# R code to do bisection search.
#  For the class Mathematics in Finance

#  http://www.math.nyu.edu/faculty/goodman/teaching/MathFin/index.html
# Author: Jonathan Goodman


solver = function( f,            #  Solve the equation f(x) = y, f is an R function
                   y,            #  y is the target value
                   a,            #  seek a solution in the interval [a,b]
                   b,
                   eps){         #  return when the uncertainty in x is < eps
                   
    it_max   = 50                #  declare failure if you do more than this many iterations
    
    famy = f(a) - y    #  famy is for "f(a) minus y"
    fbmy = f(b) - y    #  find (x) so that f(x) - y = 0
    
                                 #   stop if f does not change sign between a and b
    
    it = 0             #  the number of iterations done so far
    while ( (b-a) > eps ){
    
        c    = (a+b)*.5
        fcmy = f(c) - y          #  Evaluate f at the midpoint of the interval
        if ( famy*fcmy < 0){     #  f changes sign between a and c,  ...
            b    = c             #  ... so the new interval is [a,c]
            fbmy = fcmy          
          }  else{               #  f changes sign between c and b,  ...
            a    = c             #  ... so the new interval is [c,b]
            famy = fcmy
          }
          
        cat("a is ", a, ", b is ", b, " famy is ", famy, ", fbmy is ", fbmy, "\n")
        
        it = it + 1              #  just finished another iteration
        if ( it > it_max){       #  Please, please don't let this be an infinite loop!
            stop("solver stopping because it did too many iterations\n")
          }
      }
    return(a)
  }