naginterfaces.library.mip.ilp_​info

naginterfaces.library.mip.ilp_info(n, m, comm)[source]

ilp_info extracts more information associated with the solution of an integer programming problem computed by ilp_dense().

For full information please refer to the NAG Library document for h02bz

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/h/h02bzf.html

Parameters
nint

This must be the same argument as supplied to ilp_dense().

mint

This must be the same argument as supplied to ilp_dense().

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to ilp_dense().

Returns
blfloat, ndarray, shape

If ilp_dense() exits with the function exits successfully or = 7 or 9, the values in the array contain the lower bounds imposed on the integer solution for all the constraints. The first elements contain the lower bounds on the variables, and the next elements contain the lower bounds for the general linear constraints (if any).

bufloat, ndarray, shape

If ilp_dense() exits with the function exits successfully or = 7 or 9, the values in the array contain the upper bounds imposed on the integer solution for all the constraints. The first elements contain the upper bounds on the variables, and the next elements contain the upper bounds for the general linear constraints (if any).

clamdafloat, ndarray, shape

If ilp_dense() exits with the function exits successfully or = 7 or 9, the values in the array contain the values of the Lagrange-multipliers for each constraint with respect to the current working set. The first elements contain the multipliers (reduced costs) for the bound constraints on the variables, and the next elements contain the multipliers (shadow costs) for the general linear constraints (if any).

istateint, ndarray, shape

If ilp_dense() exits with the function exits successfully or = 7 or 9, the values in the array indicate the status of the constraints in the working set at an integer solution. Otherwise, indicates the composition of the working set at the final iterate. The significance of each possible value of is as follows.

Meaning

The constraint violates its lower bound by more than (the feasibility tolerance, see ilp_dense()).

The constraint violates its upper bound by more than .

The constraint is satisfied to within , but is not in the working set.

This inequality constraint is included in the working set at its lower bound.

This inequality constraint is included in the working set at its upper bound.

This constraint is included in the working set as an equality. This value of can occur only when .

This corresponds to an integer solution being declared with being temporarily fixed at its current value. This value of can occur only when the function exits successfully or = 7 or 9 on exit from ilp_dense().

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

ilp_info extracts the following information associated with the solution of an integer programming problem computed by ilp_dense(). The upper and lower bounds used for the solution, the Lagrange-multipliers (costs), and the status of the variables at the solution.

In the branch and bound method employed by ilp_dense(), the arrays and are used to impose restrictions on the values of the integer variables in each sub-problem. That is, if the variable is restricted to take value in a particular sub-problem, then is set in the sub-problem. Thus, on exit from this function, some of the elements of and which correspond to integer variables may contain these imposed values, rather than those originally supplied to ilp_dense().