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### determine if an expression `x' can be interpreted as numeric
is_num <- function(x) {
if (length(x) == 1) return(is.numeric(x))
if (length(x) == 2) return(is.name(x[[1]]) && is.numeric(x[[2]]))
return(FALSE)
}
### extract coefficients and variable names
coefs <- function(ex) {
### `a'
if (length(ex) == 1 && !is_num(ex))
return(list(coef = 1, var = as.character(ex)))
### `-a'
if (length(ex) == 2 && (ex[[1]] == "-" && !is_num(ex[[2]])))
return(list(coef = -1, var = as.character(ex[[2]])))
if (length(ex) == 3) {
### `2 * a'
if (ex[[1]] == "*" && (is_num(ex[[2]]) && !is_num(ex[[3]])))
return(list(coef = eval(ex[[2]]), var = as.character(ex[[3]])))
cf <- coefs(ex[[3]])
if (ex[[1]] == "-")
cf$coef <- cf$coef * (-1)
return(cf)
}
stop("cannot interpret expression ", sQuote(ex), " as linear function")
}
### extract left hand side of an expression
lhs <- function(ex) {
if (length(ex) != 1)
stop("expression is not of length 1")
if (length(ex[[1]]) != 3)
stop("expression ", sQuote(ex),
" does not contain a left and right hand side")
return(ex[[1]][[2]])
}
### extract right hand side of an expression
rhs <- function(ex) {
if (length(ex) != 1)
stop("expression is not of length 1")
if (length(ex[[1]][[3]]) == 2)
return(-ex[[1]][[3]][[2]])
rhs <- ex[[1]][[3]]
if (!is_num(rhs) || length(rhs) > 1)
stop("right hand side of expression ", sQuote(ex),
" is not a scalar numeric")
return(rhs)
}
### extract direction of the _alternative_
side <- function(ex) {
side <- as.character(ex[[1]][[1]])
if (!(side %in% c("<=", ">=", "==", "=")))
stop("does not contain ", sQuote("<=, >=, =="))
alternative <- switch(side,
"<=" = "greater",
">=" = "less",
"==" = "two.sided",
"=" = "two.sided")
return(alternative)
}
### extract coefficients and variable names
expression2coef <- function(ex) {
cf <- c()
nm <- c()
m <- rhs(ex)
x <- lhs(ex)
alternative <- side(ex)
while (TRUE) {
tmp <- coefs(x)
cf <- c(cf, tmp$coef)
nm <- c(nm, tmp$var)
### x == "A"
if (is.name(x)) break
### x == "-1"
if (is_num(x)) break
### x == "3 * A"
if (length(x) == 3 && is_num(x[[2]])) break
### x == "-3 * A"
if (length(x) == 3 && is_num(x[[2]])) break
x <- x[[2]]
}
return(list(coef = cf, names = nm,
m = m, alternative = alternative,
lhs = deparse(lhs(ex))))
}
### interpret character representations of linear functions
chrlinfct2matrix <- function(ex, var) {
if (!is.character(ex))
stop("argument ", sQuote(ex), " is not of type character")
if (!is.character(var))
stop("argument ", sQuote(var), " is not of type character")
K <- matrix(0, nrow = length(ex), ncol = length(var))
colnames(K) <- var
rownames(K) <- 1:length(ex)
m <- rep(0, length(ex))
for (i in 1:length(ex)) {
tmp <- expression2coef(parse(text = ex[i]))
if (!all(tmp$names %in% var))
stop("variable(s) ", sQuote(tmp$names[!tmp$names %in% var]),
" not found")
for (n in tmp$names)
K[i, var == n] <- tmp$coef[tmp$names == n]
m[i] <- tmp$m
if (i == 1) {
alternative <- tmp$alternative
} else {
if (tmp$alternative != alternative)
stop("mix of alternatives currently not implemented")
}
rownames(K)[i] <- tmp$lhs[1]
}
list(K = K, m = m, alternative = alternative)
}
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