Constraint

`Constraint`

Returned by Model.constraint. Rows over an expression's frame, bounded by a right-hand side.

Model.constraint(name, relation, where=None, over=None)

Argument	Meaning
`name`	the name `Solution.dual` reads it back by
`relation`	an expression, a sense and a right-hand side
`where`	a domain intersecting the rows
`over`	the rows, given explicitly

Member	Returns
`n_rows`	the number of rows it produces
`nnz`	the number of coefficients they contain
`labels_at(positions)`	the labels of the rows at those positions, per free dimension
`position_of(coords)`	the position of the row at a coordinate, one label per free dimension
`row_at(position)`	the columns, the coefficients and the lower and upper bound of the row at that position
`row_of(name)` on the `Assembled`	the position of those rows in the matrix

A row derived from the terms exists where every term has a value and the right-hand side has a value. A coefficient absent inside a sum removes a term and keeps the row. A term absent along a free dimension removes the row: a row missing one of its terms would express a constraint that was not written.

over= gives the rows explicitly instead, and a term covering some of them contributes where it has values. A condition given with where= intersects the row domain, and a row outside the condition is not produced.

The expression is symbolic, and the constraint stores the term list and no block. The expression is materialised once to compute its shape and once to write it, and it stores nothing between the two.

import numpy as np
from nimopt import Model, Param, Set, Sum

P = Set("P", np.array(["lisbon", "porto"]))
W = Set("W", np.array(["berlin", "paris", "rome"]))
supply = Param.from_dense("supply", (P,), np.array([30.0, 25.0]))

m = Model("transport")
x = m.var("x", (P, W))

rows = m.constraint("supply", Sum(W, x[P, W]) <= supply[P])
print(rows.n_rows, rows.nnz)
print(m.assemble().row_of("supply"))

Run this example

Output

2 6
slice(0, 2, None)

The right-hand side is a number, applied to every row, or a parameter over exactly the free dimensions of the constraint. A parameter gives each row its own value. A parameter over other dimensions raises ValueError, and the message gives both sets of dimensions.

import numpy as np
from nimopt import Model, Param, Set, Sum

P = Set("P", np.array(["lisbon", "porto"]))
W = Set("W", np.array(["berlin", "paris", "rome"]))
demand = Param.from_dense("demand", (W,), np.array([20.0, 15.0, 15.0]))

m = Model("transport")
x = m.var("x", (P, W))

m.constraint("supply", Sum(W, x[P, W]) <= demand[W])

Run this example

Raises ValueError

ValueError: constraint 'supply' has free dimensions ('P',); its right-hand side 'demand' is over ('W',)

Constraint​

`Constraint`