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main_par_trafo.g
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main_par_trafo.g
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ChiefParallelClearDown := function( galoisField,mat,a,b )
## inputs: a finite field, a matrix, natural nr. a,b to treat mat as axb matirx
local TaskListClearDown,
TaskListUpdateR,
TaskListUpdateM,
TaskListE,
dummyTask,
nrows,
ncols,
rows,
rank,
tmpC,
tmpR,
tmp,
bs,
A,
B,
C,
D,
E,
K,
M,
R,
X,
v,
w,
i,
j,
k,
k_,
l,
h;
##Preparation: Init and chopping the matrix mat
C := ChopMatrix( galoisField,mat,a,b );
ncols := DimensionsMat( mat )[2];
dummyTask := RunTask( function() return []; end );
TaskListClearDown := List(
[ 1 .. a ],
x -> List( [ 1 .. b ], x -> dummyTask )
);
TaskListE := List(
[ 1 .. a ],
x -> List( [ 1 .. b ], x -> dummyTask )
);
TaskListUpdateR := List(
[ 1 .. b ],
x -> List(
[ 1 .. b ],
x -> List( [ 1 .. b ], x -> RunTask( function() return rec( C := [],B:=[] ); end ) )
)
);
TaskListUpdateM := List(
[ 1 .. b ],
x -> List(
[ 1 .. a ],
x -> List( [ 1 .. b ], x -> RunTask( function() return rec( M := [],K:=[] ); end ) )
)
);
A := [];
B := [];
D := [];
E := [];
K := [];
M := [];
R := [];
X := [];
nrows := [];
for i in [ 1 .. a ] do
A[i] := [];
E[i] := [];
K[i] := [];
for k in [ 1 .. b ] do
A[i][k] := rec( A:=[],M:=[],K:=[],rho:=[],E:=[],lambda:=[] );
E[i][k] := rec( rho:=[],delta:=[],nr:=0 );
od;
for h in [ 1 .. a ] do
K[i][h] := [];
od;
od;
for i in [ 1 .. b ] do
M[i] := [];
nrows[i] := DimensionsMat(C[1][i])[2];
for k in [ 1 .. a ] do
M[i][k] := [];
od;
od;
for k in [ 1 .. b ] do
D[k] := rec( remnant:=[],bitstring:=[] );
B[k] := [];
R[k] := [];
X[k] := [];
for j in [ 1 .. b ] do
B[k][j] := [];
R[k][j] := [];
X[k][j] := [];;
od;
od;
###############################
###############################
## Step 1 ##
for i in [ 1 .. a ] do
for j in [ 1 .. b ] do
if i=1 and j=1 then
TaskListClearDown[1][1] := RunTask(
ClearDown,
galoisField,
C[1][1],
rec( remnant:=[],bitstring:=[] ),
1
);
TaskListE[i][j] := ScheduleTask(
[
TaskListClearDown[i][j]
],
Extend,
TaskResult( TaskListClearDown[i][j] ).A,
rec( rho:=[],delta:=[],nr:=0 ),
j
);
elif i=1 and j>1 then
TaskListClearDown[1][j] := ScheduleTask(
[
TaskListUpdateR[1][j-1][j]
],
ClearDown,
galoisField,
TaskResult( TaskListUpdateR[1][j-1][j] ).C,
rec( remnant:=[],bitstring:=[] ),
1
);
TaskListE[i][j] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListE[i][j-1],
],
Extend,
TaskResult( TaskListClearDown[i][j] ).A,
TaskResult( TaskListE[i][j-1] ),
j
);
elif i>1 and j=1 then
TaskListClearDown[i][1] := ScheduleTask(
[
TaskListClearDown[i-1][1]
],
ClearDown,
galoisField,
C[i][1],
TaskResult( TaskListClearDown[i-1][1] ).D,
i
);
TaskListE[i][j] := ScheduleTask(
[
TaskListClearDown[i][j]
],
Extend,
TaskResult( TaskListClearDown[i][j] ).A,
rec( rho:=[],delta:=[],nr:=0 ),
j
);
else
TaskListClearDown[i][j] := ScheduleTask(
[
TaskListClearDown[i-1][j],
TaskListUpdateR[i][j-1][j]
],
ClearDown,
galoisField,
TaskResult( TaskListUpdateR[i][j-1][j] ).C,
TaskResult( TaskListClearDown[i-1][j] ).D,
i
);
TaskListE[i][j] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListE[i][j-1]
],
Extend,
TaskResult( TaskListClearDown[i][j] ).A,
TaskResult( TaskListE[i][j-1] ),
j
);
fi;
#tmp := ClearDown( galoisField,C[i][j],D[j],i );
#D[j] := tmp.D;
#A[i][j] := tmp.A;
#if j=1 then
# bs := rec( rho:=[],delta:=[],nr:=0 );
#else
# bs := E[i][j-1];
#fi;
#E[i][j] := Extend( A[i][j],bs,j );
for k in [ j+1 .. b ] do
if i=1 and j=1 then
TaskListUpdateR[i][j][k] := ScheduleTask(
[
