C# matrix-class design (transpose method)

i'm currently working on a matrix implementation in C# . It's not a question about how sth. should work or sth. similar. It's more about the "design-part" ... So, i want to implement a function, which transposes a matrix ( http://en.wikipedia.org/wiki/Transpose ) . Easy thing thought, but it's really hard for me to choose, which implemantation way is the most elegant.

But here first a bit code of the matrix class:

namespace Math
    public class Matrix
        protected double[,] matrix;

        public Matrix(byte m, byte n)[...]
        public Matrix(Matrix matrix)[...]

        public byte M { get; private set; }
        public byte N { get; private set; }

        // Possibility 1 (changes the matrix directly)
        public void Transpose()[...]

        // Possibility 2 (getter method)
        public Matrix GetTransposed()[...]

        // Possibility 3 (property)
        public Matrix TransposedMatrix

        // Possibility 4 (static method; a bit like an operator)
        public static Matrix Transpose(Matrix matrix)[...]

And here, how you would use the different possibilities:

namespace MathTest
    class Program
        static void Main(string[] args)
            // Create a new matrix object...
            var mat1 = new Math.Matrix(4, 4);

            // Using possibility 2 (getter method, like "GetHashCode()" or sth. similar)
            var mat2 = mat1.GetTransposed();

            // Using possibility 3 (the transposed matrix is a property of each matrix)
            var mat3 = mat1.TransposedMatrix;

            // Using possibility 4 (definition and use is like an unary operator)
            var mat4 = Math.Matrix.Transpose(mat1);

            // Using possibility 1 (changes the matrix directly)

Which way would you prefer and why? Or are there even better ways to implement the transposition of a matrix?

Thank you very much!



I would rather vote for

  public Matrix Transpose() { ... }

Possibility 1

Is, IMHO, dubious since Matrix seems to be immutable (all other methods don't change it). Moreover, other operations (if you decide to implement them) e.g. arithmetics +, -, *, /, don't change the initial Matrix as well, they return a new Matrix instead.

   Matrix B = -A; // <- A doesn't changed
   Matrix D = A + B * C; // <- A, B, C don't changed
   Matrix E = F.Transpose(); // <- I hope to have F being intact as well

Possibility 2

Is the best one; I'd rather rename method from GetTransposed() to Transpose() - we usuallly, use active names - Perform, Send, Write instead of GetPerformed, GetSent etc.

  // looks better than
  // A.GetPerformed().GetValidated().GetSentTo(@"Me@MyServer.com"); 

  // The same with transpose:
  // easier to read than
  // A.GetTransposed().GetAppied(x => x * x).GetToString();
  A.Transpose().Apply(x => x * x).ToString();

Possibility 3

I, personally, don't like it because TransposedMatrix is not a property in the typical sence of its name like RowCount, ColCount, IsUnit, IsDegenrate... Instead TransposedMatrix looks very similar to functions, like Exp(), Sqrt()...

  A.ColCount; // <- property of the matrix
  A.IsDegenerate; // <- another property of the matrix
  A.ToString(); // <- is not a property: it's conversion (function) into string representation
  A.Sqrt(); // <- is not a property, square root is a function
  A.Transpose(); // <- is not a propery either: it's a function too

Possibility 4:

IMHO, sounds innaturally. My way of thinking is: "I have a matrix instance A, I want to have a transposed matrix from it, say, B, so I should do something with A". And I'll start looking for the method:

   B = A.Transpose();
   B = A.ToTransposed();
   B = A.GetTransposed();
   B = A.Rotate(); 
   B = A.Transform(...);
   B = A.DoSomething();

The static methods are good, IMHO, for creating. e.g.

   A = Math.Matrix.Zero(5); // <- Create 5x5 Matrix, all zeroes
   B = Math.Matrix.Unit(6); // <- 6x6 unit matrix

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