test/bisect.lua

   1 $debug
   2 -- bisection method for solving non-linear equations
   3
   4 function bisect(f,a,b,fa,fb)
   5  write(n," a=",a," fa=",fa," b=",b," fb=",fb,"\n")
   6  local c=(a+b)/2
   7  if abs(a-b)<delta then return c end
   8  n=n+1
   9  local fc=f(c)
  10  if fa*fc<0 then return bisect(f,a,c,fa,fc) else return bisect(f,c,b,fc,fb) end
  11 end
  12
  13 -- find root of f in the inverval [a,b]. bisection needs that f(a)*f(b)<0
  14 function solve(f,a,b)
  15  delta=1e-6     -- tolerance
  16  n=0
  17  local z=bisect(f,a,b,f(a),f(b))
  18  write(format("after %d steps, root is %.10g\n",n,z))
  19 end
  20
  21 -- our function
  22 function f(x)
  23  return x*x*x-x-1
  24 end
  25
  26 solve(f,1,2)