TaskListClearDown[i][j]
],
UpdateRow,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
C[i][k],
[],
i
);
elif i=1 and j>1 then
TaskListUpdateR[i][j][k] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListUpdateR[i][j-1][k]
],
UpdateRow,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
TaskResult( TaskListUpdateR[i][j-1][k] ).C,
[],
i
);
elif i>1 and j=1 then
TaskListUpdateR[i][j][k] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListUpdateR[i-1][j][k]
],
UpdateRow,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
C[i][k],
TaskResult( TaskListUpdateR[i-1][j][k] ).B,
i
);
else
TaskListUpdateR[i][j][k] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListUpdateR[i-1][j][k],
TaskListUpdateR[i][j-1][k]
],
UpdateRow,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
TaskResult( TaskListUpdateR[i][j-1][k] ).C,
TaskResult( TaskListUpdateR[i-1][j][k] ).B,
i
);
fi;
#tmp := UpdateRow( galoisField,A[i][j],C[i][k],
# B[j][k],i );
#C[i][k] := tmp.C;
#B[j][k] := tmp.B;
od;
for h in [ 1 .. i ] do
if i=1 and j=1 then
TaskListUpdateM[i][j][h] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListE[h][j]
],
UpdateRowTrafo,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
[],
[],
TaskResult( TaskListE[h][j] ),
i,
h,
j
);
elif i=1 and j>1 then
TaskListUpdateM[i][j][h] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListE[h][j],
TaskListUpdateM[i][j-1][h]
],
UpdateRowTrafo,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
TaskResult( TaskListUpdateM[i][j-1][h] ).K,
[],
TaskResult( TaskListE[h][j] ),
i,
h,
j
);
elif i>1 and j=1 then
TaskListUpdateM[i][j][h] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListE[h][j],
TaskListUpdateM[i-1][j][h]
],
UpdateRowTrafo,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
[],
TaskResult( TaskListUpdateM[i-1][j][h] ).M,
TaskResult( TaskListE[h][j] ),
i,
h,
j
);
else
TaskListUpdateM[i][j][h] := ScheduleTask(
[
TaskListClearDown[i][j],
TaskListE[h][j],
TaskListUpdateM[i][j-1][h],
TaskListUpdateM[i-1][j][h]
],
UpdateRowTrafo,
galoisField,
TaskResult( TaskListClearDown[i][j] ).A,
TaskResult( TaskListUpdateM[i][j-1][h] ).K,
TaskResult( TaskListUpdateM[i-1][j][h] ).M,
TaskResult( TaskListE[h][j] ),
i,
h,
j
);
fi;
#tmp := UpdateRowTrafo( galoisField,A[i][j],K[i][h],
# M[j][h],E[h][j],i,h,j );
#K[i][h] := tmp.K;
#M[j][h] := tmp.M;
od;
od;
od;
WaitTask( Concatenation( TaskListClearDown ) );
WaitTask( Concatenation( TaskListE ) );
WaitTask( Concatenation( List( TaskListUpdateR,Concatenation ) ) );
WaitTask( Concatenation( List( TaskListUpdateM,Concatenation ) ) );
for i in [ 1 .. a ] do
for j in [ 1 .. b ] do
E[i][j] := TaskResult( TaskListE[i][j] );
A[i][j] := TaskResult( TaskListClearDown[i][j] ).A;
D[j] := TaskResult( TaskListClearDown[i][j] ).D;
for k in [ j+1 .. b ] do
C[i][k] := TaskResult( TaskListUpdateR[i][j][k] ).C;
B[j][k] := TaskResult( TaskListUpdateR[i][j][k] ).B;
od;
for h in [ 1 .. i ] do
K[i][h] := TaskResult( TaskListUpdateM[i][j][h] ).K;
M[j][h] := TaskResult( TaskListUpdateM[i][j][h] ).M;
od;
od;
od;
## Step 2 ##
for j in [ 1 .. b ] do
for h in [ 1 .. a ] do
M[j][h] := RowLengthen( galoisField,M[j][h],E[h][j],E[h][b] );
od;
od;
## Step3 ##
for k in [ 1 .. b ] do
R[k][k] := D[k].remnant;
od;
for k_ in [ 1 .. b ] do
k := b-k_+1;
for j in [ 1 .. (k - 1) ] do
tmp := CEX( galoisField,D[k].bitstring,B[j][k] );
X := tmp[1];
R[j][k] := tmp[2];
if IsEmpty(X) then continue; fi;
for l in [ k .. b ] do
if not IsEmpty(R[k][l]) then
if IsEmpty(R[j][l]) then
R[j][l] :=X*R[k][l];
else
R[j][l] := R[j][l] + X*R[k][l];
fi;
fi;
od;
for h in [ 1 .. a ] do
