Other Features

Status Functions

The status function returns a symbol indicating the state of the tableau, T. The result of status(T) is one of the following:

:no_basis – no basis has been established for this tableau.
:feasible – the tableau is in a feasible state, but not optimal (rhs is nonnegative).
:infeasible – the tableau is in an infeasible state (rhs contains negative values).
:optimal – the tableau has reached a global minimization point. This supercedes :feasible.
:unbounded – the tableau has reached a feasible state, but there are no pivots; the objective function value can be arbitrarily negative. This supercedes :feasible.

These functions are superfluous but may be convenient:

in_feasible_state(T) returns true if the current basic vector is in the feasible region (including if at optimality).
in_optimal_state(T) returns true if the tableau has reached an optimal (minimal) state.

The functions make_standard and make_canonical convert a Tableau from standard to canonical, and from canonical to standard, respectively. A new Tableau is returned unless the input Tableau is already in the desired form.

make_canonical adds slack variables to create a new Tableau that is in standard form and has the same solution.
make_standard replaces each equality constraint of the form ax=b with a pair of inequality constraints ax≥b and -ax≥-b.

Miscellaneous Functions

basic_vector(T) returns the vector in which the nonbasic variables have been set to zero.
dual_basic_vector(T) returns the dual basic vector.
header(T) returns the top row of T (negative reduced costs). Does not include the 1 in column 0 nor the value in the last column.
get_Abc(T) returns the original matrix A and the vectors b and c for the standard presentation of the linear program.
get_basis(T) returns the column numbers of the current basis.
is_infeasible(T) returns true if the linear program's feasible region is empty.
is_unbounded(T) returns true if the linear program is unbounded (below).
rhs(T) returns the righthand column of T (from row 1 onward – does not include the value in row 0).
value(T) returns the objective function value of the current basic vector.
value(T,x) returns the objective function value for the vector x. May also be invoked as T(x).

Return to Start

The function restore! returns the tableau to its state when it was constructed.

julia> T
┌──────────┬───┬─────┬─────┬────────┬─────┬─────────┬──────────┐
│          │ z │ x_1 │ x_2 │    x_3 │ x_4 │     x_5 │      RHS │
│ Obj Func │ 1 │   0 │   0 │ -25/47 │   0 │ -110/47 │ 13500/47 │
├──────────┼───┼─────┼─────┼────────┼─────┼─────────┼──────────┤
│   Cons 1 │ 0 │   1 │   0 │   1/47 │   0 │   -5/47 │   400/47 │
│   Cons 2 │ 0 │   0 │   0 │ -25/47 │   1 │  -16/47 │  -600/47 │
│   Cons 3 │ 0 │   0 │   1 │  -5/47 │   0 │    3/94 │   350/47 │
└──────────┴───┴─────┴─────┴────────┴─────┴─────────┴──────────┘


julia> restore!(T)
┌──────────┬───┬─────┬─────┬─────┬─────┬─────┬─────┐
│          │ z │ x_1 │ x_2 │ x_3 │ x_4 │ x_5 │ RHS │
│ Obj Func │ 1 │ -25 │ -10 │   0 │   0 │   0 │   0 │
├──────────┼───┼─────┼─────┼─────┼─────┼─────┼─────┤
│   Cons 1 │ 0 │   3 │  10 │  -1 │   0 │   0 │ 100 │
│   Cons 2 │ 0 │   5 │   6 │   0 │  -1 │   0 │ 100 │
│   Cons 3 │ 0 │  10 │   2 │   0 │   0 │  -1 │ 100 │
└──────────┴───┴─────┴─────┴─────┴─────┴─────┴─────┘

LaTeX Output

Using LatexPrint users can get the code for pasting into a LaTeX document.

julia> using LatexPrint

julia> T
┌──────────┬───┬─────┬─────┬─────┬─────┬──────┬─────┐
│          │ z │ x_1 │ x_2 │ x_3 │ x_4 │  x_5 │ RHS │
│ Obj Func │ 1 │   0 │  -3 │  -2 │   8 │    0 │   9 │
├──────────┼───┼─────┼─────┼─────┼─────┼──────┼─────┤
│   Cons 1 │ 0 │   1 │ 1/2 │   0 │ 9/2 │ -1/2 │ 9/2 │
│   Cons 2 │ 0 │   0 │ 1/2 │  -1 │ 1/2 │  3/2 │ 5/2 │
└──────────┴───┴─────┴─────┴─────┴─────┴──────┴─────┘


julia> lap(T)
\begin{tabular}{|c|ccccc|c|}\hline 
{\Large\strut}$z$ &$x_{1}$ & $x_{2}$ & $x_{3}$ & $x_{4}$ & $x_{5}$ & RHS \\
{\Large\strut}$1$ & $0$ & $-3$ & $-2$ & $8$ & $0$ & $9$\\
\hline 
{\Large\strut}$0$ & $1$ & $\frac{1}{2}$ & $0$ & $\frac{9}{2}$ & $\frac{-1}{2}$ & $\frac{9}{2}$\\
{\Large\strut}$0$ & $0$ & $\frac{1}{2}$ & $-1$ & $\frac{1}{2}$ & $\frac{3}{2}$ & $\frac{5}{2}$\\
\hline 
\end{tabular}

Here is the LaTeX output:

Other Public Functions

Presently, these functions are exported in SimplexTableaux but might be hidden in future releases. They are not likely to be useful to the users of this module. See the doc strings for more information: