{R}^{m \times n}$	$\mathbf{C} \in \mathbb{R}^{m \times n}$

🔧 Functions

Function	Description	Input	Output
matmul(A, B)	Performs matrix multiplication between two matrices A and B.	$A \in \mathbb{R}^{l \times m}$, $B \in \mathbb{R}^{m \times n}$	$C \in \mathbb{R}^{l \times n}$
rank(A)	Calculates the rank of a matrix.	$A \in \mathbb{R}^{m \times n}$	$C \in \mathbb{R}^{1 \times 1}$
trans(A)	Computes the transpose of a matrix A.	$A \in \mathbb{R}^{m \times n}$	$C ^\mathrm{T}\in \mathbb{R}^{m \times n}$
solve(A, B)	Solves a linear system of equations of the form $Ax = B$.	$A \in \mathbb{R}^{n \times n}$, $B \in \mathbb{R}^{n \times 1}$	$x \in \mathbb{R}^{n \times 1}$
det(A)	Calculates the determinant of a Matrix	$A \in \mathbb{R}^{n \times n}$	$C \in \mathbb{R}^{1 \times 1}$
inverse(A)	Finds the inverse matrix of a square matrix A.	$A \in \mathbb{R}^{n \times n}$	$C \in \mathbb{R}^{n \times n}$
adj(A)	Computes the adjoint of a matrix	$A \in \mathbb{R}^{n \times n}$	$C \in \mathbb{R}^{n \times n}$
pm(A)	Finds Largest Eigenvalue and Eigenvector by using the power method	$A \in \mathbb{R}^{n \times n}$	String: Eigenvalue and Eigenvector
eigen(A)	Find Eigenvalue and Eigenvector of matrix A.	$A \in \mathbb{R}^{n \times n}, n \in {1, 2, 3}$	String: Eigenvalue and Eigenvector
leastq	Applies The Method of Least Squares.	$A \in \mathbb{R}^{n \times n}$, $B \in \mathbb{R}^{n \times 1}$	$x \in \mathbb{R}^{n \times 1}$
rref(A)	Converts matrix A to its reduced row echelon form.	$A \in \mathbb{R}^{m \times n}$	$C \in \mathbb{R}^{m \times n}$

🔍 Customization Guide

Adding or Modifying Functions

To add a new function or change the usage of existing functions, follow these steps:

1. Implement a Subclass of ICommand in Command.h

• Create a new subclass of ICommand in the Command.h file. Make sure to override the operate method to define the functionality of your command. For example:

class YourCommand : public ICommand {
public:
    YourCommand() {
        operand_count_ = 2;
        return_type_ = ReturnType::Operand; // or ReturnType::String
    }

    Vector operate(std::vector<Vector>& operands) override;
};

2. Register Your Command

In the WindowsForm.h file, locate the InitializeCommands() function, and register your newly implemented command using the command_factory->RegisterCommand() method. This step ensures that your command becomes available in the application. For example:

void InitializeCommands() {
    command_factory = new CommandFactory();
    // Existing vector commands
    command_factory->RegisterCommand("dot", std::make_shared<DotCommand>());
    // ...
    // Register your custom command
    command_factory->RegisterCommand("yourcommand", std::make_shared<YourCommand>());
}

By following these steps, you can easily add new mathematical functions or modify the behavior of existing functions within the application.