 # Boost :

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