Transpose matrix ada - matrix

Question

How can I transpose matrix in ADA?. I´ve tried:
procedure transpose(A: in out matrix) is
B : matrix(1..A'Last(2),1..A'Last(1));
begin
for i in A'Range(1) loop
for j in A'Range(2) loop
B(j,i):= A(i,j);
end loop;
end loop;
A := B;
end transpose;
but it doesn´t work when A isn´t a square Matrix.
Any help would be appreciated.

Answer 1

As a procedure this can never work for non-square matrices because the output is a different constrained type from the input. However you can return B from a suitable function.
function transpose(A: in matrix) return matrix is
B : matrix(A'Range(2),A'Range(1));
begin
for i in A'Range(1) loop
for j in A'Range(2) loop
B(j,i):= A(i,j);
end loop;
end loop;
return B;
end transpose;
The easiest way to create a matrix of the right constrained type for the result is a declare block:
declare
Transposed : Matrix := Transpose(A);
begin
-- operations on the transposed matrix
end;

Answer 2

You can transpose a matrix by creating a record like:
type Matrix_Type is record
Data : array (1..MAX_SIZE, 1..MAX_SIZE) of Float;
Last_Row : Positive range 1 .. MAX_SIZE;
Last_Column : Positive range 1 .. MAX_SIZE;
end record;
This record can support matrices of any m by n size up to n,m <= MAX_SIZE
Your procedure becomes:
procedure transpose(A: in out Matrix_Type) is
B : Matrix_Type;
begin
for i in 1..A.Last_Row loop
for j in 1..A.Last_Column loop
B(j,i):= A(i,j);
end loop;
end loop;
B.Last_Column := A.Last_Row;
B.Last_Row := A.Last_Column;
A := B;
end transpose;

Answer 3

The easiest way I know of is to use the Fortran convention on an intermediate array-type. (This is because Fortran convention is column-major while in Ada, it is row-major.)
Function Transpose(M : Matrix) return Matrix is
subtype Constrained is Matrix(M'Range(2), M'Range(1));
Type Xposed is new Matrix with Convention => Fortran;
Temp : Xposed := Xposed(M);
Result : Constrained with Import, Address => Temp'Address; --'
begin
Return Result;
end Transpose;