Dom::SparseMatrix_LinBox – Interface to the sparse matrix C++ library LinBox
Dom::SparseMatrix_LinBox(R) creates a domain for sparse matrices over the ring R, with computations done by http://linalg.org/linbox.
Creating the Type
Dom::SparseMatrix_LinBox(R)
Parameters:
|
R: |
a ring |
Details:
Experimental. You need to have Linbox installed separately. More precisely, our interface currently uses the little binary smithform_gap that Jean-Guillaume Dumas wrote for his gap interface. All you have to do is to download the appropriate homology binary package form http://www.linalg.org/gap.html, and put the included smithform_gap binary somewhere on your path.
Creating Elements
SparseMatrix_LinBox(n)(l)
Parameters:
|
l: |
|
Categories
Entries
|
"linbox" |
the name of the LinBox executable. |
Access Methods
matdim – size of a matrix
(Dom::SparseMatrix_LinBox(R))::matdim({dom})
Returns the size of the matrix as a list of two integers [nrows, ncols].
rank – rank of a matrix
(Dom::SparseMatrix_LinBox(R))::rank(dom m)
Returns the rank of the matrix. Computed by LinBox using blackbox method.
rankGauss – rank of a matrix
(Dom::SparseMatrix_LinBox(R))::rankGauss(dom m)
Returns the rank of the matrix. Computed by LinBox using gauss elimination.
characteristicColumns – characteristic columns of a matrix
(Dom::SparseMatrix_LinBox(R))::characteristicColumns(dom m)
Returns a list of indexes of columns of the matrix which are linearly independent. Computed by LinBox using elimination.
Here is a sample session:
Z5 := Dom::IntegerMod(5):
M:=Dom::SparseMatrix_LinBox(Z5):
M::verboseLevel := "10 10":
m:=M():
m:=m::appendRow([[4,Z5(3)]]):
m:=m::appendRow([[2,Z5(7)],[3,Z5(4)]]):
m:=m::appendRow([[1,Z5(3)],[2,Z5(8)]]):
m:=m::fix();
m::matdim();
m::file();
fprint(Unquoted, 0, shell::system("cat ".m::file()));
m::rankBlackBox(); // broken
m::rankGauss();
m::characteristicColumns();
m::_delete():
[3, 4]
"/tmp/matrix"
0 0 M
1 4 3
2 2 2
2 3 4
3 1 3
3 2 3
0 0 0
#I:D Wiedemann: Computing rank via Wiedemann algorithm
#I:D Wiedemann: Computing rank mod 5 in GF(15625).
#I:D Wiedemann: Rank 0, computed deterministically.
#I:T Wiedemann: cpu time : 0.13 seconds
#I:T Wiedemann: sys time : 0 seconds
#I:T Wiedemann: real time : 0.168739 seconds
3
#I:D Gauss Reordering: 4 x 3
#I:R Gauss Reordering: Rank : 3 over GF(5)
#I:T Gauss Reordering: cpu time : 0 seconds
#I:T Gauss Reordering: sys time : 0 seconds
#I:T Gauss Reordering: real time : 9.0003e-05 seconds
3
#I:D Gauss Reordering: 4 x 3
#I:R Gauss Reordering: Rank : 3 over GF(5)
#I:T Gauss Reordering: cpu time : 0 seconds
#I:T Gauss Reordering: sys time : 0 seconds
#I:T Gauss Reordering: real time : 0.00518698 seconds
[0, 1, 3]