##
##  b i s e c t . R
##


# bisect <- function(f, a, b, maxiter=100, tol=.Machine$double.eps^0.5)
# # Bisection search for zero of a univariate function in a bounded interval
# {
#     if (f(a)*f(b) > 0) stop("f(a) and f(b) must have different signs.")
#     x1 <- min(a, b); x2 <- max(a,b)
#     xm <- (x1+x2)/2.0
#     n <- 0
#     while (abs(x1-x2)/2.0 > tol) {
#         n <- n+1
#         if (abs(f(xm)) <= tol) break
#         if (f(x1)*f(xm) < 0) {
#             x2 <- xm
#         } else {
#             x1 <- xm
#         }
#         xm <- (x1+x2)/2.0  # xm <- x1 - f(x1) * (x2-x1) / (f(x2)-f(x1))
#         if (n >= maxiter) break
#     }
#     return(list(root=xm, f.root=f(xm), iter=n, estim.prec=abs(x1-x2)/2.0))
# }


bisect <- function(f, a, b, maxiter = 100, tol = NA)
# Bisection search, trimmed for exactness, not no. of iterations
{
    if (!is.na(tol)) warning("Deprecated: Argument 'tol' not used anymore.")
	if (f(a)*f(b) > 0) stop("f(a) and f(b) must have different signs.")
	x1 <- min(a, b); x2 <- max(a,b)
	xm <- (x1+x2)/2.0
	n <- 1
	while (x1 < xm && xm < x2 && n < maxiter) {
		n <- n+1
		if (sign(x1) != sign(x2) && x1 != 0 && x2 != 0) {
		    xm <- 0.0
		    if (f(xm) == 0.0) {x1 <- x2 <- xm; break}
		}
		if (sign(f(x1)) != sign(f(xm))) {
			x2 <- xm
		} else {
			x1 <- xm
		}
		xm <- (x1 + x2) / 2.0
	}
	return(list(root=xm, f.root=f(xm), iter=n, estim.prec=abs(x1-x2)))
}

regulaFalsi <- function(f, a, b, maxiter = 100, tol = .Machine$double.eps^0.5)
#Regula Falsi search for zero of a univariate function in a bounded interval
{
	x1 <- a;      x2 <- b
	f1 <- f(x1);  f2 <- f(x2)
	if (f1*f2 > 0) stop("f(a) and f(b) must have different signs.")

	m <- 0.5                                         # Illinois rule
	niter <- 0
	while (abs(x2-x1) >= tol && niter <= maxiter) {
		niter <- niter + 1
		x3 <- (x1*f2-x2*f1)/(f2-f1); f3 <- f(x3)

		if(f3*f2 < 0) {
			x1 <- x2;  f1 <- f2
			x2 <- x3;  f2 <- f3
		} else {
			# m <- f2/(f2+f3)                         # Pegasus rule
			# m <- if (1-f3/f2 > 0) 1-f3/f2 else 0.5  # Andersen/Bjoerk
			f1 <- m * f1
			x2 <- x3;  f2 <- f3
		}
	}
	if (niter > maxiter && abs(x2-x1) >= tol)
		cat("regulaFalsi stopped without converging.\n")
	return(list(root = x3, f.root = f3, niter = niter, estim.prec = x1-x2))
}


secant <- function(fun, a, b, ...,
                   maxiter = 100, tol = .Machine$double.eps^0.5)
# Secant search for zero of a univariate function
{
    fun <- match.fun(fun)
    f <- function(x) fun(x, ...)

	x1 <- a; x2 <- b
	f1 <- f(x1); if (abs(f1) <= tol) return(x1)
	f2 <- f(x2); if (abs(f2) <= tol) return(x1)
	n <- 0
	while (n <= maxiter && abs(x2 - x1) > tol) {
		n <- n+1
		slope <- (f2 - f1)/(x2 - x1)
		if (slope == 0) return(root=NA, f.root=NA, iter=n, estim.prec=NA)
		x3 <- x2 - f2/slope
		f3 <- f(x3); if (abs(f3) <= tol) break
		x1 <- x2; f1 <- f2
		x2 <- x3; f2 <- f3
	}
	if (n > maxiter) {
		warning("Maximum number of iterations 'maxiter' was reached.")
	}
	return(list(root=x3, f.root=f3, iter=n, estim.prec=2*abs(x3-x2)))
}