A table of data indexed by decisions

Sometimes a model needs a number from a table at a position that is not known yet: the distance between the first and the second stop of a route whose ordering the service is still choosing, or the price of an option that an integer variable picks. An ordinary R vector or matrix cannot be indexed this way. lookup_table() adds the data to the model under a name, and indexing the result with expressions, such as item_at() or an integer variable, builds an expression whose value is the entry at the positions the service chooses.

Usage

lookup_table(m, name, values)

# S3 method for class 'quicopt_table'
x[i, j]

Arguments

m

A model().

name

The table's name, unique within the model.

values

A numeric vector or matrix without NA.

x

A lookup table.

i, j

Positions in the table: numbers, or expressions such as item_at(). j only for a table made from a matrix.

Value

The table, to be indexed with [.

x[i] and x[i, j] return an expression with one element per position.

Details

A table made from a vector takes one index, and a table made from a matrix two. Each index may be a number, a vector of numbers, or an expression.

Unlike indexing an ordinary R matrix, the two indices are paired up element by element: km[1:4, 2:5] is a 4 x 4 block of a matrix km, but for a lookup table dist, dist[1:4, 2:5] has four elements, the entries [1, 2], [2, 3], [3, 4] and [4, 5]. This is what makes dist[item_at(1:4, P), item_at(2:5, P)] the four legs of a five-stop route.

The result is an ordinary expression: it can be multiplied by a cost, added up, or averaged with expectation(). An index that is not a whole number is rounded, and one outside the table is moved to the nearest end, so a continuous variable can be used as an index too.

A model with a lookup table is solved by a search, so its status is "heuristic". The whole table is sent with the model, so a very large table makes the request large.

Examples

# the distances between five stops along a road
position <- c(0, 3, 1, 4, 2)
m <- model()
dist  <- lookup_table(m, "dist", abs(outer(position, position, "-")))
route <- perm_var(m, "route", 5)
legs  <- dist[item_at(1:4, route), item_at(2:5, route)]    # the four legs of the route
minimize(m, sum(legs))

# the price of one of four options, picked by an integer variable
price  <- lookup_table(m, "price", c(3, 1, 4, 1.5))
choice <- int_var(m, "choice", lower = 1, upper = 4)
price[choice]
#> price[choice]