R Under development (unstable) (2023-12-13 r85679 ucrt) -- "Unsuffered Consequences"
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> 
>  library(rcdd)
If you want correct answers, use rational arithmetic.
See the Warnings sections in help pages for
    functions that do computational geometry.
> 
>  ### optimal solution exists -- file samplelp1.ine in cddlib ###
> 
>  hrep <- rbind(
+  c(0, 1,  1,  0,  0),
+  c(0, 1,  0,  1,  0),
+  c(0, 1,  0,  0,  1),
+  c(0, 1, -1,  0,  0),
+  c(0, 1,  0, -1,  0),
+  c(0, 1,  0,  0, -1))
> 
>  a <- c(1, 1, 1)
> 
>  lpcdd(hrep, a, minimize = FALSE)
$solution.type
[1] "Optimal"

$primal.solution
[1] 1 1 1

$dual.solution
[1] 0 0 0 1 1 1

$optimal.value
[1] 3

> 
>  ### optimal solution exists -- file samplelp2.ine in cddlib ###
> 
>  hrep <- rbind(
+  c("0",   "0", "1",  "1",  "0",  "0"),
+  c("0",   "0", "0",  "2",  "0",  "0"),
+  c("1",   "3", "0", "-1",  "0",  "0"),
+  c("1", "9/2", "0",  "0", "-1", "-1"))
> 
>  a <- c("2", "3/5", "0", "0")
> 
>  lpcdd(hrep, a)
$solution.type
[1] "Optimal"

$primal.solution
[1] "-3"  "3"   "9/2" "0"  

$dual.solution
[1] "-2"   "0"    "-7/5" "0"   

$optimal.value
[1] "-21/5"

> 
>  ### primal inconsistent problem ###
> 
>  hrep <- rbind(
+  c("0",  "0",  "1",  "0"),
+  c("0",  "0",  "0",  "1"),
+  c("0", "-2", "-1", "-1"))
> 
>  a <- c("1", "1")
> 
>  lpcdd(hrep, a)
$solution.type
[1] "Inconsistent"

$dual.direction
[1] "1" "1" "1"

> 
>  lpcdd(q2d(hrep), q2d(a))
$solution.type
[1] "Inconsistent"

$dual.direction
[1] 1 1 1

> 
>  ### dual inconsistent problem ###
> 
>  hrep <- rbind(
+  c("0", "0", "1", "0"),
+  c("0", "0", "0", "1"))
> 
>  a <- c("1", "1")
> 
>  lpcdd(hrep, a, minimize = FALSE)
$solution.type
[1] "DualInconsistent"

$primal.direction
[1] "1" "0"

> 
>  lpcdd(q2d(hrep), q2d(a), minimize = FALSE)
$solution.type
[1] "DualInconsistent"

$primal.direction
[1] 1 0

> 
>  ### negative Lagrange multipliers
> 
>  # needed because of the change in R function "sample" in R-devel
>  suppressWarnings(RNGversion("3.5.2"))
> 
>  set.seed(42)
> 
>  d <- 20
>  k <- 6
>  foo <- matrix(sample(seq(-1000, 1000), k * d, replace = TRUE), ncol = d)
>  foo <- rbind(foo, diag(d))
>  foo <- rbind(foo, - diag(d))
>  foo <- cbind(c(rep(0, k), rep(1, 2 * d)), foo)
>  foo <- cbind(c(rep(1, k), rep(0, 2 * d)), foo)
> 
>  w <- sample(seq(-1000, 1000), d, replace = TRUE)
> 
>  out <- lpcdd(d2q(foo), d2q(w))
> 
>  out$solution.type
[1] "Optimal"
> 
>  q2d(out$primal.solution)
 [1]  0.006018942 -0.683091012 -1.000000000 -1.000000000 -0.110030285
 [6] -1.000000000 -1.000000000 -1.000000000 -0.613259326 -1.000000000
[11] -1.000000000 -1.000000000 -0.683061014 -1.000000000 -1.000000000
[16] -0.815424962 -1.000000000  1.000000000 -1.000000000 -1.000000000
> 
>  x <- out$primal.solution
>  lambda <- qneg(out$dual.solution)   ### see tutorial
>  l <- foo[ , 1]
>  b <- foo[ , 2]
>  v <- foo[ , - c(1, 2)]
> 
>  ##### check gradient of Lagrangian function zero
>  all(qsign(qmq(w, qmatmult(rbind(lambda), v))) == 0)
[1] TRUE
> 
>  ##### check primal feasibility
>  slack <- qpq(b, qmatmult(v, cbind(x)))
>  all(qsign(slack) >= 0)
[1] TRUE
> 
>  ##### check dual feasibility
>  all(qsign(lambda) * (1 - l) >= 0)
[1] TRUE
> 
>  ##### check complementary slackness
>  all(qsign(slack) * qsign(lambda) == 0)
[1] TRUE
> 
>  ##### number of negative lagrange multipliers (shows exercised relevant code)
>  sum(qsign(lambda) < 0)
[1] 4
> 
> proc.time()
   user  system elapsed 
   0.10    0.07    0.17