feat: Implement Matrix , its Methods and Some Functions including Strassen Matrix Multiplication in Go

[mohit07raghav19]

Title: Implementation of Matrix and Associated Methods in Go

Description:

This pull request introduces several enhancements to the math/matrix directory:

• Matrix Data Type: Implemented a new Matrix data type in Go, providing a foundation for matrix operations.
• Matrix Methods: Developed associated methods for the Matrix data type, enabling operations such as addition, subtraction, and multiplication.
• Strassen's Algorithm: Included an efficient implementation of Strassen's Matrix Multiplication algorithm.
• Error Handling: Integrated robust error handling for matrix operations to manage incompatible inputs effectively.
• Concurrency Utilization: Leveraged Go's concurrency features for improved performance on large matrix computations.
• Test Coverage: Added comprehensive unit tests to ensure the correctness of the matrix operations and Strassen's algorithm.

Closes #661 (if applicable)

[mohit07raghav19]

@raklaptudirm , I have made the required changes in the code.
I request you to Verify the same.
Please let me know if I could do something related to it further.
Thank YOU :)

[raklaptudirm]

Note the Go idiom that you should not repeat the package name. For example, in matrix.AddMatrices, you are using the word "Matrix" twice. matrix.Add is a much simpler name and it doesn't lose any information. Change the names accordingly.

Also, you could make some simple functions that find the lenght/breadth of a matrix, given you are trying to find that multiple times.

[mohit07raghav19]

Also, you could make some simple functions that find the length/breadth of a matrix, given you are trying to find that multiple times.

@raklaptudirm
For getting the Breadth of a matrix (only valid matrix.),

// Breadth returns the number of columns in a valid matrix.
func Breadth[T any](matrix [][]T) (int, error) {
	if err := IsValid(matrix); err != nil {
		return 0, err
	}

	if len(matrix) == 0 {
		return 0, nil // Return 0 if the matrix is empty and valid.
	}

	return len(matrix[0]), nil
}

in which IsValid func is used as

// IsValid checks if a matrix is valid, meaning all rows have the same number of columns.
func IsValid[T any](matrix [][]T) error {
	if len(matrix) == 0 {
		return nil // an empty matrix is considered valid
	}

	columns := len(matrix[0]) // Number of columns in the first row.

	for _, row := range matrix {
		if len(row) != columns {
			return errors.New("invalid matrix: rows have different numbers of columns")
		}
	}

	return nil
}

and Len func returns the length only if matrix is valid.

func Len[T any](matrix [][]T) (int, error) {
	if err := IsValid(matrix); err != nil {
		return 0, err
	}
	return len(matrix), nil
}

BUT now in many functions simple len(matrix) is used After verifying that it is a valid matrix. The code can become unnecessarily extended like for
result := make([][]T, len(matrix1)) , The code would be

// checked for IsValid(matrix1) above.
    length , err := Len(matrix1) // There is _no need_ to check for a valid matrix again
    if err!=nil {
         result := make([][]T, length)
         // ... appropriate code
    }

Do I need to change them to Len or Breadth ?

[raklaptudirm]

Don't do a validity check in the Length or Breadth functions, let the user decide when to do that.

Even better, you could make matrix a type with a constructor that ensures that the number of columns in each row is the same.

[raklaptudirm]

Also fix the CI errors.

[tjgurwara99]

I haven't reviewed it fully, so will come back to this later. But I've left some thoughts on the PR 😄

[tjgurwara99]

Well done! This is looking much better now 😄

PS: you might need to make an empty commit - the update GoDoc action has stopped the execution of other actions for some reason 😓

[raklaptudirm]

A very good quality pr, LGTM :)