CoCoA » CoCoA-5

We have this constructor for matrices:

/**/  MakeMatByRows(2, 10, 1..20);
matrix([
  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
  [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
])

The usual question: a good name? MakeMultiMatByRows? MakeMatByRows?

I thought about the code for the multi block matrix.
The input checking (size compatibility) would be really tedious.
I think something like this might do most of the desired work

Define ConcatHorList(L)
  If L=[] Then Error("Empty list"); EndIf;
  If Len(L)=1 Then Return L[1]; EndIf;
  Return ConcatHor(L[1], ConcatHorList(Tail(L)));
EndDefine; -- ConcatHorList

-- Example 2:
/**/ A:=Mat(QQ, [[1,2,3], [4,5,6]]); B:=ColMat(QQ, [1,2]); C:= ColMat(QQ, [3,4]);
/**/ ConcatHorList([A,B,C]);
matrix( /*QQ*/
 [[1, 2, 3, 1, 3],
  [4, 5, 6, 2, 4]]
 )

-- Example 3;
/**/ A1:=Mat(QQ,[ [1]]); A2:=Mat(QQ,[ [2]]); A3:=Mat(QQ,[ [3]]);
/**/ A4:=Mat(QQ,[ [4]]); A5:=Mat(QQ,[ [5]]); A6:=Mat(QQ,[ [6]]);
/**/ ConcatVer(ConcatHorList([A1,A2,A3]), ConcatHorList([A4,A5,A6]));
matrix( /*QQ*/
 [[1, 2, 3],
  [4, 5, 6]]
 )

JAA wonders whether it might be appropriate to have a fairly general function for building matrices by blocks:

BlockMat(M)  --->  M
BlockMat([M1, M2, M3])  --->  ConcatHorList(M1,M2,M3)
BlockMat([[M1,M2,M3],[M4,M5,M6]])  --->  ConcatVerList([ConcatHorList(row) | row in L])

What do you think?

John Abbott wrote:

JAA wonders whether it might be appropriate to have a fairly general function for building matrices by blocks:

That's what I thought to start with, but the current solution is actually more flexible (in philosophy). I explain: I would expect BlockMat to check row and column numbers compatibility (very tedious) whether

ConcatVerList([ConcatHorList(row) | row in L])

A := RowMat([1,2,3]);  B := RowMat([0,0]);
/**/ BlockMat(A,B, B,A);  -- gives error, as it should!
/**/ ConcatVerList([ConcatHorList([A,B]),  ConcatHorList([B,A]) ]);
matrix( /*QQ*/
 [[1, 2, 3, 0, 0],
  [0, 0, 1, 2, 3]]
 )

added JAA's definition of MultiBlockMat into manual entry of BlockMat
(and also search keys)

  Define MultiBlockMat(L)
    Return ConcatVerList([ConcatHorList(row) | row in L]);
  EndDefine;

/**/  A := RowMat([1,2,3,4]);   B := RowMat([0,0]);
/**/  BlockMat(A,B, B,A);   -- !!! ERROR !!! as expected
/**/  MultiBlockMat([[A,B], [B,A]]);
matrix( /*QQ*/
 [[1, 2, 3, 4, 0, 0],
  [0, 0, 1, 2, 3, 4]]
 )

How about renaming the current BlockMat to BlockMat2x2,
and the new fn MultiBlockMat to just plain BlockMat?

Just so we don't forget: for the time being we are not planning on making a MultiBlockMat fn available in CoCoALib -- it would be tedious making up the vector of vector of matrix input data.

If in the future we let users be more flexible with rings, it may be helpful to have a BlockMat function which accepts also the ring in which the entries will reside -- the entries of the contributing matrices will be mapped automatically into that ring.

The syntax I have in mind is something like

BlockMat(R, [[Mat1, Mat2],[Mat3, Mat4]]);

This syntax appears to be coherent with other matrix ctors. Similar changes might then be needed to ConcatVer and ConcatHor, and so on.

Is this a good/sane idea?

JAA still prefers the name BlockMat to the unwieldy MultiBlockMat.
New issue for 5.0.4??

John Abbott wrote:

JAA still prefers the name BlockMat to the unwieldy MultiBlockMat.
New issue for 5.0.4??

BlockMat does another thing and has the same syntax as in CoCoALib (one-liner).
The new one would be a nightmare in C++. So we need two different names.
(we could do CoCoA5-overloading, but that's an unnecessary complication with all the things we have to do)