Types of matrices

In Scala, we will use the Breeze library to represent a matrix. A matrix can be represented as a dense or a CSC matrix.

• Dense matrix: A dense matrix is created with a constructor method call. Its elements can be accessed and updated. It is a column major, and can be transposed to convert to row major.

        val a = DenseMatrix((1,2),(3,4)) 
          println("a : n" + a) 
         val m = DenseMatrix.zeros[Int](5,5) 

        The columns of a matrix can be accessed as Dense Vectors, and    
        the rows as  Dense Matrices. 

          println( "m.rows :" + m.rows + " m.cols : "  + m.cols) 
          m(::,1) 
         println("m : n" + m) 

• Transposing a matrix: Transposing a matrix means swapping its rows and columns. The transpose of a P × Q matrix, written MT, is a Q × P matrix such that (MT ) j, I = Mi, j for every I ∈ P, j ∈ Q. Vector transpose to create a matrix row.

        m(4,::) := DenseVector(5,5,5,5,5).t 
        println(m) 

      
      a : 
      1  2  
      3  4  
      Created a 5x5 matrix
      0  0  0  0  0  
      0  0  0  0  0  
      0  0  0  0  0  
      0  0  0  0  0  
      0  0  0  0  0  
      m.rows :5 m.cols : 5
      First Column of m : 
            DenseVector(0, 0, 0, 0, 0)
            Assigned 5,5,5,5,5 to last row of m.
        
      0  0  0  0  0  
      0  0  0  0  0  
      0  0  0  0  0  
      0  0  0  0  0  
      5  5  5  5  5 

• CSC matrix: The CSC matrix is known as the Compressed Sparse Columns matrix. Each column within the CSC matrix represents a sparse vector. The CSC matrix supports all matrix operations, and is constructed using Builder.

        val builder = new CSCMatrix.Builder[Double](rows=10, 
           cols=10) 
        builder.add(3,4, 1.0) 
        // etc. 
        val myMatrix = builder.result()