Calculate the corner points for the polytope Ax<=b.
Arguments
- A
Constraint matrix.
- b
Right hand side.
- type
A character vector of same length as number of variables. If entry k is 'i' variable \(k\) must be integer and if 'c' continuous.
- nonneg
A boolean vector of same length as number of variables. If entry k is TRUE then variable k must be non-negative.
Author
Lars Relund lars@relund.dk
Examples
A <- matrix( c(3,-2, 1, 2, 4,-2,-3, 2, 1), nc = 3, byrow = TRUE)
b <- c(10, 12, 3)
cornerPoints(A, b, type = c("c", "c", "c"))
#> x1 x2 x3
#> [1,] 4.000000 4.250 6.5
#> [2,] 1.166667 0.000 6.5
#> [3,] 0.000000 0.000 3.0
#> [4,] 4.000000 1.000 0.0
#> [5,] 0.750000 2.625 0.0
#> [6,] 0.000000 1.500 0.0
#> [7,] 3.333333 0.000 0.0
#> [8,] 0.000000 0.000 0.0
cornerPoints(A, b, type = c("i", "i", "i"))
#> x1 x2 x3
#> [1,] 2 0 4
#> [2,] 2 1 6
#> [3,] 1 0 6
#> [4,] 2 3 2
#> [5,] 2 2 0
#> [6,] 1 2 0
#> [7,] 3 0 1
#> [8,] 3 0 0
#> [9,] 4 1 0
#> [10,] 2 3 3
#> [11,] 4 4 6
#> [12,] 3 3 6
#> [13,] 0 1 0
#> [14,] 0 0 0
#> [15,] 0 0 3
#> [16,] 0 1 1
cornerPoints(A, b, type = c("i", "c", "c"))
#> x1 x2 x3
#> [1,] 0 0.00 0.0
#> [2,] 0 1.50 0.0
#> [3,] 0 0.00 3.0
#> [4,] 1 2.50 0.0
#> [5,] 1 2.75 0.5
#> [6,] 2 1.25 6.5
#> [7,] 2 0.00 4.0
#> [8,] 1 0.00 6.0
#> [9,] 3 0.00 1.0
#> [10,] 3 0.00 0.0
#> [11,] 4 1.00 0.0
#> [12,] 4 4.25 6.5