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# program spuRs/resources/scripts/fixedpoint.r
# loadable spuRs function
fixedpoint <- function(ftn, x0, tol = 1e-9, max.iter = 100) {
# applies the fixed-point algorithm to find x such that ftn(x) == x
# we assume that ftn is a function of a single variable
#
# x0 is the initial guess at the fixed point
# the algorithm terminates when successive iterations are
# within distance tol of each other,
# or the number of iterations exceeds max.iter
# do first iteration
xold <- x0
xnew <- ftn(xold)
iter <- 1
cat("At iteration 1 value of x is:", xnew, "\n")
# continue iterating until stopping conditions are met
while ((abs(xnew-xold) > tol) && (iter < max.iter)) {
xold <- xnew;
xnew <- ftn(xold);
iter <- iter + 1
cat("At iteration", iter, "value of x is:", xnew, "\n")
}
# output depends on success of algorithm
if (abs(xnew-xold) > tol) {
cat("Algorithm failed to converge\n")
return(NULL)
} else {
cat("Algorithm converged\n")
return(xnew)
}
}
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