Generate Constraint Sets

Generate sets of constraint matrices (constr), right hand side elements, and numbers of equality constraints (nec) with a predefined structure

constrSet(n, set = c("sequence", "seqcontrol", "lplateau", "uplateau",
  "downturn", "williams"), direction = c("increase", "decrease"), base = 1)

Arguments

n	a (possibly named) vector of sample sizes for each group.
set	character string defining the type of constraints; one of "sequence", "seqcontrol", "lplateau", "uplateau", or "downturn"
direction	direction of the inequality constraints, either "increase" or "decrease"
base	column of the constraint matrix representing a control group

Value

a list with slots constr, rhs, and nec for each constraint definition

See also

orlm, constrMat

Examples

n <- c(10,20,30,40)
constrSet(n, set="sequence")
#> $`1<2`
#> $`1<2`$constr
#>       1 2 3 4
#> [1,] -1 1 0 0
#> 
#> $`1<2`$rhs
#> [1] 0
#> 
#> $`1<2`$nec
#> [1] FALSE
#> 
#> 
#> $`1<2<3`
#> $`1<2<3`$constr
#>       1  2 3 4
#> [1,] -1  1 0 0
#> [2,]  0 -1 1 0
#> 
#> $`1<2<3`$rhs
#> [1] 0 0
#> 
#> $`1<2<3`$nec
#> [1] FALSE FALSE
#> 
#> 
#> $`1<2<3<4`
#> $`1<2<3<4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1<2<3<4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2<3<4`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $unconstrained
#> $unconstrained$constr
#>      1 2 3 4
#> [1,] 0 0 0 0
#> 
#> $unconstrained$rhs
#> [1] 0
#> 
#> $unconstrained$nec
#> [1] FALSE
#> 
#> 
constrSet(n, set="seqcontrol")
#> $`1<2`
#> $`1<2`$constr
#>       1 2 3 4
#> [1,] -1 1 0 0
#> 
#> $`1<2`$rhs
#> [1] 0
#> 
#> $`1<2`$nec
#> [1] FALSE
#> 
#> 
#> $`1<2|1<3`
#> $`1<2|1<3`$constr
#>       1 2 3 4
#> [1,] -1 1 0 0
#> [2,] -1 0 1 0
#> 
#> $`1<2|1<3`$rhs
#> [1] 0 0
#> 
#> $`1<2|1<3`$nec
#> [1] FALSE FALSE
#> 
#> 
#> $`1<2|1<3|1<4`
#> $`1<2|1<3|1<4`$constr
#>       1 2 3 4
#> [1,] -1 1 0 0
#> [2,] -1 0 1 0
#> [3,] -1 0 0 1
#> 
#> $`1<2|1<3|1<4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2|1<3|1<4`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $unconstrained
#> $unconstrained$constr
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> 
#> $unconstrained$rhs
#> [1] 0
#> 
#> $unconstrained$nec
#> [1] FALSE
#> 
#> 
constrSet(n, set="lplateau")
#> $`1=2=3=4`
#> $`1=2=3=4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1=2=3=4`$rhs
#> [1] 0 0 0
#> 
#> $`1=2=3=4`$nec
#> [1] TRUE TRUE TRUE
#> 
#> 
#> $`1=2=3<4`
#> $`1=2=3<4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1=2=3<4`$rhs
#> [1] 0 0 0
#> 
#> $`1=2=3<4`$nec
#> [1]  TRUE  TRUE FALSE
#> 
#> 
#> $`1=2<3<4`
#> $`1=2<3<4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1=2<3<4`$rhs
#> [1] 0 0 0
#> 
#> $`1=2<3<4`$nec
#> [1]  TRUE FALSE FALSE
#> 
#> 
#> $`1<2<3<4`
#> $`1<2<3<4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1<2<3<4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2<3<4`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $unconstrained
#> $unconstrained$constr
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> 
#> $unconstrained$rhs
#> [1] 0
#> 
#> $unconstrained$nec
#> [1] FALSE
#> 
#> 
constrSet(n, set="uplateau")
#> $`1<2<3<4`
#> $`1<2<3<4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1<2<3<4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2<3<4`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $`1<2<3=4`
#> $`1<2<3=4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1<2<3=4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2<3=4`$nec
#> [1] FALSE FALSE  TRUE
#> 
#> 
#> $`1<2=3=4`
#> $`1<2=3=4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1<2=3=4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2=3=4`$nec
#> [1] FALSE  TRUE  TRUE
#> 
#> 
#> $`1=2=3=4`
#> $`1=2=3=4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1=2=3=4`$rhs
#> [1] 0 0 0
#> 
#> $`1=2=3=4`$nec
#> [1] TRUE TRUE TRUE
#> 
#> 
#> $unconstrained
#> $unconstrained$constr
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> 
#> $unconstrained$rhs
#> [1] 0
#> 
#> $unconstrained$nec
#> [1] FALSE
#> 
#> 
constrSet(n, set="downturn")
#> $`1<2<3<4`
#> $`1<2<3<4`$constr
#>       1  2  3 4
#> [1,] -1  1  0 0
#> [2,]  0 -1  1 0
#> [3,]  0  0 -1 1
#> 
#> $`1<2<3<4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2<3<4`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $`1<2<3>4`
#> $`1<2<3>4`$constr
#>       1  2 3  4
#> [1,] -1  1 0  0
#> [2,]  0 -1 1  0
#> [3,]  0  0 1 -1
#> 
#> $`1<2<3>4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2<3>4`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $`1<2>3>4`
#> $`1<2>3>4`$constr
#>       1 2  3  4
#> [1,] -1 1  0  0
#> [2,]  0 1 -1  0
#> [3,]  0 0  1 -1
#> 
#> $`1<2>3>4`$rhs
#> [1] 0 0 0
#> 
#> $`1<2>3>4`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $unconstrained
#> $unconstrained$constr
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> 
#> $unconstrained$rhs
#> [1] 0
#> 
#> $unconstrained$nec
#> [1] FALSE
#> 
#> 
constrSet(n, set="williams")
#> $`1 < 2`
#> $`1 < 2`$constr
#>       1 2 3 4
#> [1,] -1 1 0 0
#> 
#> $`1 < 2`$rhs
#> [1] 0
#> 
#> $`1 < 2`$nec
#> [1] FALSE
#> 
#> 
#> $`1 < ave(2,3)`
#> $`1 < ave(2,3)`$constr
#>       1   2   3 4
#> [1,] -1 1.0 0.0 0
#> [2,] -1 0.4 0.6 0
#> 
#> $`1 < ave(2,3)`$rhs
#> [1] 0 0
#> 
#> $`1 < ave(2,3)`$nec
#> [1] FALSE FALSE
#> 
#> 
#> $`1 < ave(2,3,4)`
#> $`1 < ave(2,3,4)`$constr
#>       1         2         3         4
#> [1,] -1 1.0000000 0.0000000 0.0000000
#> [2,] -1 0.4000000 0.6000000 0.0000000
#> [3,] -1 0.2222222 0.3333333 0.4444444
#> 
#> $`1 < ave(2,3,4)`$rhs
#> [1] 0 0 0
#> 
#> $`1 < ave(2,3,4)`$nec
#> [1] FALSE FALSE FALSE
#> 
#> 
#> $unconstrained
#> $unconstrained$constr
#>      1 2 3 4
#> [1,] 0 0 0 0
#> 
#> $unconstrained$rhs
#> [1] 0
#> 
#> $unconstrained$nec
#> [1] FALSE
#> 
#>