The Copy function copies data from one mod m Matrix or Vector to another, or to a new Matrix or Vector.

If B or order are not specified, a new output object with the same ordering as the input object A is returned. If B is not specified, the returned object has the specified ordering either C_order or Fortran_order.

If order is not specified, the copy is performed into the output object B and NULL is returned. Note that the dimensions of the object specified for A must match those specified for B.

In all cases, the datatype of the output object must match the datatype of the input object.

The ctype parameter is used to specify the type of copy to be performed. Valid options are upper for the upper triangular part of a Matrix, lower for the lower triangular part of a Matrix, and $\mathrm{uppernodiag}$ and $\mathrm{lowernodiag}$ for the corresponding copy operation without the diagonal.

Note: These copy types are only valid for square Matrices.

The Copy function allows the use of sub-Matrix and sub-Vector specifications for both input and output. For example, the function can be used to copy a row of a Matrix to a row of another Matrix, or convert a Matrix into a Vector.

Note: If A and B overlap, the behavior of Copy is undefined.

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form Copy(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][Copy](..).

$\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Modular}\right]\right)\:$

$A≔\mathrm{Mod}\left(13\,\mathrm{Matrix}\left(4\,4\,\left(i\,j\right)\mapsto \mathrm{rand}\left(\right)\right)\,\mathrm{integer}\left[\right]\right)$

$A≔\left[\begin{array}{cccc}10& 0& 8& 12\\ 2& 6& 0& 11\\ 9& 2& 11& 7\\ 4& 11& 12& 11\end{array}\right]$

$\mathrm{Copy}\left(13\,A\right)$

$\left[\begin{array}{cccc}10& 0& 8& 12\\ 2& 6& 0& 11\\ 9& 2& 11& 7\\ 4& 11& 12& 11\end{array}\right]$

$M≔\mathrm{Copy}\left(13\,A\,3\right)$

$M≔\left[\begin{array}{cccc}9& 2& 11& 7\end{array}\right]$

$\mathrm{whattype}\left(M\right)$

${\mathrm{Vector}}_{\mathrm{row}}$

$N≔\mathrm{Copy}\left(13\,A\,1..-1\,2\right)$

$N≔\left[\begin{array}{c}0\\ 6\\ 2\\ 11\end{array}\right]$

$\mathrm{whattype}\left(N\right)$

${\mathrm{Vector}}_{\mathrm{column}}$

$L≔\mathrm{Copy}\left(13\,A\,1..-1\,2..2\right)$

$L≔\left[\begin{array}{c}0\\ 6\\ 2\\ 11\end{array}\right]$

$\mathrm{whattype}\left(L\right)$

$\mathrm{Matrix}$

$B≔\mathrm{Create}\left(13\,4\,4\,\mathrm{integer}\left[\right]\right)$

$B≔\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$

$\mathrm{Copy}\left(13\,A\,3\,B\,2\right)\:$

$\mathrm{Copy}\left(13\,A\,2\,B\,3\right)\:$

$A,B$

$\left[\begin{array}{cccc}10& 0& 8& 12\\ 2& 6& 0& 11\\ 9& 2& 11& 7\\ 4& 11& 12& 11\end{array}\right],\left[\begin{array}{cccc}0& 0& 0& 0\\ 9& 2& 11& 7\\ 2& 6& 0& 11\\ 0& 0& 0& 0\end{array}\right]$

$B≔\mathrm{Create}\left(13\,4\,3\,\mathrm{integer}\left[\right]\right)$

$B≔\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

$\mathrm{Copy}\left(13\,A\,3\,B\,2\right)\:$

Error, (in LinearAlgebra:-Modular:-Copy) argument 4 has a different number of columns than required by prior arguments

$B≔\mathrm{Create}\left(13\,4\,4\,\mathrm{float}\left[8\right]\right)$

$B≔\left[\begin{array}{cccc}0.& 0.& 0.& 0.\\ 0.& 0.& 0.& 0.\\ 0.& 0.& 0.& 0.\\ 0.& 0.& 0.& 0.\end{array}\right]$

$\mathrm{Copy}\left(13\,A\,3\,B\,2\right)\:$

Error, (in LinearAlgebra:-Modular:-Copy) argument 4 has incorrect datatype

$\mathrm{Copy}\left(13\,\mathrm{upper}\,A\right)$

$\left[\begin{array}{cccc}10& 0& 8& 12\\ 0& 6& 0& 11\\ 0& 0& 11& 7\\ 0& 0& 0& 11\end{array}\right]$

$B≔\mathrm{Create}\left(13\,4\,4\,\mathrm{integer}\left[\right]\right)\:$

$\mathrm{Copy}\left(13\,\mathrm{lowernodiag}\,A\,B\right)\:$

$B$

$\left[\begin{array}{cccc}0& 0& 0& 0\\ 2& 0& 0& 0\\ 9& 2& 0& 0\\ 4& 11& 12& 0\end{array}\right]$