from application polytope
A linear program specified by a linear or abstract objective function
Scalar
: numeric type of variables and objective function
ABSTRACT_OBJECTIVE
Abstract objective function. Defines a direction for each edge such that each non-empty face has a unique source and a unique sink. The i-th element is the value of the objective function at vertex number i. Only defined for bounded polytopes.
DIRECTED_BOUNDED_GRAPH
Subgraph of BOUNDED_GRAPH
. Consists only of directed arcs along which the value of the objective function increases.
DIRECTED_GRAPH
Subgraph of GRAPH
. Consists only of directed arcs along which the value of the objective function increases.
The following defines a LinearProgram together with a linear objective for the centered square with side length 2. The directed graph according to the linear objective is stored in a new variable and the corresponding edges are printend.
> $c = new Vector([0, 1, 0]); > $p = cube(2); > $p->LP(LINEAR_OBJECTIVE=>$c); > $g = $p->LP->DIRECTED_GRAPH; > print $g->EDGES; {0 1} {2 3}
LINEAR_OBJECTIVE
Linear objective function. In d-space a linear objective function is given by a (d+1)-vector. The first coordinate specifies a constant that is added to the resulting value.
MAXIMAL_FACE
Indices of vertices at which the maximum of the objective function is attained.
The following defines a LinearProgram together with a linear objective for the centered square with side length 2 and asks for the maximal face:
> $c = new Vector([0, 1, 0]); > $p = cube(2); > $p->LP(LINEAR_OBJECTIVE=>$c); > print $p->LP->MAXIMAL_FACE; {1 3}
MAXIMAL_VALUE
Maximum value of the objective function. Negated if linear problem is unbounded.
Scalar
The following defines a LinearProgram together with a linear objective for the centered square with side length 2 and asks for the maximal value:
> $c = new Vector([0, 1, 0]); > $p = cube(2); > $p->LP(LINEAR_OBJECTIVE=>$c); > print $p->LP->MAXIMAL_VALUE; 1
The following defines a LinearProgram together with a linear objective with bias 3 for the centered square with side length 4 and asks for the maximal value:
> $c = new Vector([3, 1, 0]); > $p = cube(2,2); > $p->LP(LINEAR_OBJECTIVE=>$c); > print $p->LP->MAXIMAL_VALUE; 5
The following defines a LinearProgram together with a linear objective for the positive quadrant (unbounded) and asks for the maximal value:
> $c = new Vector([0, 1, 1]); > $p = facet_to_infinity(simplex(2),0); > $p->LP(LINEAR_OBJECTIVE=>$c); > print $p->LP->MAXIMAL_VALUE; inf
MAXIMAL_VERTEX
Coordinates of a (possibly not unique) affine vertex at which the maximum of the objective function is attained.
MINIMAL_FACE
Similar to MAXIMAL_FACE
.
The following defines a LinearProgram together with a linear objective for the centered square with side length 2 and asks for the minimal face:
> $c = new Vector([0, 1, 0]); > $p = cube(2); > $p->LP(LINEAR_OBJECTIVE=>$c); > print $p->LP->MINIMAL_FACE; {0 2}
MINIMAL_VALUE
Similar to MAXIMAL_VALUE
.
Scalar
The following defines a LinearProgram together with a linear objective for the centered square with side length 2 and asks for the minimal value:
> $c = new Vector([0, 1, 0]); > $p = cube(2); > $p->LP(LINEAR_OBJECTIVE=>$c); > print $p->LP->MINIMAL_VALUE; -1
The following defines a LinearProgram together with a linear objective with bias 3 for the centered square with side length 4 and asks for the minimal value:
> $c = new Vector([3, 1, 0]); > $p = cube(2,2); > $p->LP(LINEAR_OBJECTIVE=>$c); > print $p->LP->MINIMAL_VALUE; 1
MINIMAL_VERTEX
Similar to MAXIMAL_VERTEX
.
RANDOM_EDGE_EPL
Expected average path length for a simplex algorithm employing “random edge” pivoting strategy.
VERTEX_IN_DEGREES()
Array of in-degrees for all nodes of DIRECTED_GRAPH
or numbers of objective decreasing edges at each vertex
VERTEX_OUT_DEGREES()
Array of out-degrees for all nodes of DIRECTED_GRAPH
or numbers of objective increasing edges at each vertex