Make SwapMatrixColumns and SwapMatrixRows faster for classic matrices (lists-of-lists)

[fingolfin]

Yet another commit from an unfinished branch/PR that might be considered useful on its own: faster "early methods" for SwapRows/SwapCols using kernel methods. It is not tested thoroughly and I am not even sure we want to go in this direction, but we could e.g. use this as basis for discussions during the GAP Days

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This speeds up swap operations for plain list matrices a lot, and
even for "real" matrix objs, as the overhead of a GAP early method
is much higher than the overhead of one written in the kernel.

Now whether this gain is worth the extra complexity is another question;
though of course when doing heavy linear algebra, these row and column
can add up.

Before:

gap> mat:=IdentityMat(10,Integers);;
gap> for i in [1..1000000] do SwapMatrixColumns(mat,1,2); od; time;
326
gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
90
gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
37

gap> mat:=IdentityMat(10,GF(2));; ConvertToMatrixRep(mat);; mat;
<a 10x10 matrix over GF2>
gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
146
gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
84

After:

gap> mat:=IdentityMat(10,Integers);;
gap> for i in [1..1000000] do SwapMatrixColumns(mat,1,2); od; time;
153
gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
19
gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
45

gap> mat:=IdentityMat(10,GF(2));; ConvertToMatrixRep(mat);; mat;
<a 10x10 matrix over GF2>
gap> for i in [1..1000000] do SwapMatrixRows(mat,1,2); od; time;
116
gap> for i in [1..1000000] do tmp:=mat[1];mat[1]:=mat[2];mat[2]:=tmp; od; time;
83

[fingolfin]

The work is done and I see no harm. The idea of course is that ideally code switching to SwapMatrixRows should be penalized as little as possible for it, or even better, should benefit from it. This is clearly the case for the plist matrix. For the GF2 rep it still is a little bit slower but that could be mitigated further in the future if desired.

So I see no harm in merging this. Agreed @ThomasBreuer ?

[ThomasBreuer]

No problem with the idea and with the use of the kernel operation for matrices without holes.
I do not understand the explicit error cases in FuncSWAP_MAT_ROWS. Apparently the code deals also with holes inside the lists:

gap> l:= [ 1, 2,, 4 ];; SWAP_MAT_ROWS( l, 2, 3 ); l;
[ 1,, 2, 4 ]

(If the hole is beyond the length of the list, the result is different.)

[fingolfin]

Revised. Now we get

gap> l:= [ 1, 2,, 4 ];; SWAP_MAT_ROWS( l, 2, 3 ); l;
Error, Matrix Element: <mat>[3] must have an assigned value
not in any function at *stdin*:1
type 'quit;' to quit to outer loop
brk>

and the error handling should be consistent overall.