Transpose of a matrix

The transpose of a matrix M of m×n elements is the matrix M^T with n×m elements, where M [i, j] = M^T [j, i] for all indices of i and j. In other words the elements of the rows become the elements of the columns and vice versa. A square matrix is called symmetric, when M = M^T. The here given function returns the transpose of a matrix of the type t2dVariantArrayDouble.

Algorithm

As initial step the passed InputMatrix is controlled whether it is rectangular of not. When the test succeeds the row vectors of InputMatrix are transposed to column vectors of OutputMatrix. When the test fails the function returns FALSE. The title arrays of the rows and columns are exchanged.

Source

Function mtx_Transpose (InputMatrix : T2dVariantArrayDouble; Var OutputMatrix : T2dVariantArrayDouble) : Boolean;
// The function mtxTranspose transposes a matrix. Thus every element of a
// rectangular matrix input [y, x] is transposed to the output [x, y].
// (c) Jan Schulz, February 2004, www.code10.info
Var RunnerX    : Integer;
    RunnerY    : Integer;
    MaxCols    : Integer;
    MaxRows    : Integer;
Begin
  mtx_Transpose := False;

  // is the input matrix rectangular and get its dimensions
  If mtx_IsRectangular (InputMatrix, MaxRows, MaxCols) THen
  Begin

    // create the output matrix and swap col and row size
    mtx_Create (OutputMatrix, MaxCols, MaxRows, NAN, InputMatrix.MatrixName);

    // copy elements from Input [y, x] to Output [x, y]
    For RunnerY := High (InputMatrix.Cells) downto Low (InputMatrix.Cells) do
    Begin
      For RunnerX := High (InputMatrix.Cells [RunnerY]) downto 0 do
      Begin
        OutputMatrix.Cells [RunnerX, RunnerY] := InputMatrix.Cells [RunnerY, RunnerX];
      end;
    end;

    // set the length of the arrays for the column and row titles
    SetLength (OutputMatrix.ColTitle, High (InputMatrix.RowTitle) +1);
    SetLength (OutputMatrix.RowTitle, High (InputMatrix.ColTitle) +1);

    // copy the titles for the transposed matrix
    For RunnerX := High (InputMatrix.ColTitle) downto 0 do
        OutputMatrix.RowTitle [RunnerX] := InputMatrix.ColTitle [RunnerX];

    For RunnerY := High (InputMatrix.RowTitle) downto 0 do
      Outputmatrix.ColTitle [RunnerY] := InputMatrix.RowTitle [RunnerY];

    mtx_Transpose := True;
  end;
end;

Example

For a data matrix aInputMatrix of the type t2dVariantArrayDouble, populated with:

the call of:

aBooleanVar := mtx_Transpose (aInputMatrix, aOutputMatrix);

returns TRUE and in aOutputMatrix the transposed matrix: