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4.22.2 coneViaInequalities
Syntax:
coneViaInequalities( intmat IE )
coneViaInequalities( intmat IE, intmat E )
coneViaInequalities( intmat IE, intmat E, int flags )
Type:
- cone
Purpose:
- cone consisting of all points x, such that IE*x >= 0 in each component
and (if stated) E*x = 0;
inequalities and (if stated) equations will be transformed, getting rid of
redundancies;
flags may range between 0,..,3 defining an upper and lower bit
(0=0*2+0, 1=0*2+1, 2=1*2+0, 3=1*2+1),
if higher bit is 1, then program assumes each inequality yields a facet,
if lower bit is 1, then program assumes the kernel of E is the span of the cone,
if either bit is 0, then program computes the information itself.
Example:
| | LIB"gfanlib.so";
// Let's define a cone in R^3 given by the following inequalities:
intmat IE[6][3]=
1,3,5,
1,5,3,
0,1,-1,
0,1,1,
1,0,0,
-1,0,0;
cone c=coneViaInequalities(IE);
c;
==> AMBIENT_DIM
==> 3
==> INEQUALITIES
==> 0,1,-1,
==> 0,1, 1,
==> 1,3, 5,
==> 1,5, 3
==> LINEAR_SPAN
==> -1,0,0
==>
// Note that the last two inequalities yield x1 = 0, hence also possible:
intmat IE[4][3]=
==> // ** redefining IE **
0,1,-1,
0,1,1;
intmat E[1][3]=
1,0,0;
cone c=coneViaInequalities(IE,E);
==> // ** redefining c **
c;
==> AMBIENT_DIM
==> 3
==> INEQUALITIES
==> 0,1,-1,
==> 0,1, 1
==> LINEAR_SPAN
==> 1,0,0
==>
// each inequalities gives rise to a facet
intmat IE[2][3]=
==> // ** redefining IE **
0,1,-1,
0,1,1;
intmat E[1][3]=
==> // ** redefining E **
1,0,0;
cone c=coneViaInequalities(IE,E,1);
==> // ** redefining c **
c;
==> AMBIENT_DIM
==> 3
==> INEQUALITIES
==> 0,1,-1,
==> 0,1, 1
==> LINEAR_SPAN
==> 1,0,0
==>
// and the kernel of E is the span of the cone
intmat IE[2][3]=
==> // ** redefining IE **
0,1,-1,
0,1,1;
intmat E[1][3]=
==> // ** redefining E **
1,0,0;
cone c=coneViaInequalities(IE,E,3);
==> // ** redefining c **
c;
==> AMBIENT_DIM
==> 3
==> FACETS
==> 0,1,-1,
==> 0,1, 1
==> LINEAR_SPAN
==> 1,0,0
==>
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