Function to translate linear equations into matrix

问题:

I was wondering whether there exist any packages or other pre-built solutions for R that are capable of translating sets of linear equations into matrix form (e.g. for solution via the Gauss Seidel algorithm), similar to the equationsToMatrix(eqns,vars) function in Matlab?

An example from Matlab:

[A, b] = equationsToMatrix([x - y == 0, x + 2*y == 3, [x, y])

A =
[ 1, -1]
[ 1, 2]

b =
  0
  3

Suggestions for building blocks would be very helpful, too.

回答1:

1) This is not exactly what you are asking for but maybe it will help anyways:

library(Ryacas)
x <- Sym("x")
y <- Sym("y")
Simplify(Solve(List(x - y == 0, x + 2*y == 3), List(x, y)))

giving:

expression(list(list(x - y == 0, y - 1 == 0)))

2) If we know these are linear equations exactly of the form shown in the question then try this. The two strapply calls perform matches of the regular expression against the components of args, capture the strings matched by the portions of the regular expressions within parentheses and call the function specified as the third argument with those captured strings as arguments. We combine the strapply outputs using rbind.fill and replace any NAs it generates with zero.

library(gsubfn) # strapply
library(plyr) # rbind.fill

eqn <- function(...) {
  args <- c(...)
  x2num <- function(x, y) { # determine coefficient value as a numeric
       z <- gsub(" ", "", x)
       setNames(if (z == "-") -1 else if (z == "") 1 else as.numeric(z), y)
  }
  lhs <- strapply(args, "(-? *\\d*)[ *]*([a-z])", x2num)
  lhs <- do.call(rbind.fill, lapply(lhs, function(x) as.data.frame(t(x))))
  lhs <- as.matrix(lhs)
  lhs[] <- ifelse(is.na(lhs), 0, lhs)
  list(lhs = lhs, rhs = strapply(args, "== *(\\d)", as.numeric, simplify = TRUE))
}

# test it out
eqn("x - y == 0", "2*y == 3")

giving:

$lhs
     x  y
[1,] 1 -1
[2,] 0  2

$rhs
[1] 0 3

Update: Generalized so that now not all variables need to be in each equation and also variables can be in different orders in different equations.

回答2:

Can't tell from your example whether you just want simple linear equation solving or a more general system solver. If the latter, take a look at the BB and nleqslv packages.

You might also be interested in a "wrapper" tool written by some seriously twisted mind :-) , in the package ktsolve . This last tool lets you set up an arbitrary set of equations and back-solve for any desired set of variables.