test/limsolve_ex.R

In kkdey/classtpx: MAP Estimation using topic models in a semi-supervised set up where there are few samples with known topic proportions or known to belong to some cluster exclusively and there are samples for which no such information are available.

## limSolve tutorial

E <- matrix(nrow = 3, ncol = 3, data = c(3, 1, 2, 2, 0, 0, 1, 0, 2))
F <- c(2, 1, 8)
solve(E, F)




E2 <- rbind(E, E[1, ] + E[2, ])
F2 <- c(F, F[1] + F[2])
solve(E2,F2)  ## gives error
Solve(E2, F2) ## gives the correct output: same as above for the determined system

## over-determined system

## Overdetermined systems contain more independent equations than unknowns
## the least squares solution can be extracted using the function lsei()

##  for equalities case

A <- matrix(nrow = 4, ncol = 3, data = c(3, 1, 2, 0, 2, 0, 0, 1, 1, 0, 2, 0))
B <- c(2, 1, 8, 3)
lsei(A = A, B = B, fulloutput = TRUE, verbose = FALSE)

## for equalities + inequalities

G <- matrix(nrow = 2, ncol = 3, byrow = TRUE, data = c(-1, 2, 0, 1, 0, -1))
H <- c(-3, 2)
lsei(A = A, B = B, G = G, H = H, verbose = FALSE)

## Under-determined system

## Underdetermined systems contain less independent equations than unknowns
## we aim for the most parsimonious solution

## equalities case

E <- matrix(nrow = 2, ncol = 3, data = c(3, 1, 2, 0, 1, 0))
F <- c(2, 1)
Solve(E, F)
ldei(E = E, F = F)$X

## equalities + inequalities case

E <- matrix(ncol = 4, byrow = TRUE, data = c(3, 2, 1, 4, 1, 1, 1, 1))
F <- c(2, 2)
G <-matrix(ncol = 4, byrow = TRUE, data = c(2, 1, 1, 1, -1, 3, 2, 1, -1, 0, 1, 0))
H <- c(-1, 2, 1)
ldei(E, F, G = G, H = H)$X