# R FUNCTION "MONSOLVE", TO FIND A POSITIVE ROOT OF
#   A (NON-VECTORISED) INCREASING FUNCTION OF ONE REAL VARIABLE.
# 
# BY JEFFREY ROSENTHAL (www.probability.ca), February 2014

monsolve = function(ff, initx=1.0, numrep=10^4) {
  x = initx
  mult = 1.0
  ssgn = sign(ff(x))
  for (i in 1:numrep) {
    if (ff(x)<0) {
      x = x / runif(1)^mult
      if (ssgn<0) {
        ssgn = -ssgn
	mult = mult/2
      }
    }
    else {
      x = x * runif(1)^mult
      if (ssgn>0) {
        ssgn = -ssgn
	mult = mult/2
      }
    }
    # print(x)
  }
  return(x)
}