mtl: homegene solution

From: Hayati Ayguen (Ayguen_at_[hidden])
Date: 2001-07-15 10:52:16

hello,

being new to mtl-2.1.2-19, i have following questions:

1-
is it possible to let mtl calculate the (in)homogene solution space of a
matrix A having rank(A) < min(A.nrows(),A.ncols()) with A.nrows() !=
A.ncols() ?

2-
A being an incidence matrix describing a graph:

           { -1 , if  i == start_node( edge(j) )
  a(i,j) = { +1 , if  i == end_node( edge(j) )
           {  0 , else

would it be possible to use a sparse matrix containing no double but
integer elements for the problem above?

example for a simple small graph:
=================================

   N1  b   N2  c   N3
   +-------+-------+
   |       |       |
   |a      |g      |d
   |       |       |
   +-------+-------+
   N6  f   N5  e   N4

A(6,7) * x(1,7) = b(1,6)

specially b = transposed( 0, 0, 0, 0, 0, 0 ).

so solving A * x = 0  with following A

    [ -1 -1  0  0  0  0  0  |  0 ]
    [  0  1 -1  0  0  0 -1  |  0 ]
A = [  0  0  1 -1  0  0  0  |  0 ]
    [  0  0  0  1 -1  0  0  |  0 ]
    [  0  0  0  0  1 -1  1  |  0 ]
    [  1  0  0  0  0  1  0  |  0 ]

should led to the solution space

              [ 0 ]   [  1  0 ]
              [ 0 ]   [ -1  0 ]
              [ 0 ]   [ -1  1 ]   [ alpha1 ]
X = x0 + X1 = [ 0 ] + [ -1  1 ] * [ alpha2 ]
              [ 0 ]   [ -1  1 ]
              [ 0 ]   [ -1  0 ]
              [ 0 ]   [  0 -1 ]

for any transposed(alpha1, alpha2)

thanks in advance

Hayati Ayguen