if not IsEmpty(M[k][h]) then
if IsEmpty(M[j][h]) then
M[j][h] := X*M[k][h];
else
M[j][h] := M[j][h] + X*M[k][h];
fi;
fi;
od;
od;
od;
Print("3\n");
###############################
###############################
## Write output
# Begin with row-select bitstring named v
v := [];
rank := 0;
w := 0*[1..(DimensionsMat(mat)[1]/a) ];
for i in [ 1 .. a ] do
if IsEmpty(E[i][b].rho) then
tmp := w;
else
tmp := E[i][b].rho;
fi;
v := Concatenation( v,tmp );
rank := rank + Sum( tmp );
od;
#### Glueing the blocks of M
B := NullMat( rank,Length(v),galoisField );
rows := [];
for j in [ 1 .. b ] do
rows[j] := 0;
for i in [ 1 .. a ] do
if not IsEmpty(M[j][i]) then
rows[j] := DimensionsMat(M[j][i])[1];
break;
fi;
od;
od;
tmpR := 1;
for j in [ 1 .. b ] do
if rows[j]=0 then
continue;
fi;
tmpC := 1;
w := DimensionsMat(mat)[1]/a;
for i in [ 1 .. a ] do
if IsEmpty(M[j][i]) then
if IsEmpty(E[i][b].rho) then
tmp := w;
else
tmp := Length( E[i][b].rho );
fi;
tmpC := tmpC + tmp; continue;
#M[j][i] := NullMat( rows[j],tmp,galoisField );
else
M[j][i] := TransposedMat( RRF( galoisField,
NullMat( Length(E[i][b].rho)-
DimensionsMat(M[j][i])[2],
DimensionsMat(M[j][i])[1],galoisField ),
TransposedMat(M[j][i]),E[i][b].rho ) );
fi;
B{[tmpR .. tmpR + DimensionsMat(M[j][i])[1]-1 ]}{[tmpC .. tmpC + DimensionsMat(M[j][i])[2]-1 ]}
:= M[j][i];
tmpC := tmpC + DimensionsMat(M[j][i])[2];
od;
tmpR := tmpR + rows[j];
od;
### Glueing the blocks of R
C := NullMat( rank,ncols-rank,galoisField );
rows := [];
w := [];
for i in [ 1 .. b ] do
rows[i] := 0;
if IsEmpty(D[i].bitstring) then
w := Concatenation( w,0*[1..nrows[i]] );
else
w := Concatenation( w,D[i].bitstring );
fi;
for j in [ 1 .. b ] do
if not IsEmpty(R[i][j]) then
rows[i] := DimensionsMat(R[i][j])[1];
break;
fi;
od;
od;
tmpR := 1;
for i in [ 1 .. b ] do
if rows[i]=0 then
continue;
fi;
tmpC := 1;
for j in [ 1 .. b ] do
if IsEmpty(R[i][j]) then
if not IsEmpty(D[j].bitstring) then
tmpC := tmpC + Sum( 1 - D[j].bitstring );
elif not IsEmpty(R[1][j]) then
tmpC := tmpC + DimensionsMat(R[1][j])[2];
fi;
continue;
fi;
C{[tmpR .. tmpR + DimensionsMat(R[i][j])[1]-1 ]}{[tmpC .. tmpC + DimensionsMat(R[i][j])[2]-1 ]}
:= R[i][j];
tmpC := tmpC + DimensionsMat(R[i][j])[2];
od;
tmpR := tmpR + rows[i];
od;
C := TransposedMat( RRF( galoisField,TransposedMat(C), -IdentityMat( rank,galoisField ),w ) );
## Glueing the blocks of K
D := NullMat( Length(v)-rank,Length(v),galoisField );
X := IdentityMat( Length(v)-rank,galoisField );
rows := [];
for j in [ 1 .. a ] do
rows[j] := 0;
for i in [ 1 .. a ] do
if IsEmpty(K[j][i]) then
rows[j] := Length(E[j][b].rho) - Sum(E[j][b].rho);
else
rows[j] := DimensionsMat(K[j][i])[1];
break;
fi;
od;
od;
tmpR := 1;
for j in [ 1 .. a ] do
if rows[j]=0 then
continue;
fi;
tmpC := 1;
for i in [ 1 .. a ] do
if IsEmpty(K[j][i]) then
if IsEmpty(E[i][b].rho) then
#tmp := b;
tmp := DimensionsMat(mat)[1]/a;
else
tmp := Length( E[i][b].rho );
fi;
tmpC := tmpC + tmp; continue;
#K[j][i] := NullMat( rows[j],tmp,galoisField );
else
K[j][i] := TransposedMat( RRF( galoisField,
NullMat( Length(E[i][b].rho)-
DimensionsMat(K[j][i])[2],
DimensionsMat(K[j][i])[1],galoisField ),
TransposedMat(K[j][i]),E[i][b].rho ) );
fi;
D{[tmpR .. tmpR + DimensionsMat(K[j][i])[1]-1 ]}
{[tmpC .. tmpC + DimensionsMat(K[j][i])[2]-1 ]}
:= K[j][i];
tmpC := tmpC + DimensionsMat(K[j][i])[2];
od;
tmpR := tmpR + rows[j];
od;
D := TransposedMat( RRF( galoisField,X,
TransposedMat( CEX( galoisField,v,D )[1] ),v ) );
return rec( transformation:=B,remnant:=C,relations:=D,
pivotrows:=v,pivotcols:=w,rank:=rank);
end;